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Mathematics challenges naturalism, says math prof

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My Picture James Franklin offers insights from a new theory of Aristotelian realism at Aeon, and a new book:

Aristotelian realism stands in a difficult relationship with naturalism, the project of showing that all of the world and human knowledge can be explained in terms of physics, biology and neuroscience. If mathematical properties are realised in the physical world and capable of being perceived, then mathematics can seem no more inexplicable than colour perception, which surely can be explained in naturalist terms. On the other hand, Aristotelians agree with Platonists that the mathematical grasp of necessities is mysterious. What is necessary is true in all possible worlds, but how can perception see into other possible worlds? The scholastics, the Aristotelian Catholic philosophers of the Middle Ages, were so impressed with the mind’s grasp of necessary truths as to conclude that the intellect was 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 standard alternatives in the philosophy of mathematics have failed to account for the simplest facts about how mathematics tells us about the world we live in – nominalism by reducing mathematics to trivialities, and Platonism by divorcing it from the world, the real world of which mathematical truths form a necessary skeleton. Aristotelian realism is a new beginning. It connects the philosophy of mathematics back to the applications that have always been the fertile ground from which mathematics grows. It has a message both for philosophy and for mathematics and its teaching: don’t get blinded by shuffling symbols, don’t disappear into a realm of abstractions, just keep an eye fixed on the mathematical structure of the real world. More.

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6 Replies to “Mathematics challenges naturalism, says math prof

  1. 1
    bornagain77 says:

    Although it is easy to wax poetic about the Greek mathematical influences on modern science, the truth of the matter is that it was not until pagan Greek influences were purged from Christian culture (219 Aristotelian propositions) that modern science was finally able to reach a point of sustainable maturity in western Europe.

    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.
    http://www.scifiwright.com/201.....revisited/

    The emergence of modern science was associated with a disdain for the rationalism of Greek philosophers who pronounced on how the world should behave, with insufficient attention to how the world in fact did behave.
    – Henry F. Schaefer III

    The Christian Founders Of Science – Henry F. Schaefer III – video
    https://vimeo.com/16523153

    “Did Christianity (and Other Religions) Promote the Rise Of Science?” – Michael Egnor October 24, 2013
    Excerpt: Neither the Greeks nor Islam produced modern theoretical science. The Greeks produced sublime philosophy and mathematics, but no theoretical science. They excelled in mathematics but never applied mathematical models to the systematic study of nature.
    per evolution news and views

    Science and Theism: Concord, not Conflict* – Robert C. Koons
    IV. The Dependency of Science Upon Theism (Page 21)
    Excerpt: Far from undermining the credibility of theism, the remarkable success of science in modern times is a remarkable confirmation of the truth of theism. It was from the perspective of Judeo-Christian theism—and from the perspective alone—that it was predictable that science would have succeeded as it has. Without the faith in the rational intelligibility of the world and the divine vocation of human beings to master it, modern science would never have been possible, and, even today, the continued rationality of the enterprise of science depends on convictions that can be reasonably grounded only in theistic metaphysics.
    http://www.robkoons.net/media/.....ffd524.pdf

    Epistemology – Why Should The Human Mind Even Be Able To Comprehend Reality? – Stephen Meyer – video – (Notes in description)
    http://vimeo.com/32145998

    Atheists/Materialists simply do not believe that there is a rational overarching order to this universe to be grasped in the first place, (in fact they will argue endlessly, sometimes angrily, for multiverses, many worlds, and such epistemologically self defeating propositions)

    “If you have no God, then you have no design plan for the universe. You have no prexisting structure to the universe.,, As the ancient Greeks held, like Democritus and others, the universe is flux. It’s just matter in motion. Now on that basis all you are confronted with is innumerable brute facts that are unrelated pieces of data. They have no meaningful connection to each other because there is no overall structure. There’s no design plan. It’s like my kids do ‘join the dots’ puzzles. It’s just dots, but when you join the dots there is a structure, and a picture emerges. Well, the atheists is without that (final picture). There is no preestablished pattern (to connect the facts given atheism).”
    Pastor Joe Boot – Defending the Christian Faith – 13:20 minute mark of the video
    http://www.youtube.com/watch?v=wqE5_ZOAnKo

    ,,and thus on atheism/materialism, with its insistence on randomness/chaos at the base of all things, atheism is actually a major hindrance to the progress of science.

    “Modern science was conceived, and born, and flourished in the matrix of Christian theism. Only liberal doses of self-deception and double-think, I believe, will permit it to flourish in the context of Darwinian naturalism.”
    ~ Alvin Plantinga

    In fact, I hold that, besides belief in a transcendent Creator, that the foundational ‘made in God’s image’ belief, which is central to Christian teaching, (i.e. God incarnate in Christ Jesus!), was also a integral pillar upon which modern science was able to achieve a sustainable maturity.

    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/art.....ematicians

    “Geometry is unique and eternal, a reflection from the mind of God. That mankind shares in it is because man is an image of God.”
    – Johannes Kepler

    And I also hold that modern science, besides finding its birth in Christianity, will find its ultimate resolution in the much sought after ‘Theory of Everything’ in the resurrection event of Christ,,,

    The Center Of The Universe Is Life – General Relativity, Quantum Mechanics, Entropy and The Shroud Of Turin – video
    http://vimeo.com/34084462

    Notes:
    http://www.uncommondescent.com.....ent-490690

    Verse and Music:

    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.

    Evanescence – The Other Side (Lyric Video)
    http://www.vevo.com/watch/evan.....tantsearch

  2. 2
    OldArmy94 says:

    The existence of math and its integral interconnectedness with reality, its predictive and inherently explanatory properties and its universality is a powerful beacon to the Divine. It is an evidence that is not easily explained away by the materialist.

  3. 3
    Barb says:

    Interestingly enough, some scientists say they now have mathematical proof that the universe could have spontaneously appeared from nothing: https://medium.com/the-physics-arxiv-blog/ed7ed0f304a3

  4. 4
    bornagain77 says:

    “Joel Primack, a cosmologist at the University of California, Santa Cruz, once posed an interesting question to the physicist Neil Turok: “What is it that makes the electrons continue to follow the laws.” Turok was surprised by the question; he recognized its force. Something seems to compel physical objects to obey the laws of nature, and what makes this observation odd is just that neither compulsion nor obedience are physical ideas. (p.132) In a Landscape in which anything is possible, nothing is necessary. In a universe in which nothing is necessary, anything is possible. It is nothing that makes the electron follow any laws.
    Which, then, is it to be: God, logic, or nothing?
    This is the question to which all discussions of the Land-scape and the Anthropic Principle are tending, and because the same question can be raised with respect to moral thought, it is a question with an immense and disturbing intellectual power.
    For scientific atheists, the question answers itself: Better logic than nothing, and better nothing than God. (…) The laws of nature, as Isaac Newton foresaw, are not laws of logic, nor are they like the laws of logic. Physicists since Einstein have tried to see in the laws of nature a formal structure that would allow them to say to themselves, “Ah, that is why they are true,” and they have failed.” (p.133)
    Berlinski, The Devil’s Delusion pg. 132-133

  5. 5
    bornagain77 says:

    A few related notes about any purported ‘mathematical proof’ showing the universe could have spontaneously appeared from ‘nothing’

    Kurt Gödel – Incompleteness Theorem – video
    http://www.metacafe.com/w/8462821

    As Godel demonstrated with the incompleteness theorem, if numbers are included, there cannot be a ‘complete’ mathematical theory of everything. Even Hawking agreed at one time that there cannot be a mathematical theory of everything (a concession he has subsequently forgot)

    The nature and significance of Gödel’s incompleteness theorems – Princeton – 2006
    Excerpt: ,,Stephen Hawking and Freeman Dyson, among others, have come to the conclusion that Gödel’s theorem implies that there can’t be a Theory of Everything.,,
    http://math.stanford.edu/~fefe.....el-IAS.pdf

    Godel 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

    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/art.....ematicians

    i.e. mathematical equations specific enough to have the counting numbers do not contain the ‘truth’ within themselves but are dependent upon God for any truth inherent within them!

    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.or...../equation#

    As well, this ‘mathematical proof’ that the universe can arise out of ‘nothing’ reminds me of the last time an atheist tried to give causal power to nothing:

    Lawrence Krauss vs The Dictionary – video
    https://www.youtube.com/watch?v=iY0gC6ExG8k

    “Pale, Small, Silly, Nerdy”: NY Times Gives a Devastating Smack to New Atheists’ Favorite Cosmologist – March 2012
    Excerpt: Krauss, author of the The Physics of Star Trek and other works, has been something of a hero to the New Atheists. It will be interesting to see how they regard him now. Albert has slain the dragon, burned its body, buried the ashes, and salted the earth over the grave. He hasn’t given some superficial criticism of Krauss’s argument that is politically correct and leaves Krauss with a platform. He has not only shown why Krauss’s argument is wrong, but why it can’t be right — because it incoherently gives physical causal properties to “nothing.”
    http://www.evolutionnews.org/2.....57841.html

    Not Understanding Nothing – A review of A Universe from Nothing – Edward Feser – June 2012
    Excerpt: A critic might reasonably question the arguments for a divine first cause of the cosmos. But to ask “What caused God?” misses the whole reason classical philosophers thought his existence necessary in the first place. So when physicist Lawrence Krauss begins his new book by suggesting that to ask “Who created the creator?” suffices to dispatch traditional philosophical theology, we know it isn’t going to end well. ,,,
    ,,, But Krauss simply can’t see the “difference between arguing in favor of an eternally existing creator versus an eternally existing universe without one.” The difference, as the reader of Aristotle or Aquinas knows, is that the universe changes while the unmoved mover does not, or, as the Neoplatonist can tell you, that the universe is made up of parts while its source is absolutely one; or, as Leibniz could tell you, that the universe is contingent and God absolutely necessary. There is thus a principled reason for regarding God rather than the universe as the terminus of explanation.
    http://www.firstthings.com/art.....ng-nothing

    Of related note:

    The Universe Is Not Eternal – Johanan Raatz – March 1, 2014
    Excerpt: One thing known for certain about quantum gravity is something called the holographic principle. Precisely put, the holographic principle tells us that the entropy of a region of space (measured in terms of information) is directly proportional to a quarter of its surface area. The volume of this region is then actually a hologram of this information on its surface.
    Except this tells us something interesting about the universe as well. Entropy, or the amount of disorder present, always increases with time. In fact not only is this law inviolate, it is also how the flow of time is defined. Without entropy, there is no way to discern forwards and backwards in time.
    But if the holographic principle links the universe’s entropy and its horizon area then going back in time, all of space-time eventually vanishes to nothing at zero entropy. Thus Carroll’s argument is unsound. We already have enough knowledge about what happens beyond the BVG theorem that Craig cites. The universe is not eternal but created.
    It is interesting to note that this also undermines claims made by atheists like Hawking and Krauss that the universe could have fluctuated into existence from nothing. Their argument rests on the assumption that there was a pre-existent zero-point field or ZPF. The only trouble is that the physics of a ZPF requires a space-time to exist in. No space-time means no zero-point field, and without a zero-point field, the universe can not spontaneously fluctuate into existence.
    http://blog.proofdirectory.org.....t-eternal/

  6. 6
    Axel says:

    ‘The only trouble is that the physics of a ZPF requires a space-time to exist in. No space-time means no zero-point field, and without a zero-point field, the universe can not spontaneously fluctuate into existence.
    http://blog.proofdirectory.org…..t-eternal/’

    Don’t be a spoilsport, BA. There’s a good chap. Refuting their most basic assumption can only upset them.

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