# Mathematics influence on Philosophy

I am reading Bertrand Russell's "History of Western Philosophy" and in the chapter on Pythagoras the author commented that the influence of mathematics on philosophy is unmistakable and unfortunate. As a neophyte I am not formally studied in philosophy and was curious why Russell would characterize the impact of mathematics on philosophy as unfortunate.

Perhaps someone schooled in philosophy could shed some light. Would it be incorrect to assume that mathematics and logic would be considered intrinsic to philosophical thought?

Tags: Bertrand, Russell, mathematics

Views: 453

### Replies to This Discussion

@Simon:
RE: Logic is a property of reality.

...What do you mean "property of?"

Reality conforms to natural rules of logic.

...What are "natural rules of logic?"

Mathematics conforms to logic in the same way, and logic can be used in conjunction with mathematical rules to produce new results.

..."Producing new results" would mean you are applying an almost futuristic application towards philosophy as if it gives you something tangible. Am I interpreting that correctly?

I've tried doing equations with moral values.  See what you think of this.  I've posted it before, you may have seen it.  I can't work out whether it's superbly profound, or just random rubbish.

"balls" + humility + a good heart + integrity = beauty
"balls" + humility + a good heart + integrity + experience = wisdom

Therefore, subtracting line 2 from line 1, we have this [possible nonsense]:

experience = wisdom - beauty
(experience is wisdom without beauty)

experience - wisdom = - beauty
(experience without wisdom is ugliness)

wisdom - experience = beauty
(wisdom without experience is beauty)

"Logic is a property of reality." - in the reality we live in, there are things which are possible and things which are impossible.  It is impossible for me to be in two places at once, for example.  There is also the logic of numbers, which is an abstraction of the real world - abstracting the "threeness" of three stones, for example.

By "natural rules of logic" I mean the logic of numbers and the logic of everyday life.  The logic of physical reality.

Russell's concern is probably the same for any discipline that applies math or logic. If you set up the problem wrong; your conclusion will be wrong, even if the math or logic is correct. For instance, if you use a number line with points to represent physical distance, math tells you pencil will never reach paper.

Binary logic, used to implement computers is even more limited than real math in a sense. The only "truths" and computer "knows" are the logical binary operators OR, AND, INVERT. It can only use binary representations of real numbers. Fortunately that is almost always good enough, just don't divide by zero.

Easy to get lost in a computer program or pages of math expressions and forget the philosophy behind the problem.

You don't need math to get a bad conclusion from a flawed setup.

I suspect that he came to realize as time went by that the really sticky issues in philosophy had to do with ethics and human rights, subject areas not very susceptible to being described and analyzed in a rigorously deterministic way. I think he eventually came to agree with G.E. Moore that ethical disputes are really about attitudes not facts. Factual matters can be set up and operated on using logic. Attitudes fall into areas where logic doesn't work so well, like psychology, personal preferences, folkways, etc.

I am inclined to agree with this explanation. Hopefully I will come to understand more by what he meant as I progress through his book.

Exactly my point. If you are going to use math for Philosophy, use it correctly. Psychology very often relies on scientific methods, logical contructs, statistical data to reach conclusions. Is the defendant sane or not? Attitudes, personal preference, folkways are probably the actual underlying factors for such a determination, however we like to present data and analysis to make such decisions seem rational. Trained as an engineer, I used to get a good laugh when I read some of the dissertations that applied scientific methods to softer subjects. They seemed to be so deterministic.

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