Edward Feser on mathematics and the sense of the divine

_{Denyse O'Leary

March 15, 2020

Intelligent Design, Mathematics, Philosophy}

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Edward Feser (right) explains how mathematics illustrates some of the qualities we associate with God:

Mathematics appears to describe a realm of entities with quasi–divine attributes. The series of natural numbers is infinite. That one and one equal two and two and two equal four could not have been otherwise. Such mathematical truths never begin being true or cease being true; they hold eternally and immutably. The lines, planes, and figures studied by the geometer have a kind of perfection that the objects of our -experience lack. Mathematical objects seem -immaterial and known by pure reason rather than through the senses. Given the centrality of mathematics to scientific explanation, it seems in some way to be a cause of the natural world and its order.
How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect. [name], “Keep it simple” at First Things

Dr. Feser’s most recent book is Aristotle’s Revenge: The Metaphysical Foundations of Physical and Biological Science (2019).

See also: A simple triangle can disprove materialism. Conventional descriptions of material processes do not help much when we are trying to account for abstract thought.

and

If computers are intelligent, climbing a tree is flying That, says Edward Feser, is the take-home message from Gary Smith’s book, The AI Delusion.

Hat tip: Philip Cunningham

Comments

The reason why no computer will ever have genuine mathematical insight is because they, besides having no conscious mind, computers also have no free will. As Douglas S. Robertson explains, "Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information."
Algorithmic Information Theory, Free Will and the Turing Test - Douglas S. Robertson Excerpt: Chaitin’s Algorithmic Information Theory shows that information is conserved under formal mathematical operations and, equivalently, under computer operations. This conservation law puts a new perspective on many familiar problems related to artificial intelligence. For example, the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information. http://cires.colorado.edu/~doug/philosophy/info8.pdf
Thus since ‘secular Platonism’ is obviously false, (as well as being insane), we are necessarily back to the Christian’s presupposition that mathematics exists "because they are God’s thoughts" As Bruce Gordon explains, “the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.”
BRUCE GORDON: Hawking’s irrational arguments – October 2010 Excerpt: ,,,The physical universe is causally incomplete and therefore neither self-originating nor self-sustaining. The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,, Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.” Anything else invokes random miracles as an explanatory principle and spells the end of scientific rationality. http://www.washingtontimes.com/news/2010/oct/1/hawking-irrational-arguments/
Moreover, allowing the free will and/or Agent causality of God ‘back’ into physics, as the Christian founders of modern science originally envisioned,,,, (Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders),,, and as quantum mechanics itself now empirically demands (with the closing of the free will loophole by Anton Zeilinger and company), rightly allowing the Agent causality of God ‘back’ into physics provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead provides an empirically backed reconciliation, via the Shroud of Turin, between quantum mechanics and general relativity into the much sought after ‘Theory of Everything”.
November 2019 - despite the fact that virtually everyone, including the vast majority of Christians, hold that the Copernican Principle is unquestionably true, the fact of the matter is that the Copernican Principle is now empirically shown, (via quantum mechanics and general relativity, etc..), to be a false assumption. https://uncommondescent.com/intelligent-design/so-then-maybe-we-are-privileged-observers/#comment-688855 (February 19, 2019) To support Isabel Piczek’s claim that the Shroud of Turin does indeed reveal a true ‘event horizon’, the following study states that ‘The bottom part of the cloth (containing the dorsal image) would have born all the weight of the man’s supine body, yet the dorsal image is not encoded with a greater amount of intensity than the frontal image.’,,, Moreover, besides gravity being dealt with, the shroud also gives us evidence that Quantum Mechanics was dealt with. In the following paper, it was found that it was not possible to describe the image formation on the Shroud in classical terms but they found it necessary to describe the formation of the image on the Shroud in discrete quantum terms. https://uncommondescent.com/intelligent-design/experiment-quantum-particles-can-violate-the-mathematical-pigeonhole-principle/#comment-673178 The evidence for the Shroud's authenticity keeps growing. (Timeline of facts) - November 08, 2019 What Is the Shroud of Turin? Facts & History Everyone Should Know - Myra Adams and Russ Breault https://www.christianity.com/wiki/jesus-christ/what-is-the-shroud-of-turin.html
Verse:
Colossians 1:15-20 The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross.
bornagain77_{March 18, 2020
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As to this comment from the article:
How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world.
This view the mathematics exists "because they are God’s thoughts" and the Christian view that God created the universe and that the universe has not always existed, (as Aristotle had held), were necessary presuppositions for modern science to take root in Medieval Christian culture. As the following article notes, "contingency and rationality of the cosmos are like two pillars supporting the Christian vision of the cosmos."
The War against the War Between Science and Faith Revisited - July 2010 Excerpt: … If science suffered only stillbirths in ancient cultures, how did it come to its unique viable birth? The beginning of science as a fully fledged enterprise took place in relation to two important definitions of the Magisterium of the Church. The first was the definition at the Fourth Lateran Council in the year 1215, that the universe was created out of nothing at the beginning of time. The second magisterial statement was at the local level, enunciated by Bishop Stephen Tempier of Paris who, on March 7, 1277, condemned 219 Aristotelian propositions, so outlawing the deterministic and necessitarian views of creation. These statements of the teaching authority of the Church expressed an atmosphere in which faith in God had penetrated the medieval culture and given rise to philosophical consequences. The cosmos was seen as contingent in its existence and thus dependent on a divine choice which called it into being; the universe is also contingent in its nature and so God was free to create this particular form of world among an infinity of other possibilities. Thus the cosmos cannot be a necessary form of existence; and so it has to be approached by a posteriori investigation. The universe is also rational and so a coherent discourse can be made about it. Indeed the contingency and rationality of the cosmos are like two pillars supporting the Christian vision of the cosmos. http://www.scifiwright.com/2010/08/the-war-against-the-war-between-science-and-faith-revisited/
Perhaps the best example of just how integral this Augustinian view of mathematics, (i.e. "because they are God’s thoughts"), was for the rise of modern science is this following quote by Johannes Kepler. A quote which he made after he discovered his third law of planetary motion in 1618,
"O, Almighty God, I am thinking Thy thoughts after Thee!" - Johannes Kepler, "The Harmonies of the World.", book five - 1619 - best known for his three laws of planetary motion,
As well Kepler noted, after he discovered the first two laws of planetary motion in 1609, that this "is one of the reasons that Man is the image of God."
"Geometry is one and eternal shining in the mind of God. That share in it accorded to men is one of the reasons that Man is the image of God." - Johannes Kepler - from an open letter to Galileo Galilei - Dissertatio cum Nuncio Sidereo (1610)
Feser did an excellent job in his article of explaining exactly why God's "Divine simplicity" defeats the current mathematical philosophy in academia, i.e. "Platonism that makes no reference to God" (which) "has in recent decades come to renewed prominence in secular academic philosophy." But for me, while reading Feser's article, I kept asking myself, "What about Gödel’s incompleteness theorems'?" I think, as good as Feser's argument currently is against the current 'secular Platonism' that has risen to prominence in academia, that Gödel's incompleteness theorems can, none-the-less, add quite a bit to Feser's current argument against 'secular Platonism' . As Goldman noted in the following article, Gödel's incompleteness proofs directly implies that, "we cannot construct an (mathematical) ontology that makes God dispensable."
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/2010/08/the-god-of-the-mathematicians
And as Stanley Jaki explained in the following quote from an article entitled “Gödel and Physics”,“Clearly then no scientific cosmology, which of necessity must be highly mathematical, can have its proof of consistency within itself as far as mathematics go. In absence of such consistency, all mathematical models, all theories of elementary particles, including the theory of quarks and gluons…fall inherently short of being that theory which shows in virtue of its a priori truth that the world can only be what it is and nothing else. This is true even if the theory happened to account for perfect accuracy for all phenomena of the physical world known at a particular time.”
Gödel and Physics – John D. Barrow Excerpt (page 5-6): “Clearly then no scientific cosmology, which of necessity must be highly mathematical, can have its proof of consistency within itself as far as mathematics go. In absence of such consistency, all mathematical models, all theories of elementary particles, including the theory of quarks and gluons…fall inherently short of being that theory which shows in virtue of its a priori truth that the world can only be what it is and nothing else. This is true even if the theory happened to account for perfect accuracy for all phenomena of the physical world known at a particular time.” Stanley Jaki – Cosmos and Creator – 1980, pg. 49 http://arxiv.org/pdf/physics/0612253.pdf
Moreover, besides Gödel’s incompleteness theorems falsifying the secularist’s belief that they can construct a mathematical ontology without reference to God, besides that, when we take the secularist’s belief that he can explain the existence of mathematics, via a philosophical "Platonism that makes no reference to God", when we take that secularist’s presupposition to its logical end, we find, (as is usual with taking atheistic beliefs to their logical end), that the secularist’s presupposition commits epistemological suicide. For prime example of the ‘epistemological suicide’ is Max Tegmark’s book ‘Our Mathematical Universe’ which based on the secularist’s presupposition that they, i.e. atheists, can construct a mathematical ontology without reference to God. In critique to Max Tegmark’s 2015 book, 'Our Mathematical Universe', Sheldon Glashow, professor of Mathematics and Physics at Boston University, quips that, “I may be a blockhead but I am certainly not a mathematical structure akin to a triangle.”
A Hand-Waving Exact Science - Sheldon Glashow Excerpt: And our ToE is just one among an infinity of mathematical structures, each of them its own universe. If Tegmark is correct, there must exist a slightly different mathematical structure, whose equations are emblazoned on another T-shirt, wherein I am Tegmark’s psychiatrist rather than a physicist. I do not believe a word of it. Paraphrasing Danny, I may be a blockhead but I am certainly not a mathematical structure akin to a triangle. - Sheldon Glashow Sheldon Glashow is professor of Mathematics and Physics at Boston University and professor emeritus of Physics at Harvard University. He received the Nobel Prize in Physics in 1979. http://inference-review.com/article/a-hand-waving-exact-science
And as George Ellis remarks in the following article, “Tegmark has argued that every consistent mathematical structure exists in some disconnected universe. Tegmark also believes that nothing else exists beyond the consistent mathematical structures. Tegmark is himself nothing more than a consistent mathematical structure. This is a view that assigns to mathematical structures a degree of agency that they are not otherwise thought to possess.”
Physics on Edge - George Ellis - August 2017 Excerpt: Tegmark has argued that every consistent mathematical structure exists in some disconnected universe. Tegmark also believes that nothing else exists beyond the consistent mathematical structures. Tegmark is himself nothing more than a consistent mathematical structure. This is a view that assigns to mathematical structures a degree of agency that they are not otherwise thought to possess. http://inference-review.com/article/physics-on-edge
To repeat, “Tegmark is himself nothing more than a consistent mathematical structure. This is a view that assigns to mathematical structures a degree of agency that they are not otherwise thought to possess.” In other words, instead of mathematicians discovering mathematical laws and revealing them to other mathematicians, we instead, in effect, have consistent mathematical structures discovering themselves and then revealing themselves to other consistent mathematical structures. This assumes a degree of cognition and free will for “consistent mathematical structures”, say for euclidean geometric structures such as triangles, squares, circles, etc.. etc.., that they are not normally thought to possess. In fact, as should be needless to say, it is insane to believe as such. Moreover, since “an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms”,,,
The Limits Of Reason – Gregory Chaitin – 2006 Excerpt: Unlike Gödel’s approach, mine is based on measuring information and showing that some mathematical facts cannot be compressed into a theory because they are too complicated. This new approach suggests that what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms. http://www.umcs.maine.edu/~chaitin/sciamer3.pdf
As since Tegmark apparently believes that it is possible to have consistent mathematical structures discovering themselves and then revealing themselves to other consistent mathematical structures, then it follows that Tegmark must believe that consistent mathematical structures, (i.e. people), have the ‘potential’ attribute of ominiscience. (After all, Tegmark does believe he, the consistent mathmatical structure that he is, is on the trail of the ‘Theory of Everything’ in his book “Our Mathematical Universe”),
A Hand-Waving Exact Science - Sheldon Glashow Excerpt: According to Tegmark, our universe is (rather than merely “is described by”) the long sought “Theory of Everything, or ToE, from which all else can be derived… [S]uch a complete description must be devoid of any human baggage. This means that it must contain no concepts at all! In other words, it must be a purely mathematical theory… [An] infinitely intelligent mathematician should be able to derive the entire theory tree [including all of science, engineering, sociology, psychology etc.] from these equations alone, by deriving the properties of the physical reality that they describe, the properties of its inhabitants, their perceptions of the world, and even the words they invent. This purely mathematical theory of everything could potentially turn out to be simple enough to describe with equations that fit on a T-shirt.9” - Sheldon Glashow Sheldon Glashow is professor of Mathematics and Physics at Boston University and professor emeritus of Physics at Harvard University. He received the Nobel Prize in Physics in 1979. http://inference-review.com/article/a-hand-waving-exact-science
In short, via insanity, Tegmark. and apparently secular academia at large, has replaced God with the mathematical philosophy of ‘secular Platonism’ which, when taken to its logical conclusion, winds up in, as usual for secular presuppositions, once again in catastrophic epistemological failure Of course consistent mathematical structures do not ‘discover themselves’ much less do they reveal themselves to other consistent mathematical structures. It is people, via their immaterial minds and free will, who discover consistent mathematical structures and reveal those consistent mathematical structures to other people. As James Franklin stated, the intellect (is) immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.,,
The mathematical world - James Franklin - 7 April 2014 Excerpt: the intellect (is) immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.,,, - James Franklin is professor of mathematics at the University of New South Wales in Sydney. http://aeon.co/magazine/world-views/what-is-left-for-mathematics-to-be-about/
bornagain77_{March 18, 2020
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News, math is truly mind-blowing. KFkairosfocus_{March 17, 2020
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