“those symbols seem to come to take on meaning only because they get grounded by how they are used,” I would argue that they don’t need to be applied to anything other than pure mathematics in order to take on meaning. Therefore they are not grounded in empiricism, even if our understanding of them tends to be related to it.
If they are being applied to pure mathematics they are being used to do mathematics. Math, in an important sense, doesn’t exist when it’s not being done.
“Math, in an important sense, doesn’t exist when it’s not being done.” Can you justify this claim? What is the important sense? Would this claim not imply that the existence of mathematics is in principle dependent on one’s velocity because of special relativity? Do you think the same is true of logic? Are you a mereological nihilist? Can unconscious beings do mathematics? Sorry for all these questions, please don’t feel obliged to answer them all, but I am concerned that the belief that ‘Mathematics isn’t real other than as a human activity/mental activity’ is being propagated without being aptly defined!
Math exists in the map, not the territory. Math is a map to make sense what we experience (I phrase it this way to avoid making excess metaphysical commitments about the nature of what’s experienced). It’s an abstraction of symbols, and it’s useful to the extent it accurately models and predict what we experience. Modeling is an active task. When there’s no mind, there’s no modeling happen, and hence no math. There may well still be things happening that could be modeled by math and you could argue that the abstractions of math are latent, but they don’t meaningfully exist, as far as we know, when we’re not mathing.
“you could argue that the abstractions of math are latent” This is what almost anyone arguing that mathematics has an objective existence means by mathematics. “but they don’t meaningfully exist, as far as we know, when we’re not mathing.” I think this is clearly false; the process which you distinguish from these abstractions earlier in this comment clearly doesn’t exist when it isn’t being carried out, but the ‘latent abstractions’ are defined in a completely timeless way, so it seems wrong to apply the same reasoning to them.
What does it even mean for an abstraction not to exist? I can understand what it means to say that a particular object doesn’t exist in the sense of not being instantiated, and I can understand what it means to say that, for example, a rational number whose square is 3 doesn’t exist as an abstract platonic entity because it is a contradiction in terms, but it doesn’t seem coherent to say that 2 doesn’t exist (when it isn’t being considered. Of course one observer’s perception of it might not exist when they aren’t perceiving it, but this is not 2 itself.). What I mean by Platonic existence in this context is that there is a well-defined answer to the question of whether or not it follows from a system of axioms. Not whether or not someone has ever derived it from those axioms, or even conceived of the axioms themselves. Do you accept that there is a distinction between those questions?
I think I want to repeat my question about whether unconscious entities can do mathematics; can they?
If abstractions don’t exist, what explains the fact when we resume ‘mathing’, they continue to describe reality in a way which is consistent? If your answer involves logic, then presumably that logic which connects the two instances of a mathematician considering a theorem together does, itself , exist in the intervening time (or transcend time). At the very least, it’s dependent on the causal structure of spacetime rather than on any one observer’s notion of simultaneity.
“those symbols seem to come to take on meaning only because they get grounded by how they are used,” I would argue that they don’t need to be applied to anything other than pure mathematics in order to take on meaning. Therefore they are not grounded in empiricism, even if our understanding of them tends to be related to it.
If they are being applied to pure mathematics they are being used to do mathematics. Math, in an important sense, doesn’t exist when it’s not being done.
“Math, in an important sense, doesn’t exist when it’s not being done.” Can you justify this claim? What is the important sense? Would this claim not imply that the existence of mathematics is in principle dependent on one’s velocity because of special relativity? Do you think the same is true of logic? Are you a mereological nihilist? Can unconscious beings do mathematics? Sorry for all these questions, please don’t feel obliged to answer them all, but I am concerned that the belief that ‘Mathematics isn’t real other than as a human activity/mental activity’ is being propagated without being aptly defined!
Math exists in the map, not the territory. Math is a map to make sense what we experience (I phrase it this way to avoid making excess metaphysical commitments about the nature of what’s experienced). It’s an abstraction of symbols, and it’s useful to the extent it accurately models and predict what we experience. Modeling is an active task. When there’s no mind, there’s no modeling happen, and hence no math. There may well still be things happening that could be modeled by math and you could argue that the abstractions of math are latent, but they don’t meaningfully exist, as far as we know, when we’re not mathing.
“you could argue that the abstractions of math are latent” This is what almost anyone arguing that mathematics has an objective existence means by mathematics. “but they don’t meaningfully exist, as far as we know, when we’re not mathing.” I think this is clearly false; the process which you distinguish from these abstractions earlier in this comment clearly doesn’t exist when it isn’t being carried out, but the ‘latent abstractions’ are defined in a completely timeless way, so it seems wrong to apply the same reasoning to them.
What does it even mean for an abstraction not to exist? I can understand what it means to say that a particular object doesn’t exist in the sense of not being instantiated, and I can understand what it means to say that, for example, a rational number whose square is 3 doesn’t exist as an abstract platonic entity because it is a contradiction in terms, but it doesn’t seem coherent to say that 2 doesn’t exist (when it isn’t being considered. Of course one observer’s perception of it might not exist when they aren’t perceiving it, but this is not 2 itself.). What I mean by Platonic existence in this context is that there is a well-defined answer to the question of whether or not it follows from a system of axioms. Not whether or not someone has ever derived it from those axioms, or even conceived of the axioms themselves. Do you accept that there is a distinction between those questions?
I think I want to repeat my question about whether unconscious entities can do mathematics; can they?
If abstractions don’t exist, what explains the fact when we resume ‘mathing’, they continue to describe reality in a way which is consistent? If your answer involves logic, then presumably that logic which connects the two instances of a mathematician considering a theorem together does, itself , exist in the intervening time (or transcend time). At the very least, it’s dependent on the causal structure of spacetime rather than on any one observer’s notion of simultaneity.