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Please answer the question directly before giving an explanation.

I would like to test the definition of "love of knowledge" and its relation to individual aptitudes. According to the concept of "love of knowledge or wisdom" a philosopher should be a master of learning by approaching all possible sources, including mathematics and formal logic. In psychology, it is noted that there are regionally specific skills which are generally (not always, or exclusively) localised within one of the two hemispheres of the brain. Those who are dominant in one of the sides may be good at verbal reasoning while the other may be good at mathematical reasoning. Because of this, it is plausible to accept that not all philosophers are strong in both mathematical and verbal reasoning. This means that people have to reach an understanding of the term "love of knowledge" based on their own particular aptitudes.

Is it possible to love wisdom while neglecting the study of mathematics?

Dr Sister
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Zid
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    this also seems to be a duplicate of http://philosophy.stackexchange.com/questions/4167/does-a-philosopher-need-much-knowledge-of-mathematical-formal-logic – Dr Sister Jan 01 '13 at 07:03

2 Answers2

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Please answer the question directly before giving an explanation.

Which question? The one in the headline, or the one at the end of the question text? Because there is an interesting slippage between the two.

Clearly, no human being, philosopher or otherwise, is going to be equally conversant and skilled in all branches of knowledge.

Which means, it is all a question of degree-- in other words, we can rephrase the question as "what level of mathematical learning is a minimum for someone to function effectively as a philosopher?"

It seems to me, the appropriate response to that question is "Why do you care? What is your reason for asking?"

Michael Dorfman
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  • Good point. You are pointing to the fact there are different academic disciplines for economic reasons. Plato was aware of this. "But then again, as we know by experience, he whose desires are strong in one direction will have them weaker in others; they will be like a stream which has been drawn off into another channel. True." If you look at Kant's analytic/synthetic distinction, you will find that mathematics is a class of judgements. Which is why argue differently, see below. – RParadox Jan 01 '13 at 14:22
  • Yes, but mathematics is not the only class of judgments, and there is no indication that Kant relied on (or even had) knowledge of higher mathematics. Is there anything in Kant's writings that requires a knowledge of calculus or linear algebra? – Michael Dorfman Jan 02 '13 at 13:53
  • Well, actually the answer is yes. Kant's conception of mathematics is much deeper than even Hilbert could imagine. Not everything is written with a sign in front of the door, such as in Plato's case. Not every obvious answer is the right answer. So yes, without a very deep understanding of mathematics philosophy is impossible. It's just that someone with such an understanding would not call it "calculus" and "linear algebra". It's not by chance that the first was invented by Leibniz and the second by Descartes. – RParadox Jan 02 '13 at 15:47
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    @RParadox: I can't say I agree with this valorising of mathematics. Although Plato approves of maths (in the Republic he says 'it is a contemplation of the eternal'), but he also warns 'They...are always talking in a narrow and ridiculous manner, they confuse the ways of geometry with those of daily life'. Kant had a penetrating mind - and thats the key point, it underlines why he was a good philosopher, and no doubt he would have been a good mathematician had he chose to go in that direction. – Mozibur Ullah Jan 02 '13 at 16:03
  • Calculus & algebra have a long history - neither Liebniz nor Descartes were the first although they had important things to say about it. – Mozibur Ullah Jan 02 '13 at 16:03
  • @RParadox: There is nothing I can find in Kant's conception of mathematics that indicates he had any training in higher mathematics; in fact, I can't find anything that requires more than high school mathematics. Saying that his conception of mathematics is deeper than Hilbert's is irrelevant, because that is a matter of the philosophy of mathematics which is very different than the discipline of mathematics itself (in the same way that one does not need to be an artist to have a philosophy of aesthetics.) I see no reason an Ethicist, for example, requires training in higher mathematics. – Michael Dorfman Jan 04 '13 at 08:36
  • It's correct that you say, that you can't find anything, because it is there. The concept of mathematics by Frege and Russell is a completely different one than that of Hilbert. Hence Frege's concept-script. Concept is a Kantian term. Also I believe that the idea of philosophy of mathematics is useless. Because that is precisely what I would reject, along the lines of Leibniz. It's just sad that the logical school has been forgotten. Just because it is ignored, doesn't mean the formalists (Hilbert) are right. Putting everything in neat boxes, doesn't solve the hard problems. – RParadox Jan 04 '13 at 10:52
  • Again, I ask: can you name a portion of Kant's corpus which requires an understanding of mathematics beyond, say, the high school level? Is there any evidence you are willing to cite that higher mathematics is necessary for, say, an Ethicist? No need to drag, Frege, Russell, Leibniz or any other philosophers into the mix. – Michael Dorfman Jan 04 '13 at 16:30
  • Kant has major connections to topology, logic, category theory, starting from page 1 where he talks about the logical inference of Aristotle, which most people in high school have never heard of. – RParadox Jan 04 '13 at 19:41
  • Kant has connections to those fields, but does not rely on any advanced mathematical knowledge, and to claim that it is necessary for philosophers to study Aristotle is not a particularly novel claim. My answer to the OP stands. – Michael Dorfman Jan 05 '13 at 12:34
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“I would like to test the definition of "love of knowledge"”

The word philosophy is of Ancient Greek origin: meaning "love of wisdom." However, the etymology is not much help. The use and meaning of the word "philosophy" has changed throughout history.

“We may note one peculiar feature of philosophy. If someone asks the question what is mathematics, we can give him a dictionary definition, let us say the science of number, for the sake of argument. As far as it goes this is an uncontroversial statement. Definitions may be given in this way of any field where a body of definite knowledge exists. But philosophy cannot be so defined. Any definition is controversial and already embodies a philosophic attitude. The only way to find out what philosophy is, is to do philosophy." —Bertrand Russell, The Wisdom of the West

“Is it possible to love wisdom while neglecting the study of mathematics?”

A review of standard reference works suggests that there is a broad agreement among such sources that philosophy involves the study of the most fundamental and general concepts and principles involved in thought, action and reality. If it is possible to do philosophy while neglecting the study of mathematics depends of the kind of concepts and principles involved.

Those who are dominant in one of the sides may be good at verbal reasoning while the other may be good at mathematical reasoning. Because of this, it is plausible to accept that not all philosophers are strong in both mathematical and verbal reasoning.

It is plausible to anyone. It is a platitude.

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