# Questions tagged [philosophy]

Questions involving philosophy of mathematics. Please consider if Philosophy Stack Exchange is a better site to post your question.

788 questions
Filter by
Sorted by
Tagged with
1answer
116 views

### What formal proof systems are capable of proving $\forall x \exists y x = y$ without needing to apply $\forall$-I to $\exists y x = y$?

I am interested in some philosophical questions that depend on whether the open formula $\exists y x = y$ is a logical truth. I'm making the assumption that some logical systems are intended, in the ...
2answers
136 views

### Is there any “good” definition for what constitutes “applied mathematics”?

Is there any "good" definition for what constitutes "applied mathematics"? Wikipedia lists stuff such as statistics, optimization. However, e.g these have certainly "pure mathematical" aspects to ...
0answers
45 views

### What is the relationship between the common concept of “model” and “model” as used in Model Theory? [duplicate]

To my understanding, a model in Model Theory is an interpretation (in a form of a set or other algebraic structures) for a certain sentence S which makes S true. In everyday language, and also in ...
1answer
46 views

### Is there an accurate view on the distinction between “what mathematics can model” and what it cannot? [closed]

Is there an accurate view on the distinction between "what mathematics can model" and what it cannot? Not just in hard sciences. What about social, political questions? What's the accuracy of ...
0answers
61 views

### Why we need such a restrictions in logics?

Note:I am not competent is logic so this question may look weird to you. So as I know there are different types of logics (first-order logic, second-order...), and the difference between them is that ...
1answer
166 views

### Why do we need/use proof theory?

Note that my knowledge of both proof theory and model theory is incredibly weak. I just started learning about them using Kleene's "Mathematical logic". If I understand it correctly then one of the ...
1answer
418 views

### Choosing formal system for mathematics

I always wondered, we have many choices for choosing what kind of postulates - axioms, deduction rules, we choose for our formal system. For example, there are Hilbert style systems where there are ...
1answer
160 views

### Is mathematics a syntax?

I have read that syntax is symbol and semantics is meaning those symbols convey. Is mathematics a syntax? Where is semantics in mathematics? What gives meaning to mathematics, to those symbols I ...
1answer
101 views

### Understanding a quote from G. H. Hardy in 'A Mathematician's Apology'

I recently learned about the philosophy of constructive mathematics. In several discussions of the topic, I keep seeing a quote from G. H. Hardy's book A Mathematician's Apology; Reductio ad ...
1answer
60 views

0answers
66 views

### Can we be sure proofs have no errors?

My current understanding is that work submitted to journals has mathematicians look over it for errors. Mathematics is deductive, yet with this being the burden of proof, how can we know for sure ...
1answer
45 views

### About proofs that we cannot verify every step by hand

For something I am planning to write, I need to clarify few issues with respect to computer-aided proofs that we cannot verify every step by hand. For example, the proof for the four-color map theorem....
0answers
93 views

### Intuitionism and theoretical physics

In the book by Kleene "Introduction to Metamathematics" I have read that Poincare was intuitionist. Nevertheless, due to the fact that I am an undergraduate student in physics, I know that Poincare ...
2answers
77 views

1answer
93 views

### Metaphysical/psychological aspects of describing a formal language (mentioned in Bourbaki)

In the introduction to Bourbaki vol. 1, we read: "It goes without saying that the description of the formalized language is made in ordinary language, just as the rules of chess are. We do not ...
2answers
221 views

### Is there any “real” number that may not actually be a real because we haven't found its Dedekind cut?

I just watched a video that shows how real numbers are constructed using Dedekind cuts, and what I understood was that a real number is a subset of Q which, among a few other conditions, contains no ...
2answers
284 views

### What does it mean when we say a mathematical object exists?

I learned recently that there are mathematical objects that can be proven to exist, but also that can be proven to be impossible to "construct". For example see this answer on MSE: Does the existence ...
8answers
6k views

### Does the existence of a mathematical object imply that it is possible to construct the object?

In mathematics the existence of a mathematical object is often proved by contradiction without showing how to construct the object. Does the existence of the object imply that it is at least possible ...