I think you’re objecting to 2. I think you’re using a loose definition of “conceivable,” meaning no contradiction obvious to the speaker. I agree that’s not relevant. The relevant notion of “conceivable” is not conceivable by a particular human but more like conceivable by a super smart ideal person who’s thought about it for a long time and made all possible deductions.
1. doesn’t just follow from some humans’ intuitions: it needs argument.
Sure but then this begs the question since I’ve never met a super smart ideal person who’s thought about it for a long time and made all possible deductions. So then using that definition of “conceivable”, 1) is false (or at least undetermined).
we can make progress by thinking about it and making arguments.
I mean real progress is via proof and things leading up to a proof right? I’m not discounting mathematical intuition here but the ~entirety of the game comes from the correct formalisms/proofs, which is a very different notion of “thinking.”
Put in a different way, mathematics (at least ideally, in the abstract) is ~mind-independent.
Do you think ideal reasoning is well-defined? In the limit I feel like you run into classic problems like anti-induction, daemons, and all sorts of other issues that I assume people outside of our community also think about. Is there a particularly concrete definition philosophers like Chalmers use?
I think the argument is
I think you’re objecting to 2. I think you’re using a loose definition of “conceivable,” meaning no contradiction obvious to the speaker. I agree that’s not relevant. The relevant notion of “conceivable” is not conceivable by a particular human but more like conceivable by a super smart ideal person who’s thought about it for a long time and made all possible deductions.
1. doesn’t just follow from some humans’ intuitions: it needs argument.
Sure but then this begs the question since I’ve never met a super smart ideal person who’s thought about it for a long time and made all possible deductions. So then using that definition of “conceivable”, 1) is false (or at least undetermined).
No, it’s like the irrationality of pi or the Riemann hypothesis: not super obvious and we can make progress by thinking about it and making arguments.
I mean real progress is via proof and things leading up to a proof right? I’m not discounting mathematical intuition here but the ~entirety of the game comes from the correct formalisms/proofs, which is a very different notion of “thinking.”
Put in a different way, mathematics (at least ideally, in the abstract) is ~mind-independent.
Yeah, any relevant notion of conceivability is surely independent of particular minds
Do you think ideal reasoning is well-defined? In the limit I feel like you run into classic problems like anti-induction, daemons, and all sorts of other issues that I assume people outside of our community also think about. Is there a particularly concrete definition philosophers like Chalmers use?