All Questions

Filter by
Sorted by
Tagged with
11
votes
5answers
2k views

What are computable numbers, and what is their philosophical significance?

What are Computable Numbers? Is computability (or non-computability) some sort of technology-dependent characteristic of numbers (via e.g. Turing Machines)? What are the philosophical implications or ...
8
votes
3answers
1k views

How does Frege's definition of number solve the Julius Caesar problem?

How does Frege's definition of number solve the Julius Caesar problem? Frege's definition of number in the end of Foundation is such: the number belonging to the concept F is the extension of the ...
8
votes
2answers
308 views

What did Poincaré mean by intuition of pure number?

To what does Poincaré refer in his article Intuition and Logic in mathematics when he speaks about the intuition of pure number? He refers also to two other forms of intuition, besides the "intuition ...
5
votes
2answers
251 views

What is the difference (if any) between the concepts of natural numbers and finite cardinals?

The definition of natural numbers from Wikipedia: In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third ...
4
votes
3answers
689 views

What are the “undefinable numbers” in real analysis and philosophy?

What if any important results in real analysis make use of the notion of an "undefinable" real number? (Whatever "important" may mean to the reader.) Or is it used more in the philosophy of ...
4
votes
2answers
903 views

Is number π empirical or a priori?

I used the example of π, but this applies to other transcendental numbers as well, such as e Kant classified statements into 4 epistemic categories based on two criteria: The Analytic/Synthetic ...
4
votes
1answer
108 views

What is the difference between concepts of number and natural number?

When reading an article about Frege on Stanford Encyclopedia of Philosophy (https://plato.stanford.edu/entries/frege/#AnaStaNum), in section 2.5 I encountered the following sentence: But though ...
2
votes
4answers
750 views

Why is there so little discussion / research on the philosophy of precision?

I was thinking the other day about the difference between rational and irrational numbers, and wondering whether the distinction between them is created by leaving out discussion of precision. So for ...
2
votes
2answers
229 views

Number, Category and Set

Can it be said that a number is a category is a set? There is such a variety of ideas on numbers, categories and sets that probably anything one says about them will be controversial, but I was ...
1
vote
7answers
556 views

Do whole numbers other than zero actually exist?

Think about counting up: you start from 0. There are many decimals in between 0 and 1, actually, an infinite amount of decimals are there. So in the same way that there is no last number there is no ...
0
votes
5answers
235 views

Can anything be less than one?

Zero itself seems to be an absurd number because if there is really zero of something, then nobody has ever sensed it. But even with temperatures, we don’t really have negative and positive ...
0
votes
1answer
132 views

What was the “rigorous” definition of “number” for the Pythagoreans?

I am not sure if this is the right stackexchange for this question. However, I'm wondering about the following thing: We know n+ow that there are rational and irrational numbers. Pythagoras however, ...