Linked Questions

18 votes
6 answers
9k views

If math is so deductive, why is it so hard to discover new math?

Some considerations: The conclusions of much latter/new math may be said to be already existent within the premises of current math The importance of deduction changes depending on if math is said ...
Xeon's user avatar
  • 489
10 votes
5 answers
2k views

Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?

While reading Logicomix, I came across a scene that I don't quite understand. Russell: ...Logicians are creating elaborate ways to "say the same things in different words"...this "...
Dimen's user avatar
  • 413
7 votes
5 answers
2k views

Is mathematics analytic or synthetic?

This question is related to another question I posted but I think it requires its own treatment since of the already wide scope of the other question i.e. Is the classical theory of concepts ...
user21312's user avatar
  • 139
3 votes
5 answers
1k views

Why can anything be discovered in mathematics at all?

Imagine a Perfect Mathematician that has superhuman abilities -- if you give him or her a formal foundational system for mathematics like ZFC with all the underlying logical machinery, he or she is ...
user avatar
5 votes
4 answers
376 views

What is the value of a formal model in science?

In science we often use formal models (by which I mean a mathematical structure composed of assumptions, variables, and equations, which might be solved/simulated to derive analytical insights and/or ...
luchonacho's user avatar
3 votes
1 answer
399 views

Is the problem of logical omniscience intractable?

Vincent Hendricks and John Symons notes the following about epistemic logic: Epistemic logic gets its start with the recognition that expressions like ‘knows that’ or ‘believes that’ have systematic ...
Frank Hubeny's user avatar
  • 19.5k
1 vote
5 answers
521 views

Is the concept of information nonphysical?

To keep within the guidelines of only asking questions that have a definite answer, I will stipulate that I am asking about cases where the question has been considered in an academically respectable ...
A Raybould's user avatar
7 votes
1 answer
189 views

Can it be rational to have beliefs one knows to be inconsistent?

It seems that the answer would be yes, especially when we think about the example of the preface paradox (authors stating in prefaces "the errors that are found herein are mine alone", i.e. believing ...
mrnobody's user avatar
  • 159
3 votes
1 answer
279 views

Understanding Hintikka's scandal of deduction (as depicted by D'Agostino)

I am having trouble understanding Hintikka's Scandal of Deduction, as depicted in D'Agostino's article. According to this account, the problem stems from the fact that, while first order logic is ...
Constantly confused's user avatar
4 votes
1 answer
324 views

Was Euclid's method of proof axiomatic?

Euclid's method of proof has often been described in textbooks as axiomatic, but was it really so? And if not, how else can Euclid's method be characterized?
user avatar
4 votes
2 answers
137 views

Is a fallacy involved in perceiving the solution to a long-standing problem as simple and straightforward?

In university (or, school) we're often presented with a problem, and directly afterwards, the solution is presented. Quite often, the solutions presented for a given problem seem painfully obvious, ...
Magnus Berg Sletfjerding's user avatar
1 vote
2 answers
187 views

Is it even possible to desire something we believe is impossible?

Is it even possible to desire something we believe is impossible? What does that mean, to have something that cannot exist as an intentional object of desire? Nevertheless, people often talk about ...
user avatar
2 votes
1 answer
138 views

Why do equivalent propositions sometimes differ in apparency?

I study maths, and I have found that a useful way of thinking about two propositions A and B being equivalent is to regard them as being two different ways of saying the same thing, or equivalently, ...
legionwhale's user avatar
3 votes
1 answer
135 views

Chalmers' two-dimensional argument against materialism

I'm trying to understand David Chalmers' two-dimensional argument against materialism in philosophy of mind (here). I'm particularly confused by the paragraph (pp. 11-12) where he claims that it's not ...
Riccardo Iorio's user avatar
0 votes
1 answer
222 views

Self contradictory things that can't really exist: can they be fully conceived of?

It seems like we can conceive of self contradictory things that can exist. e.g. the proposition expressed by "this sentence is false" is self contradictory but I don't seem to have any trouble ...
user avatar

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