VIDEO: The Feb 1, 2013 Craig- Rosenberg debate: “Is Faith in God Reasonable?”

_{kairosfocus

February 2, 2013

Philosophy, Video, worldview}

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Thanks to Bornagain 77’s diligence, we are able to bring to UD’s readership, this important debate on the reasonableness (or otherwise) of theistic faith in an era dominated by Science, with Scientism an influential worldview rooted in the prestige of science:

[youtube bhfkhq-CM84]

(NB: The debate proper begins at 4 10 mins 27 48 seconds in, with the moderator’s introduction.)

Let us watch, let us reflect, let us discuss. END

PS: I have also put up the Dawkins-Williams Jan 31st 2013 debate here. (HT: SG.)

PPS: I think it worthwhile to add this David Wood video on the argument from reason:

[youtube xKX-QtEo2fI]

Comments

As a bit of an aside: over the weekend I came across a nice argument for the claim that "semantic platonism" is inexplicable unless supplemented by something like mind-body dualism. Note 1: "Semantic platonism" holds that there are real abstract universals, hence meanings, intensions, propositions, logical rules, mathematical objects, and mathematical operations must be included in any full description of the basic constituents of reality, do not depend on the existence or contents of any finite, embodied mind, and do not have the kinds of causal interactions that physical things have.) Note 2: It's not entirely clear to me that semantic platonism is the only version of semantic realism, though it is the most ontologically demanding version, and it has a well-established pedigree in Western philosophy and theology. Suppose semantic platonism were true, but that mind-body dualism were false. Then we would not be able to arrive at any awareness of the semantic entities. (Whether there could be any awareness at all if dualism were false is a separate question.) The semantic entities would inhabit a realm of being to which we had no access; we would be metaphysically alienated from logic! A few further distinctions to round out this post: I think it's a bit murky to see how one gets from semantic platonism (SP) + mind-body dualism (D) to theism (T). In order for the Craig-style inference-to-the-best-explanation move to get started, it would have to be the case that SP+D is somehow incomplete, or that needs to be explained, and that T is an adequate explanation of SP+D. So what is it that needs to be explained, if SP+D were true?Kantian Naturalist_{February 11, 2013
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F/N: The papers on theology of math -- yes, such exists and has something serious to say -- here and here are worth pondering. KFkairosfocus_{February 8, 2013
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Theism, Naturalism, and Rationality - Alvin Plantinga - video - (January 7, 2013 lecture) http://www.youtube.com/watch?v=ApvLxnHq8Zsbornagain77_{February 8, 2013
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F/N: It is easy to go in ever expanding tangential spirals on a matter like this, so let us ask ourselves, on an inference to best explanation basis, has Dr Craig made a compelling or at least reasonable case worthy of consideration? And, for the moment we can zoom in on his third of the eight arguments, as it seems relatively novel: does mathematics show a pattern of elegant and beautiful complexity that is strangely and powerfully applicable to the physical world, one that is best explained on it being integral to the design of the world per the act of a designer? Above -- starting with the emptry set {} used to generate natural numbers then the reals, then mathematical spaces of two, three and in principle n dimensions, with kinematics opening a gateway to dynamics -- I argued that, internal to God's mind, we can see in dim outline a pattern that can generate a mathematically driven world that then allows physics to be spun out by moving to instantiation. Notoriously, all else in our physical world is founded on, constrained by or at least influenced by physics, including designs that harness the materials and forces of nature (in light of constraining factors such as efficiency or cost etc) to achieve purposes -- a classic definition of what engineers do. Does the world show evidence, then of being a mathematically anchored design? Would that be a good reason for the unreasonable effectiveness of mathematics in analysing and in designs in our world? Or, what? Why? Specifically, why? KFkairosfocus_{February 7, 2013
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Box: Indeed, a most interesting result, rather similar to the spiral structure of galaxies, which is indeed rather like the spirals that can be made based on the Fibonacci numbers. Strange, beautiful and fascinating. Order amidst an appearance that has defied our ability to predict. (Note the Wiki presentation here, that yields a cloth-like pattern. I see where here at Monash uni, it is triangle numbers that may generate the spiral you note. The pic on the right shows that beyond a certain point the structure diverges to a sort of bent arm spiral but the log-spiral structure in the heart of the pattern is plain. Yet another strange pattern like the Mandelbrot set. Which generates, with appropriate colour impositions, some of the most beautiful abstract images I have seen, with a degree of structured complexity flowing from a fairly simple algorithm that defies understanding. Where also, we see how powerful the symbolism and logical connexions of mathematics are, e.g. note in the linked vid on the sharpness of the criterion, that one needs only test the fate of 0 to categorise Julia sets.) BA77: Again, some very interesting food for thought. Godel was a true maverick among mathematicians and I remember the shock of discovering his incompleteness theorems. Mathematics is irreducibly complex and mathematicians must walk by faith and not by sight! (So much for the project of utter rationalism and deductive reasoning that eliminates faith: notitia, assensus, fiducia. Our proper worldview objective is reasonable faith, not reason in place of faith and not faith in place of reason.) Phinehas: The Euthyphro dilemma -- originally developed in the context of Greek gods who were supermen, rather than the ground of being -- fails spectacularly when applied to the God who is the ground of being, our inherently good creator and Lord, who as a necessary and maximally great being is worthy of worship. That which is good is intrinsic to God's character, is not an arbitrary whim on his part, and so to live by the good, the true, the right, the reasonable, truly loving and just is a part of our reasonable service to him. (Cf. here and onward links, especially here. Note Canon Hooker's summary used by Locke to ground the framework of liberty and justice in government and civil life.) KFkairosfocus_{February 7, 2013
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@Kairosfocus (191) The spiral of Ulam shows simularity with the spirals based on the famous Fibonacci numbers, which are omnipresent in nature.Box_{February 7, 2013
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Mathematics has long intrigued man as a way to get to the ultimate truth about reality. This quest to find 'ultimate truth' through mathematics is perhaps best summarized by this quote:
"We must know — we will know!" David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries.
But alas Hilbert's (naturalistic) belief that mathematics could offer, within itself, a complete description of reality was overturned by the soft spoken Kurt Godel:
BBC-Dangerous Knowledge - Part 1 https://vimeo.com/30482156 Part 2 https://vimeo.com/30641992
Hilbert's (and every mathematician's) dream to understand the complete mystery (truth) of reality through purely mathematical means was dashed to pieces on the rock of Godel's incompleteness theorem:
Kurt Gödel - Incompleteness Theorem - video http://www.metacafe.com/w/8462821 THE GOD OF THE MATHEMATICIANS - DAVID P. GOLDMAN - August 2010 Excerpt: we cannot construct an ontology that makes God dispensable. Secularists can dismiss this as a mere exercise within predefined rules of the game of mathematical logic, but that is sour grapes, for it was the secular side that hoped to substitute logic for God in the first place. Gödel's critique of the continuum hypothesis has the same implication as his incompleteness theorems: Mathematics never will create the sort of closed system that sorts reality into neat boxes. http://www.firstthings.com/article/2010/07/the-god-of-the-mathematicians
Undeterred in this set back, many leading researchers, such as Stephen Hawking, with the unverifiable mathematical fantasy of M-theory, still believe that they can arrive at an ultimate 'naturalistic' truth for reality through purely mathematical means. And indeed, as is evidenced by Euler's identity, there could very well be a single mathematical equation to describe all of reality (although the equation would still be dependent upon God for the inherent truthfulness therein according to Godel's incompleteness theorem):
God by the Numbers - Connecting the constants Excerpt: The final number comes from theoretical mathematics. It is Euler's (pronounced "Oiler's") number: e^pi*i. This number is equal to -1, so when the formula is written e^pi*i+1 = 0, it connects the five most important constants in mathematics (e, pi, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation). These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by pi; and analysis, by e, the base of the natural log. e^pi*i+1 = 0 has been called "the most famous of all formulas," because, as one textbook says, "It appeals equally to the mystic, the scientist, the philosopher, and the mathematician.",,, The discovery of this number gave mathematicians the same sense of delight and wonder that would come from the discovery that three broken pieces of pottery, each made in different countries, could be fitted together to make a perfect sphere. It seemed to argue that there was a plan where no plan should be.,,, Today, numbers from astronomy, biology, and theoretical mathematics point to a rational mind behind the universe.,,, The apostle John prepared the way for this conclusion when he used the word for logic, reason, and rationality—logos—to describe Christ at the beginning of his Gospel: "In the beginning was the logos, and the logos was with God, and the logos was God." When we think logically, which is the goal of mathematics, we are led to think of God. http://www.christianitytoday.com/ct/2006/march/26.44.html?start=3
Yet the broken pieces of pottery within physics were not to be nearly as cooperative as the broken pottery pieces from pure mathematics were:
THE MYSTERIOUS ZERO/INFINITY Excerpt: The biggest challenge to today's physicists is how to reconcile general relativity and quantum mechanics. However, these two pillars of modern science were bound to be incompatible. "The universe of general relativity is a smooth rubber sheet. It is continuous and flowing, never sharp, never pointy. Quantum mechanics, on the other hand, describes a jerky and discontinuous universe. What the two theories have in common - and what they clash over - is zero.",, "The infinite zero of a black hole -- mass crammed into zero space, curving space infinitely -- punches a hole in the smooth rubber sheet. The equations of general relativity cannot deal with the sharpness of zero. In a black hole, space and time are meaningless.",, "Quantum mechanics has a similar problem, a problem related to the zero-point energy. The laws of quantum mechanics treat particles such as the electron as points; that is, they take up no space at all. The electron is a zero-dimensional object,,, According to the rules of quantum mechanics, the zero-dimensional electron has infinite mass and infinite charge. http://www.fmbr.org/editoral/edit01_02/edit6_mar02.htm Quantum Mechanics and Relativity – The Collapse Of Physics? – video – with notes as to plausible reconciliation that is missed by materialists http://www.metacafe.com/watch/6597379/
Yet when one allows God into math, as Godel indicated must ultimately be done to keep math from being 'incomplete', then there actually exists a very credible, empirically backed, reconciliation between Quantum Mechanics and General Relativity into the long sought after 'Theory of Everything'! ,,,, Yet it certainly is one that many dogmatic Atheists, at least the ones I've dealt with, will try to deny the relevance of instead of testing the truthfulness of it,,,
Centrality of Each Individual Observer In The Universe and Christ’s Very Credible Reconciliation Of General Relativity and Quantum Mechanics https://docs.google.com/document/d/17SDgYPHPcrl1XX39EXhaQzk7M0zmANKdYIetpZ-WB5Y/edit?hl=en_US
As a footnote; Godel, who proved you cannot have a mathematical ‘Theory of Everything’, without allowing God to bring completeness to the 'Theory of Everything', also had this to say:
The God of the Mathematicians – Goldman Excerpt: As Gödel told Hao Wang, “Einstein’s religion [was] more abstract, like Spinoza and Indian philosophy. Spinoza’s god is less than a person; mine is more than a person; because God can play the role of a person.” – Kurt Gödel – (Gödel is considered one of the greatest logicians who ever existed) http://www.firstthings.com/article/2010/07/the-god-of-the-mathematicians
bornagain77_{February 7, 2013
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KN:
Moreover, it is completely unnecessary, because one could take a more “Platonic” view, and say that the Good is not constituted by God, but that God, being all-knowing, has perfect knowledge of the Good.
If Good is not constituted by God (that is, God is the standard by which Good is measured rather than Good is the standard by which God is measured), then the first horn of the Euthyphro dilemma would be in effect. The second horn of the Euthyphro dilemma does not require divine command theory because Good is not defined by God's will or command, but by God's existence and essence and being. Good is not arbitrary because God is not arbitrary. God is immutable.Phinehas_{February 7, 2013
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KN: Pardon, but you keep making a switcheroo: OUR mental efforts. We are contingent, secondary minds. I repeat, God, by definition would be the necessary being and root of being. One, in whom we live, move and have our being, who sustains in being everywhen and everywhere. So, it is a very different thing to speak about what our minds may recognise from what the mind at the root of being would constitute. Besides, the issue is that the blogger you cited was asserting that symbolic reference is necessarily external to the mind going through the symbolising process. By showing the chain from the empty set on, I am showing that that simply is not so, in the context of such a primary mind. And, I am pointing out that in that eternal mind, truth would eternally rest. So, the assertion no 3 above in the attempted disproof is question-begging at best. and, in actuality, it is false as one -- especially the One in view -- needs not make an EXTERNAL reference to conceive and extend a world of mathematics; such truths as 2 + 3 = 5 (and the components in it) are not contingent on any given world but hold in all possible worlds. In addition, a physical world could then be instantiated on the constructs, in this case ex nihilo. KFkairosfocus_{February 7, 2013
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It is one thing to say that our mental operations disclose that there are sets, quite another to say that mental operations constitute those sets. The reason I'm so surprised at the turn this conversation has taken is that you seem to be saying that mental activity constitutes the sets themselves (not just our knowledge of them, but the sets themselves), and that seems to fly in the face of what I'd assumed would be logical platonism. Put otherwise: does esse est concipi hold of abstract entities? That's what Kairosfocus seems to be saying here, but just that is the nominalist position! I also have serious worries about the suggestion (as I interpret what Kairosfocus has written) that logic is basically divine psychology. This basically gives us a divine command theory of logic that parallels the divine command theory of ethics. On the one hand, I appreciate the recognition that logic and ethics are, at bottom, both normative sciences -- the normative science of belief and the normative science of conduct. On the other hand, I think that grounding normativity as such in the divine will threatens to empty normativity of real content, since there is nothing to constrain the exercise of the divine will. One may say that God is necessarily good, but if goodness is itself just the divine will, then appealing to the essential goodness of God is a shameless dodge. Moreover, it is completely unnecessary, because one could take a more "Platonic" view, and say that the Good is not constituted by God, but that God, being all-knowing, has perfect knowledge of the Good. That gives the theist all she needs in securing a relation between revelation and ethics, without the problems of divine command theory. (Quite frankly, divine command theory has always struck me as a 'might makes right' view -- it's just that the right is constituted by the ultimate might.) Likewise, God might have perfect knowledge of mathematical objects, or of inferential relations, without constituting them. That would still preserve the theocentric conception of knowledge, and still allow one to say that human knowledge is more or less adequate insofar as it approximates divine knowledge (though of course still limited by human finitude).Kantian Naturalist_{February 7, 2013
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KN:
(2) abstract entities are mental entities [T]his is only acceptable if we first accept (1) [If God exists, then abstract entities are divine mental entities].
I'd like to understand why you believe this to be true. And must we also fist accept (1) to get to (2a) abstract entities may be mental entities? How so?Phinehas_{February 7, 2013
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Box, Not something I have ever really looked into, strange pattern. KFkairosfocus_{February 7, 2013
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Here's the clipped portion: Mathematics and Physics – A Happy Coincidence? – William Lane Craig – video http://www.metacafe.com/w/9826382bornagain77_{February 7, 2013
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Phinehas: Pardon, I doubt you were trying to derail, but if you look up-thread you will see a derail problem of significant proportions on a very similar topic. I decided to use something that is neutral to show that symbolic reference can be within, and that is also a context that speaks onwards very powerfully indeed. I think Craig was on to something with his remarks on Mathematics. KFkairosfocus_{February 7, 2013
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KF: Sorry, my intent was not to derail your thread. I just found a certain satisfaction in the notion that, in the process of trying to discount God's existence through an appeal to the mind's need for otherness, one might merely end up supporting a traditional theological position. KN's use of "external" or "representational" reminds me a bit of the UprightBiped thread with the brouhaha over "arbitrary." It seems to me that the argument could go something like: thoughts are similar to language in that they require the "about-ness" discussed in that thread. But I think the flaw is in asserting that "about-ness" must be external to the being thinking the thoughts. It seems to me that this is patently untrue if the being has any complexity at all, including the minimal complexity of existing as three persons.Phinehas_{February 7, 2013
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Unfortunately my knowledge of mathamatics is such that completing the captcha is quite a challenge for me every time ... I was wondering though if the magic of math is also reflected in prime numbers patterns - the spiral of Ulam (1963)? See for instance this picture. On phys.org there is a report on a recent study (2009) of Bartolo Luque and Lucas Lacasa of the Universidad Politécnica de Madrid in Spain, who have discovered yet another pattern in primes that has surprisingly gone unnoticed until now. Also here is a mysterious relationship with nature “Physicists have shown that many processes in nature can be modeled as stochastic multiplicative processes, (…)”. Maybe the experts here care to comment on this.Box_{February 7, 2013
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PS: How can I forget, infinity is already involved: 1, 2, 3, . . x2 2, 4, 6 . . . That is, we have 1:1 correspondence of a set and a proper subset, leading to a transfinite cardinality. And of course any "length" can be matched to the 0 -->1 interval, and so we see continuum cardinality with the same property.kairosfocus_{February 7, 2013
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F/N 5: To span to real numbers and space, consider the interval [0,1]. To cover this, accept 0, and 1 per above. In so doing, note that 1 > 0. Now, construct an expression of form 0. abcd . . . such that in succession we make up a Baire-like tree of countably infinite depth. For convenience, at each node allow it to span {0, 1, 2, . . . 9}. Then at stage a we have ten nodes [effectively 0.1 LT 0.2 LT . . . LT 0.9]. At b we have 10 * 10 nodes. Continue, using the usual place value designation connected to fractions and decimals. We thus define an infinite succession of points that can be ordered through less than or greater than or equality as 0.499999 . . . and 0.50000 . . . denote the same number, i.e. the underlying infinite series have the same sum. BTW, the span takes in the full interval from 0 to 1, from this, where 0.0000 . . . is 0 and 0.99999 . . . is 1. We also see that the Dedekind cut will at any point have an interior value between any two points, i.e. we have arrived at the continuum. Obviously, this procedure extends to any onward gap between successive integers, as we can slide it over to 1 --> 2, etc in succession without limit. BTW, we here have some sort of a picture of why it is the continuum has a higher and non countable cardinality than the natural numbers and their derivatives up to rationals. For at any point there will be an onward transfinite tree of further numbers between neighbours. To move to 2-d space, introduce the i* operator such that i*[i*x] = -x. (it helps us to think in terms of the sketch known as the number line, but the sketch is to help us as a crutch, the logic of assertions of concepts and constructions is more fundamental.) Where, - x is that value that added to x gives 0, the additive identity element. (Just defined a negative number. If you owe $x and you pay off $x, you now owe 0.) Of course the interpretation here, first, is that i^2 = -1, i.e. sqrt - 1 has popped up. Going on, we can use the inverse to see that -1 LT 0, -2 LT -1, etc, allowing extension to the full real number line via the set of integers and the Baire-like tree. So i* i* is a rotation by pi rads or 180 degrees in this line. A line being a succession of points in a continuum. Continuum being as noted. i* is then rotation anticlockwise by pi/2 rads or 90 degrees. (This leads into the cis theta = cos theta + i* sin theta analysis on the unit circle and also the exponential form, where e^i*theta is rot by theta in AC direction pivoted on origin. I am being summary and loose but the line should be traceable. exponentiation, cos and sin are of course defined on sums of series.) Of course the Euler expression is the special case of pi rad. We now have a plane. The complex one, and we can define points in it (x, i*y) or we can simplify to (x,y). That already invites extensions to (x, y, z) and r, theta phi) etc including n dimensional vectors etc, and onward matrices. But just go back to the idea of a segment directed origin --> point (x,y) a position vector. This can be seen as sum of two base vectors, with a different definition of i and j: i*x is on x axis, j*y is along y axis. We go to a z axis with k*z. Any 3-d point is now the vector sum. (And yes I know there is a road through Quaternions.) Such a point can move in succession by defining a succession in time, t. Thus kinematics. Onward we can define bodies as clusters of points, and assign inertia, force energy, momentum, angular momentum etc etc. Notice, we are here still in a conceptual abstraction frame, but are already seeing how these things can map over into the physical world. We define functions and relationships as per usual, with a function being a mapping from one set to another [which can be a replicate of the same] with the requirement of non ambiguity. The above is of course not rigorous and axiomatically presented, it is more of a modelling exercise, but one that is getting to the same place as a more rigid derivation would. It is intuitive but reasonably grounded. And, here we are, we have space, time, bodies, kinematics, dynamics, discretisation, continuum, rotation, translation, oscillation, transients, fields, fluxes, etc all ready to pop out. We are now on very familiar turf and there is no need to further elaborate. KFkairosfocus_{February 7, 2013
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F/N 4: More thoughts. Let us think together on these things. KFkairosfocus_{February 7, 2013
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Thanks kf that's a keeper: As to Alexander Vilenkin commenting on the beauty of mathematics being ideally suited for describing our physical universe (particularly e^ipi+1=0),, He probably does not realize just how deeply true what he wrote for e^ipi+1=0 actually is: 0 = 1 + e ^(i*pi) is found to govern the 'macro' structure of the universe: Michael Denton – Mathematical Truths Are Transcendent And Beautiful – Square root of -1 is built into the fabric of reality – video http://www.metacafe.com/watch/4003918 I find it extremely strange that the enigmatic Euler's identity, which was deduced centuries ago, would find such striking correlation to how reality is actually found to be structured by modern science. In pi we have correlation to the 'sphere of the universe' as revealed by the Cosmic Background radiation, as well pi correlates to the finely-tuned 'geometric flatness' within the 'sphere of the universe' that has now been found. In 'e' we have the fundamental constant that is used for ascertaining exponential growth in math that strongly correlates to the fact that space-time is 'expanding/growing equally' in all places of the universe. In the square root of -1 we have what is termed a 'imaginary number', which was first proposed to help solve equations like x2+ 1 = 0 back in the 17th century, yet now, as Michael Denton pointed out in the preceding video, it is found that the square root of -1 is required to explain the behavior of quantum mechanics in this universe. The correlation of Euler's identity, to the foundational characteristics of how this universe is constructed and operates, points overwhelmingly to a transcendent Intelligence, with a capital I, which created this universe! It should also be noted that these mathematical constants, pi,e, and square root -1, were at first thought by many to be completely transcendent of any material basis, to find that these transcendent constants of Euler's identity in fact 'govern' material reality, in such a foundational way, should be enough to send shivers down any mathematicians spine. notes: It is also interesting to note that 'higher dimensional' mathematics had to be developed before Einstein could elucidate General Relativity, or even before Quantum Mechanics could be elucidated; The Mathematics Of Higher Dimensionality – Gauss and Riemann – video http://www.metacafe.com/watch/6199520/ The Unreasonable Effectiveness of Mathematics in the Natural Sciences - Eugene Wigner - 1960 Excerpt: We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity.,,, The two theories operate with different mathematical concepts: the four dimensional Riemann space and the infinite dimensional Hilbert space, http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html Centrality of Earth Within The 4-Dimensional Space-Time of General Relativity - video http://www.metacafe.com/w/8421879 Dr. Quantum - Double Slit Experiment & Entanglement - video http://www.metacafe.com/watch/4096579 The Galileo Affair and the true "Center of the Universe" Excerpt: I find it extremely interesting, and strange, that quantum mechanics tells us that instantaneous quantum wave collapse to its 'uncertain' 3D state is centered on each individual conscious observer in the universe, whereas, 4D space-time cosmology (General Relativity) tells us each 3D point in the universe is central to the expansion of the universe. These findings of modern science are pretty much exactly what we would expect to see if this universe were indeed created, and sustained, from a higher dimension by a omniscient, omnipotent, omnipresent, eternal Being who knows everything that is happening everywhere in the universe at the same time. These findings certainly seem to go to the very heart of the age old question asked of many parents by their children, “How can God hear everybody’s prayers at the same time?”,,, i.e. Why should the expansion of the universe, or the quantum wave collapse of the entire universe, even care that you or I, or anyone else, should exist? Only Theism, Christian Theism in particular, offers a rational explanation as to why you or I, or anyone else, should have such undeserved significance in such a vast universe. [15] Psalm 33:13-15 The LORD looks from heaven; He sees all the sons of men. From the place of His dwelling He looks on all the inhabitants of the earth; He fashions their hearts individually; He considers all their works. https://docs.google.com/document/d/1BHAcvrc913SgnPcDohwkPnN4kMJ9EDX-JJSkjc4AXmA/edit as well,,, Kurt Gödel - Incompleteness Theorem - video http://www.metacafe.com/w/8462821 Taking God Out of the Equation - Biblical Worldview - by Ron Tagliapietra - January 1, 2012 Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties. 1. Validity . . . all conclusions are reached by valid reasoning. 2. Consistency . . . no conclusions contradict any other conclusions. 3. Completeness . . . all statements made in the system are either true or false. The details filled a book, but the basic concept was simple and elegant. He summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem. Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation. Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3). http://www.answersingenesis.org/articles/am/v7/n1/equation# Verse: John 1:1-5 In the beginning was the Word(Logos), and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. In him was life, and that life was the light of all mankind. The light shines in the darkness, and the darkness has not overcome it.bornagain77_{February 7, 2013
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BA, thanks. I am having a strange vision of the beauty, power, truth and unity of Math forming in my mind, joined to a vision of eternity, infinity and more, multiplied by the one and the many. Things I did in entirely different disciplines are -- live, in process, this is evidently a visitation to the mind as promised some years ago (personal promises are real and delivered upon . . . ) -- reconstructing themselves into facets of a brilliant diamond. A strange and yet familiar experience of live synthesis, triggered by KN's challenge, for which I must thank him in the providence of the God he does not yet fully acknowledge -- note that Naturalism -- but who is obviously calling out to him from a deep past of covenantal heritage. May he hear that still, small persistent voice as CSL did in 1929. KFkairosfocus_{February 7, 2013
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Thanks kf, will read it,,, you may appreciate this off topic short video: Hazor - Israel Aerials - video https://vimeo.com/59008952bornagain77_{February 7, 2013
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F/N 4: A reader. note the neutrality issue.kairosfocus_{February 7, 2013
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F/N 3: BA77, you will love the related argument here by harvey1. KFkairosfocus_{February 7, 2013
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F/N 2: This, by C. Stephen Evans, is maybe a closer step to what I am thinking, inter alia:
Beneficial Order and Teleological Arguments for God DOI:10.1093/acprof:oso/9780199217168.003.0004 This chapter argues that the theistic natural sign of “beneficial order” lies at the foundation of many of the teleological arguments for God's existence. This sign provides more content about God than the sign of cosmic wonder. Various forms of the argument are examined and developed, including the classic one given by Aquinas. The “fine?tuning” of the physical universe, while it may provide support for a teleological argument, is not a natural sign, because it fails the Wide Accessibility Principle test [--> this sets hostage the cogency of a case to the politics of willful objectionism] . Darwinian evolutionary theory does not undermine the claim that beneficial order is a theistic natural sign [--> But the underlying, common a priori materialism tends to lead to that perception]. The chapter concludes by showing that Hume and Kant, both of whom rejected teleological arguments as proofs [--> explanatory inference per comparative difficulties is about warrant and reasonable faith, not deductive proof], still recognized the force of the sign that lies at the heart of the arguments. This fact, combined with our own experiences, gives us good reason to think that beneficial order is a theistic natural sign.
You will see my caveats on a first look. My basic point is that the elegant unity provided by mathematics and its inherently abstract nature, multiplied by the necessity of key mathematical results, that confers a causeless, eternal nature to them -- note, there are no possible worlds in which 3 + 2 = 5 will fail to hold good, even a world empty of physical objects (but I reckon from the context of a credibly contingent world in which we exist as embodied minded contingent creatures that points to an underlying necessary being as ground of the reality we experience] -- point to a unifying mind behind reality. One that is as necessary as a being and so as eternal as the mathematics in it. KFkairosfocus_{February 7, 2013
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F/N 2: Without endorsing it just now -- i.e. I invite discussion -- the following skeletal may be a place to begin:
#8) ARGUMENT FROM MATHEMATICS. Premise 1) Evidence for design within mathematics would point to a teleological source of mathematics. Premise 2) There is evidence for design within mathematics. _____________________________________ Therefore, [3, conclusion:] there is a teleological source of mathematics. {Augment: Where also, the relevant features of mathematics express necessary relationships true in any possible world.} {DISCUSSION:] Premise 1 is pretty obvious since actual design always requires a teleological source. Premise 2 is true because there are many examples of evidence for design within mathematics …
1) Euler`s formula. 2) The Mandelbrot set. 3) The mathematical relationship between Fibonacci numbers and nature. 4) The mathematical relationships between man and his relationship to the natural world (for example,the mass of the earth is midway between the mass of the observable universe and the mass of the atom). 5) The fact that mathematics can actually describe the universe in a coherent way with simple mathematical equations.

Maybe, this might be a place to begin from. But, I think this misses the issue of the powerful unifying force that mathematics captures and the sort of concerns I have been expressing in this thread. It does hint at some of that, e.g. the Euler expression. KFkairosfocus_{February 7, 2013
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F/N: let me clip the just linked, from Craig:
1. The Cosmological Argument from Contingency The cosmological argument comes in a variety of forms. Here’s a simple version of the famous version from contingency: Everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. If the universe has an explanation of its existence, that explanation is God. The universe exists. Therefore, the universe has an explanation of its existence (from 1, 3). Therefore, the explanation of the universe’s existence is God (from 2, 4). Now this is a logically airtight argument. That is to say, if the premises are true, then the conclusion is unavoidable. It doesn’t matter if we don’t like the conclusion. It doesn’t matter if we have other objections to God’s existence. So long as we grant the three premises, we have to accept the conclusion. So the question is this: Which is more plausible—that those premises are true or that they are false? 1.1. Premise 1 Consider first premise 1. According to premise 1, there are two kinds of things: things which exist necessarily and things which are produced by some external cause. Let me explain. Things that exist necessarily exist by a necessity of their own nature. It’s impossible for them not to exist. Many mathematicians think that numbers, sets, and other mathematical entities exist in this way. They’re not caused to exist by something else; they just exist necessarily. By contrast, things that are caused to exist by something else don’t exist necessarily. They exist contingently. They exist because something else has produced them. Familiar physical objects like people, planets, and galaxies belong in this category. So premise 1 asserts that everything that exists can be explained in one of these two ways. This claim, when you reflect on it, seems very plausibly true. Imagine that you’re hiking through the woods and come across a translucent ball lying on the forest floor. You’d naturally wonder how it came to be there. If one of your hiking partners said to you, “Don’t worry about it! There isn’t any explanation of its existence!”, you’d either think he was crazy or figure that he just wanted you to keep moving. No one would take seriously the suggestion that the ball existed there with literally no explanation. Now suppose you increase the size of the ball in this story to the size of a car. That wouldn’t do anything to satisfy or remove the demand for an explanation. Suppose it were the size of a house. Same problem. Suppose it were the size of a continent or a planet. Same problem. Suppose it were the size of the entire universe. Same problem. Merely increasing the size of the ball does nothing to affect the need of an explanation. Since any object could be substituted for the ball in this story, that gives grounds for thinking premise 1 to be true. It might be said that while premise 1 is true of everything in the universe, it is not true of the universe itself. Everything in the universe has an explanation, but the universe itself has no explanation. Such a response commits what has been aptly called “the taxicab fallacy.” For as the nineteenth-century atheist philosopher Arthur Schopenhauer quipped, premise 1 can’t be dismissed like a taxi once you’ve arrived at your desired destination! You can’t say that everything has an explanation of its existence and then suddenly exempt the universe. It would be arbitrary to claim that the universe is the exception to the rule. (God is not an exception to premise 1: see below at 1.4.) Our illustration of the ball in the woods shows that merely increasing the size of the object to be explained, even until it becomes the universe itself, does nothing to remove the need for some explanation of its existence. One might try to justify making the universe an exception to premise 1. Some philosophers have claimed that it’s impossible for the universe to have an explanation of its existence. For the explanation of the universe would have to be some prior state of affairs in which the universe did not yet exist. But that would be nothingness, and nothingness can’t be the explanation of anything. So the universe must just exist inexplicably. This line of reasoning is, however, obviously fallacious because it assumes that the universe is all there is, that if there were no universe there would be nothing. In other words, the objection assumes that atheism is true. The objector is thus begging the question in favor of atheism, arguing in a circle. The theist will agree that the explanation of the universe must be some (explanatorily) prior state of affairs in which the universe did not exist. But that state of affairs is God and his will, not nothingness. So it seems that premise 1 is more plausibly true than false, which is all we need for a good argument. 1.2. Premise 2 What, then, about premise 2? Is it more plausibly true than false? Although premise 2 might appear at first to be controversial, what’s really awkward for the atheist is that premise 2 is logically equivalent to the typical atheist response to the contingency argument. (Two statements are logically equivalent if it’s impossible for one to be true and the other one false. They stand or fall together.) So what does the atheist almost always say in response to the contingency argument? He typically asserts the following: A. If atheism is true, the universe has no explanation of its existence. Since, on atheism, the universe is the ultimate reality, it just exists as a brute fact. But that is logically equivalent to saying this: B. If the universe has an explanation of its existence, then atheism is not true. So you can’t affirm (A) and deny (B). But (B) is virtually synonymous with premise 2! (Just compare them.) So by saying that, given atheism, the universe has no explanation, the atheist is implicitly admitting premise 2: if the universe does have an explanation, then God exists. Besides that, premise 2 is very plausible in its own right. For think of what the universe is: all of space-time reality, including all matter and energy. It follows that if the universe has a cause of its existence, that cause must be a non-physical, immaterial being beyond space and time. Now there are only two sorts of things that could fit that description: either an abstract object like a number or else an unembodied mind. But abstract objects can’t cause anything. That’s part of what it means to be abstract. The number seven, for example, can’t cause any effects. So if there is a cause of the universe, it must be a transcendent, unembodied Mind, which is what Christians understand God to be. 1.3. Premise 3 Premise 3 is undeniable for any sincere seeker after truth. Obviously the universe exists! 1.4. Conclusion From these three premises it follows that God exists. Now if God exists, the explanation of God’s existence lies in the necessity of his own nature, since, as even the atheist recognizes, it’s impossible for God to have a cause. So if this argument is successful, it proves the existence of a necessary, uncaused, timeless, spaceless, immaterial, personal Creator of the universe. This is truly astonishing! 1.5. Dawkins’s Response So what does Dawkins have to say in response to this argument? Nothing! Just look at pages 77–78 of his book where you’d expect this argument to come up. All you’ll find is a brief discussion of some watered down versions of Thomas Aquinas’ arguments, but nothing about the argument from contingency. This is quite remarkable since the argument from contingency is one of the most famous arguments for God’s existence and is defended today by philosophers such as Alexander Pruss, Timothy O’Connor, Stephen Davis, Robert Koons, and Richard Swinburne, to name a few.4 [The New Atheism and Five Arguments for God]
Here he simply adverts to mathematical objects as necessarily existing as a serious view among mathematicians. Does someone have a link where he elaborates, or someone else does, other than my own sketchy discussion above? KFkairosfocus_{February 7, 2013
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Phineas, the triune concept of God is a systems conception, of complex unity, e.g. cf. the curious legend of Patrick and the shamrock. Where the problem of the one and the many as a key characteristic of the world, is itself another deep problem in phil and worldviews, one that -- cf discussion here and here -- the triune concept of God addresses on a comparative difficulties basis with other major options. But, this is not a context and forum for going off on such a potentially contentious theological and ideological battle debate, there is far more than enough on the table already with Craig's Mathematics point. I have only given the links so that you may pursue per your own interests. BTW, for the Craig debate fans, is this a new point for Craig to make in his debates? [I see a curious link here.] KFkairosfocus_{February 7, 2013
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KN: Let me continue, after a bit of the old biologically necessary downtime. The set concept is that we can have unambiguously definable collections [notice the concession to Lord Russell's Village Barber paradox], including first the empty one. There is no reason why a set of relevant collections -- where the required act of clustering is a conceptual operation that can be physically instantiated (a very familiar pattern to modellers) -- cannot be carried out mentally. As for concept, I think this may help:
concept [?k?ns?pt]n 1. an idea, esp an abstract idea the concepts of biology 2. (Philosophy) Philosophy a general idea or notion that corresponds to some class of entities and that consists of the characteristic or essential features of the class 3. (Philosophy) Philosophy a. the conjunction of all the characteristic features of something b. a theoretical construct within some theory c. a directly intuited object of thought d. the meaning of a predicate 4. (Engineering / Automotive Engineering) (modifier) (of a product, esp a car) created as an exercise to demonstrate the technical skills and imagination of the designers, and not intended for mass production or sale [from Latin conceptum something received or conceived, from concipere to take in, conceive] Collins English Dictionary – Complete and Unabridged © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003
In short, I am using the term well within its normal meaning, and that meaning is precisely a mental one. Where, in particular, the concept of an unambiguously definable clustering that happens to be empty is quite feasible: {}, the empty set. Think of the abstract singleton {*} then remove its sole member. The successor operations already laid out are similarly mental ones, of deceptively simple form:
{} --> 0 {0} --> 1 {0, 1} --> 2 {0, 1, 2} --> 3, etc [even this is deceptively simple, it denotes, without limit! The transfinite nature of the successively built up collection is immediately implied.] I have already outlined how counting then emerges by simply chaining the successive numerals for the sets: 0, 1, 2, 3, . . . and making a match, pictorial, verbal [algebraic if you will . . . (this is the hard part, and we see why Algebra is both powerful and hard], oral or physical From the set of numbers, we then are able to construct all else by injecting further ideas and constructions. THAT TAKES US TO PARTICLE KINEMATICS, AND TO GET TO PHYSICS WE "SIMPLY" ADD INERTIA, FORCE, BODIES, ENERGY ETC AND THEN WE CAN MOVE FROM A MODEL WORLD TO A MATERIAL ONE. The mathematical linkages will then play out by the logic involved. Then, also, remember, just how closely integrated this is, shockingly integrated: Euler: 0 = 1 + e^i*pi In close connexion with this, we see the world of the frequency domain, and the wider one that via Laplace integrates transient behaviour. In that domain, d/dt --> s*[] and Integral - dt is [1/s]*[]. Hence turning differential equation based analysis into sophisticated algebra with dynamical implications. Also, this can be discretised through the bridge to the Z transform, and the whole vista of digital signal processing opens up. In these domains, issues on stability drop out, and pole and zero location determine dynamic behaviour. The operation 1/z has the definition unit delay, and can then be directly instantiated in a network of elements. That is, we are here at the point of a comprehensive discrete time model of systems. I will not bother with the extension that runs through the partial differential into the world of PDE's, the continuum, fields etc. Just say that fluids and electromagnetism, as obvious first applications, rest on that via the powerful mathematical operations, div, grad and curl etc. Mix in vectors and matrices which can be populated with essentially arbitrary elements, including those from the above domains, and we can do shocklingly powerful things. Sprinkle on tensors while we are really going at it. Run in the other direction and we are at the provinces of logic and set theory, which turn out to be absolutely foundational to the field.
And, yes, I freely confess to the framework of thinking God's thoughts after him as a paradigm for doing Math and science. Yes, I freely acknowledge that others out there can and do use the above abstractions and operations etc, without that framework. But, I would like to see their grounding of it. (In other words, I am again raising the issue of worldview grounding.) However, all of this is to a certain extent distractive. The actual task in view on the claimed proof was to address the claim of externality as inherent to symbolisation and abstract conceptualisation based on it. It should be clear from the above, that once there is a framework in which symbolic thoughts need have no external reference, then the pivotal premise 3 falls to the ground, a fatal stake through its heart. Let me again clip from 136, which was taken from the online argument you pointed to with approval, that God is claimed to be conceptually impossible:
CIGEC.1: For all entities designated God, that entity had conscious mental states and there were no external objects. CIGEC.2: Representational content is a necessary condition of conscious mental states. CIGEC.3: The existence of external objects is a necessary condition of representational content. CIGEC.3.1: NOTE – Strict internalism about representational content seems challenging given the further state of the discourse. However, a dispute would be possible to challenge (3). CIGEC.4: The existence of external objects is a necessary condition of conscious mental states. (Hypothetical Syllogism; 2, 3) CIGEC.5: Necessarily, for all entities/states of affairs, either there are no external objects or there are conscious mental states. (Material Implication; 4) CIGEC.5.1: Since this is operating in a modal system, the extraction of the necessity operator is important. This seems justified (on with the exclusive ‘or’ operator) by fact that we are concerned with a necessary condition in (4). CIGEC.6: It is not possible that there is some entity that had conscious mental states and there were no external objects. (Modal Equivalence; 5) CIGEC.7: Therefore, there are no possible entities designated God.
See the point of my use of a counter-example? What seems to have gone wrong is, first, the confusion of our ontological status with that of a Mind at the root of being. We do represent external objects and we do form symbols for them internally, by extensions of pictures. However, that is not necessary, and it is doubly not so for the sort of being "in whom we live and move and have our being." That is why the construction of the field of numbers and other relevant mathematical objects by starting with the concept of unambiguously definable collection, and then using the empty set to actually successively construct, is important. I think that the abstract entity and its operations and relationships, constraints etc can be reasonably understood as being held in a mind. Can you identify and explain coherently and explicitly another way in which such can have a legitimate, credibly real status? (As in, just last evening, in discussing with my son on this discussion, I had him say the words circle square. Then, I asked him to draw me one. We can easily enough say words that are incoherent and incapable of being instantiated, abstractly or physically. Which brings us back to the Barber paradox, where set theory ran into a crucial difficulty. Allow set overlap and the collections are unambiguous, but the situation forbids that, and behold with that seemingly simple step we are at a point where the whole idea is in deep trouble and has to be reformulated.) I think this exchange has been very useful and it happens to be also illustrating what lurks in Craig's argument that the effectiveness of Mathematics is one of the cluster of convergent facts or issues etc that cumulatively point on inference to best explanation, to God. Let's hear your onward thoughts and those of others who have an interest. KFkairosfocus_{February 7, 2013
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Your nominalism is showing. ;)Mung_{February 6, 2013
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