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We were talking somewhere about people’s views on Hegel, and I mentioned how analytic philosophy defined itself in its opposition to Hegel. Here’s Russell:
In philosophy ever since the time of Pythagoras there has been an opposition between the men whose thought was mainly inspired by mathematics and those who were more influenced by the empirical sciences. Plato, Thomas Aquinas, Spinoza, and Kant belong to what may be called the mathematical party; Democritus, Aristotle, and the modern empiricist from Locke onwards, belong to the opposite party. In our day a school of philosophy has arisen which sets to work to eliminate Pythagoreanism from the principles of mathematics, and to combine empiricism with an interest in the deductive parts of human knowledge. The aims of this school are less spectacular than those of most philosophers in the past, but some of its achievements are as solid as those of the men of science.
The origin of this philosophy is in the achievements of mathematicians who set to work to purge their subject of fallacies and slipshod reasoning. The great mathematicians of the seventeenth century were optimistic and anxious for quick results; consequently they left the foundations of analytical geometry and the infinitesimal calculus insecure. Leibnitz believed in actual infinitesimals, but although this belief suited his metaphysics it has no sound basis in mathematics. Weierstrass, soon after the middle of the nineteenth century, showed how to establish the calculus without infinitesimals, and thus at last made it logically secure. Next came Georg Cantor, who developed the theory of continuity and infinite number. “Continuity” had been, until he defined it, a vague word, convenient for philosophers like Hegel, who wished to introduce metaphysical muddles into mathematics. Cantor gave a precise significance to the word, and showed that continuity, as he defined it, was the concept needed by mathematicians and physicist. By this means a great deal of mysticism, such as that of Bergson, was rendered antiquated. (Chapter XXXI of “A History of Western Philosophy” (1945))
Thanks, interesting.
With the advantage of hindsight, we have to note that the second part of this sentence here is plain wrong:
Leibnitz believed in actual infinitesimals, but although this belief suited his metaphysics it has no sound basis in mathematics.
But apart from such nitpicking: I can entirely understand the opposition to Hegel. If indeed he was “right”, then he did not explain why and how, and then it is correct not to take his insights by faith. If our interpretation at Science of Logic, following Lawvere’s lead, is roughly right, then Hegel was like a man in the Stone Age talking to his fellows about Lorentz transformations like an oracle. A seer, a prophet. Not a philosopher and certainly not a scientist.
The problem with prophets is: they may be entirely right and yet it may be impossible to tell until much later.
Collingwood writes of Eddington in his 1928 Gifford lectures
The discovery by a very distinguished scientist that there are grains of sense in Hegel’s Naturphilosophie, and that he feels himself obliged to apologize for having made the discovery, is a sign of the times. How far was the habitual and monotonous execration of Hegel by nineteenth century scientists due to the fact that he violently disliked the science of his own day, and demanded the substitution for it of a physics, which it turns out, was to be in effect the physics that we have now?
He also writes somewhere about Hegel’s foresight that scientists have to work things out in their own time.
Hm, interesting. Could you recall a bit more of the context? I don’t quite understand who feels obliged to apologize for what. And what is meant by “the physics that we have now”, and how does it turn out to be in effect what Hegel demanded?
The particular anticipation here was Hegel’s complaint against the Newtonian picture that taking planets to be kept in their orbits by the operation of ’forces’ is to consider them like stupid children pushed and pulled into place at drill, and that in fact they move freely. Eddington observes that Hegel was right according to general relativity.
The general thrust of Collingwood’s piece is to show that good metaphysics is unearthing the presuppositions of the best science of the day and investigating its internal tensions. Kant had done the former for Newtonian physics, and Hegel was pointing out a tension.
Interesting.
Sorry for the sudden silence, and it will last a bit longer. Am helping a newborn on its way from nothing into being.
Well! If that’s a way of announcing your fatherhood, then congratulations!!
Yes, congratulations, unless Urs has suddenly changed careers to midwifery.
Congratulations! I was thinking it might have been a birth of a more mathematical kind causing your silence, but that’s not really your style.
Thanks to you all. I didn’t want to make much of an announcement, but then I thought I should express the cause of my abrupt change of behaviour. Speaking of forces that push and pull.
But now I happen to have a spare minute. I’d like to get back to the topic of this post. Just a second…
Okay, in the attempt to collect some of the above discussion, I have started at Georg Hegel a section Perception of Hegel’s Naturphilosophie
In the first two paragraphs this has some comments that are mine, and then follow the quotes that David provided above, with brief comments and links.
This is not meant to be in final state. Please feel invited to edit and expand. In particular I am not sure if I am recounting the second quote accurately (haven’t seen the original text yet).
Congratulations!! Who’s next? (-:
I’ve made some small adjustments.
We could add negative comments about Hegel at will, not all being that illuminating.
E.g., John Stuart Mill, in his letter of November 4, 1867 to Alexander Bain, wrote:
Besides these I have been toiling through Stirling’s Secret of Hegel. It is right to learn what Hegel is & one learns it only too well from Stirling’s book. I say "too well" because I found by actual experience of Hegel that conversancy with him tends to deprave one’s intellect. The attempt to unwind an apparently infinite series of self–contradictions, not disguised but openly faced & coined into [illegible word] science by being stamped with a set of big abstract terms, really if persisted in impairs the acquired delicacy of perception of false reasoning & false thinking which has been gained by years of careful mental discipline with terms of real meaning. For some time after I had finished the book all such words as reflexion, development, evolution, &c., gave me a sort of sickening feeling which I have not yet entirely got rid of.
Thanks, I have briefly added that quote to Georg Hegel, too. Maybe these quotes are the more interesting the more we say what impact they had. I gather that Russell is worth quoting as he was a champion of analytic philosophy, I suppose. How about Mill?
Also, do we have further instances of people later finding unexpected value in reading Hegel, similar to the Eddington quote?
stub for analytic philosophy, just to satisfy links
What should one do with the page for Bertrand Russel given that it should be Bertrand Russell with 2 ls, and the latter already exists?
Sorry, fixed now.
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