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# Questions tagged [numbers]

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### What is a number? Is human's cognition sense allowed us to know numbers?

I know number is an abstract object. But I am not satisfied. Let's take number 1 represents any wholesome unit that we consider, say a goat .Then we say number 2 as 2 of that wholesome unit, here 2 ...
751 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 ...
52 views

### Does the real line mean that the start and end points of any line must exist?

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line https://en.wikipedia.org/wiki/Real_number We consider the set of real numbers, ...
230 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 ...
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 ...
137 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 ...
557 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 ...
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, ...
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 ...
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 ...
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 ...
697 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 ...
113 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 ...
1k 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.
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 ...
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 ...