one way to think about this is that if you're saying that in a world without concrete entities there would also be no sets, then you (arguably) need some way of distinguishing between "the set of all sets" and "the set of all sets not members of themselves". If you're a Platonist, this is simple, because you just say that there existed an abstract, non-concrete entity called "the set of all sets", and there did not exist such an entity called "the set of all sets not members of themselves".
-----Original Message----- From: PEN-L list [mailto:[EMAIL PROTECTED] Behalf Of Devine, James Sent: 15 October 2004 03:08 To: [EMAIL PROTECTED] Subject: Re: Dialectics/Phil of Math Daniel Davies wrote:>>> I don't think this would be right. For example, if there were no concrete entities, there would still be an abstract entity called "the set of all concrete entities", and you could make true or false statements about it (like "it's an empty set"). If you were a Platonist.<<< I answered: >> if there were no concrete entities, I couldn't make statements at all, of either the true or false variety.<< JKS writes: >So? That doesn't mean the statements you could make if you existed wouldn't be true or false.< Assuming that JKS isn't engaged in willful misunderstanding, I guess my prose is really, really, bad. What I said is that if there were no concrete entities, I couldn't make statements at all. Because I _couldn't_ exist without violating the assumption that "there are no concrete entities." JKS continues: > Even when there wasn't anybody, say in the first few seconds of the big bang and for several billion years thereafter, the proposition ... "No conscious life exists" was true.< but in that case, there _were_ concrete entities (the monoblock that's exploding and then its pieces). JKS: >All the propositions that could ever be exist, though of course only an infinutesmal fraction of them will ever be said or thought. ....< propositions are mental states. How can propositions exist without minds? Now we _can_ say that (after the Big Bang, at least), some propositions that we _now_ think about were empirically true. I'd bet that "E = m c squared" fit empirical reality before Einstein thought it up -- and before sentient beings arose that were able to think about such matters. But saying that "a proposition we now posit was true" is different from saying "the proposition _existed_." Similarly, saying that 2 + 2 = 4 applied before sentient beings developed mathematical principles is different from saying that mathematical principles exist independent of our minds. (It's a mistake to confuse our consciousness of something for that something.) Among other things, it's quite possible that our mathematical principles turn out to be wrong in some sense (or at least incomplete). Our mathematical principles do not correspond to the abstract nature of empirical reality _exactly_ because we don't (and can't) know the world exactly. (By the way, even simple math depends on assumptions (just as the number of planets orbiting the sun depends on assumptions). If you take a piece of chalk and break it in half, you suddenly have two pieces of chalk. But it's the same chalk! so 1 = 2. ) JKS:>There, Ian, I'm really scary -- I am not only realistic about maths, I'm realistic about propositions! ...< JKS, I'd say that you heed a very specific kind of realism, idealist realism (Platonism), rather than realism in general. Jim Devine > >> > I wrote: > I would guess that abstract "entities" don't exist > separate from concrete entities. Rather, they are > characteristics of the latter. > > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
