by AmagicalFishy » Mon Oct 06, 2014 11:47 am
lahvak wrote:What you probably wanted to say is "for some m".
Oh, whoops—my mistake! I did not catch that, haha.
I've never heard of the sand heap in that paradox having an infinite number of grains, though; is that something I've just been missing? The reason the assumption-statement would be true (whether it be for a sand heap or a party) is because of the lack of definition for either. If one defined a party as "A gathering of 40 people," then removing a single person from a 40-person party would stop it from being a party (but then there'd be no Sorite's Paradox in the first place).
The paradox a bit more intuitive when one considers a heap of sand, but the same kind of definition can resolve it. Surely, removing a grain of sand from a heap of 1,000,000,000,000 grains does not make it
not a heap. And, similarly, removing one more grain of sand does not.
But, if we defined a "heap" as 999,999,999,998 grains or more, then removing a third grain of sand would make it not a heap.
Once you definitively define (!) things, there isn't much of a paradox.
[quote="lahvak"]What you probably wanted to say is "for [b]some m[/b]".[/quote]
Oh, whoops—my mistake! I did not catch that, haha.
I've never heard of the sand heap in that paradox having an infinite number of grains, though; is that something I've just been missing? The reason the assumption-statement would be true (whether it be for a sand heap or a party) is because of the lack of definition for either. If one defined a party as "A gathering of 40 people," then removing a single person from a 40-person party would stop it from being a party (but then there'd be no Sorite's Paradox in the first place).
The paradox a bit more intuitive when one considers a heap of sand, but the same kind of definition can resolve it. Surely, removing a grain of sand from a heap of 1,000,000,000,000 grains does not make it [i]not[/i] a heap. And, similarly, removing one more grain of sand does not. [i]But[/i], if we defined a "heap" as 999,999,999,998 grains or more, then removing a third grain of sand would make it not a heap.
Once you definitively define (!) things, there isn't much of a paradox.