Summations Only

*Edited*Are you guys trying to figure out if math is objective/subjective? Edited by Chuck77, : No reason given.Edited by Chuck77, : No reason given.Edited by Chuck77, : No reason given.Edited by Chuck77, : No reason given.Edited by Chuck77, : No reason given.

Not really. I think the three of us agree that maths is objective.So then it becomes an exercise in philosophical navel gazing about the nature of existence and whether the objectivity of maths means that mathematical entities can be said to "exist" in some sense that is independent of minds. Are mathematical entities aspects of objective reality - That sort of thing.Or - To put it another way - Do we invent or discover maths?

Ok. I guess that's the question for a lot of things not just math. Is it a different debate than the one for god(s) or is this one a little more objectivly based? Well, obviously it is more objective but is it along those lines?It's kind of like the tree in the forest analogy? If no one is around to observe it does math still exist? Or is it soley a human invention?Would there still be a certain number that describes light years or is it something we came up with to better understand the universe. Or does the universe compel us to use math to try understand things about it. Without math would we be able to figure certain things out or is math a product of our environment.I'm rambling now. Am I anywhere in the ballpark of what you guys are talking about?Edited by Chuck77, : No reason given.

Hmm ... I'd say that we discover math and that mathematical entities don't exist. We are not discovering things, which exist, but facts, which are true.

So mathematical entities are not realistic if no one discovers them? So then 2+2=4 is a fact that was never discovered? It didn't exist until someone brought it into existance?

No, that's not what I said. A fact can be true before someone discovers it.But facts are not real, they're true.Things are real or not real (e.g. hats, unicorns, respectively). Statements are true or false (e.g. "Hats exist"; "Unicorns exist").Mathematical truths are true, not real, because they're statements, not things.

So 2+2=4 is a concept?

Yes. To be precise, the truth here is that within the system of natural numbers, 2 + 2 = 4. Now the fact that the system of natural numbers can be used to model some aspects of our experience is merely a scientific discovery, and is not true a priori.

If these facts are properties of reality then they are "things". Not physical "things". But "things" which can meaningfully be said to "exist" and thus be discovered.But the fact that I feel the need to splatter inverted commas all over the place when writing that should tell you that I am not entirely convinced of that myself.

Yeah - Sort of.Rahvin was making the case for maths having a purely empirical basis. I am sort of putting forward the case for mathematical realism. Dr A is making a distinction between facts that can be discovered and things which can be discovered. I suspect the difference between him and I is a semantic one based on whether or not facts are "things" that can be said to "exist".Unfortunately the philosophical area of ontology is fraught with such distinctions and as a result is mostly navel gazing nonsense. But it can still be "fun"......

Well, what do you mean by "properties of reality"?Consider the following statement: "If all snufflepuffs are frungible, and all frungible things are blurple, then all snufflepuffs are blurple".This is a fact (which is true). Is there a thing (which exists) corresponding to the fact?

Yes. Logic.Does logic exist? Is logic a property of reality?

Well, that's a bit broad. Would you say that the "thing" corresponding to Pythagoras' theorem was math?

Maybe so. But that, I suspect, is what all this boils down to. If we discover rather than invent maths then it is because ultimately maths is our method of exploring the logic innate in reality. Or something like that. To Pythagoras theorem specifically I guess the "thing" we are specifically applying logic to is the geometric form known as a triangle.But in your Snufflepuff example there was nothing that makes it specific to Snufflepuffs. In fact you would be better off generalising your statement to something like:If ALL X are Y and ALL Y are Z Then ALL X are ZA simple and generic statement of pure logic that applies to the frungibleness of snufflepuffs or anything else which meets the same logical criteria.

No, you'd have been better off if I did that. That's why I talked about snufflepuffs. Snufflepuffs are clearly not the things the syllogism is true of, since they aren't things; and on the other hand those who vaguely imagine a Platonic world of mathematical and logical truths will tend to baulk at the idea of my premises and conclusion sitting there in their logical relationship waiting for me to come along and enunciate it.