Well I see you read it over the good paper. That’s great. The thing that strikes me the most about the paper is how much of a “mind is more than matter and machine” kind of guy Gödel really was. One might think that his theorem was hijacked by religious zealots to support an extreme view that wasn’t his own. These notes pretty much put that to rest. Chalk up another one of the greats to anti- methodological materialism. Virtually all of his most explicit comments (and what we know about him) seem to point to the fact that he was a true Platonist of the modern era. Perhaps he could be referred to as a neo-Platonist. In any event he used Husserl’s phenomenology as a launching pad to help grow his philosophical views (Platonism) into what he saw as a modern synthesis. You KF are a believer in self referential experience as a means of deriving senses and truths that result in pure reason- so you must be able to appreciate his phenomenological venture. I like this quote by KG-

“I do not fit into this century.”

I would have loved to see what he would have thought about the works of Behe and Dembski. Can you imagine that obsessive genius mind getting hold of biological data and the NFL theorems? DE would be over in a week; maybe less.

An excerpt from the Rodriguez-Consuegra review of Wang’s 1996 presentation on Godel’s philosophy [Modern Logic, Vol 8 nos 3 – 4 (May 2000 – Oct 2001), pp. 137 – 152] may be helpful, and certainly help us see a wider frame of possibilities than we are wont to if we are in thralldom to he evolutionary materialist paradigm:

From the publication of Wang’s From mathematics to philosophy in 1974 we know Godel’s main arguments against any possible attempt to identify minds and computers (in the context of his comments about Turing machines). They were: that the use of the mind is in constant development, while computers are static; that the states of every computer are necessarily finite, while mental states might converge to infinity because of their development, and that there may exist mental procedures which are not mechanical in nature (he was obviously thinking of mathematical intuition, which for Godel cannot be reduced to any mechanical procedure). [HT, Frosty]

It would be helpful to understand the point of the above if we see a further excerpt:

“Even if the finite brain cannot store an infinite amount of information, the spirit may be able to. The brain is a computing machine connected with a spirit” (p. 193). As usual then, Godel was much more cautious in his publishable writings than in his private reflections.

Reverting to monads [which Godel consciously used], Godel is seeing the observable functions of the human mind as a result of a composite whole that embraces entities from a physical and a spiritual world. The brain is the mind’s input/output computer that interfaces with the empirical, materially embodied world, in effect. And to support that idea, in his 1951 Gibbs lecture, he has in effect used the results of his theorems to show that mechanical axiom-theorem-proof approaches cannot exhaust the range of credibly knowable mathematical truth. He then presented the implications as a “dilemma”:

either the system of all demonstrable propositions (subjective mathematics) surpasses all machines, or the system of all true mathematical propositions (objective mathematics) surpasses subjective mathematics. If the first, the human mind cannot be reduced to the brain; if the second, mathematical objects and facts cannot be our creation, so they are independent of our mental acts. Obviously enough, both alternatives were to be unacceptable for materialists, so they together may be indirectly argued in favour of spiritualism.

Worth a few thoughts.

And, the thoughts will bring us back to the issue that mathematico-logical reasoning, conclusions and associated decisions require the reality and correspondence to the empirically observed world of entities that are radically different from the elements and characteristic interactions and laws or necessity or of chance of the material world. Worse, when we try to sort out first principle propositions and systematise the rest by deductive inference, we see that for realistically rich axiomatic systems, we run into incompleteness and/or incoherence.

Thus, the world of propositions, truths etc is irreducibly complex in the sense of resistance to finite, coherent axiomatisation and algorithmic inference to implications. That in turn raises serious questions on the nature of mathematical and related truths, reasoning and knowledge. Questions that point away from the materialistic picture of the world – it turns out to be far too simple to correspond to major aspects of reality.

Not least, let us observe that faith and reason are not clashing opposites, but are deeply intertwined in the deepest roots of our thought life.

GEM of TKI

“My incompleteness theorem makes it likely that mind is not mechanical, or else mind cannot understand it’s own mechanism. IF my result is taken together with the rationalistic attitude which Hilbert had and which was not refuted by my results, then [we can infer] the sharp result that the mind is not mechanical. This is so, because, if the mind were a machine, there should, contrary to this rationalistic attitude, exist number-theoretic questions undecidable for the human mind.”

So either the mind isn’t a machine (what Gödel and I subscribe to) or there are number theoretic questions undecidable for the human mind. I the second is true that materialism is grated a new stay in that the mind may just simply be inadequate. But if Gödel is right then the idea of a mechanically deducible mind and universe is a non-reality. I should also point out that if the second possibility is correct this means that still epistemologically the mind will be incapable of understanding itself because it will be able to deduce true propositions. The only exception is that those propositions are “undecidable.” That means the mind still can not be viewed in a complete formal way even if materialism is true.

So materialism is either false as Gödel inferred, or it is true but we will never be able to fully prove it.

My point was that I feel both are a little bit like two sides of the same coin. If we can’t prove it then how do we know it’s possibly true? This leads me to appeal to other evidences on the question of the origin of mind like those regarding the big bang and the appearance of information and form into matter which is not capable of producing or comprised of the stuff that designs or accounts for form. I see Gödel’s proof as clearly a leap away from a materialistic reductionist reality and a step in the right direction towards nonmaterial reality of the mind. He of course thought is was even more than a step in the right direction. He thought it was a proof.

Remember he said as an undergraduate that he wanted to produce a mathematical result that would have meta-mathematical implications and consequences so that Platonism could be proven as the true reality of being and rationality. Gödel said he wanted to do for mathematics what Newton did for physics. And guess what, he did.

If the mind can transcend sets then no set can contain it. Since no set can contain it, it cannot be formalized. If it cannot be formalized is cannot be deduced.

In this sense the mind cannot be proven to operate in any particular mechanical way because whatever axioms that you use to represent its range- that is the “sets”- they will either be themselves incomplete or will lead to a eventual contradiction. as KF puts it so beautifully…

“…no sufficiently rich as to be useful mathematically anchored system can be complete relative to a set of coherent axioms, and [b] there is no constructive procedure for getting to a known coherent set of axioms, even where these are incomplete.”

So we have said what it proves but what does it really mean?

To quote from Yourgrau’s book AWWT

“…the system should be complete, in the sense that all true statements expressible within the system (under a suitable interpretation) should be derivable from the axioms. To prevent circularity, the system in which consistency is to be proved must not itself employ any mathematically suspect or controversial procedures that could render its own consistency suspect. It must be, to use Hilbert’s invented term, not exactly finite but rather “finitary,” in the sense that its proofs must be in principle surveyable by sense experience and must not at any point appeal to an abstract, completed infinity of the kind proposed by Cantor.”

So it cant be contradictory, it cant be infinite, and it MUST be complete.

Since logic is not and then later arithmetic was proven to also share the same fate- knowledge is left up to true induction through intuitions and the like, to give us the sense perceptions that we use to come to formalistic proofs. In this sense to me the world begins to look more like an experience or a thought than a provable material process. It is here that I say the mind cannot be reduced and is, it seems, more than matter. The self experience of phenomenological consciousness is not materialistic in that it is self referential and matter does not display any such capacity in utero. So it seems to be that mind is more than matter. To say my conclusion in the reverse “if it could be demonstrated that a formalistic complete proof could show how the system of consciousness arose and functions as a material process then it would fallow that mind is simply a material machine.”

Thanks to Gödel I can rest assured.

I gather from his quotes especially the one that started this discussion…

“At any rate it has not been proved that there are arithmetical questions undecidable by the human mind. Rather what has been proved is only this: Either there are such questions or the human mind is more than a machine. In my opinion the second alternative is much more likely.”

that as I siad before

“That’s right… epistemologically a complete mechanization of consciousness is logically and arithmetically impossible.”

is true and that what you said

“I am telling you it is my understanding that he was not saying anything like that.”

misses the thrust and the point.

[I] think what is throwing “you” off is this part of his comment…

“it has not been proved that there are arithmetical questions undecidable by the human mind”

What he means is that perhaps the mind can “know” and therefore, to use his word, “decide” all things but that some cannot be mechanically formalized into complete expressions that are provable within themselves. THis means that any mechanical, material explanation of consciousness would have to appeal to richer axioms or intuitions that do not exist within the system to complete it.

The first possiblity of his dialectic refers to concepts, numbers- but the second refers to the system by which those numbers can be formalistically proved meaningful. My focus was not on whether we can or can not understand or rationalize all things but that all things cannot be proven in a material mechanically reductionist model that say Dawkins would subscribe to.

The one place I go further is that I take the ontological point behind Godle and assume it true for the mind. Any why not? The mind ontologically exists to me and I see no reason why it should not be freed by incompleteness as well. Call it “irreducible complexity of the nonmaterial consciouness.”

“It was to be expected that my proof would be taken up by religion sooner or later. This is justified in a certain sense.”

From what I gather up until the end of his life he remained a deep believer. Though I think he died an atheist. But for most or all of his life he believed like Newton that the world was made to be understood and was in fact like the mind, rational. That is he didn’t just think that the mind was rational because of evolution, but that the world , like the predictable effects
of gravity, was meant even perhaps designed to be understood. Here at some last Gödel quotes to consider…

“Human reason will develop in all directions.”

“Religions are mostly bad, but religion is good.”

“My philosophical views:
1.The world is rational.”

“That’s right…epistemologically a complete mechanization of consciousness is logically and arithmetically impossible.”

I am telling you it is my understanding that he was not saying anything like that.”

We he simply is because if you cannot show how the mind works with some deductive logical analysis then your model cannot be proved. Gödel’s proof is about deduction and it was Hilbert’s hope to prove deduction as a system rich enough to deal with all things. Consciousness will never be proven mechanistically- simple as that- and it cannot be proven as such then why should be think it TRULY so? In fact Gödel was convinced that the mind was more than could be contained in it- as clearly expressed in that quote. Hence, my conclusion fallows like the night to the day. Gödel’s proof is that strange place where epistemology and ontology meet vis-a-vis.

Thanks to DK, EM MA, JT etc and of course Frosty, SB, etc for a useful thread that has prompted then contributed to the development of appendix 6, the always linked, on mind and matter [and thence morality].

This thread is now winding down, but it has served to show again to the discerning reader just where the balance on the merits lies on the key matters raised above. I see some further remarks, though, and think it is worthwhile noting a few hopefully final observations:

1] DK, 199: I don’t despise theologians. I noted only that they have sectarian beliefs that I disagree with and that they would be lost without metaphysics.

And, post-Lakatos et al, and in light of the underlying implications of say methodological naturalism for how they too often look at the world, evolutionary materialist scientists have no metaphysical commitments that they would be “lost without”?

That is, sadly, the objection is plainly selectively hyperskeptical, and shows the underlying prejudice that I spoke of. Perhaps, though, I spoke too sharply: “dismisses” may be a better term.

2] “What is your warrant for “the credibility of the mind?”

From one perspective, this looks a lot like an attempt to turn around the burden of proof, serving to distract from the self-referential incoherence difficulties of evolutionary materialism as highlighted above [and in the draft appendix 6 the always linked], once it has to address the nature and origin of mind. But, we can look at the matter from a philosophical perspective as a call to comparative difficulties analysis, across factual adequacy, coherence and explanatory power.

Let us use the latter view for the moment, noting that this is addressed to me as an individual with his own worldview and associated presuppositional framework of first plausibles articulated into a story of the world and our place and mission in it. In my case, a Judaeo-Christian, theistic worldview [anchored in the end principally through knowing God as a person, in relationship based ont eh risen Christ, and historically by the resurrection, attested to by 500+ eyewitnesses and associated power flowing across the centuries of history above and beyond all the failures, sins and limitations of the Christian church as a very human institution. The glory yet shines out through the cracks in the “clay pots” . . .

Such a framework is theistic, and sees our cosmos as a creation by a supremely Intelligent, wise and powerful designer, a creation that brims over with his signature style. Thus, it is not surprising that there is an intelligible, mathematically, empirically and logically discernible order to the cosmos, and that we are placed and adapted to discover it at least in part, using minds that are made in the image of the Mind who formed the worlds.

Indeed, historically, this is the precise worldview that in a unique time and place then generally known as Christendom, gave birth to the still ongoing scientific revolution. Newton's General Scholium to his Principia -- cf here App 4 the always linked -- states that historically foundational scientific view aptly, even eloquently:

. . . This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. And if the fixed stars are the centres of other like systems, these, being formed by the like wise counsel, must be all subject to the dominion of One; especially since the light of the fixed stars is of the same nature with the light of the sun, and from every system light passes into all the other systems: and lest the systems of the fixed stars should, by their gravity, fall on each other mutually, he hath placed those systems at immense distances one from another.

This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont to be called Lord God pantokrator , or Universal Ruler . . . And from his true dominion it follows that the true God is a living, intelligent, and powerful Being . . . He is not eternity or infinity, but eternal and infinite; he is not duration or space, but he endures and is present. He endures for ever, and is every where present; and by existing always and every where, he constitutes duration and space . . . God is the same God, always and every where. He is omnipresent not virtually only, but also substantially; for virtue cannot subsist without substance. In him are all things contained and moved [i.e. cites Ac 17, where Paul evidently cites Cleanthes] . . . It is allowed by all that the Supreme God exists necessarily; and by the same necessity he exists always, and every where. [i.e accepts the cosmological argument to God.] . . . . We have ideas of his attributes, but what the real substance of any thing is we know not. In bodies, we see only their figures and colours, we hear only the sounds, we touch only their outward surfaces, we smell only the smells, and taste the savours; but their inward substances are not to be known either by our senses, or by any reflex act of our minds [notice his awareness of the limitations of empirical thought and his anticipation of the noumenal-phenomenal challenge]: much less, then, have we any idea of the substance of God. We know him only by his most wise and excellent contrivances of things, and final cause [i.e from his designs]: we admire him for his perfections; but we reverence and adore him on account of his dominion: for we adore him as his servants; and a god without dominion, providence, and final causes, is nothing else but Fate and Nature. Blind metaphysical necessity, which is certainly the same always and every where, could produce no variety of things. [i.e necessity does not produce contingency] All that diversity of natural things which we find suited to different times and places could arise from nothing but the ideas and will of a Being necessarily existing [That is, implicitly rejects chance, Plato's third alternative and explicitly infers to the Designer of the Cosmos.] . . . And thus much concerning God; to discourse of whom from the appearances of things, does certainly belong to Natural Philosophy.

Onlookers, no prizes for guessing why this passage is not commonly mentioned when discussions on the roots of ID thought come up!

3] PS to JT: on the implications of Godel . . .

I raised Marks’ remarks on Godel and other topics as a matter of interest primarily.

FYI, the central implication of the incompleteness theorems is that [a] no sufficiently rich as to be useful mathematically anchored system can be complete relative to a set of coherent axioms, and [b] there is no constructive procedure for getting to a known coherent set of axioms, even where these are incomplete.

As a direct consequence, mathematico-deductive reasoning loses all claim to certainty of proof.

We may know with high confidence and good warrant, but we must never confuse our degree of certitude with certainty. Thus, mathematicians, computer scientists and scientists all must live and work by trust relative to core first plausibles, i.e points of faith. And so wisdom is to be open-minded and open-hearted about this, for we are finite and fallible. So, in the end, we all live by such faith-points, the cores of our worldviews, and wisdom is to be aware that the first undeniable truth is this: error exists, which means that truth exists but we may at least in part be mistaken about it.

Reason and belief are inextricably intertwined in the roots of our worldviews and intellectual careers.

Here endeth the lesson.

Grace to all, and thanks again . . .

GEM of TKI

The only perfect model of a human brain would be another human brain subject to the exact same stimuli at the same time and the same place, which is impossible.

Something else I wanted to point from FrostN’s Godel quote:

“At any rate it has not been proved that there are arithmetical questions undecidable by the human mind. Rather what has been proved is only this: Either there are such questions or the human mind is more than a machine. In my opinion the second alternative is much more likely”.

So, to Godel, the idea that there could be arithmetical questions undecidable by a human mind was apparently just too incredible for him to fully accept. In fact he asserts that in his opinion it is much more likely that it is not the case, i.e. that man must therefore be something more than a mechanism. His personal viewpoint seems to be only explainable by some culturally-conditioned hubris that would ascribe God-like attributes to our species by default. Furthermore his personal viewpoint is nothing that by any means he claims are implies to have proven.

In the presentation you supplied, only by the vaguest and briefest allusions does the author imply that we can infer somehow that man transcends mechanism:

“There are some things we know exist that we can prove we will ever know. Most doubt a computer will ever write a deeply meaningful poem or a classic novel.”

That’s it – the only remark in the entire presentation that touches on the subject of dualism.

To me, it is just kind of pathetic for someone to consider “Ode to a Cloud”, e.g. “Oh Cloud! How doest thou traverse the endless sky… blah blah blah…” and exalt that as some indelible mark of Godhood in the human race.

Could a computer ever come up with something so brilliant? Could a human ever write a first-hand account of what it feels like to be dog? If not, would that mean a dog is superior to a human? Would it prove a dog isn’t a mechanism? Can two things that are different be the same?

Here’s an interesting discussion from The Straight Dope on “the seven basic literary plots”