Why I Majored in Philosophy Despite Everyone Telling Me Not To (2013)

I'm not sure if that's really true about mathematicians lacking rigour.

I do recall a logic professor of mine jokingly say that mathematicians were afraid of logicians, and (more seriously) that the former thought the latter were unnecessarily precise. (I hope I'm remembering this right and not misrepresenting what he said)

I'm not sure about the superiority in rigour in the rest of philosophy (even if we narrow the meaning of that term to just analytic philosophy, some of whom sure are fond of their logic, symbols and attempting to sound "scientific" or rigorous). If anything, I'd say those analytic philosophers have math (or hard science) envy.

You're right about mathematicians not being very interested in the foundations of math. That's a consequence of the failure of the great foundational project in the early 20th century. From what I understand, most mathematicians have decided that such a foundation is not possible, and view themselves as moving on to doing the very practical business of math anyway. After all, the lack of a foundation has not prevented them from achieving many interesting (and often useful) results.

That said, there has continued to be interest in foundations for math from some logicians, and (at least according to my logic professor) it still might be possible to found math on logic yet. That's quite a bit out of my league, however, so I'm afraid I can't elaborate much. But if you're interested in that, I do recommend taking some courses in symbolic logic and in the philosophy of math.

This is one of my favorite hacker news comments ever.

Maciej, you’re a treasure.

I can only assume his persona and commentary is an elaborate satirical parody of the snooty narcissistic philosopher (but you never know.. Poe’s Law and all that). To quote from saintzozo’s website:

Mathematics is easy.

If you think it's hard, you are retarded.

proof

Any true mathematical statement is logically equivalent to the axiomatic framework within which it occurs. If you do not understand such a statement, there are only two possibilities:

1. You do not understand the axioms.

Axioms are chosen so that they are evident a priori (eg. the probability of all disjoint events must sum to unity). If all the axioms are not clear to you, there is something seriously wrong with your reasoning faculties.

2. You do not understand logic.

If you understand the axioms, then the only thing that could prevent you from understanding a true mathematical statement is an inability to reason logically. Such a crippling deficiency defines what it means to be retarded.

This case analysis exhaustively proves that if you don't understand math, you are retarded. ■

corollary

Now one must be wary of students formally enrolled in programs of study devoted to mathematics (and its bastard child, computer science).

These people misunderstand mathematics (read: are retarded) to such an extent that they have resorted to paying other people money for instruction in the obvious. [...]

I hope you realize that your statement is absolutely loaded with philosophical undertones. A few examples:

- Is being deluded bad? If so, what is it that makes being deluded bad? You might say "Oh come on! Of course it's bad! We can all see that!" But is that just your opinion, or is it objectively bad? If it's objectively true that I ought to have an accurately informed view of reality instead of being deluded, what is this ought-making property? What grounds it? Is it a moral duty (e.g., I ought not murder), or an intellectual duty (e.g., I ought to think Austin is the capital of Texas)? Is there a difference between moral and intellectual duties?

- Why is philosophy for delusional people, instead of rational people? Surely you recognize that "philosophy is for delusional people" is itself a philosophical statement!

- Being deluded assumes a theory of truth, and an epistemological theory (how we come to know what we know). You seem to know that philosophy is for delusional people -- on what grounds do you know it? What counts as justification for this belief, and how would you account for Gettier counterexamples to warrant?

- I imagine you don't count all fields of study as being reserved for the delusional. What about math or science? If it is the case that math and science are legitimate sources of knowledge, but philosophy is not, how do you justify this claim? You can't prove it mathematically, or verify it in a laboratory. Thus, this scientistic view is self-refuting -- and surely that's for really delusional people!