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.
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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
News, math is truly mind-blowing. KF
As to this comment from the article:
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.”
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,
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.”
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.”
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.”
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.”
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.”
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”,,,
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”),
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 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.”
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.”
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”.
Verse: