Is your claim that because the mind is itself physical, any idea stored in a mind is necessarily reducible to something physical?
Indeed, the mind seems empirically to be something we experience due to the workings of visibly finite machine.
My mind contains a concept of 4 which is pretty dang useful, I can visualize 4 in so many ways and see it so often in reality without even trying to look for it. My mind’s concept of 1000 doesn’t suck, but is starting to look more like fluid measure (continuously variable) than discrete. With neocortical help I can improve my concept of 1000 around the edges, learning what 1000 dollars looks like, or a thousand grains of sand, or 1000 people in a stadium, but the amount of the conception of 1000 that my mind actually misses, when held side by side with my conception of 4 is, I think, very obvious.
I can think of 10 billion, which is more than the neurons in my brain, 100 billion which is more than the cells in my body (including the bacteria), 10 trillion (which is more than the neuronal interconnections in my brain) but all of these concepts are so fuzzy as to be honored primarily in the logarithm base 10. That is, virtually the only thing I know about 10 billion is that it is 10x as much as 1 billion, and similar such indirect conceptions.
My point in this is that if we think about how we actually think about numbers, the physicalism seems clear, including the limits in clarity we might expect as we exceed the number of parts of the physical system we are using for doing such thinking.
So how, then, do we come up with theorems about different kinds of infinities if our conceptions of these things are so finite? I believe it to be true (please correct me) that
1) the number of things we know about infinities is quite finite (maybe 1000 things at most?)
2) the proofs we use to know these finite number of things about infinities are also quite finite (comprising perhaps 10,000 pages, perhaps 100,000 to prove everything humans know about math, including everything we know about infinities)
PUNCHLINE:
Therefore it is very suggestive to think the physical substrate is a gigantic part of the story, and I am at a loss to see an opening for any serious contribution from a non-physical source.
Indeed, the mind seems empirically to be something we experience due to the workings of visibly finite machine.
My mind contains a concept of 4 which is pretty dang useful, I can visualize 4 in so many ways and see it so often in reality without even trying to look for it. My mind’s concept of 1000 doesn’t suck, but is starting to look more like fluid measure (continuously variable) than discrete. With neocortical help I can improve my concept of 1000 around the edges, learning what 1000 dollars looks like, or a thousand grains of sand, or 1000 people in a stadium, but the amount of the conception of 1000 that my mind actually misses, when held side by side with my conception of 4 is, I think, very obvious.
I can think of 10 billion, which is more than the neurons in my brain, 100 billion which is more than the cells in my body (including the bacteria), 10 trillion (which is more than the neuronal interconnections in my brain) but all of these concepts are so fuzzy as to be honored primarily in the logarithm base 10. That is, virtually the only thing I know about 10 billion is that it is 10x as much as 1 billion, and similar such indirect conceptions.
My point in this is that if we think about how we actually think about numbers, the physicalism seems clear, including the limits in clarity we might expect as we exceed the number of parts of the physical system we are using for doing such thinking.
So how, then, do we come up with theorems about different kinds of infinities if our conceptions of these things are so finite? I believe it to be true (please correct me) that 1) the number of things we know about infinities is quite finite (maybe 1000 things at most?) 2) the proofs we use to know these finite number of things about infinities are also quite finite (comprising perhaps 10,000 pages, perhaps 100,000 to prove everything humans know about math, including everything we know about infinities)
PUNCHLINE: Therefore it is very suggestive to think the physical substrate is a gigantic part of the story, and I am at a loss to see an opening for any serious contribution from a non-physical source.