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Questions tagged [numbers]

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0
votes
5answers
224 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 ...
5
votes
1answer
99 views

Square of Opposition with percentages?

What happens if you replace the statements of the Traditional Square of Opposition with "percentages of the subject term"? Do all the relationships from the Traditional Square of Opposition still ...
2
votes
3answers
278 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
1answer
119 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, ...
8
votes
2answers
198 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
1answer
101 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 ...
0
votes
0answers
174 views

When philosophers talk about numbers, do they mean cardinal or ordinal numbers?

Often, when philosophers talk about numbers, they consider the existence of numbers and what they really are, but they don't specify which of the two meanings of number they actually use. Why is that? ...
11
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 ...
7
votes
1answer
569 views

What are functions in the Peano axioms?

I'm posting this here because it's more of a philosophical question than a mathematical one. In set theory, we define a function as a particular type of set; and since the natural numbers are defined ...
5
votes
3answers
105 views

How do our minds divide spaces and create “entities?”

I've been thinking about how any object can be split into infinitely smaller pieces and how we may say that there is a particular object or entity, but it has an upper portion and lower portion. In ...
5
votes
2answers
671 views

Why is 2+2=4 a necessary truth?

A necessary truth is something which is true in all possible worlds. How can we be sure that there is no other universe where 2+2=4 can be untrue.
13
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 ...
5
votes
2answers
754 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 ...
10
votes
2answers
292 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
4answers
633 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 ...