Mathematics

Mathematical logic : The final sacrifice on the altar of materialism

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A friend, watching a serial thriller, The Oxford Murders, jotted down this interesting bit of dialogue between a professor who holds the Darwinist view of the brain (shaped for fitness, not for truth) and a design-based one (design in mathematics is real, and the brain is designed to apprehend it):

Elijah Wood is sitting in a lecture hall listening to a professor discuss the significance of Wittgenstein and the Tractatus Logico-Philosophicus.

Professor: There is no way of finding a single absolute truth, an irrefutable argument that might help to answer the questions of mankind. Philosophy, therefore, is dead. Because “Whereof we cannot speak, thereof we must be silent.”

[Elijah Wood raises his hand]

Professor: Oh, it seems that someone does wish to speak. It appears you are not in agreement with Wittgenstein. That means either you have found a contradiction in the arguments of the Tractatus, or you have an absolute truth to share with us all.

Wood: I believe in the number Pi.

Professor: I’m sorry, I didn’t understand you. What was it you said you believed in?

Wood: In the number Pi, in the Golden Section, the Fibonacci Series. The essence of nature is mathematical. There is a hidden meaning beneath reality. Things are organized following a model, a scheme, a logical series. Even the tiny snowflake includes a numerical basis in its structure. Therefore, if we manage to discover the secret meaning of numbers, we will know the secret meaning of reality.

Professor: Impressive! Translating his words into the Queen’s English, we find ourselves faced with a fresh, rousing defense of mathematics, as if numbers were pre-existing ideas in reality. Anyway, this is nothing new. Since man is incapable of reconciling mind and matter, he tends to confer some sort of entity on ideas, because he cannot bear the notion that the purely abstract only exists in our brain. The beauty and harmony of a snowflake — how sweet! The butterfly that flutters its wings and causes a hurricane on the other side of the world. We’ve been hearing about that damn butterfly for decades, but who has been able to predict a single hurricane? Nobody!

Tell me something: Where is the beauty and harmony in cancer? What makes a cell suddenly decide to turn itself into a killer metastasis and destroy the rest of the cells in a healthy body? Does anyone know? No. Because we’d rather think of snowflakes and butterflies than of pain, war or that book. Why? Because we need to think that life has meaning, that everything is governed by logic and not by mere chance. If I write 2 then 4 then 6, then we feel good, because we know that next comes 8. We can foresee it, we are not in the hands of destiny. Unfortunately, however, this has nothing to do with truth. Don’t you agree? This is only fear. Sad, but there you go.

It strikes me that if the purely abstract exists only in one’s brain, it still exists. And – unlike a mere delusion – abstract mathematics has great power when embodied in the world of nature.

What would you ask the professor?

12 Replies to “Mathematical logic : The final sacrifice on the altar of materialism

  1. 1
    Collin says:

    I think that the professor does not adequately appreciate consciousness. He does not adequately consider Descartes’ reasoning that “I think, therefore, I am.”

    I have been told that the essence of philosophy is merely being always curious, always asking questions. That is what Socrates did. For this professor, philosophy must be dead because he has finished asking questions.

  2. 2
    bornagain77 says:

    That Professor reminds me of this Professor:

    Albert Einstein vs. professor – video
    http://www.youtube.com/watch?v=OxWXvh6OVB8

  3. 3
    bornagain77 says:

    Furthermore, the professor, from his materialistic perspective, cannot explain why the base of ‘material’ reality is dictated by a mathematical form:

    Finely Tuned Big Bang, Elvis In The Multiverse, and the Schroedinger Equation – Granville Sewell
    http://www.metacafe.com/watch/4233012/

  4. 4
    Meleagar says:

    Two questions I’d ask the professor:

    1. “Why are you still talking?”
    2. “Why should we listen to you?”

  5. 5
    Bruce David says:

    I would ask, “Professor, how do you know that what you say is true? How do you that ‘There is no way of finding a single absolute truth’?”

    In philosophic inquiry, the first question that must be answered is epistemological, not metaphysical: “How do we know?” “What is real knowledge?” Until we can answer that, we can conclude nothing at all.

    The tradition of Western philosophy for the most part looks to reason, or rational argument, as the source of real knowledge. The problem with that answer is that reason must have first principles from which to work, as Euclid discovered and which has been the modus operendi of mathematics ever since. And when people disagree over the truth of anything, the disagreement is almost always in the area of first principles (although they often don’t recognize this fact). The question is, how can we arrive at knowledge of first principles?

    So how do we know anything? What do you think?

  6. 6
    vividbleau says:

    “There is no way of finding a single absolute truth,”

    I would ask the professor if this ia an absolutely true statement?

    Vivid

  7. 7
    stvnhthr says:

    If there is no absolute truth I would ask the professor to uphold that standard when he grades my midterm.

  8. 8
    Collin says:

    It would be funny if the student just walked out of the class and if the professor stopped him he would say, “Didn’t you just tell me this class was worthless?”

  9. 9
    UrbanMysticDee says:

    Bruce David and vividbleau may have been hinting at this already, but the professor’s argument is logically self-refuting.

    He says “There is no way of finding a single absolute truth, an irrefutable argument that might help to answer the questions of mankind.”

    This statement is either true or false (“P ? ¬P”) by the law of the excluded middle. If his statement is true, that there is no way of finding an absolute truth, then an absolute truth does exist, namely, that there is no way of finding an absolute truth, and his argument is self-contradictory. If his statement is false, then an absolute truth exists, namely that it is possible to find an absolute truth. Either way absolute truth exists and the professor’s argument falls apart.

  10. 10
    UrbanMysticDee says:

    I notice that some symbols do not show up (in the P or not P formula). Please bear this in mind when reading my response.

  11. 11
    allanius says:

    The professor is correct, although probably for the wrong reasons. Wittgenstein was making a simple point that was acknowledged by all major philosophers in the modern era: intellect and its value judgments about “the good” are divided between intellect and sense. See the beginning of Descartes’ famous book. It’s the very first thing he says.

    Perhaps it is not widely known that Wiggenstein was a rather fervent—if unorthodox—Christian. His beef was with Hegel and the synthetic method, not with God. But that’s just the problem. Wittgenstein clung to the square root of 2 because of its resistance to any ratio of value.

    In the mathematical analysis of nature irrationality inevitably intrudes. The seeming ideality of the circle cannot be expressed in mathematic terms. It must be expressed as a ratio, and ratios are not ideal. Ratios resist any attempt to harmonize intellect and sense. And that’s a problem for philosophers.

    What is “the good” (or “absolute truth”? Is it pure reason, as Plato claimed, pure intellect? If so, it cannot be applied to nature. In order to obtain pure valuations, nature must be negated, because our analysis of nature does not produce ideal (rational) numbers. But then “truth” is plagued with the nothingness seen in Idealism and its step-child, Rationalism.

    The only alternative to pure negation is to claim that truth is a purely active ratio of reciprocal causes—basically a ratio of intellect and sense. The Absolute Idea is said to be a synthesis of thesis and antithesis, but in real life it is impossible for any synthesis or ratio to overcome the love of resistance and ideality seen in someone like Wittgenstein. From his point of view, the Absolute Idea is nothing more than another construct to be overthrown by invoking the irrationality of the square root of 2.

    Classical philosophy was deeply divided between Plato and Aristotle and their methods of discerning “the good.” Descartes tried to overcome this dividedness by blending philosophy with the new science, but the results of this great endeavor were also divided. Descartes’ insistence on pure intellect leads to nothingness, while Kant’s notion of transcendental ratios cannot overcome nothingness and its force of resistance.

    That’s why Nihilism became acceptable in the end. Nihilism is simply a denial of absolute truth. Philosophers realized that the modern attempt to overcome the shortcomings of classical philosophy by blending philosophy with science had failed to produce a satisfactory description of absolute truth, and so they decided to negate it, which is the position of the professor above.

    Those who could not be happy with Hegel’s Absolute Idea squared off into two schools. The atheists followed Nietzsche down the path of pure negation and openly embraced nothingness as the means of creating “new gods and new ideals.” Those of a more religious nature followed Husserl and Wittgenstein and clung to resistance as a sign of the existence of a transcendent intellect and of ideas that exceed the grasp of men.

    ID is a silver bullet when it clings to the obvious to resist materialsm: the existence of design in nature. Why compromise it by trying to turn back the clock and embrace teh failed endeavor of philosophy?

  12. 12
    Collin says:

    allanus,

    Is there any intellectual endeavor that does not have its basis in philosophy? I don’t think that ID can rest on its criticism of materialism. It must offer a substitute.

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