As far as I know it’s an open question of how LLMs learn language. It’s clearly different from humans because they don’t have the same kind of learning-from-sense-experience process that we do to ground the meaning of words defined in terms of other words. It’s possible they don’t learn words the same way we do and the sense in which an LLM gives a word meaning is different from how a human does it, and maybe that happens in such a way as to be meaningful even if humans and LLMs can communicate and each experiences the other as producing words that they interpret as grounded in the way they ground meaning.
As for mathematical concepts made out of relationships to each other, the story from the human perspective is the same: grounded in experience with words that back up those other words. When we try to do mathematics where everything floats free, it’s possible, but those symbols seem to come to take on meaning only because they get grounded by how they are used, which, arguably, is what humans do, so maybe that’s what LLMs do, too, only they don’t have the point-at-a-thing-to-know-it operation, so their use of words have meaning grounded in use, but not use to describe sensory experience.
“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.
As far as I know it’s an open question of how LLMs learn language. It’s clearly different from humans because they don’t have the same kind of learning-from-sense-experience process that we do to ground the meaning of words defined in terms of other words. It’s possible they don’t learn words the same way we do and the sense in which an LLM gives a word meaning is different from how a human does it, and maybe that happens in such a way as to be meaningful even if humans and LLMs can communicate and each experiences the other as producing words that they interpret as grounded in the way they ground meaning.
As for mathematical concepts made out of relationships to each other, the story from the human perspective is the same: grounded in experience with words that back up those other words. When we try to do mathematics where everything floats free, it’s possible, but those symbols seem to come to take on meaning only because they get grounded by how they are used, which, arguably, is what humans do, so maybe that’s what LLMs do, too, only they don’t have the point-at-a-thing-to-know-it operation, so their use of words have meaning grounded in use, but not use to describe sensory experience.
“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.