Let me add that, here on Earth, we have the Pirahas of the Amazon rainforest who don't have any use for natural numbers, not even the number 1, nor of the existential or universal quantifiers (which Hume, I think, argued were required for grounding the practice of counting). — Pierre-Normand
Breifly, on this - Do you know if this is something that is in Daniel Everett's discussion of the Piraha language? — StreetlightX
M is the Platonic world of math. The problem, though, is that this world is essentially full of junk. The vast majority of it is simply useless, and of no interest to anyone whatsoever. — StreetlightX
The fluid intelligence diffused over the Jupiter-like planet, could have developed mathematics without ever thinking about natural numbers. — StreetlightX
The most general definition of mathematics I know is that it is a study of structures/relations. — litewave
Arguably, we reason the way we do because the world is certain way for us to reason about it. — Marchesk
but the recognition that the world is a certain way for us to reason about — Pierre-Normand
Why would it only be a certain way for us? Do we really think that evolution or general relativity is a certain way for us, as opposed to being a certain way for the universe? — Marchesk
So his argument is that the Platonic world of math doesn't exist because it is... uninteresting? :lol: — litewave
Sure, but what sorts of things are structures and relations? Do they exist in themselves rather like intelligible forms in Platonic heaven? If you assume that they are universals that exist by themselves, quite independently from the constitutive roles of our practices of reasoning and discussing about them, then, in that case, you are begging the question in favor of mathematical Platonism. — Pierre-Normand
My point was there are reasons to think the structures and relations we use math to model exist in the world independent of us, since they led to us existing. — Marchesk
Relations are objects that hold between other objects (those other objects may be relations or non-relations). Relations are inseparable from the objects between which they hold. — litewave
Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
As long as there are any objects in the external reality, there are also relations between them, in the external reality. Relations and the objects between which they hold are inseparable. — litewave
Of course, the reality of an abstraction would only depend on its utility to us if the abstraction were not independently real to begin with. — Pneumenon
But anyway, the thrust of the argument is: if we took the results of all possible axiomatic systems, agglomerated them into one giant object, then granted that object independent existence - what would it look like? It would contain all kinds of bizarre crap, navigating through this world you'd hardly ever find an axiomatic system which resembled anything like our own. — fdrake
So his argument is that the Platonic world of math doesn't exist because it is... uninteresting? — litewave
There are other foundations of mathematics which are currently in use. — fdrake
in category theory, the category Set is a subcategory of the category of relations, — fdrake
Lots of irrealists about math make this argument. "Well, it's not useful, so these abstractions aren't real." Of course, the reality of an abstraction would only depend on its utility to us if the abstraction were not independently real to begin with. — Pneumenon
But anyway, the thrust of the argument is: if we took the results of all possible axiomatic systems, agglomerated them into one giant object, then granted that object independent existence - what would it look like? It would contain all kinds of bizarre crap, navigating through this world you'd hardly ever find an axiomatic system which resembled anything like our own. — fdrake
In set theory, all relations are defined as sets. — litewave
Yes, most of it might not be beautiful or useful but we are talking about metaphysics, which I don't think depends on subjective notions of beauty or usefulness. — litewave
th. The main thrust is simply that most mathematical objects aren't worthy of study, — fdrake
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