Log24

Tuesday, November 1, 2005

Tuesday November 1, 2005

Filed under: General,Geometry — Tags: , — m759 @ 9:00 PM
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The above seal is from an ad (pdf) for an Oct. 21 lecture, "The Nature of Space," by Sir Michael Atiyah, sponsored by the American Mathematical Society.

The picture in the seal is of Plato's Academy.

"The great philosopher Plato excluded from his Academy anyone who had not studied geometry.  He would have been delighted to admit Sir Michael Atiyah, who was for a time Savilian Professor of Geometry at Oxford…"

 

Would he?

Sir Michael Atiyah's
Anti-Platonism

"Mathematics is an evolution from the human brain, which is responding to outside influences, creating the machinery with which it then attacks the outside world. It is our way of trying to reduce complexity into simplicity, beauty and elegance….

I tend to think that science and mathematics are ways the human mind looks and experiences– you cannot divorce the human mind from it. Mathematics is part of the human mind. The question whether there is a reality independent of the human mind, has no meaning– at least, we cannot answer it."

— Sir Michael Atiyah, interview in Oslo, May 2004

"For Plato, the Forms represent truth, or reality…. these Forms are independent of the mind: they are eternal, unchanging and perfect."

—  Roy Jackson (pdf)

Atiyah's denial of a reality independent of the human mind may have something to do with religion:

"Socrates and Plato were considered 'Christians before Christ'; they paved the way for the coming of Christianity by providing it with philosophical and theoretical foundations that would be acceptable to the western mind.
    In the analogy of the cave, the sun represents the Form of the Good. In the same way that the sun is the source of all things and gives light to them, the Form of the Good is over and above the other Forms, giving them light and allowing us to perceive them. Therefore, when you have awareness of the Form of the Good you have achieved true enlightenment. In Christianity, the Form of the Good becomes God: the source of all things."

— Roy Jackson, The God of Philosophy (pdf)

See also the previous entry.
 

Tuesday November 1, 2005

Filed under: General — Tags: , — m759 @ 12:00 PM

Antidote to Atiyah

In a recent talk, "The Nature of Space," Sir Michael Atiyah gave a misleading description of Plato's doctrine of "ideas," or "idealism."  Atiyah said that according to Plato, ideas reside in  "an imaginary world–  the world of the mind," and that what we see in the external world is "some pale reflection" of ideas in the mind.

An antidote to Atiyah's nonsense may be found in the Catholic Encyclopedia:

"So it came to pass that the word idea in various languages took on more and more the meaning of 'representation,' 'mental image,' and the like. Hence too, there was gradually introduced the terminology which we find in the writings of Berkeley, and according to which idealism is the doctrine that ascribes reality to our ideas, i.e. our representations, but denies the reality of the physical world. This sort of idealism is just the reverse of that which was held by the philosophers of antiquity and their Christian successors; it does away with the reality of ideal principles by confining them exclusively to the thinking subject; it is a spurious idealism…."

Atiyah contrasts his mistaken view of Plato with what he calls the "realism" of Hume.  He does not mention that Plato's doctrine of ideas is also known as "realism."  For details, see, again, the Catholic Encyclopedia:

"The conciliation of the one and the many, the changing and the permanent, was a favourite problem with the Greeks; it leads to the problem of universals. The typical affirmation of Exaggerated Realism, the most outspoken ever made, appears in Plato's philosophy; the real must possess the attributes of necessity, universality, unity, and immutability which are found in our intellectual representations. And as the sensible world contains only the contingent, the particular, the unstable, it follows that the real exists outside and above the sensible world. Plato calls it eîdos, idea. The idea is absolutely stable and exists by itself (ontos on; auta kath' auta), isolated from the phenomenal world, distinct from the Divine and human intellect…. The exaggerated Realism of Plato… is the principal doctrine of his metaphysics."
 
Atiyah's misleading remarks may appeal to believers in the contemptible religion of Scientism, but they have little to do with either historical reality or authentic philosophy.

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