# mathematical-philosophy's questions - English 1answer

253 mathematical-philosophy questions.

### 14 Variable-centric logical foundation of calculus

Since calculus originated long before our modern function concept, much of our language of calculus still focuses on variables and their interrelationships rather than explicitly on functions. For ...

### 6 what's the point of cubical type theory?

I have been following through the development of homotopy type theory since 2013 because I was really interested in the foundation of mathematics. The novel idea of combining programming with homotopy ...

### 15 Is PA consistent? do we know it?

1) (By Goedel's) One can not prove, in PA, a formula that can be interpreted to express the consistency of PA. (Hopefully I said it right. Specialists correct me, please). 2) There are proofs (...

### Criterion of completeness

Wittgenstein (PR 181) talks about a criterion of completeness for the irrationals. I am trying to understand what this might mean. Completeness of the reals, in the decimal number system, is the ...

### 5 Ultrainfinitism, or a step beyond the transfinite

Cantor has, in the immortal words of D. Hilbert, given all of us a paradise (or perhaps, I would rather say, a great vacation spot), the TRANSFINITE. $\aleph_0, \aleph_1,\aleph_2\dots$ the lists ...

### 49 The Logic of Buddha: A Formal Approach

Buddhist logic is a branch of Indian logic (see also Nyaya), one of the three original traditions of logic, alongside the Greek and the Chinese logic. It seems Buddha himself used some of the features ...

### -3 What is the intuitive notion that ZF-Extensionality-Foundation+Collection can be said to capture? [closed]

This question has been moved to philosophy.stackexchange.com I'll try to abbreviate it here: the question asks about the "informal notion" that the fragment of $\text{ZFC}$ that is axiomatized by ...

### 28 Excellent mathematical explanations

8 answers, 4.683 views mathematical-philosophy big-list
In the Stanford Encyclopedia of Philosophy there is an entry on mathematical explanation. The basic philosophical question is: What makes a proof explanatory? Two main "models" of mathematical ...

### 37 Can a problem be simultaneously polynomial time and undecidable?

The Robertson-Seymour theorem on graph minors leads to some interesting conundrums. The theorem states that any minor-closed class of graphs can be described by a finite number of excluded minors. As ...

### 7 Identity types: What makes Intuitionistic Type Theory *intuitionistic*?

In the opening passage of Martin-Löf's (1975) he famously says that "the theory of types with which we shall be concerned is intended to be a full scale system for formalizing intuitionistic ...

### 40 Do set-theorists use informal set theory as their meta-theory when talking about models of ZFC?

Here, Noah Schweber writes the following: Most mathematics is not done in ZFC. Most mathematics, in fact, isn't done axiomatically at all: rather, we simply use propositions which seem "intuitively ...

### 27 Category of categories as a foundation of mathematics

In Lawvere, F. W., 1966, “The Category of Categories as a Foundation for Mathematics”, Proceedings of the Conference on Categorical Algebra, La Jolla, New York: Springer-Verlag, 1–21. ...

### 39 Categorical foundations without set theory

Can there be a foundations of mathematics using only category theory, i.e. no set theory? More precisely, the definition of a category is a class/set of objects and a class/set of arrows, satisfying ...

### 47 Lawvere's “Some thoughts on the future of category theory.”

In Lecture Notes in Mathematics 1488, Lawvere writes the introduction to the Proceedings for a 1990 conference in Como. In this article, Lawvere, the inventor of Toposes and Algebraic Theories, ...

### 6 where can you find Grothendieck's “Recoltes et Semailles”?

Where can you find Grothendieck's "Recoltes et Semailles"? Is it available anywhere?