Through this argument, I am not saying that numbers do not exist, but am merely illustrating the idea that it is possible that numbers do not necessarily exist. — Abecedarian
However, possible worlds are conceived as discrete entities — Mentalusion
1. Any possible world that is intelligible is such that it contains some structure and form.
1a. All possible worlds are intelligible
2. At least some aspect of all structure and form is inherently quantifiable
3. Anything quantifiable is capable of being expressed numerically
4. All possible worlds contain aspects that are capable of numeric expression
5. The capacity for expressing numbers is sufficient for numbers to exist (whether or not anyone uses them or has discovered how to use them)
6. Numbers exist in all possible worlds
7. Therefore, numbers necessarily exist — Mentalusion
1a is probably false, depending on what you mean by intelligible. Lots of worlds are presumably unintelligible if their structure is such that it runs very counter to our own universe. So say a universe where objects are clearly distinguished would probably appear as very unintelligible to most or all people. But if by "intelligible" you mean "coherent" (i.e. not logically trivial) then 1a is true. — MindForged
2 & 3 are suspicious because there are different ways of assigning quantity to thing. Numbers are not the same thing across all mathematical formalisms, and so it does not follow that some numerical system that is apt to one particular possible world is applicable to all of them. — MindForged
I mean as little as possible by it so as to leave open to interpretation what it could mean. Most generally, I take just to mean "capable of being understood" whether by humans or any other rational creature. My intuition for its truth is that any "world" that were completely incapable of being conceptualized in any way by any kind of rational creature would not qualify as a world at all. It would essentially be chaos. — Mentalusion
Agree about the math formalism, but I don't see why the premise wouldn't work with whatever theory of numbers you accept, whether platonic, intuitionist, whatever. Are you suggesting it makes sense to suppose there could be different possible worlds where, say, constructivist , platonic, etc. interpretations hold in each? I guess my assumption is you would first have to decide what you think numbers are before running off to look for them in different possible worlds. — Mentalusion
I used to think that numbers were invented components of the numerical language which mathematics used to express logic or principles of nature. Now, I think part of it is true. — BrianW
OK, so which part have you recognised as being false? — Pattern-chaser
I no longer think numbers were invented. I'm now inclined to think numbers are an expression of a relationship which has always existed in nature, and which we discovered. — BrianW
Where in the scientific space-time universe is "two"? — Pattern-chaser
Numbers don't have to exist for a mathematician to say that the square root of 2 is irrational or that 2 is equal to 4 divided by 2. — Walter Pound
2 = 2 is true without 2 being a real entity. — Walter Pound
Numbers don't have to exist for a mathematician to say... — Walter Pound
The symbol "2" is not itself 2... — Walter Pound
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