At least for geometrical forms, the abstractions may be intrinsic to the mind, even if they don’t exist outside it.
In The Man Who Mistook His Wife for a Hat, there’s a description of a man who lost the ability to visually recognize ordinary objects, though he could still see. The one description suggest that he just saw geometry.
In Crashing Through, which is about a man who lost his sight at age 3 and recovered it in middle age and which has a lot about recovered vision and the amount of processing it takes to make sense of what you see, there’s mention of some people who are very disappointed when they recover their sight—they’re constantly comparing the world to an idea of it which is perfectly clean and geometrical.
In The Man Who Mistook His Wife for a Hat, there’s a description of a man who lost the ability to visually recognize ordinary objects, though he could still see. The one description suggest that he just saw geometry.
I’m a little confused: did is visual field lose focus such that, instead of seeing the details on objects and their imperfections he actually just saw idealized geometric figures?
One problem with this as evidence of the possibility that geometric forms could exist only in the human mind is that it presumably only applies to a rather narrow class of geometric forms. It would be weird if the geometric forms we have innate access to had a different ontological status from forms that can’t be instantiated in the human mind: like a 1000-sided polygon or something in 4+ dimensions.
What I meant was that, if people have simple geometric forms built deep into their minds, then it would be tempting to conclude that math has an objective eternal existence because it feels that way.
In any case, I found the actual quote, and I’ve very uncertain that it suggests what I thought it did. It seems as though the man was at least as sensitive to simple topology as geometry, However, people don’t romanticize topology.
I had stopped at a florist on my way to his apartment and bought myself an extravagant red rose for my buttonhole. Now I removed this and handed it to him. He took it like a botanist or morphologist given a specimen, not like person given a flower.
“About six inches in length,’ he commented. ‘A convoluted red form with a linear green attachment.’
‘Yes,’ I said encouragingly, ‘and what do you think it is, Dr P.?’
‘Not easy to say.’ He seemed perplexed. ‘It lacks the simple symmetry of the Platonic solids, although it may have a higher symmetry of its own… I think this could be an inflorescence or flower.’
‘Could be?’ I queried.
‘Could be,’ he confirmed.
‘Smell it,’ I suggested, and he again looked somewhat puzzled, as if I had asked him to smell a higher symmetry. But he complied courteously, and took it to his nose. Now, suddenly, he came to life.
‘Beautiful!’ he exclaimed. ‘An early rose. What a heavenly smell!’ He started to hum ‘Die Rose, die Lillie…’ Reality, it seemed, might by conveyed by smell, not by sight.
I tried one final test. It was still a cold day, in early spring, and I had thrown my coat and gloves on the sofa.
‘What is this?’ I asked, holding up a glove.
‘May I examine it?’ he asked, and, taking it from me, he proceeded to examine it as he had examined the geometrical shapes.
‘A continuous surface,’ he announced at last, ‘infolded on itself. It appears to have’ – he hesitated – ‘five outpouchings, if this is the word.’
It’s a wonderful extract in any case. It is fascinating to see someone describing the world without anything more than the phenomenology of his surroundings. It is interesting that the concepts he had access to were mathematical and geometric- that these concepts involve a part of the brain separate from the part that involves more complex and obviously learned concepts like shoe, glove, and flower does seem important to keep in mind when evaluating the evidence on this issue. You’re right that this fact could lead to us positing a false ontological difference… though of course there are those who will say “gloveness” and “flowerness” are abstract objects as well. The fact that these concepts are processed in different parts of the brain could also be taken as evidence for the distinction in that different evolutionary processes generated these two kinds of concepts. I’m not sure how to interpret this. Good for keeping in mind though.
In The Man Who Mistook His Wife for a Hat, there’s a description of a man who lost the ability to visually recognize ordinary objects, though he could still see. The one description suggest that he just saw geometry.
Googling it looks like maybe he just had visual agnosia? Which doesn’t really entail what you’re saying. That would mean that he could see normally but just couldn’t recognize figures as objects with names and functions. Or are you saying the details of objects disappeared and all that was left were the basic geometric forms?
On problem with this as evidence of the possibility that geometric forms could exist only in the human mind is that it presumably only applies to a rather narrow class of geometric forms. It would be weird if the geometric forms we have innate access to had a different ontological status from forms that can’t be instantiated in the human mind: like a 1000-sided polygon or something in 4+ dimensions.
At least for geometrical forms, the abstractions may be intrinsic to the mind, even if they don’t exist outside it.
In The Man Who Mistook His Wife for a Hat, there’s a description of a man who lost the ability to visually recognize ordinary objects, though he could still see. The one description suggest that he just saw geometry.
In Crashing Through, which is about a man who lost his sight at age 3 and recovered it in middle age and which has a lot about recovered vision and the amount of processing it takes to make sense of what you see, there’s mention of some people who are very disappointed when they recover their sight—they’re constantly comparing the world to an idea of it which is perfectly clean and geometrical.
I’m a little confused: did is visual field lose focus such that, instead of seeing the details on objects and their imperfections he actually just saw idealized geometric figures?
One problem with this as evidence of the possibility that geometric forms could exist only in the human mind is that it presumably only applies to a rather narrow class of geometric forms. It would be weird if the geometric forms we have innate access to had a different ontological status from forms that can’t be instantiated in the human mind: like a 1000-sided polygon or something in 4+ dimensions.
What I meant was that, if people have simple geometric forms built deep into their minds, then it would be tempting to conclude that math has an objective eternal existence because it feels that way.
In any case, I found the actual quote, and I’ve very uncertain that it suggests what I thought it did. It seems as though the man was at least as sensitive to simple topology as geometry, However, people don’t romanticize topology.
Here’s the passage, which I had not remembered as well as I thought:
It’s a wonderful extract in any case. It is fascinating to see someone describing the world without anything more than the phenomenology of his surroundings. It is interesting that the concepts he had access to were mathematical and geometric- that these concepts involve a part of the brain separate from the part that involves more complex and obviously learned concepts like shoe, glove, and flower does seem important to keep in mind when evaluating the evidence on this issue. You’re right that this fact could lead to us positing a false ontological difference… though of course there are those who will say “gloveness” and “flowerness” are abstract objects as well. The fact that these concepts are processed in different parts of the brain could also be taken as evidence for the distinction in that different evolutionary processes generated these two kinds of concepts. I’m not sure how to interpret this. Good for keeping in mind though.
Googling it looks like maybe he just had visual agnosia? Which doesn’t really entail what you’re saying. That would mean that he could see normally but just couldn’t recognize figures as objects with names and functions. Or are you saying the details of objects disappeared and all that was left were the basic geometric forms?
On problem with this as evidence of the possibility that geometric forms could exist only in the human mind is that it presumably only applies to a rather narrow class of geometric forms. It would be weird if the geometric forms we have innate access to had a different ontological status from forms that can’t be instantiated in the human mind: like a 1000-sided polygon or something in 4+ dimensions.