I'm not a mathematician so maybe this is a dumb question. Not even sure if this is considered more philosophical. What makes numbers a "real" metaphysical truth? And I mean just beyond the symbols we use to describe numbers, which I know are a construct of the human mind (the symbols themselves, I mean).I can sort of wrap my head around the laws of logic, for example, but what exactly makes "2 + 2= 4"? I know that if I see 4 apples, there are "4 of that certain thing" but I'm having trouble defining what that 4 actually is and why it's considered "real" as opposed to just humans coming up with a universal measurement.
I'm not a Platonist, so i think they're not literally real like how a chair is real.
>>16553979Nothing. You’re saying garbage pseud nonsense. Natural numbers are canonically constructed from the empty set via an iterative procedure called the von Neumann ordinals.>but what exactly makes "2 + 2= 4”the definition of 4. See Peano axioms. You could write 2 + 2 =elephant if you really wanted to. That’s not some deep mathematical truth but a convention.
>>16554047but what is a chair though? the chair is the information about the chair. there's no difference between a rock and a chair, with no humans around. we care about that approximate arrangement of atoms. because we draw use from it.outside of humans the chair doesn't exist, even if the structure itself persists. it's no use to anyone, it's just something along with everything else in here.thus, the chair is the information encoded in that arrangement, not the atoms themselves.
>>16554063>Rock no chair until Grog sit>Ergo, Grog no like 4>Checkmate, Ogg
>>165540904 exists only when you need it
>>16553979>I can sort of wrap my head around the laws of logic, for example, but what exactly makes "2 + 2= 4"?Logic makes it so. Math is logic applied to a set of axiomatic assumptions.>What makes numbers a "real" metaphysical truth?It's not.Both logics, and mathematic axioms, are empirical truths, in that they are true because our experiences so far reproduce these patterns. Math is an excerise in assumption that if these patterns persist what would be the conclusions.If the universe suddenly decides to go full Chaos and everything turns into a DMT trip, then everything we know thus far goes out the window.
>>16554051>You could write 2 + 2 =elephant if you really wanted toI don't think you understood what I'm asking. That's why I made the distinction of the symbols we use for numbers(1, 2, 3, 4, etc.) and the concept itself (numbers). Because otherwise, I'd just dismiss this whole thing and say it's just a construct of the mind when it clearly isn't. >>16554047I know they're not real like a chair is real. That's why I said metaphysical, which mathematics is considered to be.
>>16554110The concept of natural numbers itself can be understood via this iterative set procedure. It could be understood as as a semigroup (without the zero) or a monoid (with the zero). That’s how these things are thought about in mathematics and nobody does all this irrelevant wankery you’re engaging with in this thread. It’s simply a set with certain axiomatic properties on it.
>>16554109>Both logics, and mathematic axioms, are empirical truthsBut wouldn't those empirical truths be the way that you measure the things themselves and not the idea itself of a number? Meaning, saying that something is 100lbs is an objective truth but that the symbol of "100" and unit of "lbs" is the empirical part, which are man-made constructs.And can I ask how logic is an empirical truth? Sorry, it's kinda hard to put what I'm thinking into words. I'm probably way in over my head but I've been thinking about this a lot.
>>16554110>metaphysicalThat's a fancy word, what does it mean again? "Doesn't exist in reality?" Oh wow, it's just like the phrase "not real"
>>16554121Fair enough. It's not wankery, I'm just genuinely curious if there was an answer to this. I've heard the claim that mathematics is an objective truth and not mentally constructed like, say, a political ideology and wanted to see why it was considered so.
>>16554128I know that but never mind. I don't think I know how to write what I'm thinking into words kek I'm a pleb when it comes to math so sue me.
>>16554130>I've heard the claim that mathematics is an objective truth and not mentally constructedNone of this is of any relevance. Idk what you mean by an objective truth in this context and why something mentally constructed cannot be an objective truth. The syllogism “All unicorns’ dicks taste of cotton candy. Jack is a unicorn. Therefore Jack’s dick tastes of cotton candy” is true. May I see Jack the unicorn and his cotton-candy tasting dick?
>>16554133I was being sarcastic, but the answer really is that simple. Numbers aren't real in the same way a chair is. You could say the concepts of numbers are real, but that's true of literally anything you can think of (by definition)
>>16554135You want to suck off a unicorn?I think there's a board for that already...
>>16554122>But wouldn't those empirical truths be the way that you measure the things themselves and not the idea itself of a number?>Meaning, saying that something is 100lbs is an objective truth but that the symbol of "100" and unit of "lbs" is the empirical part, which are man-made constructs.Man-made constructs are not a problem empirically so long as the symbols exhibit a consistent ratio with what it is representing.For example, take "4 - 3 = 1". Empirically there are 4 apples on the table, you eat 3, and there is only 1 left. The "4 - 3 = 1" is a man-made construct that symbolizes this chain of empirical experience faithfully, proven by the fact there is only 1 apple left as per the "1" prediction of the mathematical operation.>And can I ask how logic is an empirical truth?Because the vast majority of our experiences follow logics, and can therefore, be predicted by logics. This fact makes it an empirical truth. Empirical is simply what is true by experience.And like I said, if hypothetically our universe goes haywire someday, logics then cease to be an empirical truth.That is the "how". As for "why" is logics an empirical truth. Why does our experiences/the universe thus far seem to follow logical patterns. That is the real philosophical question of the ages.
>>16554095Grog and wife invite Ogg and wife for dinosaur rib BBQ. How many rocks do they need so that everyone has a place to sit around the bigger rock?
>>16554138the chair is as real as 4. or as fake as 4. the chair is information used with atom arrangements. that's where we draw use from it.4 is useful in mathematics, it's real there. it's useful information that you apply in different ways, chair with atom arrangements, 4 in math.you could also make a 4 out of atoms, and it would be useful for decorative purposes, or to convey information. though its use as a material object is more abstract than the chair. unless you use the chair to also convey information, and not actually sit on it. ok shit's confusing
>>16554159>the chair is as real as 4literally turn it over
>>16553979>What makes numbers a "real" metaphysical truth?They're not "real". Human (and some animal) brains have just evolved to use some shortcuts in order to survive in the wild and "number" is just a label used by language using humans to refer to this system of shortcuts used by the brain.
>>16554145Thanks for the explanation, this made me understand it better. Screencapped for future reference. >>16554138Fair enough. Thanks
>>16554051No. The Vonn Neumann ordinals form a model of arithmetic (numbers), which the Peano axioms are an axiomatization of. You could pull another model out of your ass and if it satisfied the Peano axioms, then it’d be just as good for doing mathematics with, though it may have some extra behavior in some cases. There is no canonical model of arithmetic even in set theory, you can have many different ones that all behave the same.The axioms are a way to pin down the wanted behavior of arithmetic, and the model tells us that we got something that actually behaves the way we want it to (like arithmetic). But it is always a model "of an axiomatization of arithmetic/numbers", where "arithmetic/numbers" refers to an apriori somehow intuitively understood concept.In a similar way there is even no "true" canonical model of set theory itself, the Vonn Neumann universe is just one possible. And again it’s just formally pinning down the intuitive concept of set that already existed before.
>>16553979>I'm not a mathematician so maybe this is a dumb questionNo that's a good question anon. As far as I'm concerned numbers aren't 'real' as much as they are patterns that we use to predict things. Patterns are only provable by observation as there is nothing we can point to other than the fact that it works every time.
