Questions tagged [mathematical-logic]

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7 votes
2 answers

Why aren't Kripke semantics "syntax in disguise"?

The Wikipedia article on Kripke semantics suggests that they were considered a major breakthrough in part because algebraic semantics were seen as merely "syntax in disguise". But Kripke ...
3 votes
2 answers

Does logic give us a single definitive and universal answer for comparing the odds of unlikely events?

As an amateur who has interest in logic and mathematics I've been reading about the concept of different probability perceptions. I'd like to have your opinions over the subject below. When it comes ...
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3 votes
0 answers

Is the overlap between Yoneda's lemma and Peirce's pragmatic maxim known?

In philosophy, particularly in ethics, the pragmatic maxim (WP) states that an object may be considered solely in terms of its effects on the surrounding context. In the special case of ethics, the ...
  • 191
2 votes
2 answers

Per Mathematical Structuralism, can a pure mathematical theory have semantics that is not closed on isomorphism?

This question is the philosophical side of a question that I've recently posted to MathOverflow. Here, I'm specifically asking about the output of Mathematical Structuralism on that question that I'll ...
  • 389
1 vote
4 answers

Why do many philosophers state their arguments without using mathematics or formal language?

I am an amateur lover of philosophy and a researcher in physics and computer science. When reading a book of philosophy, I always find it frustrating that philosophers are so polysemous and ambiguous ...
1 vote
1 answer

Philosophy books for mathematicians

Are there any books on philosophy that make relatively heavy use of math? I'm not looking for anything on formal epistemology, logic, or philosophy of math. Two examples of books that fall in the ...
0 votes
1 answer

Why is conjunction interposed with intersection instead of union?

My philosophical background going into set theory was heavily laden with Kantian and neo-Kantian elements, so one of my essential premises was read off the following passage from the first Critique [...
0 votes
0 answers

is there such a thing as non-constructive computational “proof”?

For the problems which can’t modified into a constructive proof, is there some useful notion of proving them to some computational approximation? I’m referencing: “Interpretations come at a cost: for ...
  • 1,601
-6 votes
3 answers

Can we logically derive a value for 0÷0? [closed]

I have a "proof" that 0÷0 = 2: 0÷0 = (100 - 100) ÷ (100 - 100)   = (10⋅10 - 10⋅10) ÷ (10⋅10 - 10⋅10)   = (10² - 10²) ÷ 10(10 - 10)   = (10 + 10)(10 - 10) ÷ 10(10 - 10)   = (10 + 10) ÷ 10   =...