Best Philosopher?

[Solus_vistor]

Notwithstanding Sokal, Lacan has raised interesting questions about what it means to be a human being, and, specifically, what it means to be a “speaking” being.

You might want to look at one of the secondary resources mentioned in my posting #21 (perhaps Zizek or Forrester).

Lacan is a genuine intellectual, well versed in continental philosophy (Hegel, Heidegger, Sartre) as well as Freud.

But I have a feeling I’m not being very persuasive.

Perhaps I should not have used the term “serious scholar”. After all nonody doubts Richard Dawkins’ expertise as an evolutionary biologist, in spite of his “delusions” about religion and God that he is very public about. Actually the same about Alan Sokal, whose recent book Beyond Hoax (OUP 2008) displays an “understanding” of religion comparable to Lacan’s “understanding” of mathematics. The difference is perhaps that in case of mathematics the superficiality or even ignorance is more obvious since in distinction to religion there are no world-view, cultural and emotional factors involved (certainly not to that extent).

To put it differently, if somebody wanted to impress his readers with his multilingual capabilities by quoting a text in Hungarian, and then it would turn out that the quote is just a more or less arbitrary collection of words that no person speaking Hungarian could make sense of, that somebody’s general credibility would be tarnished.

I do not think I shall try to understand Lacan, since I already tried to understand Derrida and Foucault without success. Partly the same about Heidegger. Perhaps I am too old for that.

 

[levinas12]

The difference is perhaps that in case of mathematics the superficiality or even ignorance is more obvious since in distinction to religion there are no world-view, cultural and emotional factors involved (certainly not to that extent).

Actually, culture may play a big role in mathematics. For example, Spengler argued that the “body” (albeit idealized) was the horizon of both Greek art and Greek mathematics. Numbers and geometrical figures remained for the Greeks highly specific. Plato, with his theory of forms, is not an exception. There is a Platonic form for the circle, for the triangle, for the square - for the number 2, the number 3, etc - even for the “odd” and “even” - but there is not a form for an indefinite variable x (as understood in modern algebra. Even in Diophantus, the ‘x’ in the equation always stands for a particular number. For more on this, see Jacob Klein.

So one can argue that the Greek understanding of mathematics is quite different from the modern understanding. And this reflects a major cultural shift.

To see this, all you have to do is compare Hilbert’s formalistic axiomatics with Euclid’s.

 

[Palamas]

Yes, Josef Pieper is great.

 

[Solus_vistor]

Actually, culture may play a big role in mathematics. For example, Spengler argued that the “body” (albeit idealized) was the horizon of both Greek art and Greek mathematics. Numbers and geometrical figures remained for the Greeks highly specific. Plato, with his theory of forms, is not an exception. There is a Platonic form for the circle, for the triangle, for the square - for the number 2, the number 3, etc - even for the “odd” and “even” - but there is not a form for an indefinite variable x (as understood in modern algebra. Even in Diophantus, the ‘x’ in the equation always stands for a particular number. For more on this, see Jacob Klein.

So one can argue that the Greek understanding of mathematics is quite different from the modern understanding. And this reflects a major cultural shift.

To see this, all you have to do is compare Hilbert’s formalistic axiomatics with Euclid’s.

I agree that not only the Greek understanding of mathematics but of many other things (in what today we call natural science) is quite different from the modern understanding. In particular, topology,countable sets, irrational and imaginary numbers, mathematical logic etc - concepts that Sokal accuses Lacan of confusing and abusing - did not exist in ancient Greece. So I don’t see the relevance of your first paragraph.

I spent most of my life teaching mathematics to Asian engineering students (in Australia), and I can assure you that our different cultural backgrounds played practically no role, which certainly would not have been the case had I tried to convert them to my religion.

 

[Qoeleth]

I am very surprised at the answere given for modern Catholic philosophers.

I recommend Etienne Gilson and Jacques Maritain. Fr. and Professor Joseph Koterski at Fordham University is also a great modern teacher and philosopher.

While not Roman Catholic, I would also recommend Mortimer Adler and Eric Voegelin. They are certainly better than Camus and Derrida.

Camus and Derrida for expressed (more so than created) the world-view of modern humanity- and both have had a particular focus on man’s relationship with the transcendent. Both speak from the heart and soul, not simply the head. They have something to say about God which makes can make sense to the modern world.

 

[levinas12]

I agree that not only the Greek understanding of mathematics but of many other things (in what today we call natural science) is quite different from the modern understanding. In particular, topology,countable sets, irrational and imaginary numbers, mathematical logic etc - concepts that Sokal accuses Lacan of confusing and abusing - did not exist in ancient Greece. So I don’t see the relevance of your first paragraph.

I spent most of my life teaching mathematics to Asian engineering students (in Australia), and I can assure you that our different cultural backgrounds played practically no role, which certainly would not have been the case had I tried to convert them to my religion.

I was merely responding to the issue of cultural “neutrality” and certain activities, e.g., technology, and certain disciplines, e.g., mathematics.

There is a school of thought that each period of history has its horizon. Including the present one.

Characterizing a horizon is difficult. Heidegger, for example, uses a term, Gestell , to describe the horizon of the present age with its emphasis on “technological” mastery of nature. But Gestell is more than technological prowess - it’s an entire way of looking at being (e.g., Nietzsche’s will-to-power).

You and the Asian students may share the “same” horizon (the Gestell), without necessarily sharing the same religion.

Of course, there is a lot of room for discussion here. The “horizonality” of human understanding is itself susceptible to relativism. But there may be a way around this.

 

[Solus_vistor]

I was merely responding to the issue of cultural “neutrality” and certain activities, e.g., technology, and certain disciplines, e.g., mathematics.

There is a school of thought that each period of history has its horizon. Including the present one.

Characterizing a horizon is difficult. Heidegger, for example, uses a term, Gestell , to describe the horizon of the present age with its emphasis on “technological” mastery of nature. But Gestell is more than technological prowess - it’s an entire way of looking at being (e.g., Nietzsche’s will-to-power).

You and the Asian students may share the “same” horizon (the Gestell), without necessarily sharing the same religion.

Of course, there is a lot of room for discussion here. The “horizonality” of human understanding is itself susceptible to relativism. But there may be a way around this.

I cannot disagree since none of this contradicts my original contention that

The difference is perhaps that in case of mathematics the superficiality or even ignorance is more obvious since in distinction to religion there are no world-view, cultural and emotional factors involved (certainly not to that extent).

Lacan and his critics (as well as I and my students) lived in the same century - call it “shared the same horizon” - when mathematics, at least in the West, was more generally accepted as useful in everyday life than any particular religion. There are people who have difficulties understanding mathematics at certain levels, however a Richard Dawkins preaching against mathematics and its basic ideas would not have much success. That is all that I wanted to say about the difference between mathematics and any particular religion.

 

[levinas12]

I cannot disagree since none of this contradicts my original contention that

Lacan and his critics (as well as I and my students) lived in the same century - call it “shared the same horizon” - when mathematics, at least in the West, was more generally accepted as useful in everyday life than any particular religion. There are people who have difficulties understanding mathematics at certain levels, however a Richard Dawkins preaching against mathematics and its basic ideas would not have much success. That is all that I wanted to say about the difference between mathematics and any particular religion.

 

[levinas12]

… in case of mathematics … in distinction to religion there are no world-view, cultural and emotional factors involved (certainly not to that extent).

I think we are disagreeing.

I am arguing that Greek mathematics and modern mathematics belong to two different world views (or horizons). Different “conceptualities” are at work. So, one could say, in the spirit of Thomas Kuhn, the history of mathematics is as discontinuous as the history of physics or cosmology. In each of these histories, there’s been a radical paradigm shift.

Now this opens up a related discussion. Is mathematics, like everything else, ideologically driven? For example, is there a relationship between modern mathematics and capitalism? Both seem to focus on indeterminate variables. In modern algebra, the variable can “stand for” for anything (numbers, classes, relations, manifolds, etc). Or for “nothing” (Hilbert).

And, in capitalism, money becomes equally abstract and indeterminate. It is no longer mercantilist, no longer “signifies” quantities of gold and silver. Like the algebraic variable, money can “stand for” anything or for nothing, is a “pure” signifier without a transcendental "signified, is no longer anchored in something “real”. Money is now caught up in a system of pure differences (see Saussure). Think of “financial” derivatives.

 

[Solus_vistor]

I think we are disagreeing…

No, I think we are talking past each other. digressing from my original objection that Lacan uses mathematical terms and concepts he does not understand.

I am arguing that Greek mathematics and modern mathematics belong to two different world views (or horizons). Different “conceptualities” are at work.

They certainly belong to different times, (together with many other things) as I have already stated. I might not be sure about what horizon means but I do not think it is equivalent to worldview, the English translation of the German Weltanschauung that I, so to say, grew up with. In particular, I don’t understand what you mean by mathematics (in distinction to philosophy of mathematics) “belonging” to a worldview.

So, one could say, in the spirit of Thomas Kuhn, the history of mathematics is as discontinuous as the history of physics or cosmology. In each of these histories, there’s been a radical paradigm shift.
Now this opens up a related discussion.

Indeed, applicability of Kuhn’s paradigm shifts to (pure) mathematics (in the same sense as it is applied to natural and social science) opens a can of worms that is unrelated to the topic of this thread and cannot be dealt with in a few words.

is there a relationship between modern mathematics and capitalism?

I am not sure I understand what you mean, unless you mean to say that there are mathematical models applied in economic, fiscal, etc analyses, the answer to which is obviously yes.

Both seem to focus on indeterminate variables. In modern algebra, the variable can “stand for” for anything (numbers, classes, relations, manifolds, etc). Or for “nothing” (Hilbert).

If by modern you mean algebra taught to contemporary (or last century’s) undergraduate (not high school) students of mathematics, then they are warned that “indeterminate” and “variable” are two different concepts that should not be confused. I just randomly found this reference - mathoverflow.net/questions/33865/indeterminate-x-in-abstract-algebra-ring-theory - that should explain the difference.

And, in capitalism, money becomes equally abstract and indeterminate. It is no longer mercantilist, no longer “signifies” quantities of gold and silver. Like the algebraic variable, money can “stand for” anything or for nothing, is a “pure” signifier without a transcendental "signified, is no longer anchored in something “real”. Money is now caught up in a system of pure differences (see Saussure). Think of “financial” derivatives.

If this mean to illustrate that mathematical models can be useful in “capitalism”, meaning contemporary economical theories, then as I said, I agree.

 

[levinas12]

If by modern you mean algebra taught to contemporary (or last century’s) undergraduate (not high school) students of mathematics, then they are warned that “indeterminate” and “variable” are two different concepts that should not be confused.

I’m not sure I understand clearly the distinction between “indeterminate” and “variable” which you mentioned. I did read the cite but it might be beyond my level of competence.

If you could unpack it a bit, I would be appreciative. But I know I’ve created a digression.

When I called the modern variable “indeterminate”, I meant only that, by standing for an infinite range of numbers, it contrasts with Diophantus whose “x” is always limited to a specific number, e.g., 3.

Spengler makes the case that the Greeks were captivated by the finite, the visible with defined boundaries, etc. whereas the modern Europeans were caught up in the infinite.

But pressing this further. Today, we are Faustian, driven by Nietzsche’s insatiable, “infinite” will-to-power over nature. Whereas the Greeks respected limits, abhorred the infinite (what they called the “apeiron”).

One mathematical expression of the modern love of the infinite: Euler’s power series, or, even better, Cantor’s infinite stack of infinities.

But there’s a deeper dimension at work here. Contrary to Hardy, modern mathematics is never pure; it’s always applied. Because what’s driving the “enterprise” is technological mastery of nature. It’s engineers all the way down.

Why else was calculus, for example, invented?

And this technological Gestell explains why the US having a hissy fit that its students are falling behind their peers in other parts of the world.

The Greeks would have been uncomfortable with all this. Look at what happened to Prometheus, or Oedipus. Hubris invites lightning strikes.

 

[Solus_vistor]

I’m not sure I understand clearly the distinction between “indeterminate” and “variable” which you mentioned. I did read the cite but it might be beyond my level of competence.

If you could unpack it a bit, I would be appreciative. But I know I’ve created a digression.

The concept of indeterminate in distinction to unknown or variable is (or was in my generation) usually taught to second year pure mathematics students, i.e. those who take courses in abstract, in distinction to high school, algebra. So it is not an easy concept to explain. In en.wikipedia.org/wiki/Indeterminate_(variable you will find what the indeterminate is NOT, though I am not sure how illuminating the examples there are.

When I called the modern variable “indeterminate”, I meant only that, by standing for an infinite range of numbers, it contrasts with Diophantus whose “x” is always limited to a specific number, e.g., 3.

I am not sure what Diophantus actually wrote, however Diophantine equations are equations in which only integer solutions are allowed, i.e. the variable x can take only integer values.

Spengler makes the case that the Greeks were captivated by the finite, the visible with defined boundaries, etc. whereas the modern Europeans were caught up in the infinite.

Well, not only ancient Greeks but not even “modern” mathematicians had a satisfactory understanding of the (quantitative, in distinction to qualitative used in theology) concept of infinity until Cantor. By the way, since the advent of computers, finite mathematics has somehow come to the forefront, since computers cannot solve differential equations but are very good at solving difference equation that approximate them.

But pressing this further. Today, we are Faustian, driven by Nietzsche’s insatiable, “infinite” will-to-power over nature. Whereas the Greeks respected limits, abhorred the infinite (what they called the “apeiron”).

Again, this probably refers to the qualitative meaning of infinity, different from the quantitative used in mathematics and mathematical models of physical reality

Contrary to Hardy, modern mathematics is never pure; it’s always applied. Because what’s driving the “enterprise” is technological mastery of nature. It’s engineers all the way down.

The distinction between pure and applied mathematics is standard, al least in the English speaking world (in the continental tradition one omits the adjective “pure” when speaking of mathematics). Example: “If X is three times as old as his son, but in 10 years time he will be only twice as old, how old is X” is problem in applied mathematics, whereas 2*(x/3+10)=x+10 is the corresponding problem in pure mathematics.

I am not sure where did Hardy say that, but I suppose he meant by applied what is more often referred to as applicable, and in this sense, of course, pure mathematics must be applicable to be of practical use.

 

[levinas12]

I am not sure where did Hardy say that, but I suppose he meant by applied what is more often referred to as applicable, and in this sense, of course, pure mathematics must be applicable to be of practical use.

Hardy prided himself on the practical “uselessness” of his work.

Of course, there is some irony in the fact that prime numbers subsequently became the basis for cryptography.

The distinction between “pure” and “applied” goes back to the ancient Greek philosophers. For them, the highest human activity was contemplation (in imitation of the Prime Mover). Practical activity (even political activity) was of a “lower rank”.

In modern times, beginning with Bacon and Hobbes (and also Descartes), a reversal took place. Practical activity (e.g., “making”) replaced “contemplation” as the highest human activity.

This reversal reflected the loss of a non-human dimension of truth. Now everything was seen “anthropocentrically”.

The Copernican revolution didn’t displace man at all. To the contrary, Nature now became a huge technological space … the deep meaning of “extension” in Descartes.

However, in Hardy’s insistence on “pure” mathematics, you can still hear a faint echo of contemplation.

 

[Solus_vistor]

Hardy prided himself on the practical “uselessness” of his work.

Of course, there is some irony in the fact that prime numbers subsequently became the basis for cryptography.

Instead of looking for the exact quote from the book, let me quote from en.wikipedia.org/wiki/A_Mathematician’s_Apology which agrees with what you are saying:

For Hardy, the most beautiful mathematics was that which had no practical applications in the outside world (pure mathematics) and, in particular, his own special field of number theory. Hardy contends that if useful knowledge is defined as knowledge which is likely to contribute to the material comfort of mankind in the near future (if not right now), so that mere intellectual satisfaction is irrelevant, then the great bulk of higher mathematics is useless.

This is a view expressed in 1940, and not only cryptography as you rightfully point out, but also much of computer science since then has “vindicated” number theory. Things have changed since Hardy: Many years ago when I wrote my PhD I was convinced that it was just an exercise in the “aesthetics” of mathematics (differential geometry). Today concepts I was working with, that had been “invented” by pure mathematicians only a few decades before, have become the building blocks of much of contemporary theoretical physics. Hence Eugene Wigner’s famous maxim about the “unreasonable effectiveness of mathematics” meaning that much of what is a priori created as “useless” pure mathematics becomes a posteriori very useful for applications in physics (lately also biology) and hence in technology.

[Hence my contention that religion, in particular Christianity, should be seen as the “pure mathematics” of social sciences (political theory, sociology etc.). However, few understand what I mean by that.]

Actually, in distinction to my generation - which saw a clear distinction between pure and applied mathematicians - today much of very abstract “pure” mathematics is being created on the go by young theoretical physicists.

The distinction between “pure” and “applied” goes back to the ancient Greek philosophers. For them, the highest human activity was contemplation (in imitation of the Prime Mover). Practical activity (even political activity) was of a “lower rank”.

In modern times, beginning with Bacon and Hobbes (and also Descartes), a reversal took place. Practical activity (e.g., “making”) replaced “contemplation” as the highest human activity.

This reversal reflected the loss of a non-human dimension of truth. Now everything was seen “anthropocentrically”.

The Copernican revolution didn’t displace man at all. To the contrary, Nature now became a huge technological space … the deep meaning of “extension” in Descartes.

I agree, however I do not see how this bears on the usefulness or not of modern (pure) mathematics.

 

[levinas12]

I agree, however I do not see how this bears on the usefulness or not of modern (pure) mathematics.

The “practical” may end up pushing out the “theoretical”.

For example, take quantum mechanics. What deep meaning is involved? Who cares? The equations work and that’s what matters.

Pragmatism reigns supreme.

But once the “theoretical” is gone, the “practical” will shrivel up.