Will that exclude your ‘vague shape’ example, and probably your ‘proof’ example?
It would exclude the vague shape example but I think it fails for the proof example.
Your reasoning suggests that if X is false, it would be impossible for me to imagine someone proving X. I think that is contrary to what most people mean when they say they can imagine something.
It’s not clear what your reasoning implies when X is true. Either
I cannot imagine someone proving X unless I can imagine all the steps in the proof
I can imagine someone proving X as long as X is true, since having a proof would be a logical possibility as long as X is true
1) is also contrary to what most people think of as imagining. 2) would mean that it is possible me to not know whether or not I am imagining something. (I imagine someone proving X and I don’t know if X is true. 2) means that if X is true I’m “really imagining” it and that if X is false, I am not.)
Your reasoning suggests that if X is false, it would be impossible for me to imagine someone proving X. I think that is contrary to what most people mean when they say they can imagine something.
Well, say I argue that it’s impossible to write a story about a bat. It seems like it should be unconvincing for you to say ‘But I can imagine someone writing a story about a bat...see, I’m imagining Tom, who’s just written a story about a bat.’ Instead, you’d need to imagine the story itself. I don’t intend to talk about the nature of the imagination here, only to say that as a rule, showing that something is logically possible by way of imagining it requires that it have enough logical granularity to answer the challenge.
So I don’t doubt that you could imagine someone proving that E-triangles have more than 180 internal degrees, but I am saying that not all imaginings are contenders in an argument about logical possibility. Only those ones which have sufficient logical granularity do.
I would understand “I can imagine...” in such a context to mean that it doesn’t contain flaws that are basic enough to prevent me from coming up with a mental picture or short description. Not that it doesn’t contain any flaws at all. It wouldn’t make sense to have “I can imagine X” mean “there are no flaws in X”—that would make “I can imagine X” equivalent to just asserting X.
The issue isn’t flaws or flawlessness. In my bat example, you could perfectly imagine Tom sitting in an easy chair with a glass of scotch saying to himself, ‘I’m glad I wrote that story about the bat’. But that wouldn’t help. I never said it’s impossible for Tom to sit in a chair and say that, I said that it was impossible to write a story about a bat.
The issue isn’t logical detail simpliciter, but logical detail relative to the purported impossibility. In the triangle case, you have to imagine, not Tom sitting in his chair thinking ‘I’m glad I proved that E-triangles have more than 180 internal degrees’ (no one could deny that that is possible) but rather the figure itself. It can be otherwise as vague and flawed as you like, so long as the relevant bits are there. Very likely, imagining the proof in the relevant way would require producing it.
And you are asserting something, you’re asserting the possibility of something in virtue of the fact that it is in some sense actual. To say that something is logically impossible is to say that it can’t exist anywhere, ever, not even in a fantasy. To imagine up that possibility is to make it sufficiently real to refute the claim of possibility, but only if you imagine, and thus make real, the precise thing being claimed to be impossible.
It would exclude the vague shape example but I think it fails for the proof example.
Your reasoning suggests that if X is false, it would be impossible for me to imagine someone proving X. I think that is contrary to what most people mean when they say they can imagine something.
It’s not clear what your reasoning implies when X is true. Either
I cannot imagine someone proving X unless I can imagine all the steps in the proof
I can imagine someone proving X as long as X is true, since having a proof would be a logical possibility as long as X is true
1) is also contrary to what most people think of as imagining. 2) would mean that it is possible me to not know whether or not I am imagining something. (I imagine someone proving X and I don’t know if X is true. 2) means that if X is true I’m “really imagining” it and that if X is false, I am not.)
Well, say I argue that it’s impossible to write a story about a bat. It seems like it should be unconvincing for you to say ‘But I can imagine someone writing a story about a bat...see, I’m imagining Tom, who’s just written a story about a bat.’ Instead, you’d need to imagine the story itself. I don’t intend to talk about the nature of the imagination here, only to say that as a rule, showing that something is logically possible by way of imagining it requires that it have enough logical granularity to answer the challenge.
So I don’t doubt that you could imagine someone proving that E-triangles have more than 180 internal degrees, but I am saying that not all imaginings are contenders in an argument about logical possibility. Only those ones which have sufficient logical granularity do.
I would understand “I can imagine...” in such a context to mean that it doesn’t contain flaws that are basic enough to prevent me from coming up with a mental picture or short description. Not that it doesn’t contain any flaws at all. It wouldn’t make sense to have “I can imagine X” mean “there are no flaws in X”—that would make “I can imagine X” equivalent to just asserting X.
The issue isn’t flaws or flawlessness. In my bat example, you could perfectly imagine Tom sitting in an easy chair with a glass of scotch saying to himself, ‘I’m glad I wrote that story about the bat’. But that wouldn’t help. I never said it’s impossible for Tom to sit in a chair and say that, I said that it was impossible to write a story about a bat.
The issue isn’t logical detail simpliciter, but logical detail relative to the purported impossibility. In the triangle case, you have to imagine, not Tom sitting in his chair thinking ‘I’m glad I proved that E-triangles have more than 180 internal degrees’ (no one could deny that that is possible) but rather the figure itself. It can be otherwise as vague and flawed as you like, so long as the relevant bits are there. Very likely, imagining the proof in the relevant way would require producing it.
And you are asserting something, you’re asserting the possibility of something in virtue of the fact that it is in some sense actual. To say that something is logically impossible is to say that it can’t exist anywhere, ever, not even in a fantasy. To imagine up that possibility is to make it sufficiently real to refute the claim of possibility, but only if you imagine, and thus make real, the precise thing being claimed to be impossible.