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Q: “What does the design theory debate have to do with the law of non-contradiction (LNC)?” A: “A lot!”

The latest flare-ups in the debates over design theory in and around UD have pivoted on the Law of non-contradiction; one of the most debated classical principles of logic.

Why on earth is that so?

The simple short answer is: if we are to make progress in debates and discussions, we must be at minimum agreed on being reasonable and rational.

In more details, LNC is one of a cluster of first principles of right reason that are pivotal to core rationality, and for years now, debates over design theory issues have often tracked back to a peculiar characteristic of the evolutionary materialist worldview: it tends strongly to reject the key laws of thought, especially, identity, excluded middle and non-contradiction, with the principle of sufficient reason (the root of the principle of causality) coming up close behind.

What is sadly ironic about all of this, is that hose who would overthrow such first principles of right reason do not see that they are sawing off the branch on which we must all sit, if we are to be rational.

Why do I say this?

Let me first excerpt a discussion on building worldviews, as I recently appended to a discussion on quantum mechanics used to try to dismiss the law of non-contradiction:

____________

>>. . . though it is quite unfashionable to seriously say such nowadays (an indictment of our times . . .), to try to deny the classic three basic principles of right reason — the law of identity, that of non-contradiction, and that of the excluded middle — inevitably ends up in absurdity.

For, to think at all, we must be able to distinguish things (or else all would be confusion and chaos), and these laws immediately follow from that first act of thought.

A diagram showing the world split into two distinct labelled parts, A and NOT-A, will help us see how naturally this happens:

Laws of logic in action as glorified common-sense first principles of right reason

If at a given moment we distinctly identify and label some thing, A — say, a bright red ball on a table — we mark a mental border-line and also necessarily identify NOT-A as “the rest of the World.” We thus have a definite separation of the World into two parts, and it immediately and undeniably holds that:

(a) the part labelled A will be A (symbolically, [A => A] = 1),
(b) A will not be the same as NOT-A ( [A AND NOT-A] = 0); and
(c) there is no third option to being A or NOT-A ( [A OR NOT-A] = 1).

So, we see how naturally the laws of (a) identity, (b) non-contradiction (or, non-confusion!), and (c) the excluded middle swing into action. This naturalness also extends to the world of statements that assert that something is true or false, as we may see from Aristotle’s classic remark in his Metaphysics 1011b (loading the 1933 English translation):

. . .   if it is impossible at the same time to affirm and deny a thing truly, it is also impossible for contraries to apply to a thing at the same time; either both must apply in a modified sense, or one in a modified sense and the other absolutely.

Nor indeed can there be any intermediate between contrary statements, but of one thing we must either assert or deny one thing, whatever it may be. This will be plain if we first define truth and falsehood. To say that what is is not, or that what is not is, is false; but to say that what is is, and what is not is not, is true; and therefore also he who says that a thing is or is not will say either what is true or what is false. [Emphases added]

So, we can state the laws in more or less traditional terms:

[a] A thing, A, is what it is (the law of identity);
[b] A thing, A, cannot at once be and not-be (the law of non-contradiction);
[c] A thing, A, is or it is not, but not both or neither (the law of the excluded middle).

In short, the diagram helps take the “mystery” out of the laws, showing us why they make sense. [Cf. responses to objections  here.]  In 1011b, too, Ari gives us a bonus, by aptly defining truth:  to say that what is is, and what is not is not, is true.(As a note for logicians: we are here specifically speaking with reference to the experienced world of credibly real things, so extensions to empty-set contexts in which questions over contrasted empty sets — that is, quite literally: no-thing –  arise, are irrelevant for the moment. That is, we deal here with the classic square of opposition. Then, once we see what follows from dealing with a world of real categories with at least one member each, we may then extend to the case of empty sets and see how much of a difference this possibility makes.)A fourth key law of sound thought is the principle of sufficient reason , which enfolds  the principle of cause and effect. Schopenhauer in his Manuscript Remains, Vol. 4, notes that: Of everything that is, it can be found why it is.”The fire tetrahedron (an extension of the classic fire triangle) is a helpful case to study briefly:

The fire tetrahedron as a model of cause, with a cluster of four necessary, and jointly sufficient causal factors

For a fire to begin or to continue, we need (1) fuel, (2) heat, (3) an oxidiser [usually oxygen] and (4) an un- interfered- with heat-generating chain reaction mechanism. (For, Halon fire extinguishers work by breaking up the chain reaction.) Each of the four factors is necessary for, and the set of four are jointly sufficient to begin and sustain a fire. We thus see four contributory factors, each of which is necessary [knock it out and you block or kill the fire], and together they are sufficient for the fire.

We thus see the principle of cause and effect. That is,

[d] if something has a beginning or may cease from being — i.e. it is contingent — it has a cause.

Common-sense rationality, decision-making and science alike are founded on this principle of right reason: if an event happens, why — and, how? If something begins or ceases to exist, why and how? If something is sustained in existence, what factors contribute to, promote or constrain that effect or process, how? The answers to these questions are causes.

Without the reality behind the concept of cause the very idea of laws of nature would make no sense: events would happen anywhere, anytime, with no intelligible reason or constraint.
As a direct result, neither rationality nor responsibility would be possible; all would be a confused, unintelligible, unpredictable, uncontrollable chaos. Also, since it often comes up, yes: a necessary causal factor is a causal factor — if there is no fuel, the car cannot go because there is no energy source for the engine. Similarly, without an unstable nucleus or particle, there can be no radioactive decay and without a photon of sufficient energy, there can be no photo-electric emission of electrons: that is, contrary to a common error, quantum mechanical events or effects, strictly speaking, are not cause-less.
(By the way, the concept of a miracle — something out of the ordinary that is a sign that points to a cause beyond the natural order — in fact depends on there being such a general order in the world. In an unintelligible chaos, there can be no extra-ordinary signposts, as nothing will be ordinary or regular!)

However, there is a subtle facet to this, one that brings out the other side of  the principle of sufficient reason. Namely, that there is a possible class of being that does not have a beginning, and cannot go out of existence; such are self-sufficient, have no external necessary causal factors, and as such cannot be blocked from existing. And it is commonly held that once there is a serious candidate to be such a necessary being, if the candidate is not contradictory in itself [i.e. if it is not impossible], it will be actual.

Or, we could arrive at effectively the same point another way, one which brings out what it means to be a serious candidate to be a necessary being:

If a thing does not exist it is either that it could, but just doesn’t happen to exist, or that it cannot exist because it is a conceptual contradiction, such as square circles, or round triangles and so on. Therefore, if it does exist, it is either that it exists contingently or that it is not contingent but exists necessarily (that is it could not fail to exist without contradiction). [--> The truth reported in "2 + 3 = 5" is a simple case in point; it could not fail without self-contradiction.] These are the four most basic modes of being and cannot be denied . . . the four modes are the basic logical deductions about the nature of existence.

That is, since there is no external necessary causal factor, such a being — if it is so — will exist without a beginning, and cannot cease from existing as one cannot “switch off” a sustaining external factor. Another possibility of course is that such a being is impossible: it cannot be so as there is the sort of contradiction involved in being a proposed square circle. So, we have candidates to be necessary beings that may not be possible on pain of contradiction, or else that may not be impossible, equally on pain of contradiction.

In addition, since matter as we know it is contingent, such a being will not be material. The likely candidates are: abstract, necessarily true propositions and an eternal mind, often brought together by suggesting that such truths are held in such a mind.

Strange thoughts, perhaps, but not absurd ones.

So also, if we live in a cosmos that (as the cosmologists tell us) seems — on the cumulative balance of evidence — to have had a beginning, then it too is credibly caused. The sheer undeniable actuality of our cosmos then points to the principle that from a genuine nothing — not matter, not energy, not space, not time, not mind etc. — nothing will come. So then, if we can see things that credibly have had a beginning or may come to an end; in a cosmos of like character, we reasonably and even confidently infer that a necessary being is the ultimate, root-cause of our world; even through suggestions such as a multiverse (which would simply multiply the contingent beings) . . . >>

____________

[Added, Feb 21:] Let us boil this down to a summary list of six first principles of right reason in a form we could write out on the back of the proverbial envelope, with a little help from SB:

{{Consider the world:

|| . . . ||

Identify some definite A in it:

|| . . . (A) . . . NOT-A (the rest of the world) . . . ||

Now, let us analyse:

[1] A thing, A, is what it is (the law of identity);

[2] A thing, A, cannot at once be and not-be (the law of non-contradiction). It is worth clipping Wiki’s cites against known interest from Aristotle in Metaphysics, as SB has done above:

1. ontological*: “It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect.” (1005b19-20)

[*NB: Ontology, per Am HD etc, is "The branch of metaphysics that deals with the nature of being," and the ontological form of the claim is talking about that which really exists or may really exist. Truth is the bridge between the world of thoughts and perceptions and that of external reality: truth says that what is is, and what is not is not.]

2. psychological: “No one can believe that the same thing can (at the same time) be and not be.” (1005b23-24)

3. logical: “The most certain of all basic principles is that contradictory propositions are not true simultaneously.” (1011b13-14)

[3] A thing, A, is or it is not, but not both or neither (the law of the excluded middle).

[4] “to say that what is is, and what is not is not, is true.” (Aristotle, on what truth is)

[5] “Of everything that is, it can be found why it is.” (Principle of sufficient Reason, per Schopenhauer.)

[6] If something has a beginning or may cease from being — i.e. it is contingent — it has a cause.* (Principle of causality, a direct derivative of 5)
_________

*F/N: Principles 5 & 6 point to the possibility of necessary, non contingent beings, e.g. the truth in 2 + 3 = 5 did not have a beginning, cannot come to an end, and is not the product of a cause, it is an eternal reality. The most significant candidate necessary being is an eternal Mind. Indeed, down this road lies a path to inferring and arguably warranting the existence of God as architect, designer and maker — thus, creator — of the cosmos. (Cf Plato’s early argument along such lines, here.)}}

It would seem that the matter is obvious at this point.

Indeed, as UD’s blog owner cited yesterday from Wikipedia, testifying against known predominant ideological interest:

The law of non-contradiction and the law of excluded middle are not separate laws per se, but correlates of the law of identity. That is to say, they are two interdependent and complementary principles that inhere naturally (implicitly) within the law of identity, as its essential nature. To understand how these supplementary laws relate to the law of identity, one must recognize the dichotomizing nature of the law of identity. By this I mean that whenever we ‘identify’ a thing as belonging to a certain class or instance of a class, we intellectually set that thing apart from all the other things in existence which are ‘not’ of that same class or instance of a class. In other words, the proposition, “A is A and A is not ~A” (law of identity) intellectually partitions a universe of discourse (the domain of all things) into exactly two subsets, A and ~A, and thus gives rise to a dichotomy. As with all dichotomies, A and ~A must then be ‘mutually exclusive’ and ‘jointly exhaustive’ with respect to that universe of discourse. In other words, ‘no one thing can simultaneously be a member of both A and ~A’ (law of non-contradiction), whilst ‘every single thing must be a member of either A or ~A’ (law of excluded middle).

The article (which seems to have been around since about 2004) goes on to say:

What’s more, since we cannot think without that we make use of some form of language (symbolic communication), for thinking entails the manipulation and amalgamation of simpler concepts in order to form more complex ones, and therefore, we must have a means of distinguishing these different concepts. It follows then that the first principle of language (law of identity) is also rightfully called the first principle of thought, and by extension, the first principle reason (rational thought).

Schopenhauer sums up aptly:

The laws of thought can be most intelligibly expressed thus:

  1. Everything that is, exists.
  2. Nothing can simultaneously be and not be.
  3. Each and every thing either is or is not.
  4. Of everything that is, it can be found why it is.

There would then have to be added only the fact that once for all in logic the question is about what is thought and hence about concepts and not about real things.  [Manuscript Remains, Vol. 4, "Pandectae II," §163. NB: Of course, the bridge from the world of thought to the world of experienced reality is that we do live in a real world that we can think truly about. Going further, there are things about that world that are self-evidently true, starting with Josiah Royce's "Error exists."]

And again:

Through a reflection, which I might call a self-examination of the faculty of reason, we know that these judgments are the expression of the conditions of all thought and therefore have these as their ground. Thus by making vain attempts to think in opposition to these laws, the faculty of reason recognizes them as the conditions of the possibility of all thought. We then find that it is just as impossible to think in opposition to them as it is to move our limbs in a direction contrary to their joints. If the subject could know itself, we should know those laws immediately, and not first through experiments on objects, that is, representations (mental images). [On the Fourfold Root of the Principle of Sufficient Reason, §33.]

Similarly, Lord Russell states:

1. Law of identity: “Whatever is, is.”

2. Law of noncontradiction: “Nothing can both be and not be.”

3. Law of excluded middle: “Everything must either be or not be.”

(The Problems of Philosophy, p. 72)

The matter should be clear enough, and simple enough.

Sadly, it is not. There are some who would now say, of course you can define a logical world in which this is an axiom and by definition be true but that has nothing to do with reality.

That is why I had to further respond this morning:

____________

>>Let us start with a basic point, as can be seen in the discussion here on in context: the first step in serious thinking about anything, is to make relevant distinctions, so for each such case we divide the world into A and not-A.

(Notice the example of a bright red ball on a table. Or, you can take: Me and not-Me, etc etc. It helps to start with the concrete and obvious so keep that nice red ball you got when you were say 6 months old in mind.)

Once there is a clear distinction, the relevant laws of thought follow directly, let’s illustrate:

World: || . . . ||

On identifying a distinct thing, (A), we distinguish:

|| (A) . . . NOT-A . . . ||

From this seemingly simple and commonsensical act of marking a distinction with a sharp border so to speak, the following follows, once A is indeed identifiably distinct at a given time and place under given circumstances:

(a) the part labelled A will be A (symbolically, [A => A] = 1),

(b) A will not be the same as NOT-A ( [A AND NOT-A] = 0); and

(c) there is no third option to being A or NOT-A ( [A OR NOT-A] = 1).

Or, in broader terms:

[a] A thing, A, is what it is (the law of identity);

[b] A thing, A, cannot at once be and not-be (the law of non-contradiction);

[c] A thing, A, is or it is not, but not both or neither (the law of the excluded middle).

And since there is a tendency to use classical quotes, let me cite one, from Paul of Tarsus, on the significance of all this, even for the very act of speech, the basis for reasoned, verbalised thought:

1 Cor 14:6 Now, brothers, if I come to you and speak in tongues, what good will I be to you, unless I bring you some revelation or knowledge or prophecy or word of instruction? 7 Even in the case of lifeless things that make sounds, such as the flute or harp, how will anyone know what tune is being played unless there is a distinction in the notes? 8 Again, if the trumpet does not sound a clear call, who will get ready for battle? 9 So it is with you. Unless you speak intelligible words with your tongue, how will anyone know what you are saying? You will just be speaking into the air. 10 Undoubtedly there are all sorts of languages in the world, yet none of them is without meaning. 11 If then I do not grasp the meaning of what someone is saying, I am a foreigner to the speaker, and he is a foreigner to me. 12 So it is with you. Since you are eager to have spiritual gifts, try to excel in gifts that build up the church . . .

In short, the very act of intelligible communication pivots on precisely the ability to mark relevant distinctions. Indeed, the ASCII code we use for text tells us one English language alphanumeric character encodes answers to seven yes/no questions, why it takes up seven bits. (The eighth is a check-sum, useful to say reasonably confident that this is accurately transmitted, but that is secondary.)

So, let us get it deep into our bones: so soon as we are communicating or calculating using symbols, textual or aural, we are relying on the oh so often spoken against laws of thought. This BTW, is why I have repeatedly pointed out how when theoretical physicists make the traditional scratches on the proverbial chalk board, these principles are deeply embedded in the whole process.

These are not arbitrary mathematical conventions that can be made into axioms as we please, they are foundational to the very act of communication involved in writing or speaking about such things.

Beyond that all the attempts to wander over this and that result of science in a desperate attempt to deny or dismiss actually rely on what they would dismiss. They refute themselves through self-referential incoherence.

For instance, just now, someone has trotted out virtual particles.

Is this a distinct concept? Can something be and not be a virtual particle under the same circumstances?

If so, the suggested concept is simply confused (try, a square circle or a triangle with six corners); back to the drawing-board.

(But of course there are effects that are traced to their action, so they seem to have reality as entities acting in our world below the Einstein energy-time threshold of uncertainty. The process that leads us to that conclusion is riddled with the need to mark distinctions, and to recognise that distinctions mark distinct things.)

And, BTW, we can extend to the next level. The number represented by the numeral, 2, is real, but it is not itself a physical entity; it just constrains physical entities such that something with twoness in it can be split exactly by the half into equal piles.

Similarly, the truth asserted in the symbolised statement: 2 + 3 = 5 constrains physical reality, but is not itself a material reality built up of atoms or the like. All the way on to 1 + e^pi*i = 0, etc; thence the “unreasonable: effectiveness of ever so much of mathematics in understanding how the physical world works. That is, we have a real, abstract world that can even specify mathematical laws that specify what happens and what will not happen. Even, reliably.

All of this pivots on the significance of marking distinctions.

So, those who seek so desperately to dismiss the first principles of right reason, saw off the branch on which they must sit.

It is a sad reflection on our times, that we so often find it hard to see this.

I know, I know: “But, that’s DIFFERENT!” (I am quoting someone caught up in a cultic system, in response to correcting a logical error.)

No. It is NOT actually different, but if we are enmeshed in systems that make us think errors are true, the truth will — to us — seem to be wrong.

Which is part of why en-darkening errors are ever so entangling.

It takes time and effort for a critical mass of corrections to reach breaking point and suddenly we see things another way. In that process, empirical cases are crucial.

But, there is another relevant saying: experience is a very good teacher, but his fees are very dear. Alas for fools, they will learn from no other.

Sadly, there are yet worse fools who will not even learn from experience, no matter how painful.

But then; it is ever so for those bewitched by clever, but unsound, schemes.

I hope that a light is beginning to dawn.>>

____________

Now, it will come as no surprise to see that I come down on the therapeutic side not the litmus test side of the issue of using the LNC as a test of rationality and fitness to discuss matters.

That is, I hold that this particular confusion is so commonplace that the key issue is to help those enmeshed, recognising that this is going to take time and effort. In that context, it is the specifically, persistently and willfully disruptive, disrespectful, deceitful and uncivil who should face disciplinary action for cause; in defence of a civil forum where important ideas can be discussed civilly. For contrasts on why that is necessary, cf YouTube and the penumbra of anti-ID sites.

Having said that, what is on the table now is rationality itself.

That is how bad things are with our civilisation at the hands of its own intellectual elites.

Do you see why I speak of a civilisation facing mortal danger and all but fatally confused in the face of such peril?

And of course the weapon of choice for the willful confus-ers is to get us to swallow an absurdity. That guarantees loss of ability to discern true from false, sound from unsound, right from wrong. Then, also, when we are told the truth, because we have been led to believe a lie, we will often resist the truth for it will seem to be obviously false.

No wonder, the prophet Isaiah thundered out, nigh on 2800 years ago:

Isa 5:20 Woe to those who call evil good
and good evil,
who put darkness for light
and light for darkness,
who put bitter for sweet
and sweet for bitter.

 21 Woe to those who are wise in their own eyes
and clever in their own sight . . .

We would do well to heed these grim words of warning, before it is too late for our civilisation. END

F/N: For those puzzling over issues raised in the name of quantum theory or the like, I suggest you go here for a first examination.

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128 Responses to Q: “What does the design theory debate have to do with the law of non-contradiction (LNC)?” A: “A lot!”

  1. KF is correct that logic in general, and the LNC in particular, is binary and dichotomous: it divides the world into a clearly defined A and not A.

    The problem is that the real world is not like that – many things exist over a spectrum where there is no natural dividing line. Therefore when we categorize things into A and not A, we create an artificial overlay on top of reality – an abstraction that is of course very useful in many ways, but also misleading and inaccurate in ways and at times.

    That’s why, as I’ve explained in other posts, we need to distinguish the logic itself from the application of the logic within a model of reality. The logic is inviolate, but the model may be flawed. In particular, the obligation to dichotomize that logic places upon us can in fact be a major impediment to understanding due to its tendency to lead to simplistic and inadequate distinctions.

  2. Aleta: The problem is that the real world is not like that – many things exist over a spectrum where there is no natural dividing line.

    You don’t understand the discussion, which is not about A in transition from A to something else, or whether A is “partially” in some given state. For example, one can ask whether it is true or not that a bucket of water is full. This can be asked while it is full, while it is not full and currently being emptied, and while empty. However, the original question, “is it full?” has a binary answer. The question “how full is it”, which has many answers, is different than the question “is it full?”, which only has one.

    The LNC holds.

  3. I didn’t say that the LNC didn’t hold. I said there are practical difficulties at times in applying it to the real world because it is not clear exactly what real-world state that A represents.

    I gave an example in another post of the proposition A = “X is a point on a mountain.” The LNC holds: (“X is a point on a mountain” and “X is not a point on a mountain.”) is false. However, answering the question about a particular point Xo: is Xo on a mountain is not at all clearcut, and would involve some arbitrary decisions. My point in response to the opening post is that logic necessarily dichotomizes, and thus can misrepresent the world. This is not a flaw in logic itself, but rather a complication in applying logic to propositions about the real world.

  4. The problem is that the real world is not like that – many things exist over a spectrum where there is no natural dividing line. Therefore when we categorize things into A and not A, we create an artificial overlay on top of reality – an abstraction that is of course very useful in many ways, but also misleading and inaccurate in ways and at times.

    A simple example would be nice.

  5. is Xo on a mountain is not at all clearcut

    Why, precisely?

  6. This seems obvious. The is no natural dividing line between mountain and non-mountain, and in fact no natural and certain definition of what constitutes a mountain.

    How would you define mountain with a set of criteria that would allow any observer to determine whether point X was on a mountain or not?

  7. is Xo on a mountain is not at all clearcut

    Why, precisely?

    (this may wind up as a double post. the comment function is wonky right now for me.)

  8. The better question is: How would you define mountain? It’s your proposition, and your responsibility.

    So, what is a mountain?

  9. Brent,
    We already know that mountains form over long periods of time as the earth’s plates collide. So clearly there are many states of “mountain” (i.e. whether something is a mountain is not a binary question).

    Do you disagree? Do you think that something is always objectively either a mountain of not a mountain?

  10. last line should read: mountain or not a mountain.

  11. Hmmm. Asking me to provide a definition of mountain misses the point, I think. You asked for an example, and I gave one. You asked why, precisely, that the proposition “Xo on a mountain” is not at all clearcut. My answer is that there is no clearcut definition of a mountain, nor criteria for establishing that a point Xo is on one. Obviously I can’t give a clearcut definition if my position is that there isn’t one.

    The reason I asked you for a definition is because you didn’t seem to understand this problem (You asked, “why precisely”.) So the question is, I suppose, do you think a clearcut operational definition of “point Xo is on a mountain” can be given?

    And remember, the bigger point here, of which this is an example, is that logic, and the LNC, works with clearcut distinctions between A and ~A, and therefore we run into problems when we try to apply logic, at times, to things that don’t have those clearcut dividing lines.

  12. I’ll wait for an answer to my question @8. Thanks.

  13. This just beggars belief.

    For anyone to propose that X is on a mountain, if there is no way to define mountain, is just to say that the person making the proposition is a moron. OR!!! That we must rely on the person making the proposition to define what THEY MEAN when THEY say “mountain”.

  14. You not getting this, Brent, and of course I’m can’t answer 8, as explained above, so I think our discussion is over.

  15. I didn’t say that the LNC didn’t hold. I said there are practical difficulties at times in applying it to the real world because it is not clear exactly what real-world state that A represents.

    What I’m hearing is that for the LNC to apply – A and NOT A cannot both be true, identical definitions must be assumed for each instance of A. It doesn’t matter if the definitions are ambiguous or even wrong.

    Doesn’t that go without saying? It’s implicit in any definition of the LNC. The use of such notation as “A and NOT A” would be pointless and make no sense if A isn’t always A, regardless of whether A is accurate, inaccurate, or ambiguous.

  16. Aleta, if you are making a proposition, it is up to you to be clear on your terms. You gave the example of “Xo is on a mountain”. It is therefore up to you to clarify your terms. Once you do, there is no ambiguity.

    And, even in the midst of ambiguity, LNC is unaffected. People can argue about the properness, wisdom, clarity, or definiteness of terms from now until the mountains erode, but the problem is completely beside the point of LNC.

    While men argue their terms, it will be true that they are arguing their terms. It will be true that it is disputed whether Xo is on a mountain. The LNC applies, still, even in the midst of non-clarity.

  17. I think there are two different meanings of the word “apply” here. Within the world of pure logic, as kf explained in the OP, in order to apply the LNC the definition of A must be the same for both A and not A, as Scott says. No question about that. And, as he says, this is true even if “the definitions are ambiguous or even wrong.”

    However, when we want to apply logic as a tool to help us understand what is true about the world, if the definitions we use are ambiguous or wrong, we won’t get the best understanding we can.

    The word “apply” is being applied to two different context in the paragraphs above: in the first within abstract logic itself, as a closed system of symbols, and in the second with respect to the model that uses language to map portions of the real world onto the logic.

  18. Brent, my answer to Scott addresses your last post also.

  19. However, when we want to apply logic as a tool to help us understand what is true about the world, if the definitions we use are ambiguous or wrong, we won’t get the best understanding we can.

    Let’s remove the first part about logic. We have, then:

    “If the definitions we use are ambiguous or wrong, we won’t get the best understanding we can.”

    It is still true. Logic has nothing to do with the ambiguity of statements per se. All you’re saying is that ambiguous statements are ambiguous statements. And I’m happy you are, because you are affirming the LNC when you do.

  20. Aleta, if all you’re saying is that reasoning from an ambiguous statement is likely to lead us to incorrect conclusions, fine. But what exactly does that have to do with anything?

    It’s like getting a wrong answer on a math quiz not because you did the math incorrectly, but because you thought the teacher said 7+18 rather than 7+80. Are you going to throw out the rules of arithmetic? Obviously not. So what is your problem here exactly?

  21. Yes, I am affirming the LNC, because “Logic has nothing to do with the ambiguity of statements per se”. I agree with that, whole-heartedly.

    That’s why logic alone can’t get us good understanding of the world: garbage in, garbage out is always a possibility.

    That’s the point I’ve been trying to make: when we apply logic to the real world, we have to assess the truth of our propositions on various grounds if we want to productively then use them in arguments that use logical principles.

  22. –Aleta: “The problem is that the real world is not like that – many things exist over a spectrum where there is no natural dividing line.”

    Give me an example of something that “exists over a spectrum where there is no natural dividing line” between existence and non-existence.

  23. With respect to @22, do not appeal to quantum mechanics, which you do not understand. I want a practical example in the macro world.

  24. Well Aleta, it looks like the gig is up. You’re now down to saying only that we should be clear with terms, which is, in my opinion, not at all what you were hoping to imply (or infer) from the beginning.

    But please explain to Stephen what you’re actually saying just in case I’m wrong.

  25. How can you tell me I don’t understand quantum mechanics, Stephen?

    And what is your background in the subject? Do you think you understand more than I do, and if you think so, why do you think that?

    Virtual particles are my example of something for which there may not be a clearcut division between existence and non-existence. I’ve made no claim about there being any practical difficulties with “A exists” for A in the macro world, and I’ve accepted “the moon exists” as a perfectly valid proposition to which to apply the LNC: if you ask, “can the moon exist and not exist at the same time,” I’m quite happy to say No.

    And, for what it’s worth, my interest in this topic goes beyond the LNC to the larger topic of the difference between logic as a self-contained symbolic system and logic as a tool for use with propositions, stated in words, about the real world.

  26. I don’t think there is any “gig” to be up, although I’ve gotten the feeling that people keeping wanting to think I’m defending a position that I am not. My first post in this thread ended with

    In particular, the obligation to dichotomize that logic places upon us can in fact be a major impediment to understanding due to its tendency to lead to simplistic and inadequate distinctions.

    That says more than “we should be clear with terms”, but being clear with terms would certainly fall under issues I’m trying to address.

  27. Aleta: “How can you tell me I don’t understand quantum mechanics, Stephen?”

    I will, for the sake of argument, and for the moment, assume that you are an expert in quantum mechanics so that you can no longer use your outrage as a stalling tactic.

    Now, back to my question.

    –Aleta: “The problem is that the real world is not like that – many things exist over a spectrum where there is no natural dividing line.”

    Without appealing to quantum mechanics, a subject that lends itself to obfuscation, I want you to support your claim: Give me an example of something that exists over a spectrum where there is no natural dividing line” between existence and non-existence.

    Please answer.

  28. Stephen writes, “I will, for the sake of argument, and for the moment, assume that you are an expert in quantum mechanics so that you can no longer use your outrage as a stalling tactic.”

    I haven’t expressed any outrage, and I’ve not claimed to be an expert – you’re exaggerating, Stephen. You said that I didn’t understand QM, and at an educated layperson level, that is false.

    You write, “Without appealing to quantum mechanics, a subject that lends itself to obfuscation, I want you to support your claim: Give me an example of something that exists over a spectrum where there is no natural dividing line” between existence and non-existence.”

    QM isn’t an obfuscation – it’s an example that challenges your position. If you don’t want to consider QM, fine, but please don’t dismiss serious and pertinent points as obfuscations. Among other things, this is why I asked you about your background – to someone not knowledgeable about QM, addressing some of the philosophical issues it brings up may seem obfuscatory, but I don’t think that’s my fault.

    You write, “Please answer.”

    I already did. In post 25, I wrote “I’ve made no claim about there being any practical difficulties with “A exists” for A in the macro world, and I’ve accepted “the moon exists” as a perfectly valid proposition to which to apply the LNC: if you ask, “can the moon exist and not exist at the same time,” I’m quite happy to say No.”

    Is that not clear enough?

  29. Why do you keep stalling? You said,

    –Aleta: “The problem is that the real world is not like that – many things exist over a spectrum where there is no natural dividing line.”

    Without appealing to quantum mechanics, give me an example of one of those “many things” that “exist over a spectrum where there is no natural dividing line” between existence and non-existence.”

    Please answer.

  30. Folks:

    Passing by for a moment.

    We must notice the circumstance at work: we must be able to determine that something is A; which leads to the rest being not A. We cannot have A in the same sense and time etc being both so and not so.

    And this is real world not just an airy fairy world of logic.

    That fast moving out of control car rushing towards you on the street is there, and you had better take its existence seriously, if you want to survive; and jump out of the way.

    There are such things as fuzzy sets, where we may define partial membership, but again, how do we get tot he math to do that? By the old fashioned way.

    And, if A is a 60% bald head, it is either there or not there as that, but not both in the same sense and time. That is confusion.

    We may have the uncertainty of position and momentum of an object, but that quantum analysis gets there the old fashioned way, and we have a limit to our ability to learn the whereabouts and/or motion of an object, not that the object is not real.

    When it comes to Schroedinger’s poor cat or the like, there are several ways to interpret the result, but he one that makes the very least sense is the notion that the cat exists in a superposed alive-and-dead state. Indeed, we could have a little vid cam in the box observing friend cat. That would not violate physics. It would show a living cat, maybe all the way though the hour in the chamber, maybe we will see the hammer hit the vial and poor tabby collapses spectacularly.

    But never will we see the case of tabby being in a ghostly superposition of living and dead states.

    There are superposed states, starting of course with classical waves. That a plucked, stretched string is a superposition of travelling waves moving left and right does not mean it is in a contradictory state, just that we analyse the node and antinode pattern on superposed travelling waves with reflection and phase inversion at a fixed end.

    So, if we see signs that our 30 micron paddle is vibrating at a frequency that is apparently a superposition of two states, why should that be being in contradictory states at once? What of the ring molecular orbital of the benzine ring, or the like for COOH etc? one thing is for sure, if we were to do a video micrograph, we would not see it both vibrating and not vibrating! (And, it is big enough to videotape — maybe by passive IR emissions so we do not interfere with the dynamics. We could do the same for the cat too.)

    We have a major problem here, that needs to be addressed, root and branch.

    GEM of TKI

  31. F/N: if you want a real conundrum try Russell’s barber paradox: the two classes of men in the village: (i) those who shave themselves, (ii) those who do not shave themselves and are shaved by the barber. So, who shaves the barber? That inescapable unambiguity led to redefining sets as clearly definable collections. A poorly expressed collection is not a set; you do not have a definition merely because you can say something in words; no more than can you have a six pointed triangle.

  32. Oh, I see what the confusion is, I think, Stephen.

    When I wrote, “The problem is that the real world is not like that – many things exist over a spectrum where there is no natural dividing line”, I meant a spectrum of some other quality, not the quality of existence. I followed this up with an example of the quality of “being a point on a mountain” in post 3.

    I did not mean that there were many things that existed over a spectrum where there is no natural dividing line “between existence and non-existence.” I didn’t say that, and I didn’t mean to imply it, but I see that that is how you have been interpreting it. I hope this clears up what I meant.

  33. –Aleta: “The problem is that the real world is not like that – many things exist over a spectrum where there is no natural dividing line”, I meant a spectrum of some other quality, not the quality of existence. I followed this up with an example of the quality of “being a point on a mountain” in post 3.”

    Excuse me, but your answer makes no sense. You have already conceded, without qualification, that the moon cannot exist and not exist at the same time. You didn’t ask for a definition of the moon’s qualities prior to acknowledging the point because definitions about the moon’s qualities are irrelevant. There is no need to define the qualities of a moon in order to know that a moon cannot exist and not exist, just as there is no need to define the qualities of a mountain in order to know that a mountain cannot exist and not exist.

    Yet you waste our time arguing that the LNC cannot be applied to a mountain in the same way that it can be applied to the moon. It is a time-wasting exercise to make it appear as if there might be exceptions to the LNC in its application and you have wasted 20+ posts to support that irrational non-argument. Please stop it.

  34. Kairosfocus: Good stuff, boss. One hitch though in that the LNC is ‘not both’ and the LEM is ‘not neither’. The LoI being ‘not both and not neither’.

  35. Aleta:

    The problem is that the real world is not like that – many things exist over a spectrum where there is no natural dividing line. Therefore when we categorize things into A and not A, we create an artificial overlay on top of reality – an abstraction that is of course very useful in many ways, but also misleading and inaccurate in ways and at times.

    The machine you typed that post on is unavoidably binary and dichotomous. And yet it can compute everything that can be computed; if you accept Church-Turing.

    It is fine to state that there are things we cannot compute feasibly or at all. But if we cannot compute them with nasty dichotomy then we cannot compute them with a sliderule either. And so mathematics is out for that topic, as is any hope of modelling or prediction. Thus goes all of science for the same topic.

    Otherwise there is nothing in your objections that are dispositive and that were not answered specifically by Aristotle a half millenia before Christ got his sandals on. Save one: Virtual particles and photons. But it is not the case that they do and do not exist. Hypothetically they come into being, mature, and then get out. Much like birth, growth, and death. So your point there holds so long as you admit that you do and do not exist. Not that I can state it, claim it, or believe it Gettier. But that you do and will claim it.

  36. Stephen, you are clearly not trying to understand me. Among other thing, you say, “Yet you waste our time arguing that the LNC cannot be applied to a mountain in the same way that it can be applied to the moon,” which is not something I have said.

    There is a sure fire way to you to stop having your time wasted, which is to not even bother to read my posts, much less reply to them. If people keep responding to my posts, I’ll reply; if they don’t I will most likely go away again – I came back because this subject of the relationship between logic (and math) and the world is of great interest to me.

  37. As Brent indicated, but did not pursue, a corollary to LNC is division and definition. When we discuss the nature of some thing we must separate that thing from all other things and indicate what we are referring to when we discuss it. It is “that thing” and not “some other thing”. If it is a “mountain” we must define “mountain” as distinct form all other things. If “that thing” is a “virtual particle” it is the thing we refer to when we use the term “virtual particle” and not some other thing.

    We may not always comprehend the nature of “that thing” well enough to provide a proper definition but we can at least point to “that thing” and indicate that is what we are discussing and not other thing. But “that thing” is what it is and not “some other thing”.

    Therefore we must invoke the LNC. It is what is it is and it is not what it is not. It cannot, at the same time and in the same sense, be what it is and what it is not. Our comprehension of what it is will, no doubt, increase as we study it, but it will remain what it is regardless of our level of comprehension.

  38. Brent says, “When we discuss the nature of some thing we must separate that thing from all other things and indicate what we are referring to when we discuss it. It is “that thing” and not “some other thing”. If it is a “mountain” we must define “mountain” as distinct form all other things.”

    In general, I agree with this. I am trying to point to the problem of “defining mountain.” If we want to talk about the 50 highest mountains in the world, that’s a pretty easy definition. However, I don’t think it is possible to “define mountain” precisely enough, with objectively useable criteria, that we could determine where the dividing line between particular mountains and their surrounding non-mountains are. That is, we can create the category called “mountain” and use it in logical thinking, but when we do so we implicitly assume that there is a clearcut mountain/non-mountain boundary, when in the real world there isn’t such a boundary.

    This is a simple truth about knowledge: the map, or model, of the world, which includes all of the propositions, stated in language, that we manipulate with logic is not the same as the world itself; and many of the dividing lines we draw to distinguish A from not A are sometimes artificial and even arbitrary.

    dgosse writes, “Therefore we must invoke the LNC.” Yes, whenever we talk about things we invoke the LNC – I have said nothing to argue against this. However, given that we can hold erroneous beliefs and still manipulate them in a logically correct manner, we have to realize that there is more than logic to knowledge.

  39. Oops, it was dgosse I was quoting in post 38, and responding to, not Brent. Sorry.

  40. –Aleta: “There is a sure fire way to you to stop having your time wasted, which is to not even bother to read my posts, much less reply to them.”

    Why do you keep stalling and evading. I repeat:
    There is no need to define the qualities of a moon in order to know that a moon cannot exist and not exist, just as there is no need to define the qualities of a mountain in order to know that a mountain cannot exist and not exist– meaning that there is no difference in the application for either with respect to the LNC. Hence, your entire irrational framework comes tumbling down.

  41. Great post Kairos!

  42. Aleta:

    However, I don’t think it is possible to “define mountain” precisely enough, with objectively useable criteria, that we could determine where the dividing line between particular mountains and their surrounding non-mountains are.

    And you have an objectively usable criteria to determine where the dividing line between objectively usable and unusable criteria lies? Anything that can be quantified is precise enough for that quantification.

    That is, we can create the category called “mountain” and use it in logical thinking, but when we do so we implicitly assume that there is a clearcut mountain/non-mountain boundary, when in the real world there isn’t such a boundary.

    You’d obviously taken courses to unthink in college; that much was apparent before you noted your interest in logic and math. But this philosophist objection of yours was, once again, covered by Aristotle. Your objection has been neither valid, nor sound, for two thousand, five hundred-or-so years counting.

    … and many of the dividing lines we draw to distinguish A from not A are sometimes artificial and even arbitrary.

    No, precisely not. You’re not talking about A and not-A. You’re talking about A and A’, where A’ is a separate claim about a different subject than the not-A that you wish it to represent. This is a well known fallacy noted all the way back in the time of…

    Yeh, you know the rest by now.

  43. Hi Maus: Thanks, the issue on LEM is that some are proposing something on the border so to speak. If there is a genuine dichotomy, there is no third intermediate or bridging state. (And it is actually wider than being true/false, we have existence involved too — think of that red ball on the table; though T/F is included.) KF

  44. Hi Aleta
    Division and definition are, to a certain extent, arbitrary. That is why definition is important, even if defition is only pointing at an object and saying “that thing”. As we look at that thing we try to define it in a manner which is acceptable to both parties.

    For “mountain” we migh define it as a “rasied portion of the earth extending 1000 ft higher at its summit, excluding that portion less than 100 ft, above the nearest plain.” This definition is totally arbitrary, made at the time of writing by me, without reference to any dictionary, and is sufficient for discussion if you accept it. If you fidn it inadequate we can redefine it until both of us are satisfied with the result. Once the definition of mountain is settled we can discuss the attributes of that object we call “mountain”.

    Even the term “mountain” is an arbirary sign in English which indicates a “raised portion of the earth”. It is something totally different in Chinese, French, or German. But the object to which the different terms refer is still a “raised portion of the earth”.

    When we are dealing with obscure or abstract concepts we might encounter extra difficulty defining the term to each others satisfaction but with people of good will it should not prove insurmountable.

  45. –Aleta: “That is, we can create the category called “mountain” and use it in logical thinking, but when we do so we implicitly assume that there is a clearcut mountain/non-mountain boundary, when in the real world there isn’t such a boundary.”

    If you really believe that nonsense, then why don’t you apply that same standard to the moon? Why don’t you say, “we can create the category called “moon” and use it in logical thinking, but when we do so we implicitly assume that there is a clearcut moon/non-moon boundary, when in the real world there is no such boundary.”

    Don’t you realize that your linguistic fog has been penetrated? (Oh wait, don’t answer that question because you will use it as an excuse to avoid the first one),

  46. Response to post 40:

    Stephen, I’m not quite sure what irrational framework you are talking about, but you keep repeating yourself about things I did not say, and not addressing what I have said, so I will keep repeating, in different ways, the point I am trying to make.

    Let me try this way:

    In the original post; kf showed a diagram of A surrounded by a distinct boundary line, and everything else in the world labelled not A. Then he wrote, “If at a given moment we distinctly identify and label some thing, … we mark a mental border-line and also necessarily identify NOT-A as “the rest of the World.” We thus have a definite separation of the World into two parts.”

    I agree with this.

    So, in the case of a mountain, if we could in fact directly transfer this mental borderline onto the world itself, there would be a distinct boundary around the mountain (although not a real line of course) so that for any point we could say with certainty that this point Xo is or is not part of the mountain. The mental borderline, and dichotomous logic in general, divides the world, in respect to any particular proposition, into two separate parts.

    Wkipedia describe this thusly: “Because the law of identity partitions its logical Universe into exactly two parts: a “logical object” and everything else, it creates a dichotomy wherein the two parts are “mutually exclusive” and “jointly exhaustive”

    So, for logical objects, the boundary line is clearcut.

    But the real world is not like that. There is no clearcut line that one could draw using any particular definition, or set of criteria, concerning whether a point was on the mountain or not. There is a gradation between points clearly on the mountain and those clearly not on the mountain, but no clear dividing line. The real mountain is different then the “logical mountain” in this regard.

    So when we think about the mountain, and manipulate symbolic statements about mountains, we are working with the logical mountain that has a mental borderline that separates it from not a mountain. Such use of logic can be extremely useful.

    But the logical mountain is not the real mountain, and the real mountain will always have properties and particulars that are not contained in the logical mountain, no matter how refined our logical model of mountains become.

  47. F/N: of course in a digital age, we know that a sufficient number of organised yes/no dichotomies suffices to describe and specify any specifiable entity. In other words, by chaining Y/N questions we can specify anything of interest that is describable. KF

  48. To Maus: perhaps instead of just referring to Aristotle, you could explain the errors you think I’m making and explain how Aristotle resolved them. Otherwise, your posts aren’t useful.

  49. Aleta:

    Nope, there are real and potential objects in this world, and these objects exist or do not exist but not both nor neither.

    You may have a problem giving a precising [necessary and sufficient, detailed description] definition of “mountain,” but that does not prevent us from identifying cases and judging others by family resemblance. And in every one of these cases, the mountain exists.

    Mt Ranier, Mt Suribachi, Catherine’s peak in Ja’s Blue Mtns, Katie Hill behind me and blocking the view to the big bad boy down south of where I sit, and Mt Fuji all exist, they do not have a shadowy intermediate state simply because you or we have a problem making a precising definition.

    Once there is a sensible commonality to cases that leads to a concept that can be labelled in general, and individual cases can be tagged as we please, i.e. each case can be labelled as all of these mountains are, we have enough to see that Mt Fuji is, or is not, but not both.

    Or more specifically, before a certain week in August 1883, there were some mountains on the island of Krakatoa in Sundai straights. then, kaboom, and it was not. Something fresh is there now, Anak Krakatoa. Son of . . .

    Thus, the concept and the law are meaningful for mountains.

    KF

  50. 50
    material.infantacy

    I’ve been enjoying the comments on this thread. I’m just adding my take on many points already raised and answered, and some still being debated. Thinking about why something must be or not be, and not both, whether in physical or abstract realms, I’ve been considering sets.

    If we let S be integers from 0…9, we have a set that looks like this:

    S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

    Defining A as all members of S that are less than 5, we get the following set:

    A = {x | x ∈ S, x < 5} = {0, 1, 2, 3, 4}

    This gives rise to the complement of A, denoted here A’, called “not A”, which is everything from S that is not in A:

    A’ = {x | x ∈ S, x ∉ A} = {5, 6, 7, 8, 9}

    It is plain that what is A is A, and what is A’ is A’, and what is A is not A’, and what is A’ is not A. These aspects of this relationship are obvious and necessary. From this there is no escape.

    Here’s the rub however. Demonstrations such as this do not prove the LNC, they rely on it. Before I ever got around to defining these sets and their relationships, I needed to assume that ‘=’ means ‘is’ and that ‘/’ means ‘not’. The basis for the reasoning, for which something so obvious is derived, must be assumed beforehand. Everyone does this by necessity, everyday, whether they claim to accept the LNC or not.

    A’ = {x | x ∈ S, x ∉ A} = {x | x ∈ S, x ≥ 5} = {5, 6, 7, 8, 9}

    The LNC must already be present in the spaces between all the symbols which are used to express a relationship such as the above. It must be assumed as axiom, that what is, is, and what is not, is not. This forms the basis for all reasoning whatsoever. Nothing in the above makes sense if ‘=’ doesn’t denote “true” and ‘/’ doesn’t denote “negation”, and if 5 isn’t 5, and if 4 isn’t less than 5, and if A’ can be comprised of the members of A.

    The LNC cannot be proven or demonstrated, it is an axiom which exists prior to reasoning itself. Everyone relies upon the assumption it is true, whether admitted or not, whether physical or abstract. The LNC is the foundation upon which all reasoning and perception exists. It cannot be denied. Inaccurate or incomplete definitions do not change it.

    Again, we can define S as being the set of all trees on the earth:

    S = {t1, t2, t3, …, tn}

    and “supertrees” as being any tree greater than 250 feet in height from its base.

    ST = {x | x ∈ S, height(x) > 250 ft.}

    That we can’t determine the members of ST with 100% fidelity does not diminish the LNC in any way. There might be a tree which grows out of a slope, which is greater than 250 ft in height, but only if measured from the lowest downhill point; if we measure from the uphill point, it’s less than 250 ft. In another instance, the supertree candidate exists in a perpetually windy vicinity, and it’s top is always swaying such that it’s measurements are never accurate enough to positively place it in the group. This difficulty is with our criteria, not with the LNC, which must be assumed in order to establish the very criteria we are calling upon.

    Neither of these examples challenge the LNC, because we must use the LNC to determine them in the first place. They don’t even speak to the issue. That some things are difficult to define or measure does not change the fact that in order to reason that anything at all is one way or another, or that some qualities are difficult to determine, or that trees are trees, or that 250 feet is 250 feet, all rely on the LNC being axiomatically true.

    To deny the supremacy of the LNC over reasoning and observation is to invoke it. To deny anything at all is to invoke the LNC. To affirm anything is to invoke it. To believe in anything or nothing also invokes the LNC. The assertion “nothing is true” relies on ‘nothing’, ‘is’, and ‘true’ all denoting specific properties of being which call upon the LNC in order to establish their “is-ness.” To argue that a thing is either true or not true may very well be reasonable. To argue that true is not always true, that in some cases “true != true”, is self-referentially absurd.

    The claim that the moon can exist and then suddenly not exist does not deny the LNC. It relies on it. As dubious as the claim is, it can be put to the test with observation based on reasoning based on the LNC. To claim that the moon can both exist and not exist at the same time, is to utter profanities against the sane.

  51. Folks, I am not arguing about whether mountains exist or not, or whether they can exist and not exist at the same time (they can’t.) You guys seem to be arguing against something I’m not saying – like I’m some kind of surrogate for discussions you had earlier with others, but not addressing what I am saying.

    kf says, “they do not have a shadowy intermediate state simply because you or we have a problem making a precising definition.”

    Of course, and I’ve said nothing about any “shadowy intermediate states”: I just said there a difference, significant in my opinion, between the enforced dichotomies of logical objects – black-and-white distinctions, and the more amorphous and un-well-defined boundaries of real objects. All the points on the earth are very real – their existence is unquestioned, but whether they are on or off the mountain is in some cases an arbitrary decision – no matter how precise our definition of mountain, there will always be points whose status as on or off is not clear. There is no natural boundary between the mountain and the non-mountain. Mountain is an abstract category, and we impose it upon the unified reality of the landscape.

    So my interests here, again, are in how we create models of the world, using language, logic and math, and the ways those models are accurate and useful. In particular, I am trying to point to some of the inherent limitations of the process, so that we don’t lose sight of the fact that our models of reality are not reality itself.

  52. –Aleta: “There is no clearcut line that one could draw using any particular definition, or set of criteria, concerning whether a point was on the mountain or not. There is a gradation between points clearly on the mountain and those clearly not on the mountain, but no clear dividing line. The real mountain is different then the “logical mountain” in this regard.”

    Unbelievable. The law of non-contradiction, it seems, doesn’t apply to a mountain because no one has stipulated where its base begins and where the ground ends. By that same reasoning, the law of non-contradiction doesn’t apply to the Atlantic Ocean because no one has stipulated where its water’s edge ends and where its tributary begins.

    With postmodernists, I always have to reduce the question to its most basic form.

    Aleta, does Mount Everest exist? Yes or No

    Aleta, can Mount Everest exist and not exist at the same time? Yes or No

    Aleta, does the Atlantic Ocean exist? Yes or No

    Aleta, can the Atlantic Ocean exist and not exist at the same time? Yes or No.

    Please answer all four questions.

  53. material.infantacy:

    A’ = {x | x ? S, x ? A} = {5, 6, 7, 8, 9}

    It is plain that what is A is A, and what is A’ is A’, and what is A is not A’, and what is A’ is not A. These aspects of this relationship are obvious and necessary. From this there is no escape.

    A necessary caveat here since it came up earlier: Treating A and A’ as contradictories here is proper and precise strictly because it is provable that A’ is synonymous with ¬A. If the domain is not definite then this does not hold casually and negation must be treated as a denial rather than as an affirmative of an unknown complement.

    This is significantly exacerbated regardless when dealing with first-order quantifiers and cardinalities less than 2.

  54. Aleta:

    To Maus: perhaps instead of just referring to Aristotle, you could explain the errors you think I’m making and explain how Aristotle resolved them. Otherwise, your posts aren’t useful.

    My most sincere apologies, I was making the erroneous assumption that I was referring to a common point of reference and did not mean it be the name dropping of authoritate.

    The discussion on the difference of A, A’, and ¬A above should really cover the bases I think. It’s all a reference to contradictories, contraries, and subcontraries. Or, those things from which first-order quantifiers and other modal operators are constructed.

    If there’s something specific that this doesn’t cover let me know and I’ll do the long-winded bit for it.

  55. 55
    material.infantacy

    Aleta, The crux of the issue as I see it is whether mountain boundaries, or trees, or superpositions, or particles blinking out of existence have anything to say about the LNC.

    So my interests here, again, are in how we create models of the world, using language, logic and math, and the ways those models are accurate and useful. In particular, I am trying to point to some of the inherent limitations of the process, so that we don’t lose sight of the fact that our models of reality are not reality itself.

    Certainly. Modeling aspects of reality — objects, processes — will have inherent limitations. As well, the models that are built by our perception to simulate reality are very likely an approximation to “true reality.” However while this notion of true reality in juxtaposition to our perceptual models of it reveals possible inaccuracies, it’s our notion of true reality itself as having an ontological superiority over our perception of it, that demonstrates that the LNC proceeds our perception of reality as the method with which we draw any conclusion whatsoever. That being the case, our perception of reality has no dominion over the LNC, because the law proceeds any perceptions — it is used to conform our perceptual models to the one perfect archetype of true reality.

    I hope that made some kind of sense.

  56. 56
    material.infantacy

    Maus, thanks for the clarification. By indefinite domain, do you mean some sort of infinite set, or just a set whose members are not entirely known, or may not be known?

  57. –Aleta: “Folks, I am not arguing about whether mountains exist or not, or whether they can exist and not exist at the same time (they can’t.) You guys seem to be arguing against something I’m not saying – like I’m some kind of surrogate for discussions you had earlier with others, but not addressing what I am saying.”

    Oh sure. It’s just a coincidence that everyone here formed the wrong impression and that you were simply misunderstood at every step all along the way. Now that you finally acknowledge that a mountain cannot exist and not exist at the same time, and that you were wasting our time with that example, do you have any other examples to challenge the application of the LNC, or will you acknowledge that its application is universal so that we can finally end this ridiculous dance.

  58. In response to 52: Stephen, you still don’t get what I’m saying.

    You write, “Unbelievable. The law of non-contradiction, it seems, doesn’t apply to a mountain because no one has stipulated where its base begins and where the ground ends.”

    No – the above last few posts are not even in reference to the LNC and the existence of things. I’ve never said the LNC doesn’t apply – it’s a fundamental principle of logic. What I’ve said is that applying it to real-word situations can present various types of difficulties – not difficulties with the LNC itself, but with the meaning, truth, and applicability of the propositions about the real world in question. I’m not going to repeat all that.

    You write, “With postmodernists, I always have to reduce the question to its most basic form.” Hmmm, I don’t consider myself a post-modernist, although I might have a few beliefs that fit that category. But that’s neither here nor there at this point.

    “Aleta, does Mount Everest exist? Yes or No” Yes

    “Aleta, can Mount Everest exist and not exist at the same time? Yes or No” No

    “Aleta, does the Atlantic Ocean exist? Yes or No” Yes

    “Aleta, can the Atlantic Ocean exist and not exist at the same time? Yes or No.” No

    I think I’ve answered questions like this quite a few times now.

  59. Response to 57.

    Stephen writes, “Now that you finally acknowledge that a mountain cannot exist and not exist at the same time, and that you were wasting our time with that example, do you have any other examples to challenge the application of the LNC”

    I have never denied that a mountain cannot exist and not exist at the same time, and my example about points on the mountain was not meant to be a challenge to the LNC.

    I am not wasting your time – you are wasting your own time persisting in reading into my posts things that are not there.

    Show me a place in my posts where I’ve meant to challenge the LNC, or have made this claim about the moon.

  60. I went back and read my long opening post on another thread, here at http://www.uncommondescent.com.....ent-420703, as well as my opening posts in this thread.

    I affirmed the validity of the LNC multiple times, and never denied it. The concerns I’ve raised are of a different nature – they have not been challenges to the LNC. I think the evidence for this is clear.

    Stephen is either not reading my posts, or reading them poorly, or just projecting his beliefs about what he thinks I am saying.

    Perhaps he can show me differently by quoting my posts, by I really think he has just set me up as an advocate for a position I don’t hold.

  61. material.infantacy:

    By indefinite domain, do you mean some sort of infinite set, or just a set whose members are not entirely known, or may not be known?

    Any domain in which the definition of membership is sketchy and/or the quantification over the individuals is sketchy. Which can include finite sets as well.

    Dedekind cuts and ratios are one example. Such that if C is the cut then we may have A, which is strictly less than the cut, and B which is strictly greater than the cut. Obviously then A and B are not contradictories as C exists between them in all cases. In this instance we know the domain but find it impossible to construct a complement as a substitute for ¬A under a number of conditions. Any range, region, or ratio taken in a fuzzy manner is in the same condition by construction.

    Otherwise it is any case in which the domain itself is not amenable to things. For temperature if it is not hot then we are warm, lukewarm, cool, cold. There are a number of opposites within that domain that are all related to one another. But if the domain is poorly, or too broadly, defined then we end up in the condition in which ¬hot implies Mitt Romney. Which is intentionally absurd, but should clarify things.

    In the broadest sense, if the complement cannot be proven to be a proper complement, and its members cannot be well defined, then negation cannot be taken as an affirmative of that complement. In general if you’re trying to make the statements A and A’, such that you want A’ to represent ¬A, then you should treat A and A’ as unspecified contraries or subcontraries until you’ve satisfied which, both, or neither of the LEM and LNC that they satisfy. The LNC doesn’t hold between subcontraries and the LEM doesn’t hold between contraries. Iff both hold, then you have shown that they are contradictories and may treat them as such.

  62. –Aleta: “I affirmed the validity of the LNC multiple times, and never denied it. The concerns I’ve raised are of a different nature – they have not been challenges to the LNC. I think the evidence for this is clear.”

    To put this thing behind us, all you have to do is say that the LNC is universally applicable, meaning that it applies to every instance in the real world–no exceptions. Clearly, you did not acknowledge that fact until we smoked it out of you. Indeed, even at this late date, you have not acknowledged the point in explicit terms.

    On the other hand, if, as you say, your concerns were of a “different nature,” then you should have emphasized the fact early on. What you seemed to say, and what everyone was hearing was that the LNC is reliable as a logical construct but not always reliable with respect to the real world. Not true. Not even close.

  63. –Aleta: “I affirmed the validity of the LNC multiple times, and never denied it.”

    The only thing that you have affirmed multiple times is your subjective and incomplete formulation of the LNC. In effect, you redefine the LNC and then commit to your redefinition.

  64. Aleta,

    If your concern was of a different nature, why did you post at all. The only substantive thing that I could get out of what you’ve said is that we should be unambiguous. I’ll note, you were very ambiguous in pointing that out.

  65. I don’t want to speak for Aleta, but my take is that there are two related but separate issues. One is the LNC, a rule of logic in the form ‘A can not be not-A at the same time’. I don’t think anybody here, banned or not, has denied the validity of this logical statement.

    The second issue that I think Aleta is driving at, is the question if there could be anything in the real world that can not be captured in the simple form ‘A or not-A’. Importantly, if there would indeed be something in existence that does not fit into that particular box, would the LNC still apply to it?

    It goes back to earlier points made by eigenstate about the difference between the map and the territory. We humans love distinguishing, classifying, labeling. We do it all the time, consciously and unconsciously. And the moment we classify something as ‘A’ and oppose it to everything that we classify a ‘not A’ the LNC comes into play and always holds.

    A valid question in my mind is to what extent these classifications are a true refection of reality, or at least to some extent merely a consequence of how our minds, and importantly our languages, operate in this reality. Note that I am emphatically NOT saying that there is nothing in reality that can be sharply defined and classified – of course the class of such objects contains many such things. The point is, does this class cover absolutely everything, or are there certain things, phenomena, whatever you want to call them, that defy such classification, defy having to be ‘A or not A’, and are therefore exempt from (NOT violating!) the LNC?

    fG

  66. Folks:

    one of the things I find interesting about this thread is the lack of discussion across yesterday of the principle of sufficient reason and its derivative, that of causality.

    Why do you think that is so, especially as this is directly connected to design issues.

    In particular, to cosmological design inference, but also to the tendency to want to pull functionally specific complex organisation and associated information out of the hat of chance and necessity.

    Any thoughts?

    KF

  67. folks:

    A lurking issue in all the above — we seemingly need to dig deep to do the uprooting, lest the bit we leave in the ground springs back up, hardy as ever — is I think one of the ugly ditches so beloved of modern thought, here, that between mental activity and the external world as it is, between the phenomenal and noumenal worlds.

    To those clinging to this ditch, examples such as how we manipulate symbols to discuss the real world plainly do not register.

    You recall my speaking long since, of physicists scratching symbols in defined relationships on chalkboards and pointing out the self-referential nature of discussions on these topics. Above, people are showing the same in discussions on what can we define and what about the continuum type situation. In each case we are showing how even attempts to deny LNC or safely lock it away in an airy fairy logic game world, rely on it and its two stable-companions from the very outset.

    Never mind pointing out somewhere that even in a Zadeh, fuzzy border set we have a defining relationship that assigns fractional membership. And yes, by constructing such a model we can have something 10% hot, 30% warm, 60% cold and trigger an effective crisp control response by doing a tea blend of the control actions for the ideal cases so defined.

    All of these real world interactions of the intelligent mind rely on the bridge between the world of thought and the world of experienced reality.

    But, if you are thinking in light of Kant’s cut, you will still think nope the gap is not bridged. It is un- bridgeable.

    Therein lieth the rub: self-referential incoherence. Kant and others are here committing one of those little errors in the beginning that spring up into ugly chasms of error cutting wide swaths across out life of thought and experience alike.

    Here is the overlooked problem of self-referentiality: to assert that we know and can know naught of the external world as it is, is to already and inescapably claim to know something about the external world, its alleged un-know-ability. So, which is it, we can know something about the external world (and indeed we can make errors in so claiming to know), or we truly cannot know in which case we could not even know that much.

    Or, as William Lane Craig pointed out in his debates with Gerd Ludemann:

    insofar as these . . . assumptions include Kant’s strictures on the scope of scientific knowledge, they are deeply, fatally flawed. For Kant must at least be claiming to have knowledge of the way some things (e.g., the mind and its structures and operations) exist in themselves and not merely as they appear; he confidently affirms that the idea of God, for instance, has the property of unknowability. [10] So the theory relies on knowledge that the theory, if it was true, would not — could not — allow. [ Jesus' Resurrection: Fact or Figment, ed. Paul Copan (Downer's Grove, IL: IVP, 2000), p. 13. NB: Ref. [10] is to Plantinga’s Warranted Christian Belief, pp. 3 – 30, and is shortly followed by a reference to F. H. Bradley’s gentle but stinging opening salvo in his Appearance and Reality, 2nd Edn.: that “The man who is ready to prove that metaphysical knowledge is impossible has . . . himself . . . perhaps unknowingly, entered the arena [of metaphysics] . . . . To say that reality is such that our knowledge cannot reach it, is to claim to know reality.” (Clarendon Press, 1930), p.1]

    Given the self referential absurdity, and the patent confusion, the answer should be plain.

    We can and even do in many cases know about the external world.

    Indeed, utterly abstract principles like 2 + 3 = 5, routinely and reliably strictly constrain what can be at all in that world. There is no possible world in which we can have heap A, two tokens, and heap B, three tokens, then push together and not get five tokens in the new heap we have so formed. It is only sheer familiarity that blinds us to how astonishing such a finding truly is.

    Thence, with elaboration, the so-called “unreasonable” effectiveness of mathematics in science, engineering and day to day life.

    There are using abstract, conceptual realities that do control what can be in this or any other possible world.

    And, as one of these, it so happens that once we can identify an item A, and distinguish it by whatever means from the rest of the world, under the usual rules of consistency in meaning etc:

    (a) the part labelled A will be A (symbolically, [A => A] = 1),
    (b) A will not be the same as NOT-A ( [A AND NOT-A] = 0); and
    (c) there is no third option to being A or NOT-A ( [A OR NOT-A] = 1).

    Such holds whenever an A exists. It is a necessary constraint on what is possible, once A exists as a distinct thing, even if it may have fuzzy borders. try this one: where does your arm end and the trunk of your body begin? Your nose? Your leg? sure, you can identify ever so many border zone points that you could debate what they are till the cows come home, but that has not changed the realities that we have arms, noses and legs etc. A nose is a nose and not also a non-nose. Something is nose or not nose but not both or neither. Regardless of fuzziness of the border.

    This point will hold even where we struggle to decide if this is indeed A.

    If it IS A in truth, the three principles apply. Our limitations as finite and fallible do not stop those consequences from actually following, they are just our limitations.

    GEM of TKI

  68. F/N: One of the inevitable talking points here, is that we are indulging in “black and white thinking.” But in fact the opposite of white is not black, it is NOT-White. Green, red, purple, yellow etc in any shade will do [think in terms of the classic CIE "tongue of colour" colour space model used for say colour TV theory, with a white point in the middle of the spectrum locus and the line of purples . . . if you are not at the white point, you are not in white territory at all . . . though of course we do see definition of a colour temperature "white"]. And sure there may be a spectrum of greys between black and white, but that does not mean that white and black are not distinct. KF

  69. Stephen writes, “On the other hand, if, as you say, your concerns were of a “different nature,” then you should have emphasized the fact early on”

    I did. The second line of my first long post on the subject was “I’d like to provide what is perhaps a broader perspective on the subject, or one that at least adds a few more elements to the discussion.”

    Major sentences in the ensuing post were things like

    “The LNC is a truth about propositions in the abstract, as elements of a logical system, as opposed to the truth or meaningfulness of the propositions themselves as they relate to the world.”

    and

    “So the point is not whether logic is true or not (there is no doubt about the logical validity of the LNC),but rather what is the relationship between logic and the world, and/or what is the nature of our use of logic as we investigate the world.”

    So I think I pretty clearly, “early on”, stated

    a) my support for the LNC, and
    b) my interest in another question concerning the difference about logical rules about propositions and the nature of the propositions themselves in respect to the real world.

    I won’t summarize the rest of the post, but I will repeat that you have been consistent in not getting, for whatever reason (I won’t repeat the possibilities for those, either) the distinctions I wanted to discuss, being focused as you have been on thinking I was attacking something I was not. I will agree with you that further discussion is a waste of time, though – I need to move on with my life.

  70. to faded glory

    Thanks for the feedback and support. I agree with almost all of your post: the main topic for me is the way in which our maps, or models, of the universe, which depend on creating categories which have sharp boundaries in accordance with the nature of logic, are or are not adequate representations of reality, with an emphasis on the ways in which this makes it hard for us to talk about and understand things which have fuzzy boundaries, or which exist over a continuous spectrum in respect to some quality. (Long sentence, I know, but this is a recap before I get out of here.)

    However, I don’t agree that I was trying to argue that virtual particles were somehow exempt from the LNC. The original arguments that happened before I starting posting on Thursday had been about applying the LNC to statements about existence, and previous posters (apparently – I didn’t read any of those previous posts) had mentioned quantum states.

    This summer I read a lot about this topic: Feynman’s “QED”, “Shrodinger’s Cat” and Schrodinger’s Kittens” by Gribbin, “The Hunting of the Quark” by Riordan, and “Dreams of a Final Theory” by Weinberg. All of these people, deeply familiar with the topic, had interesting things to say about how QM raises issues about what is reality at the quantum level and what is the nature of our knowledge about that reality.

    So when I was discussing virtual particles here, I was not questioning the logical validity of “virtual particles exist and do not exist” – that is logically impossible. Rather I was discussing the real world meaning of “exist” and wondering whether it is a concept that we can cleanly apply to virtual particles.

    In my first post back on Thursday, I wrote,

    In this case, then, if one were to ask if it possible to say “that a virtual particle can exist and not exist at the same time”, I would say this: within the world of logic where A = “a virtual particle exists”, the proposition is logically impossible, but as a statement about the real world that statement is problematic and uncertain, not because the logic is faulty (the LNC can’t be wrong), but because the model we have between our logical constructs and the real world is inadequate.

    So note, I was not even here saying there was a problem with the LNC – I was saying that the proposition A = “a virtual particle exists” might have fuzzy boundaries, not clearcut ones, in a way unlike anything in the macro world.

    So, again, fg, nice seeing the virtual you here on the internet, and thanks for your comments.

  71. Aleta: So I think I pretty clearly, “early on”, stated

    –”a) my support for the LNC, and

    –b) my interest in another question concerning the difference about logical rules about propositions and the nature of the propositions themselves in respect to the real world.”

    Yes, I know. [b] was meant to cancel out [a] so that you could try to have it both ways. You accept the Law of NonContradiction as a non-negotiable rule for the “map”, but not for the “territory” That is why you made the distinction in the first place.

    When pressed for an example of how the territory confounds the map, you introduced the “mountain” as an example–an exception to the LNC in the real world. But when you were called on it, you reversed your position and admitted that it does, indeed, conform to the rule after all, claiming to have been misunderstood all along. What nonsense.

    I provided you with the opportunity to clear things up when I said this: “To put this thing behind us, all you have to do is say that the LNC is universally applicable, meaning that it applies to every instance in the real world–no exceptions.”

    An intellectually honest person would have responded to that request because it is a requirement for the LNC. As we know, though, you reject the point, but you will not be forthcoming and say so. Clearly, you believe that there are exceptions, but strategically you feel compelled to remain silent about your convictions on the matter.

    Rhetorically, you say that you accept the LNC, but in reality you reject its universal application. Everything else you write is calculated to obfuscate. Naturally, faded glory agrees with you and defends you. Why wouldn’t he? He is in the same camp and is the last person that would call you out.

  72. Oh sure. It’s just a coincidence that everyone here formed the wrong impression and that you were simply misunderstood at every step all along the way.

    Who is “everyone?” Aleta seems to be making some very, very finely hair-splitting point, while repeating acceptance of the LNC over and over. And that point doesn’t seem to have any direct bearing on matters related to design, evolution, or origins. Granted, I can be really slow to catch on, but I just don’t get the problem.

  73. I had thought I was done with this discussion, but someone elsewhere made a comment about the topic that gave me a new thought, and perhaps a better way of making one of the points I was trying to make.

    So giving that I will be archiving this thread to preserve my thoughts and the arguments of others, for the record here is an additional point:

    In logic, the LNC can be stated as (A and ~A) = false. Let’s look at this from a truth table point of view.

    The LNC is a conjunction: two statements connected by “and.” As we all know, the truth table for a conjunction is “T and T = T”, and all other combinations (TF, FT, and FF) = F.

    Further more, the truth table for negation is “A = T ==> ~A = F” and vice versa.

    Therefore, the LNC can be seen as a combination of the rules for a conjunction and for negation: if A is true, the LNC is (T and F), which is F, and if A is false, the LNC is (F and T), which is also F.

    This is pure symbolic logic, and I don’t think there are any problems or uncertainties about it.

    Now let us apply this to the real world, where A is a proposition about the real world. Of course, the same reasoning applies: if A is true, ~A is false, and the LNC holds, and vice versa is A is false.

    But what if A is meaningless: what if A is a proposition that has no truth value in respect to the real world? What can we say then? All we can say, I think, is that if we knew that A was true or false, then the LNC would hold, but as long as A is meaningless, it is meaningless to even apply the LNC. Only statements which can be assigned a truth value can be represented within the logical framework described above. If A is meaningless, so is ~A, and (A = meaningless and ~A = meaningless) is meaningless, not false.

    The same thoughts apply to propositions about the real world that may be true, or may not: they may be incomplete, ambiguous, possibly true but unverified yet, etc. As long as they don’t have a truth value, they can’t be incontrovertibly represented by a logical formalism included the LNC.

    That is, and this is a point I made earlier, with additional clarity (to me) in light of this discussion.

    1. Within the world of logic, the LNC is absolutely and always true, because in that world, A is a proposition that is either true or false.

    2. In the application of logic to real-world, the LNC can apply only if proposition A can be meaningfully said to be true or false.

    This is in fact how we use logic to investigate the real world. We create a hypothesis about something we think might be true. We then consider it as true, and thus make it subject to the laws of logic, which are only about propositions which are true or false. Then we manipulate the logic to reach new conclusions. Then we go out in the world and test those conclusions. If they also appear to be true, or in fact seem very certainly to be true, then we have evidence that our original proposition is true. The more certain we are about the truth value of our propositions, the more they properly they come under the domain of logic.

    This is what I’ve meant by building models of the real world: we built up a set of propositions that we have evidence to believe are true, both because of empirical evidence and because that when they are treated as true, they “hang together” logically with other evidence and other propositions that we believe are true.

    Thanks to the person who stimulated these thoughts.

  74. @Aleta,
    Your last comment sounds reasonable. Its like the statement, “This sentence is false.” The sentence itself is not referring to a class of thing which can be true or false. It has no content about the world. It makes about as much sense as saying, ” this coffee mug is false.” The only sense i can make of it if it indeed does have real content,would be that it means,” This sentence is not real” in which case it would be false and would not lead to any paradox. As it is usually formulated, “this sentence is false” is meaningless since there is nothing in the sentence which can be verified to be true or false and therefore saying it is one or the other is nonsense. I note that some philosophers have tried to use the liar paradox as well as the ambiguity of language as a means to dispense with the LNC. Just take a look at the stanford encyclopedia of philosophy page on dialetheism. They fail in my opinion.

    If what you were trying to say all along was that you cant meaningfully apply the lnc to meaningless statements, then I agree and I do believe this debate was unnecessary.

  75. I may as well sum up this problem:

    Aleta, the problem is that, at some point, you bought into the epistemological skepticism that teachers in the secular academy inculcate into their students. Unfortunately and decisively, they persuaded you that the “map” is not a reliable indicator of the “territory.” Granted, the map is not a “perfect” indicator, but that is another matter. You are confusing reliability with perfection.

    In fact, our minds provide us with a reliable image of the essence of the physical entities we experience through our senses. If think you are looking at a tree, that is because you are looking at a tree, not just a organic pile of wood standing tall. Your knowledge of that tree may not be perfect, but it is reliable in the sense that you rightly perceive that you are looking at a tree.

    To know that the Law of non-contradiction pertains to every instance in the real world, one needs only to possess a reliable map, not a perfect map. You have been trained to believe that the mind, or your mental map, is unreliable– that if forms arbitrary images of “whatever kind of thing may be out there.” For that reason, you perceive an unduly wide gap between the map and the territory.

  76. 76
    material.infantacy

    “…I just don’t get the problem.”

    Scott, my take is, one cannot reason without the LNC. So when exceptions to the law are invoked, it seems quickly forgotten that one cannot reason about exceptions to the law without making use of the law. It’s not a matter of whether one can apply an objective standard of “true” and “false” to every situation without error or inaccuracy. It’s a question about whether any perception of an aspect of reality can sidestep analysis and evaluation which relies on the LNC in order to occur.

    I believe the problem here, is that one cannot “choose” whether or not to apply the LNC. It is assumed in our reasoning; and any observation about anything, anywhere, is based on reasoning. When it comes to making observations, there are not two domains, the logical and the actual. Every observation we make about reality must pass through perception; and perception itself relies upon the laws of reason. If one reasons that the LNC does not apply in some cases, because reality is different from our perception of it, one has committed two errors. The first is assuming that any observation of reality can be made independent of perception. The second is assuming that by making use of reasoning one can rationally choose whether or not to apply the LNC.

    I’m fairly new to this subject, so I may have missed the mark. However since “true = true”, and “true != false”, and “false = false” cannot be proved, it must be taken as axiom (rational) or disregarded altogether (irrational). It cannot be selectively applied, because attempting to do so invokes the very axiom being toyed with. The LNC is not merely a tool that we can make use of in order to aid our reasoning — it is the very foundation of that reasoning. The LNC does not proceed from our ability to reason. Our ability to reason proceeds from the wisdom embodied in the LNC.

    Either the laws of reason have dominion over all perception and observation, or we cannot trust perception in the slightest. There exists truth, and there exists falsehood. If one believes such, then reason, hence the LNC, precedes perception / observation / evaluation every time, without equivocation. There is no way to trust perception — or assign any truth value to an observation — without assuming the laws of reason. Once we attempt to evaluate anything we observe, the LNC has already spoken. It cannot be denied.

  77. Oh for crying out loud people, everyone knows that the law of non-contradiction cannot be applied to meaningless statements. I have made that point many times on other threads. It is a distraction and an obfuscation. There is nothing at all subtle about that point.

    The question is whether the law of non-contradiction pertains to ALL INSTANCES OF THINGS EXISTING IN THE REAL WORLD–WITHOUT EXCEPTION. All Aleta has to do is say “yes,” and the matter will be settled. She refuses to acknowledge the point.

  78. Scott Andrews 2, Kuartus

    The issue of ambiguity and imprecise meaning with respect to the LNC has been dealt with elsewhere. Here is an example from another thread:

    –David:

    –“Is ID essentially religious?”

    StephenB :You are not effectively using the language to express your meaning, possibly because you don’t know very much about ID. If you mean ID science, the answer is no. Also, the word “essentially” is ambiguous. It leaves too much room for interpretation, which does not lend itself to deductive analysis.

    –”This question LOOKS like a straightforward yes or no question, but it’s far from one. What do we mean by “essentially” or by “religious”? These questions matter. To paraphrase one Supreme Court justice, reasonable, intelligent and knowledgeable people can legitimately disagree about the meaning of all but the most trivial statements. And what’s discussed here is certainly not trivial.”

    StephenB: The question was not properly crafted. No would could possibly discern its (your) meaning. If you are asking, “Does ID methodology assume, presuppose, or depend on religious faith in any way,” then the answer is no. That question can be tested for logical validity. ID methodology either presupposes religious faith or it doesn’t. There is no excluded middle ground. If you could show, for example, how ID methodology does presuppose, or depend on, or assume religious faith, you would prove conclusively that my claim is false.

    –“In the case of Jupiter, this is very true. But instead of Jupiter, let’s substitute things like “justice” or “God” or “the greatest good for the greatest number.” There is without question considerable ambiguity as to whether such things “exist” in any absolute sense.”

    StephenB: Again, one must know something about the subjects being discussed. I would have no difficulty applying the law of non-contradiction to any of them.

    Examples:

    Plato wrote about Justice in the “Republic.” Either he did or he didn’t. It can’t be both.

    According to Christian tradition, a Divine God took on a human nature. Either He did or he didn’t. It can’t be both.

    Utilitarianism is a form of consequentialism. That statement is either true or false. It cannot be both true and false.

    So the issue of meaningless or ambiguous statements has been dealt with elsewhere. The question on the table, which is the question for Aleta is this:

    Does the law of non-contradiction pertains to ALL INSTANCES OF THINGS EXISTING IN THE REAL WORLD–WITHOUT EXCEPTION. Yes or no.

    After all this time, I think I deserve an answer.

  79. “pertains” above = pertain

  80. Aleta:

    But what if A is meaningless: what if A is a proposition that has no truth value in respect to the real world? What can we say then?

    That the proposition: “A is a proposition” is false. And that the alternate proposition “It is not the case that A is a proposition.” is true.

    The same thoughts apply to propositions about the real world that may be true, or may not: they may be incomplete, ambiguous, possibly true but unverified yet, etc.

    There is no possibly true, incompletely true, or ambiguously true. If it is correct in all its particulars then it is true. If not then it is false. And a separate discussion can be had about all the myriad ways it could be false.

    As long as they don’t have a truth value, they can’t be incontrovertibly represented by a logical formalism included the LNC.

    LP, K3 and other ternary logics that include a ‘z’ state for “indeterminate/malformed/unknown” still obey the LNC. You’re again inventing problems long solved and making appeal to the impossibility of the existence of solutions despite those solutions existing. Not that these are necessary unless you attempt to assign truth-values to things that aren’t truth-bearers in the first place. A necessary problem for databases only.

    This is what I’ve meant by building models of the real world: we built up a set of propositions that we have evidence to believe are true, both because of empirical evidence and because that when they are treated as true, they “hang together” logically with other evidence and other propositions that we believe are true.

    We believe, each of us individually, what we believe because we believe it. There is at no time a need for empiricism, “evidence”, peer pressure or cohesiveness. It is also nowhere near factual — that is empirical or evidentiary as you like — that human beings avoid contradictory beliefs. Your argument in this thread is evidence for that if you demand it for yourself.

  81. I should point out that the exasperation I expressed at 77 was not, in any way, directed at material.infantacy. On the contrary, my post just happened to follow his. On the contrary, his remarks were relevant, well written, and spot on.

  82. 82
    material.infantacy

    Thanks Stephen, appreciated. No worries, I didn’t take your comment that way. I understood you to be commenting specifically on meaningless statements’ applicability to the LNC. m.i.

  83. Stepehn writes, “Oh for crying out loud people, everyone knows that the law of non-contradiction cannot be applied to meaningless statements.”

    So if it were decided that “virtual particles exist” were a meaningless proposition – that existence as we understand it for all other objects just didn’t apply, then the statement “virtual particles exist and virtual particles don’t exist” would be meaningless, not false: that is, the LNC wouldn’t apply to the statement.

    Is that a correct conclusion based on what you wrote, Stephen?

  84. Aleta:

    So if it were decided that “virtual particles exist” were a meaningless proposition – that existence as we understand it for all other objects just didn’t apply, then the statement “virtual particles exist and virtual particles don’t exist” would be meaningless, not false: that is, the LNC wouldn’t apply to the statement.

    If it was decided that ‘exist’ as we understand it for all other objects did not apply to virtual particles then it is not true that ‘virtual particles exist’. It’s not a meaningless statement, it is simply false.[1] And you are once again denying the LNC out one side of your neck while claiming you don’t on the other.

    Which is no problem since that’s merely a dialetheia and thus it is proven that the LNC doesn’t hold, eh?

    So far you’ve demonstrated that you are ignorant of Aristote, ignorant of the underpinning of Frege’s work with First-Order logic, and have yet to demonstrate that you even have a passing familiarity with Hilbert deductions bolted on top of Frege’s baby.

    What you have demonstrated is repudiation of the LNC, ignoratio elenchi, fallacies of change of subject and many question. So it’s well past the time that you be continually treated as honest but misguided.

    So since you have such a happy hook on empiricism and evidence then it is time for you to prove that you are not thoroughly mendacious: Put or up or shut up, produce a valid example, a single witness or piece of evidence, to support your claims.

    [1] Post script here is that you’re equivocating, also a fallacy.

  85. Aleta, I notice that you continue to avoid my definitive question, which I have asked, or alluded to, at least five times, comfirming your unwillingness to dialogue in good faith. You have proven by your evasive silence that you do not accept the Law of Non-Contradiction, in spite of your rhetorical claims to the contrary. I had no trouble penetrating your linguistic fog.

  86. At the (fairly certain) risk of incurring more of your wrath, maus, there would be, in my layperson’s mind, a difference between saying “virtual particles exist” is false and “virtual particles exist” is meaningless.

    To say that “virtual particles exist” is false would, it seems to me, imply that virtual particles were the kind of thing that potentially could exist, and potentially might not, but to say that “virtual particles exist” is meaningless would imply that existence was just not a property that even potentially is applicable to virtual particles.

    Also, here’s a second point in response to Stephen’s remark that “everyone knows that the law of non-contradiction cannot be applied to meaningless statements.”

    Within logic itself, as opposed to applying logic to the world, the LNC does apply to meaningless statements. In fact, within logic itself, the meaning of a proposition is irrelevant. The statements (the moon exists and the moon does not exist) and (fuddledoms are beeble and fuddledoms are not beeble) are entirely equivalent statements within logic itself: they are just examples of (A and~A) in which if A is true, ~A is false, and vice versa, without any concern for whether A is something that, in the real world, could even have a truth value attached to it.

  87. And Stephen, I have answered your definitive questions. See post 58.

  88. Aleta:

    To say that “virtual particles exist” is false would, it seems to me, imply that virtual particles were the kind of thing that potentially could exist, and potentially might not, but to say that “virtual particles exist” is meaningless would imply that existence was just not a property that even potentially is applicable to virtual particles.

    “Aleta is a child molester.” According to you this claim is not wrong, just meaningless. But if we agree that this claim is wrong, then it is ‘false’, that it would imply that you were possibly a child molester anyways.

    So if we say that it is ‘false’ that you are a child molester then you, by your argument, claim that you are both a child molester and not a child molester. Repudiating the LNC.

    And if we say that it is ‘meaningless’, since you are quite obviously not a child molester, then your argument is that the LNC doesn’t apply because you are not a child molester. In which case it must be the, LEM by inference, and so you are a child molester. Once again repudiating the LNC.

    Therefore I accept your argument that you claim you are a child molester. And you accept mine that you are not. And no contradictions were harmed in the typing of this post.

    Which slightly mischaracterizes your argument. As you will properly note that it only implied that it was ‘possible’ for you to be a child molester. But if it implies that it is possible, then it also implies that it is possible that you are not. In which case you are neither a child molester nor not a child molester but the superposition of the possibility. Thus, you are and and are not still. Once again repudiating the LNC.

    Of course an utterance that makes no claim is not a proposition in the first place. While I maintain that a claim is made by putting forth “Aleta is a child molester.” your statement is that no claim was made at all. And thereby you have made no claims in this entire thread and will make no claims going forward.

    Within logic itself, as opposed to applying logic to the world, the LNC does apply to meaningless statements.

    Oops. So much for that then. Therefore, your claim here implies the possibility that the LNC does not apply to meaningless statements.

    Before we get onto to unclaiming what is unpossible in unlogic we really ought first square away just what you think ‘true’, ‘false’ and ‘meaningless’ are once your equivocations are stripped away.

  89. Meaningless schmeaningless!

    The LNC, I would say, does apply to meaningless statements. That is, either a statement is, or is not, meaningless; not both. If there is disagreement about the meaning, or lack of it, in a statement, it isn’t that the LNC doesn’t apply, just that we need to make sure the statement is clear.

    The problem isn’t with the LNC applying to a meaningless statement at all. The problem is only in clarifying the statement so that we can see HOW the LNC applies to it; i.e. is it a contradiction in itself, in relation to another statement, or to other truths or facts.

    Again, as I said in post #19, all Aleta has said is that ambiguous statements are ambiguous statements.

  90. Simple and clear:

    It is never a question of whether the LNC applies, but only, in some cases, how it applies.

  91. Dang it!

    I guess I should clarify “how”. Sometimes people take “how” to mean “whether”.

    So, “how” means does it affirm a statement as non-contradictory, or contradictory.

  92. F/N: It seems one of the roots of confusion we must uproot is the difference between what is (or, what was) and what we may or do know about it, how confidently.

    So, let’s note:

    1 –> What is or was is a matter of reality.

    2 –> To accurately describe reality is to speak the truth — saying of what is/was that it is/was, and of what is/was not that it is/was not.

    3 –> A proposition (in the logical sense) is the implied truth claim in a statement, which may require some appreciation of context and clarification etc.

    4 –> A proposition may or may not be accurate to reality, so it would be accordingly true or false. (And of course we may make compound propositions by chaining such together with various connectives.)

    5 –> By contrast the state of our knowledge of what is true or false, and the degree of warrant that can or does attach to that knowledge, is a matter of epistemology, not truth proper. That is, for instance, it is possible for something to be true and not known to be true, or for something to be false and not known to be false.

    6 –> So, we may properly distinguish — that dichotomising chop again! — the question true/false, from the question known/unknown, and the further question, with what degree of warrant.

    7 –> The laws of thought in view relate to truth and falsehood, not our degree of knowledge of what is true or false, much less the confidence we have on that.

    8 –> And very properly so, for we must be clear that truth and falsity exist before we can ask and seriously answer to what extent do we apprehend such, on what warrant. And indeed the process of warranting is strongly premised on confidence in reality and truth as being accurate to reality.

    9 –> So, whether a proposition is true or false has nothing to do with whether we know that it is so, to what degree of confidence.

    10 –> And once we know a statement to be a potential truth-bearer, then it will be either true or false, but not both nor neither.

    11 –> Going further, we know (as was discussed above yesterday) that propositions, as potentially true assertions about reality, point beyond the world of thought to the world of existence. Indeed a true proposition is one that accurately refers to what is/was etc.

    12 –> And, a warranted, credibly true proposition — something that we can reasonably claim to know, like 2 + 3 = 5, or that water is made up of H2O molecules, or that angular momentum is conserved under relevant circumstances, or that bad money will normally drive good money out of circulation, or that Napoleon was once Emperor of France, or that there was once a figure living among us known as Jesus of Nazareth, who proverbially “suffered under Pontius Pilate” — is one that a responsible and reasonable person will acknowledge as referring to reality, not just a vapour of thought.

    13 –> So also, once we see that labels may be properly and recognisably attached to things that do exist [here we simply choose the label A for convenience], we can see the six key laws of thought attaching to the world of such things by way of accurate reference:

    Consider the world:
    || . . . ||

    Identify some definite A in it:

    || . . . (A) . . . NOT-A (the rest of the world) . . . ||

    Now, let us analyse:

    [1] A thing, A, is what it is (the law of identity);

    [2] A thing, A, cannot at once be and not-be (the law of non-contradiction);

    [3] A thing, A, is or it is not, but not both or neither (the law of the excluded middle).

    [4] “to say that what is is, and what is not is not, is true.” (Ari, on what truth is)

    [5] “Of everything that is, it can be found why it is.” (Principle of sufficient Reason, per Schopenhauer.)

    [6] If something has a beginning or may cease from being — i.e. it is contingent — it has a cause. (Principle of causality, a direct derivative of 5, which points to the possibility of necessary, non contingent beings, e.g. the truth in 2 + 3 = 5 did not have a beginning, cannot come to an end, and is not the product of a cause, it is an eternal reality. The most significant candidate necessary being is an eternal Mind. Indeed, down this road lies a path to inferring and arguably warranting the existence of God as architect, designer and maker — thus, creator — of the cosmos. Cf Plato’s early argument along such lines, here.)

    14 –> Of course, Schroedinger’s poor cat (or the like) may be trotted out to try to make it seem that something can be and not be in the same sense at the same time. But in fact if we were to put an IR camera in the box to record the course of events in that dark chamber [i.e. a passive sensor], at no time would we ever record a ghostly superposition of a living and a dead cat, it would be alive, and if unlucky, once the RA source triggers the hammer to break the vial of prussic acid, we may see it collapse and die. That we, external observers do not know, does not mean that the reality is of an imagined superposition of possibilities; superpositions are real [and as familiar as the stretched, vibrating string with nodes and antinodes], but they are not superpositions of existence and non-existence. (For more on quantum issues, cf here.)
    ___________

    What is or what is not, is different from what we know or may observe about it.

    GEM of TKI

  93. F/N 2: Similarly, it seems the question of the reality of virtual particles is on the table. I therefore suggest that we should first consider that exchange forces to create force effects are seen as being due to virtual particles, and that something like the Casimir effect [which has apparently been observed] point to the reality of such particles, even though we may not directly observe them.

    I should note, too, that the whole province of origins sciences studies the remote and unobserved past, and is seen as scientific. Observability is not to be confused with reality or knowability, though of course it is accompanied by a weaker degree of warrant.

    Let us clip Sci Am on the Casimir Effect:

    To understand the Casimir Effect, one first has to understand something about a vacuum in space as it is viewed in quantum field theory. Far from being empty, modern physics assumes that a vacuum is full of fluctuating electromagnetic waves [which are of course quantised, i.e. photons] that can never be completely eliminated, like an ocean with waves that are always present and can never be stopped. These waves come in all possible wavelengths, and their presence implies that empty space contains a certain amount of energy–an energy that we can’t tap, but that is always there.

    Now, if mirrors are placed facing each other in a vacuum, some of the waves will fit between them, bouncing back and forth, while others will not. As the two mirrors move closer to each other, the longer waves will no longer fit–the result being that the total amount of energy in the vacuum between the plates will be a bit less than the amount elsewhere in the vacuum. Thus, the mirrors will attract each other, just as two objects held together by a stretched spring will move together as the energy stored in the spring decreases.

    This effect, that two mirrors in a vacuum will be attracted to each other, is the Casimir Effect. It was first predicted in 1948 by Dutch physicist Hendrick Casimir. Steve K. Lamoreaux, now at Los Alamos National Laboratory, initially measured the tiny force in 1996.

    It is generally true that the amount of energy in a piece of vacuum can be altered by material around it, and the term “Casimir Effect” is also used in this broader context. If the mirrors move rapidly, some of the vacuum waves can become real waves. Julian Schwinger and many others have suggested that this “dynamical Casimir effect” may be responsible for the mysterious phenomenon known as sonoluminescence . . .

    And again, the same source, in a second article, argues:

    Virtual particles are indeed real particles. Quantum theory predicts that every particle spends some time as a combination of other particles in all possible ways. These predictions are very well understood and tested.

    Quantum mechanics allows, and indeed requires, temporary violations of conservation of energy, so one particle can become a pair of heavier particles (the so-called virtual particles), which quickly rejoin into the original particle as if they had never been there. If that were all that occurred we would still be confident that it was a real effect because it is an intrinsic part of quantum mechanics, which is extremely well tested, and is a complete and tightly woven theory–if any part of it were wrong the whole structure would collapse.

    But while the virtual particles are briefly part of our world they can interact with other particles, and that leads to a number of tests of the quantum-mechanical predictions about virtual particles. The first test was understood in the late 1940s. In a hydrogen atom an electron and a proton are bound together by photons (the quanta of the electromagnetic field). Every photon will spend some time as a virtual electron plus its antiparticle, the virtual positron, since this is allowed by quantum mechanics as described above. The hydrogen atom has two energy levels that coincidentally seem to have the same energy. But when the atom is in one of those levels it interacts differently with the virtual electron and positron than when it is in the other, so their energies are shifted a tiny bit because of those interactions. That shift was measured by Willis Lamb and the Lamb shift was born, for which a Nobel Prize was eventually awarded.

    Quarks are particles much like electrons, but different in that they also interact via the strong force. Two of the lighter quarks, the so-called “up” and “down” quarks, bind together to make up protons and neutrons. The “top” quark is the heaviest of the six types of quarks. In the early 1990s it had been predicted to exist but had not been directly seen in any experiment. At the LEP collider at the European particle physics laboratory CERN, millions of Z bosons–the particles that mediate neutral weak interactions–were produced and their mass was very accurately measured. The Standard Model of particle physics predicts the mass of the Z boson, but the measured value differed a little. This small difference could be explained in terms of the time the Z spent as a virtual top quark if such a top quark had a certain mass. When the top quark mass was directly measured a few years later at the Tevatron collider at Fermi National Accelerator Laboratory near Chicago, the value agreed with that obtained from the virtual particle analysis, providing a dramatic test of our understanding of virtual particles . . .

    Now what that is saying is in effect that we have warrant for claiming to know that such virtual particles exist and have observable effects. There are of course the usual debates back and forth on warrant and alternative views, but we can see that the evidence is generally held to point to a reality.

    But in fact even that debate is simply to confirm that the claim virtual particles exists is a potential truth bearer and to show that on balance, physicists assign to it the epistemological value: credibly true, per empirical warrant.

    Even before we can do such, the very fact that such a thing is a potential reality, means that the relevant laws of thought apply, were used in analysis and were used in evaluating the evidence that warranted the belief that this is real.

    GEM of TKI

  94. F/N 3: laying out the list of six laws like the above should make the connexion to debates over design theory clear enough. First, that a necessary being credibly lies aback of a contingent cosmos points to the question of what would be a causally sufficient explanation of the credibly contingent and finely tuned for C -chemistry, aqueous medium life we inhabit (and this holds even in the face of multiverse speculations). Second, we have to ask, what is a causally reasonable and adequate explanation of the observed functionally specific, complex organisation and associated information (including digitally coded algorithmic information) in cell based life, on the gamut of our observed cosmos. That something comes from nothing — non-being — is not a reasonable explanation. So, explanations that boil down to such, are not credible. In short, at multiple levels, there is no free lunch. KF

  95. kairosfocus:

    F/N 1.12: Thereby we know that Islam is correct in all particulars and everything is as Allah (pbuh) will it. If the global plurality or majority (argumentum ad populum) is not sufficient as ‘reasonable and responsible’ then a definition is needed for which select minority (argumentum my populum) it is that this refers to.

    F/N 2: Observation of effects that could be caused by something that may or may not exist beyond its pedagogical use as analogous explanans is not the same as observing the cause itself. There’s no more pedagogical problem with virtual photons than there is with the Bohr model or Newton’s notions. But they are all wrong and known so. As to particle physics it need only be noted that the decay products are outside the statistical bounds entailed by the theory. And thus, if we follow antiquated notions like Michelson and Morely, the theory is false and right where it hurts for this point on photons hanging with Morpheus in the Matrix.

    If we follow Plato down the rabbit hole in Meno and Theatetus there’s a sound point to be made that knowledge proper is a logical account and a demonstration. Without the logical account you may not have knowledge, but you still have a demonstration. Without demonstration you have the Philosophistry at Stanford. With neither you’ve Dialetheism, which is the running sore in these Laws of Thought posts.

    F/N 3: We have to ask nothing, we have to show. Which is the point I’m after about Theatetus: If there’s no show, then there’s no tell. If it is true that there is no Creator God then it is simply true that there is not. If it is true that there is a Creator God then it is simply true that there is. None of the consequents can affirm any absinthe-fueled antecedent that can be dreamed in the reaching minds of men.

    The cut here is that there is nothing at all the matter with holding any belief, about anything, you like until you start making claims about patent medicine, technological artifacts, economics, law and governance. If you’ve got something to sell, or something you’re forcing Catholics to buy, then it’s show n’ tell time. Otherwise, keep your conscience as you like.

    It’s noteworthy, perhaps, that I’m doing little more here than bemoaning the same thing that Bacon did in his own day in the Novum Organon. Whether that’s just a constant churn in the human experience or a strictly constant feature I wouldn’t dare say.

  96. 96

    Another great post by kairosfocus, casting the relentless, cold light of reason into the dim, vague fog of materialist, post-modern thinking.

  97. –Aleta: “And Stephen, I have answered your definitive questions. See post 58.”

    You did not answer my question. At 58 you finally conceded, with no small amount of prompting, that neither the moon nor Mount Everest nor an ocean can exist and not exist at the same time. That answer will not do since other things exist other than those three.

    The question is whether the law of non-contradiction pertains to ALL INSTANCES OF THINGS EXISTING IN THE REAL WORLD–(moons, mountains, oceans and EVERYTHING ELSE). Yes or no.

  98. I’ve been reading some discussions about this topic elsewhere, and they have been useful, and in some cases enlightening – I get into these discussions to learn, both from others and from my own attempts to express my thoughts, and so I learn new ways of thinking about things from what others have to say.

    So here are some further thoughts.

    Your very questions assumes that there is a absolute link between classical logic and reality, and I’ve been arguing that that is not the case: there are ways in which classical logic is a very powerful tool, and there are ways where its use hinders our understanding, because of the necessity to dichotomize that it entails.

    Furthermore, as someone remarked elsewhere, Aristotle’s logic presupposes a particular metaphysics in which “things” and “properties” and “existence” are assumed. Modern physics perhaps challenges that metaphysics.

    Also, as someone else, a different someone else, remarked elsewhere, “it strikes me as a startling hubris to insist a priori that a system of logic devised by Aristotle must be capable of expressing every possible true state of affairs, and that phenomena that are inexpressible within that system therefore cannot exist.”

    In my first post I talked about the difference between a Platonic view and what I called there (surely inaccurately) an Aristotelian view. You are a Platonist in that you believe that logic comes first, and imprints itself upon the world in an incontrovertible way: that logic somehow imposes itself on reality. I believe reality came first, and that logic has been developed to help talk about, and thus understand, that reality – logic has been abstracted out of the nature of the world based on our experiences. If we discover some aspect of reality that doesn’t fit a logic built upon ancient metaphysics based on objects and their properties, then so be it. Reality wins, and our logical tools must be amended to help us understand that reality.

    Again, as I have repeatedly said (and I am absolutely sure there is really no use in saying it again) , it is not the LNC itself that is in question, but rather our use of it in relationship to propositions about the world. You don’t even think such a dichotomy exists: for you, if logic says it, reality must follow, but I think there is a difference between logic and its use.

    If we are willing to look at the world in a way that is compatible with classical logic (which we do virtually all the time), then if we form our propositions carefully, we can use logic to build models of understanding about the world – this process has been highly successful. But modern physics has shown us situations where reality just does not behave “logically”, in which case it may be better to adopt a different logical language rather than force our understanding of reality into what is, at the quantum level, an outdated metaphysics.

  99. Maus:

    I’ll say but little on Islam other than to point that a lot of its pivot is historical and on its founder and era, so the evaluation of its truth claims will hinge on that. For which I suggest here as one significant view. But, that’s O/T for UD, even on a phil issue.

    As touching science, the matter is simple: science seeks to provide an empirically reliable and at least possibly true description and explanation of our world. It provides a provisional warrant, and so a weak form, open-ended body of knowledge. That body is useful because of its empirical reliability, but we know already that empirical reliability of a model’s outputs says nothing about the ultimate truth of its assumptions and explanatory constructs etc.

    As in, affirming the consequent is still a formal fallacy, even when dressed up in a lab coat.

    Next, there are of course all sorts of phil views and even anti-phil views that can be held. What is at stake here is actually a matter of glorified common sense [what is implied in being able to identify something as a distinct thing in the world with a stable identity), but I reserve that for my following comment to Aleta.

    All best

    KF

  100. Aleta:

    I must take up your:

    Your very questions assumes that there is a absolute link between classical logic and reality, and I’ve been arguing that that is not the case: there are ways in which classical logic is a very powerful tool, and there are ways where its use hinders our understanding, because of the necessity to dichotomize that it entails.

    Furthermore, as someone remarked elsewhere, Aristotle’s logic presupposes a particular metaphysics in which “things” and “properties” and “existence” are assumed. Modern physics perhaps challenges that metaphysics . . .

    Pardon, Aleta, but there is no empty assumption involved, there is a big difference between assumptions and self-evident truths that are seen to be so based on our experience of the world and are also seen to be necessarily so on pain of absurdity. You are giving me the distinct impression that you have not read the original post, and where it comes from, much less the earlier markup on ES’s arguments about quantum mechanics. If you only come here to trumpet talking points and do not actually interact with the course of discussion, then that is not helpful..

    You seem to despise “dichotomising,” but you happen to have a stable identity as an individual and a name, whether or not it is an Internet Handle. That’s not a question-begging assumption that can be dismissed, that is an easily observed reality that we dare not dismiss, on pain of absurdity.

    You are therefore a relevant case in point: It is not possible for you to be and not be in the same sense at the same time. It is not possible for you to be neither there nor not there.

    One or the other of Aleta exists and Aleta does not exist will be true, but not both and not neither.

    So, let us reprise the summary form the OP that I just updated from earlier today:

    Consider the world:
    || . . . ||

    Identify some definite A in it:

    || . . . (A) . . . NOT-A (the rest of the world) . . . ||

    Now, let us analyse:

    [1] A thing, A, is what it is (the law of identity);

    [2] A thing, A, cannot at once be and not-be (the law of non-contradiction);

    [3] A thing, A, is or it is not, but not both or neither (the law of the excluded middle).

    [4] “to say that what is is, and what is not is not, is true.” (Ari, on what truth is)

    [5] “Of everything that is, it can be found why it is.” (Principle of sufficient Reason, per Schopenhauer.)

    [6] If something has a beginning or may cease from being — i.e. it is contingent — it has a cause. (Principle of causality, a direct derivative of 5, which points to the possibility of necessary, non contingent beings, e.g. the truth in 2 + 3 = 5 did not have a beginning, cannot come to an end, and is not the product of a cause, it is an eternal reality. The most significant candidate necessary being is an eternal Mind. Indeed, down this road lies a path to inferring and arguably warranting the existence of God as architect, designer and maker — thus, creator — of the cosmos. Cf Plato’s early argument along such lines, here.)

    Now what from that list is a matter of dubious assertions of question-begging assumptions?

    That something identifiable exists is a fact of experience, antecedent to labelling it, e.g. a bright red ball on a table, or Aleta.

    That thing is itself.

    It is not both itself and something else. Nor is it neither itself nor something else. It is itself.

    Now, we do have superpositions and uncertainties etc in physics, but that is not to be equated with the superposition of existence and non-existence [as some have imagined for Schroedinger's poor cat], or the like. And, when the physicists set out to do the calculations, they are locked down to treating the symbols as distinct things with distinct specific relationships, on pain of chaos and confusion leading to nonsense.

    And I still see lurking int he background the idea that Kant’s ditch between the phenomenal world of mental experience and the noumenal world of things in themselves, is still there in your mind, in the guise of a gap between language and reality that is unbridgeable. Pardon, but as was shown above yesterday I think, that is self-refuting by being self-referentially incoherent.

    Of course, you can choose to ignore that, but all this would show is that you would be clinging to the demonstrably absurd.

    Please, think again.

    GEM of TKI

  101. 101

    If we discover some aspect of reality that doesn’t fit a logic built upon ancient metaphysics based on objects and their properties, then so be it. Reality wins, and our logical tools must be amended to help us understand that reality.

    How would you go about discovering something that cannot be identified as itself and not anything/everything else (principle of identity)?

  102. WJ:

    I should add my comment on the particular attempt to tell “truth” by the clock you addressed.

    That is of course a fallacy, in and of itself.

    But also, you will observe that A — how ironic that is — has dichotomised off that ancient metaphysics she would dismiss. In other words AM is itself in her view and not NOT-AM also, or whatever fashionable claim. So, we see that A cannot in practice operate other than on the basis of what she — I infer here on the name — would reject.

    H’mmm . . .

    KF

  103. –Aleta: “Your very questions assumes that there is a absolute link between classical logic and reality, and I’ve been arguing that that is not the case: there are ways in which classical logic is a very powerful tool, and there are ways where its use hinders our understanding, because of the necessity to dichotomize that it entails.”

    Aleta, Of course there is a link between logic and reality. It is your irrational claim to the contrary that sustains your confusion. Let me try to unwrap this for you.

    On the one hand, you claim that no reliable (absolute is the wrong word) link exists between logic and the real world on the grounds that the “map” is different from the “territory.” On the other hand, you temporarily reverse your position each time we start getting into examples. You admit, for example, that the moon, which exists in the real world, cannot exist and not exist at the same time. In making that admission, you are conceding that logic and the world are, indeed, linked, insofar as the moon’s existence is concerned. In other words, you are admitting, with respect to the LNC, that no decisive gap exists between the map and the territory.

    Later on, under unrelenting pressure, you finally acknowledged that logic and the world are also linked insofar as real-world mountains and real-world ocean’s are concerned. In spite of your earlier protests, it didn’t matter whether we can identify where the mountain (or ocean) begins and the land (or tributaries) end. You came to recognize, I hope, that those “objections” were not, shall we say, richly conceived. Again, there was no significant gap between the map and the territory.

    So, my question is designed to revive your intellectual capabilities to a point that you will understand that the link between logic and reality, at least in the context of the LNC, doesn’t turn on, off, and back on again. If it is true for some things, it is true for all things. My question was designed to help you understand that we can extend our list of those things already acknowledged to pertain to the LNC 9Jupiter, the moon, the mountain, and the ocean)–to ALL things. Here it is for the eight time:

    Does the law of non-contradiction pertain to ALL INSTANCES OF THINGS EXISTING IN THE REAL WORLD–(moons, mountains, oceans and EVERYTHING ELSE). Yes or no

    Just say yes and let’s end this madness.

  104. As far as things existing (or not) on a spectrum are concerned:

    A seed is not a tree,
    A sprouted seed is not a tree,
    But at some point a seed sprouts and is a sprout at some later point the sprout becomes a sapling and at a yet later point the sapling becomes a tree. It is never both a tree and not a tree in the same sense and at the same time (LNC)
    Yet it is not clear exactly when the tree begins to exist.

    Similarly for a single water molecule to droplet to drop to puddle to pond to lake to sea to ocean.

    I can imagine Aleta’s “Xo on a mountain” example in a similar way… even with some extra fuzziness. This is not to doubt whether the mountain exists or not in the same sense at the same time. For sake of discussion we can talk about a real mountain that exists, let’s say Mount Shasta in Northern California. At what point can one say that Xo is ON Mt. Shasta or not?

    Another example is Four Corners (the arbitrary point where the states Arizona, Colorado, New Mexico and Utah meet) One can stand in all four states in the same sense at the same time yet not be in any particular state. I have done it and I didn’t poof out of existence in a flash due to a violation of LNC.

    Then there is wave-particle duality and the double slit experiment which, when combined with the photoelectric effect, really seem to tax the LNC. But I won’t discuss those just yet.

  105. I’m in agreement about ending this madness, Stephen. See you some other time.

  106. kairosfocus:

    But, that’s O/T for UD, even on a phil issue.

    No worries, I only mentioned as an example of the largest philosophical set of which I’m aware. Can I assume from your latest two responses that you’re simply looking for ‘reasonable and responsible’ as good faith and sportsmanship in debate?

  107. –Aleta: “I’m in agreement about ending this madness, Stephen. See you some other time.”

    Translation: I will never answer your question.

  108. Well, Aleta had to retreat back to quantum physics. So I found these few comments spot on:

    KF said:

    ” . . . empirical reliability of a model’s outputs says nothing about the ultimate truth of its assumptions and explanatory constructs etc.

    “As in, affirming the consequent is still a formal fallacy, even when dressed up in a lab coat.”

    And:

    “Now, we do have superpositions and uncertainties etc in physics, but that is not to be equated with the superposition of existence and non-existence [as some have imagined for Schroedinger's poor cat], or the like. And, when the physicists set out to do the calculations, they are locked down to treating the symbols as distinct things with distinct specific relationships, on pain of chaos and confusion leading to nonsense. “

    William J Murray said:

    “How would you go about discovering something that cannot be identified as itself and not anything/everything else (principle of identity)?”

    Throughout the thread, I often referred to the LNC where it would probably have been more proper to refer to the LoI (law of identity) because they are so interrelated. But, I think it is wiser to first press this LoI upon Aleta and those who look to quantum mechanics for an escape hatch from reality.

  109. 109

    Another question to ask some of them is if there are 4-sided triangles in any universe, or if 2+3=5 in all possible universes. Then ask them, if that rule just describes things we happen to find in our exterior reality, then why can we not find – somewhere, in this universe or another, that 2+3=180, or that triangles have 4 sides?

    I mean, logic is just the man imposing his brutal, patriarchal mind-control on the people, y’know? Logic is prison, bro. Reality is beyond our conceptualization of it! I mean, besides the fact that we can conceive of it enough to know it’s beyond our ability to .. eh, gimme another brewski.

  110. KF,

    Embarrassingly, I just now did read fully the OP. I skimmed it due to time constraints when I first opened it, and upon seeing Aleta’s comment just couldn’t refrain from jumping in.

    Thanks for a very, very good read and explanation of things that, as you said, are sadly still in need of explaining.

  111. Brent: Thanks, this and related threads are a revelation on just how deep-rooted the rot that ails our civilisation is. KF

  112. UT:

    You have raised some interesting points. I note:

    1 –> I emphasise elsewhere the difference between a real contradiction and a gap in our concepts, by asking if one can at just one point on earth, stand to the due north of London — England, Bridgetown — Barbados and Kingston — Jamaica.

    2 –> At first, this seems impossible; until we remember that the Earth is a ball, not a flat object. So, go to the north pole and stand there. If unity and diversity refer to different aspects of an object, phenomenon or situation, they do not stand in contradiction. (This is of course central to the triune understanding of God central to Christian theology.)

    3 –> So, it is possible to stand at a point of convergence and be “in” multiple states without contradiction. But if “in” were to mean solely in, that would be a different matter as that would exclude intersecting a border.

    4 –> The sense in which A is I, and you are you has that exclusive property: you as an identity, cannot intersect with me as an identity in the same sense and time.

    5 –> Being a mole on or next to a nose is a related case: we do not have a defined knife-edge point or borderline that is generally agreed, UNLIKE (MOST) BORDERS OF STATES. And indeed if you look at the map of Arabia, you will still see some undefined border zones; as used to be much more common.

    6 –> We could define a knife edge line which would allow our mole to intersect the border or we could use the Zadeh fuzzy zoning with an overlap so a point/mole could be 60% nose, 30% mouth and 10% cheek. (This last is commonly used in control theory.) Indeed, we could use this to map out where people think each of these zones ends, coming up with a sort of social consensus map. But where sharp definition is important [have you ever seen a real estate dispute that required a resurvey of a lot?], we will usually agree on a border.

    7 –> This does not change that a unique point is itself, not something else and not both.

    8 –> The tree example you gave is similar, with change over time. The border between seed and seedling, or seedling and sapling, or sapling and tree are linked by steadily acting processes and are fuzzy. That does not change the fact that the white guava tree or the cashew tree or the mango, soursop and sugar apple trees behind where I type, each had a unique identity through these processes. Hence the significance of beginning from the act of identification, the fact of identity and recognising the need to have the circumstances duly recognised and consistent in dealing with a case. (This tends to be obscured in using symbols, but in the real world it is vital.)

    9 –> As for quantum examples, they are discussed here at first level — before this post was attempted — as has been repeatedly linked above. We deal with wavicles [and I lean towards some vague version on Copenhagen, on grounds of the extravagances of branching worlds], which do interact with both slits and influence the resolution that marks the dot pattern on a screen. Superposition of waves is not to be confused with superposition of existence and non-existence [Scroedinger's cat and all that]. Virtual particles are real enough to be a part of observable effects. And much more. The quantum world is strange, but no stranger in the end than other aspects of the problem of the one and the many in an evidently coherent cosmos.

    KF

  113. WJ: a triangle’s got a top and a beneath, so there: FIVE sides, hic! KF

  114. And if we call the tail of a sheep a leg, how many legs will it have?

  115. to StephenB: the answer to your question is at http://theskepticalzone.com/wp/?p=296#comment-3715

  116. Aleta, I visited the other website, but you did not answer the question. You simply rationalized your evasion.

    The LINK between LOGIC and REALITY is INHERENT in Law of non-Contradiction, which includes the logical, the psychological, and the ONTOLOGICAL.

    You want to keep the logical aspect and abandon the ontological aspect, which is just another way of trying to have it both ways, claiming to accept the law it while abandoning it at the same time.

    Here is Aristotle’s formulation:

    1. ontological: “It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect.” (1005b19-20)

    2. psychological: “No one can believe that the same thing can (at the same time) be and not be.” (1005b23-24)

    3. logical: “The most certain of all basic principles is that contradictory propositions are not true simultaneously.” (1011b13-14)

    To reject the ontological aspect of the Law of non-contradiction, or to limit it to the realm of the logical, is to deny the law of non-contradiction. You have, therefore, abandoned rationality. I do not discuss science or any other important matter with irrational people. I simply make reference to the fact and move on.
    ________
    An important note, worthy of remarking, SB. KF

  117. The above reference was from Wikipedia.

  118. Just the part about Aristotle, not all of it.

  119. F/N: It is probably worthwhile to hear Ari himself in Metaphysics, per Jowett:

    __________

    >> . . . the most certain principle of all is that regarding which it is impossible to be mistaken; for such a principle must be both the best known (for all men may be mistaken about things which they do not know), and non-hypothetical. For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect; we must presuppose, to guard against dialectical objections, any further qualifications which might be added. This, then, is the most certain of all principles, since it answers to the definition given above. For it is impossible for any one to believe the same thing to be and not to be, as some think Heraclitus says. For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject (the usual qualifications must be presupposed in this premiss too), and if an opinion which contradicts another is contrary to it, obviously it is impossible for the same man at the same time to believe the same thing to be and not to be; for if a man were mistaken on this point he would have contrary opinions at the same time. It is for this reason that all who are carrying out a demonstration reduce it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms . . . .

    “There are some who, as we said, both themselves assert that it is possible for the same thing to be and not to be, and say that people can judge this to be the case. And among others many writers about nature use this language. But we have now posited that it is impossible for anything at the same time to be and not to be, and by this means have shown that this is the most indisputable of all principles.-Some indeed demand that even this shall be demonstrated, but this they do through want of education, for not to know of what things one should demand demonstration, and of what one should not, argues want of education. For it is impossible that there should be demonstration of absolutely everything (there would be an infinite regress, so that there would still be no demonstration); but if there are things of which one should not demand demonstration, these persons could not say what principle they maintain to be more self-evident than the present one . . . .

    if all contradictory statements are true of the same subject at the same time, evidently all things will be one. For the same thing will be a trireme, a wall, and a man, if of everything it is possible either to affirm or to deny anything (and this premiss must be accepted by those who share the views of Protagoras). For if any one thinks that the man is not a trireme, evidently he is not a trireme; so that he also is a trireme, if, as they say, contradictory statements are both true. And we thus get the doctrine of Anaxagoras, that all things are mixed together; so that nothing really exists. They seem, then, to be speaking of the indeterminate, and, while fancying themselves to be speaking of being, they are speaking about non-being; for it is that which exists potentially and not in complete reality that is indeterminate. But they must predicate of every subject the affirmation or the negation of every attribute. For it is absurd if of each subject its own negation is to be predicable, while the negation of something else which cannot be predicated of it is not to be predicable of it; for instance, if it is true to say of a man that he is not a man, evidently it is also true to say that he is either a trireme or not a trireme. If, then, the affirmative can be predicated, the negative must be predicable too; and if the affirmative is not predicable, the negative, at least, will be more predicable than the negative of the subject itself. If, then, even the latter negative is predicable, the negative of ‘trireme’ will be also predicable; and, if this is predicable, the affirmative will be so too.

    “Those, then, who maintain this view are driven to this conclusion, and to the further conclusion that it is not necessary either to assert or to deny. For if it is true that a thing is a man and a not-man, evidently also it will be neither a man nor a not-man. For to the two assertions there answer two negations, and if the former is treated as a single proposition compounded out of two, the latter also is a single proposition opposite to the former . . . .

    those who ask for an irresistible argument, and at the same time demand to be called to account for their views, must guard themselves by saying that the truth is not that what appears exists, but that what appears exists for him to whom it appears, and when, and to the sense to which, and under the conditions under which it appears. And if they give an account of their view, but do not give it in this way, they will soon find themselves contradicting themselves. For it is possible that the same thing may appear to be honey to the sight, but not to the taste, and that, since we have two eyes, things may not appear the same to each, if their sight is unlike. For to those who for the reasons named some time ago say that what appears is true, and therefore that all things are alike false and true, for things do not appear either the same to all men or always the same to the same man, but often have contrary appearances at the same time (for touch says there are two objects when we cross our fingers, while sight says there is one)-to these we shall say ‘yes, but not to the same sense and in the same part of it and under the same conditions and at the same time’, so that what appears will be with these qualifications true. But perhaps for this reason those who argue thus not because they feel a difficulty but for the sake of argument, should say that this is not true, but true for this man. And as has been said before, they must make everything relative-relative to opinion and perception, so that nothing either has come to be or will be without some one’s first thinking so. But if things have come to be or will be, evidently not all things will be relative to opinion.-Again, if a thing is one, it is in relation to one thing or to a definite number of things; and if the same thing is both half and equal, it is not to the double that the equal is correlative. If, then, in relation to that which thinks, man and that which is thought are the same, man will not be that which thinks, but only that which is thought. And if each thing is to be relative to that which thinks, that which thinks will be relative to an infinity of specifically different things.

    “Let this, then, suffice to show (1) that the most indisputable of all beliefs is that contradictory statements are not at the same time true, and (2) what consequences follow from the assertion that they are, and (3) why people do assert this. Now since it is impossible that contradictories should be at the same time true of the same thing, obviously contraries also cannot belong at the same time to the same thing. For of contraries, one is a privation no less than it is a contrary-and a privation of the essential nature; and privation is the denial of a predicate to a determinate genus. If, then, it is impossible to affirm and deny truly at the same time, it is also impossible that contraries should belong to a subject at the same time, unless both belong to it in particular relations, or one in a particular relation and one without qualification . . . >>
    __________

    We have been those roads of thought long since, in the footsteps of such men.

    KF

  120. –Aleta: “Just the part about Aristotle, not all of it.”

    Well, actually, Aleta, in depends on which day of the week we are interacting. First, you reject the ontological aspect of the LNC when you define your general position (the map is not the territory). On the other hand, when we ask you about Jupiter moons, and mountains, you accept the ontological aspect, contradicting your original position. (Suddenly, there is no gap between logic and reality). Then, when we correct you with examples and ask you to extend the ontological part to all existing things, you revert back to a total denial of the ontological aspect altogether. (Oops, there’s that gap again). As I say, your position is completely irrational. It cannot be defended.

  121. If logic was not linked to the real world, we could advance VALID arguments, but we would be powerless to advance SOUND arguments. An argument is valid if its structure is flawless, meaning that its conclusion infallibly follows from its premises. However, a valid argument may or may not be sound, that is, it may or may not contain true premises. An argument is SOUND if it is valid and if it contains only true premises, that is, premises that accurately reflect the real world. Clearly, if logic was not linked to the real world, there would be no such thing as a true premise and, therefore, no such thing as a sound argument. Anyone who cannot, or will not, grasp this point is incapable of rational thought.

  122. Reply at http://theskepticalzone.com/wp/?p=296#comment-3841, including an explanation of why I’m responding there, not here.

  123. Aleta, I feel sorry for you because I don’t believe that you are not capable of rational thought. Let me know if I can ever help you.

  124. Oops, I mean, I don’t believe that you are capable of rational thought. My offer for help still goes, however.

  125. Onlookers:

    Sad to say, our civilisation has plainly gone mad, and the chief inmates are running the asylum.

    Let me hasten to add: this is not to indict those victims of the willful, irresponsible implanting of the absurd into the collective mindset of our civilisation who we see coming here and over at blogs and sites in the penumbra surrounding UD.

    It is, rather, to diagnose a disease of the mind that could easily be fatal for our civilisation.

    SB, above is ever so right, to point out that we are seeing a rejection of soundness — and thus truth — in thought.

    The conclusion of a valid argument follows properly from its premises, and so if the premises are true, a valid argument standing on true premises will have true conclusions. Where, the truth says of what is that it is, and of what is not, that it is not. And of course, where we may have adequate warrant for certain claims to be certain that they are true, or at least be morally confident enough to see that to treat them as false would be irresponsible or even dangerous.

    For instance, science inevitably rests on a pattern of thought that is formally fallacious: If Theory, T, then Observations and predictions, O + P, but since we see O + P, then we infer T. That is T => (O + P), (O + P) therefore t. Let (O + P) = X and we can see where if T = “Tom is a Cat” And X = “Tom is an animal” the structure is immediately and obviously a fallacy:

    T => X (If Tom is a cat then Tom is an Animal)
    X (Tom is an animal)
    _____________________

    T (Tom is a cat)

    This is of course the affirming of the consequent.

    But, in practice, the explanation T we construct may be so well tested and empirically reliable, that we would be foolish to ignore it. For instance, think about pharmacology and the drugs we take for our ailments, which are developed using the said same scientific approach, warts and all.

    T is therefore seen as warranted as empirically reliable, and to be worthy of confidence per empirical tests though necessarily at most provisional. That is why physics has undergone two major revolutions in 350 years, and may be on the verge of a third if those recent faster than light neutrino observations pan out on cross-checking.

    But, what happens where scientific investigations traipse into fields where we cannot make such cross-checking observations?

    Too often, in fields such as origins science, it leads to the ideologisation of science. For instance, on origins science, it is easy to show that he empirically reliable source of functionally specific complex organisation and associated information is design, but because the implications cut across dominant schools of thought in origins science [which deals with the remote and unobservable deep past] we see a stout defence of the evolutionary materialist status quo that too often does not shun to resort to the most dirty rhetorical and propaganda techniques. (Indeed, that is why UD’s mods have to be so stringent, all too often. And it is why several key contributors here generally decline invitations to wade into the tainted fever swamps, other than to perhaps serve a notice of record.)

    But now, we are seeing something deeper than the above.

    Reasoned thought itself is under attack in this ultra-/post- modern era.

    So bad is this, that there are ever so many who think that something is wrong if one sticks up for longstanding, self-evidently true and indisputably certain first principles of right reason. (Did you notice how Aristotle described the concept of self-evident first principles of right reason in the clip from last night? [Read above.])

    Lest we forget (I know, I know, this cuts across what we have been ever so confidently taught by the professed wise and brilliant, complete with convincing — but misleading — talking points and claimed proof cases), let me again clip the basic summary developed above:

    Consider the world:

    || . . . ||

    Identify some definite A in it:

    || . . . (A) . . . NOT-A (the rest of the world) . . . ||

    Now, let us analyse:

    [1] A thing, A, is what it is (the law of identity);

    [2] A thing, A, cannot at once be and not-be (the law of non-contradiction). It is worth clipping Wiki’s cites against known interest from Aristotle in Metaphysics, as SB has done above:

    1. ontological*: “It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect.” (1005b19-20)

    [*NB: Ontology, per Am HD etc, is "The branch of metaphysics that deals with the nature of being," and the ontological form of the claim is talking about that which really exists or may really exist. Truth is the bridge between the world of thoughts and perceptions and that of external reality: truth says that what is is, and what is not is not.]

    2. psychological: “No one can believe that the same thing can (at the same time) be and not be.” (1005b23-24)

    3. logical: “The most certain of all basic principles is that contradictory propositions are not true simultaneously.” (1011b13-14)

    [3] A thing, A, is or it is not, but not both or neither (the law of the excluded middle).

    [4] “to say that what is is, and what is not is not, is true.” (Aristotle, on what truth is)

    [5] “Of everything that is, it can be found why it is.” (Principle of sufficient Reason, per Schopenhauer.)

    [6] If something has a beginning or may cease from being — i.e. it is contingent — it has a cause.* (Principle of causality, a direct derivative of 5)
    _________

    *F/N: Principles 5 & 6 point to the possibility of necessary, non contingent beings, e.g. the truth in 2 + 3 = 5 did not have a beginning, cannot come to an end, and is not the product of a cause, it is an eternal reality. The most significant candidate necessary being is an eternal Mind. Indeed, down this road lies a path to inferring and arguably warranting the existence of God as architect, designer and maker — thus, creator — of the cosmos. (Cf Plato’s early argument along such lines, here.)

    These six claims, once we reasonably understand them in light of our experience of the world, will patently be seen as true, and necessarily so on pain of absurdity. So soon as we can identify something, A as a definite object, A is itself, not something else at the same time and in the same sense. Similarly, the understanding of what truth is, is the ordinary and reasonable meaning: telling it like it is. And if something is, there is a reasonable question: why, which can be answered. That answer, for something that begins or may cease, is that it has a cause, and this raises the root question of beings that are necessary, and have no cause. (Cf the previous discussion in the ID Foundations series, here.)

    This then points to the question, what best explains the contingent cosmos we observe, which turns out to be fine-tuned for C-chemistry, cell based life. Cosmological design thought and theory therefore point to a designer and builder of our observed cosmos.

    That we inescapably find ourselves under moral government [those who protest this, inevitably demonstrate this by appealing to moral considerations] strongly raises the issue that the only worldview worth having is one in which there is a foundational IS that grounds OUGHT. This leads many serious thinkers to accept the best explanation as being that the designer and maker of the cosmos is an inherently good, wise, loving and just Creator God.

    These are serious and even compelling arguments, so such generic theism is not to be tartly dismissed as idiocy, ignorance, stupidity or worse — precisely what the New Atheists, unfortunately, are ever so quick to do. Too often, in the crudest, most uncivil and disrespectful or disruptive ways.

    Now, we have put some big questions on the table. They are going to be hard to answer. But then, that is actually one definition of philosophy: the organised attempt to provide sensible and systematic answers to the hard questions posed by our existence and predicaments.

    So also, let us remind ourselves: if we swallow and believe a keystone absurdity, it becomes our sheet anchor for what we think is the truth. Then, unfortunately, when the real truth — what Francis Schaeffer called “true truth” — comes along, it necessarily will not conform to the absurdity we have swallowed. SO, IF WE HAVE BEEN LED TO BELIEVE KEY ABSURDITIES, IT WILL LEAD US TO DOUBT, DISPUTE AND EVEN REJECT THE REAL TRUTH WHEN WE SEE IT.

    This brings to mind three key warnings from that much despised book of ancient but all too relevant wisdom, the Judaeo-Christian scriptures:

    Prov. 16:22 Understanding is a fountain of life to those who have it,
    but folly brings punishment to fools.

    23 A wise man’s heart guides his mouth,
    and his lips promote instruction.[b]

    24 Pleasant words are a honeycomb,
    sweet to the soul and healing to the bones.

    25 There is a way that seems right to a man,
    but in the end it leads to death.

    Isa 5:18 Woe to those who draw sin along with cords of deceit,
    and wickedness as with cart ropes . . .
    20 Woe to those who call evil good
    and good evil,
    who put darkness for light
    and light for darkness,
    who put bitter for sweet
    and sweet for bitter.

    21 Woe to those who are wise in their own eyes
    and clever in their own sight.

    Eph 4:17 So I tell you this, and insist on it in the Lord, that you must no longer live as the Gentiles do, in the futility of their thinking. 18 They are darkened in their understanding and separated from the life of God because of the ignorance that is in them due to the hardening of their hearts. 19 Having lost all sensitivity, they have given themselves over to sensuality so as to indulge in every kind of impurity, with a continual lust for more. [cf Rom 1:18 - 32]

    Yes, I know, I know, many will be irritated or worse by seeing these nuggets of wisdom from a book they despise. Talking points on Creationism in cheap tuxedos are being warmed up to be trotted out as we speak — where, of course there will be nothing on a priori evolutionary materialist atheism lurking in the holy lab coat. But, obviously, that knee-jerk rage at God does not change the force or relevance of those classic bits of wisdom we so desperately need to heed that have just been cited.

    One thing is sure, the exchanges above make it painfully plain why we need a therapeutic approach to the ills of the world of reasoned thought that haunt our civilisation.

    We are desperately sick as a civilisation.

    The question, is, whether we are willing to take the medicine that can cure our ails, before it is too late.

    The jury is still out on that.

    GEM of TKI

  126. F/N: I skimmed the thread and OP that Aleta has now repeatedly linked. I can see that from the outset they are making the little error at the beginning that Adler has highlighted, and which is discussed in more details here: failing to recognise the reality of self-evident truths of right reason, and in particular the first principles of right reason.

    For instance, in the OP, Dr Liddle remarks:

    They are indeed axiomatic – in other words, they are axioms on which a certain form of logic is based. Now I’m no logician, but I am capable of seeing that if we assume those axioms are true, we can construct a logical language in which useful conclusions can be drawn, and useful computations performed.

    But there are some propositions that simply are not possible in that language, because those axioms themselves are based on more fundamental assumption: that we know what an “object” is; that we know what “time” is – in other words, that we know what “is” is . . .

    Let me clip Wikipedia, speaking against its known ideological interest:

    In epistemology (theory of knowledge), a self-evident proposition is one that is known to be true by understanding its meaning without proof.

    Some epistemologists deny that any proposition can be self-evident. For most others, the belief that oneself is conscious is offered as an example of self-evidence. However, one’s belief that someone else is conscious is not epistemically self-evident . . . .

    A self-evident proposition cannot be denied without knowing that one contradicts oneself (provided one actually understands the proposition). An analytic proposition cannot be denied without a contradiction, but one may fail to know that there is a contradiction because it may be a contradiction that can be found only by a long and abstruse line of logical or mathematical reasoning. Most analytic propositions are very far from self-evident. Similarly, a self-evident proposition need not be analytic: my knowledge that I am conscious is self-evident but not analytic . . . .

    For those who admit the existence [i.e. reality] of abstract concepts, the class of non-analytic self-evident truths can be regarded as truths of the understanding–truths revealing connections between the meanings of ideas.

    That is, a self-evident truth is one that — providing we understand what is being said in light of our undeniable (and self-referential) experience of the world as intelligent, language-using, knowing and communicating creatures — we see is so, and that it MUST be so, on pain of obvious absurdity if we try to deny it. That is, these are foundational truths that we know or should know are so and must be so. So, to willfully reject such a truth is to implant an absurdity in the heart of our reasoning, and to open ourselves up to that en-darkenment of heart and mind that leads us to reject truth because we have swallowed an error.

    The reality of such truths is too often disputed, so let us give a key case, Warranted Credible Truth no 1, per Josiah Royce via Elton Trueblood: error exists.

    This is of course an all too familiar and universally accepted truth. That’s why we have arguments over what is correct!

    But there is a subtler and highly instructive side to it: it is UNDENIABLY true, on pain of self-referential absurdity. That is, if we try to deny that error exists, as a test, we immediately have a choice of which of two claims is in error: (a) that error exists, or (b) that error does not exist. One of these must be in error, on the common sense understanding that even philosophers must respect.

    And obviously, the correct one is (a), as it affirms what we have seen is undeniably so: error exists.

    Now, that looks trivial, doesn’t it?

    NOT.

    WCT 1 implies that truth exists, and undeniably true truth exists. Warranted credible truth — knowledge — exists. So, those who wold dismiss the reality of truth, or the know-ability of truth beyond seeming true to me or you, etc, are in error.

    This actually cuts a wide swath across many popular worldview level opinions: radical relativism and its many friends and kissing cousins.

    In addition, “error” is not a tangible reality: we cannot touch error as such, though we may see cases of error. Just like we cannot touch two as such though we may touch glyphs that represent it and illustrate with concrete cases. Reality is not to be conflated with physicality; and indeed it is precisely because mathematics often captures logical, abstract facets of reality, that we so often see its awesome power in science, engineering and even day to day life.

    Going further, we have in hand a case where we can see for ourselves that axioms are not always arbitrary and merely evaluated on being useful. Some axioms are warranted and credible as self-evident truths. So, the notion that we are free to select whatever axioms we want and then just look to see if it works well enough to be useful, crashes to the ground in flames.

    For, there are what Aristotle identified as the most certain of all truths, truths that are certain and know-able to all on pain of patent self-referential absurdity.

    It so happens that he first principles of right reason belong to exactly that category of truths.

    Now of course, one of the points that are being disputed is that: “we know what an “object” is; that we know what “time” is – in other words, that we know what “is” is . . .”

    This actually inadvertently shows what is at stake here: if we reject the first principles of right reason, our ability to communicate itself disintegrates into a chaos. (So, apply Kant’s Categorical Imperative here . . . ) But in fact, we premise our whole structure of knowledge on the undeniable self-referential and in-common common sense facts of human existence, which includes that we can and do communicate using language and keystone concepts such as our ability to answer to who or what [objects], to when [time] and to existence or non existence [is]. Or else, who is speaking, what does s/he say, and about what, when, where, and how accurately, how well warranted, evaporate in a chaos of confusion and contention.

    In short, we are patently seeing absurdity piled upon absurdity here.

    But of course, the underlying question on the issue being touted is that such words defy precising definitions that state necessary and sufficient conditions that infallibly tell us what they mean and/or operations that we can use to observe or measure them, etc. And, a selectively hyperskeptical voice can have great fun making such efforts at definition seem ridiculous.

    The only problem is that the process of making or challenging such definitions alike would depend on the common sense recognition of what these things mean. That is the one pushing such skeptical talking points is being self-referentially incoherent.

    So, are we locked into a circle of confusion and begged questions, with knowledge and reason themselves evaporating?

    Not at all.

    We start from the reality that we exist as intelligent and communicating creatures in a real world, and that we recognise many concepts on the basis of knowing cases, intuiting connexions and using that abstracted pattern to identify further cases on family resemblance. This process obviously can err, but the very fact of error is a case of existence and of truth existing and of knowable truth existing. So, we know well enough what things are, both concrete things and abstract ones of the order of the truth in the statement 2 + 3 = 5.

    We know full well that we can recognise cases of such things, and mark them off with labels, like A.

    Once that is done, we know full well that A is distinct from NOT-A, just as Dr Liddle is distinct from the rest of the world: her husband, her cat, her car, her workplace, her blog etc etc.

    In short, we see the basic laws of thought swinging into action, as has been repeatedly described and explained. And, in a case where to deny such is to end immediately in self-referential absurdity.

    What is more, if I were to take what Dr Liddle wrote and say that it means the opposite, she would rightly object that I am distorting what she said.

    In short, she full well knows that in relevant cases we know the difference between an assertion and its denial.

    She knows or should know that if one stands at the four-state point or the like, one can be “in” four states at once, but only if we take “in” in an inclusive sense. If we take “in” in the exclusive sense, that is not possible, and so the problem being posed turns out to be a case of needing to be clear what we are asking about.

    And of course there are things that shade off into one another, indeed Aristotle discussed white and black and grey in the very passage in Metaphysics we have been talking about. Does that mean there is no difference between white and black, or that something can be white and not white in the same sense and time etc?

    Patently not.

    That stricture on being in the same sense and time etc, is an invitation to be precise enough to mark whether we are equivocating when we say A and NOT-A. As Ari himself observed:

    . . . the most certain principle of all is that regarding which it is impossible to be mistaken; for such a principle must be both the best known (for all men may be mistaken about things which they do not know), and non-hypothetical. For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect; we must presuppose, to guard against dialectical objections, any further qualifications which might be added. This, then, is the most certain of all principles, since it answers to the definition given above. For it is impossible for any one to believe the same thing to be and not to be, as some think Heraclitus says. For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject (the usual qualifications must be presupposed in this premiss too), and if an opinion which contradicts another is contrary to it, obviously it is impossible for the same man at the same time to believe the same thing to be and not to be; for if a man were mistaken on this point he would have contrary opinions at the same time. It is for this reason that all who are carrying out a demonstration reduce it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms . . . .

    We did not suddenly see things that Aristotle was blind to, in the past 100 or so years!

    So, plainly, the issue is that we must recognise that here are such things as self evident truths, including the first principles of right reason.

    On pain of chaos, and obvious breaches of common sense that amount to patent absurdity.

    KF

  127. Hello kf,

    I see you linked to the ID foundations post regarding cosmological fine tuning. If i may ask, what is the difference between the cosmological fine tuning hypothesis and the privileged planet hypothesis? Is the latter a special case or subset of the former or does it stand separately?

  128. K: There are several cosmological fine tuning cases [many of which stand or fall separately from one another but form a cumulative case like mutually supportive stands of a rope of reasoning, not a chain that is no stronger than its weakest link . . . ], and the privileged planet hypothesis is just one of these. Actually, several. And, you will see that in the linked, I emphasise something that stands apart from the usual list of points. Namely, the cosmological significance of water and the first four elements in abundance, H, He, O, C. Add N more or less the fifth element and we have reached proteins, fats, carbohydrates etc in aqueous medium. But this is an off-topic, requested clarifying footnote, not an invite to a separate discussion in a vitally important thread. If you want or need more ask me to post a new thread on that. KF

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