## Does a Background in Mathematics Make One a Better Philosopher?

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I was a Philosophy major as an undergrad and became obsessed with the beauty of rigorous argumentation. There I didn't take a single class listed under the Mathematics department and was almost exclusively interested in Ethics.

Now, two years later, I have quit my job to pursue a Masters Degree in Pure Mathematics (after much self-study and a semester of expensive post-baccalaureate work). While I find the subject (and more importantly the process) of Mathematics absolutely beautiful, I feel that my true love will always be for Philosophy.

Still, I feel that studying math has made me a much better critical thinker, and I am tempted to argue that studying Mathematics has made me a better Philosopher as well (although I haven't had time to really test this claim). In particular, the study of Mathematics has taught me mental strategies to (i) grasp concepts which aren't as easily intuitive as those in philosophy, (ii) to be even more concise in my argumentation, and (iii) to feel comfortable introducing suitable notation on my own to simplify my thoughts and get me to the heart of problems.

1. Do people have experience with (or know of others who have the experience with) studying Mathematics and finding that it contributed positively towards their ability to do philosophy (above and beyond the opportunity cost of actually studying more philosophy)?

2. Are there any examples of modern professional philosophers who have non-trivial backgrounds in Mathematics?

3. Would obtaining a Masters in Pure Mathematics improve one's chances of being admitted to Philosophy grad school?

"In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it... – Quinn Culver – 2012-09-16T01:31:42.120

"...So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures; so in the mathematics, that use which is collateral and intervenient is no less worthy than that which is principal and intended." John Fauvel and Jeremy Gray (eds.) A History of Mathematics: A Reader, Sheridan House, 1987. – Quinn Culver – 2012-09-16T01:32:07.330

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You might find some interesting stuff in here: What should philosophers know about math and natural sciences?

– stoicfury – 2012-07-31T19:31:47.767

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I feel it's pretty obvious that doing math gives you experience with deduction systems. The question as posted could be translated into "has need to do more practical work an influence on doing philosophy". Moreover, the need to do some practical work in some specific fields will be the reason for many to get into philosphy in the first place. If one is involved with the deconstruction of certain structures, may it be economics or universal algebra, one might easily find oneself tapping on questions in the realm of philosophy.

Regarding the second question, Saul Kripke or Hilary Putnam comes to mind. And also many linguists or AI people also have one foot in mathematics and one in philosophy. Douglas Hofstadter, to name a known one.

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As a computer science student with a mathematics minor, I must agree with @RexKerr.

Math is truly the only language in which one can fully understand the observable laws of the universe. It is a language whose symbols are written by humans, but whose meaning potentially carries the weight of universal law. A philosopher who wishes to legitimately comment on the nature of the universe should first have a full understanding of how the observed universe operates.

As for mathematician/philosophers I would recommend Douglas Hofstadter. His book Goedel, Escher, Bach is one of the greatest books I've ever read. (Also try I Am A Strange Loop)

5"Math is truly the only language in which one can fully understand the observable laws of the universe." Somewhere, aliens are laughing. :P – stoicfury – 2012-07-31T06:57:30.837

Though it's possible an alien race's mathematics may be more advanced and written with different symbols, the laws they describe will be identical to the ones we do. That's the beauty of math :) – degausser – 2012-07-31T08:49:51.520

7My point was that your confidence in the human intellect's ability to discern *ultimate truths* is the hallmark anthropocentrism and grossly under-appreciates 3 millennia of literature on philosophical skepticism. :P +1 for GEB though, good book. :) – stoicfury – 2012-07-31T19:16:06.297

2+1 for setting me straight with a very fair comment. In the end, you are correct. All I can say is that it is my belief that human observation/intellect is reliable – degausser – 2012-07-31T19:38:48.573

3@stoicfury - Given the equivalence of computability (c.f. Turing machine), aliens have very few options for not using math. Either they are using something equivalent, something strictly drastically more powerful in ways we don't understand (in which case it's hard to claim they're "not using math"), or something so impoverished that it is hard to see how it could cover the observable laws of the universe (given that you can make good approximations of Turing machines using those laws). No, I think we already know: if there are aliens, they use math to understand the laws of the universe. – Rex Kerr – 2012-08-01T14:10:28.090

@RexKerr Well said. This was the idea that I was originally trying to convey. I think the real issue was that, while humans can observe how the system in which we live acts and apply these observations accordingly, there is no way to show that our observations give us the full picture, the "ultimate truth" of everything. For example, it is technically possible that the curvature of our universe is caused by a giant hand squeezing the universe and that this hand is, by nature, imperceptible to humans (silly example but I'm sure you get the idea). Not my belief, but valid nonetheless. – degausser – 2012-08-01T14:37:44.703

1@RexKerr The above example was actually pretty poor since I realize the curvature of the universe is a matter of debate (and in fact it is quite possibly flat). The idea is there may be a process that is, by nature, is imperceptible to humans which makes reality appear and behave the way it does. Not that dissimilar to the idea of a god. – degausser – 2012-08-01T14:59:40.867

1Yes, what degausser speaks of in the above 2 comments is certainly a key part what I was referring to. This level of philosophical skepticism is irrefutable and—no matter how much we learn and discover—will always leave us with the question in the back of our minds, "What if there's more?" Put most simply: Can you ever know that you know everything? – stoicfury – 2012-08-02T19:45:42.487

1@stoicfury - You can't get away from computability. Something more isn't not doing math, it's just doing math and more. Something less is inadequate based on existing observations. This sort of mathless "what if there's more" is therefore on the same footing as nihilism and Descartes' demon: formally possible, but practically useless. (Other types of "what if there's more" can be much more enlightening.) – Rex Kerr – 2012-08-07T17:34:05.483

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## MATHS

Maths helps us to:

1. Deal with consistency

• It helps us to work strictly within relevant boundaries.
2. provide calculation for other field of knowledge, since maths deals with basic calculation.

• Calculating physics, economics, shopping on Mall, buy T-Shirt, etc, follow rules on maths (can be provided by Maths).

## PHILOSOPHIZING

Philosophizing mostly (not always) deals with:

1. Premises and conclusions

• Maths can be used to provided consistent relational on reasoning.
2. Any field of knowledge

• Maths can be used to provide consistent relational on reasoning from different point view

It helps us making an adjustment on different field of knowledge by providing premises from different point of view with consistent relational as proved (provided) by maths calculation.

Conclusions:

• Maths helps us to provide consistent argumentation.

• Since maths can provide consistent argumentation, then it may help us to trust assertion better than previously. Furthermore maths will strongly force us to make an implementation of what we trust to achieve better possibilities for better life.

## WEAKNESSES OF MATH

1. Maths may be used to provide consistent argument with clear distinction as long as it deals with correct assertion (premise)

1.1. For example: stating there are two cats from me and two cats from yours and it's equal there are four cats (whether several of them, alive or not)

But this could be wrong, if we say "sorry, five cats from me (not two cats) and two cats from yours". But the final calculation still has consistent relational as the consequences, that "therefore there are seven cats".

1.2. When maths calculates wrong assertions on law of physics (for example past assertion on law of physics might be differ from current assertions), then it will make maths just as variables that gives inconsistency on the result.

2. It's just analysis and far away from control our emotions directly, which mean that to be an expert on maths doesn't make someone a wise person. In philosophy, we need more than just analyzing or something we forgot.

For example, we know the benefit on meditation. It's scientific technique that will change our brain chemistry, further our emotions and the way we interact.

We may be using maths to calculate how meditation is valuable for us, by comparing calculation before and after meditation and providing exact argument that increasing benefits on meditating exist. But maths won't help the situation that would excite us to practice meditation.

## The points are:

• A better philosopher is not just presenting argument, but how to make those arguments applicable to ourselves or others, and how to increase our abilities for better survival and better enjoyment. Placing ourselves without further development for better survival and better enjoyment, it's not part of philosopher, but strongly related to just theoretical.

• Accuracy on maths depends on how accurate we perceive something

Therefore asking "Does a Background in Mathematics Make One a Better Philosopher?" can be answered 'Yes' by supporting our argument with consistent relational*** & widening our chance to use argumentation from any field of knowledge (different point of view) without losing its consistency to widen our adjustment and hopefully increase our accuracy on perceive dency (since formulated under maths rules), as long as:

1. We perceive differences better than previously.

2. We have an **open minifferences (and eventually increase our accuracy on reasoning using maths).

3. Maths must not just present strong argument to us, but it must help us to (increase our trust, excitement to) realise something for better survival and better enjoyment.

Without these, maths is just an analyzing tools without making any progress that is in line with the purpose of philosophy (love wisdom).

From your experience Seremonia, do you know many math students reading philosophy? All people I know have background in Human sciences. – p.a. – 2012-08-02T17:07:40.427

Hi @p.a. Very rare, only one, the rest learning philosophy just to fulfill curiosity, and quickly abandoned because of philosophical thought was considered as word games that can be misleading. Only one of my very best friend insist to learn philosophy to answer philosophical question for personal matter. – Seremonia – 2012-08-02T17:37:15.590

@ceremonia all people I know are from humanities and most of all legal backgrounds. Maths grads are mostly geek. But maybe I m an exception. – p.a. – 2012-08-03T14:41:31.770

@p.a. Maybe it will make you thinking proportionally on both sides. That's great – Seremonia – 2012-08-03T15:25:07.060

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It depends on your defintion of "better philosoher." I was an undergraduate philosophy major at SUNY and did not do much mathematics--I did some logic. I was not particularly good at it.

Then I went to graduate school in philosophy and determined that the fashion at the time was analytic philosphy. I felt in order to do good "academic" philosophy--I had to do lots of symbolic logic, history of logic, set theory, that type of thing.

I failed. I gave it up.

So in summary, if you want to be a good "academic" philosopher, I would recommend lots of mathematics since a considerable part of the history of philosophy contains mathematical thinkers like DesCarte, Whitehead, Russel, Frege, etc. Of course, you will end up in a rarefied academic atmosphere where very few people know what the hell you're talking about, but that may be ok depending on your goals.

The other option is "independent" philosopher. I don't think you need a ton of mathematical background to be an free lance "public intellectual," in fact, this could be a detriment in communicating your ideas.

The Sage of Wake Forest

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Having a degree in maths I can say that they dont contribute towards apprehension of philosophy anymore than economics or sociology or history might do. Induction, deduction, abstraction and systems thinking exists in all domains.

3My experience with those fields is almost wholly different from yours. Induction, deduction, and abstraction were present in abundance in mathematics, and almost comical in comparison in their application in sociology and history. – Rex Kerr – 2012-07-30T15:08:39.767

1I cannot see how memorizing Bernoulli differential equations makes me understand Kant better. – p.a. – 2012-08-01T07:30:31.293

2If all you did was memorize differential equations of various forms, I think you missed out on a lot in your maths degree. – Rex Kerr – 2012-08-01T14:06:02.667

Indeed. Some courses are indeed demanding as per memorization. – p.a. – 2012-08-01T19:42:40.427