Let's say 200 years ago it was discovered that gold has the atomic number 79.
My claim: possibility is conceivability without known defeaters.
201 years ago it was possible (because it was conceivable) that gold had any atomic number except for the ones which they'd already mapped (hydrogen=1, helium=2 were known defeaters against gold being 1 or 2). Note: and they may have known of some upper bound of stability which it couldn't be bigger than. So it may have been possible for the atomic number to be greater than 2 but less that (e.g.) 250.
Today it is not possible that gold has any atomic number other than 79 because the notion of any other weight is defeated by the evidence we've collected. Today's child may think it is possible that gold could have any atomic weight, but the child's claim would be incorrect relative to what today's educated people know. Also, the well educated adult from 201 years ago's claim is incorrect relative to today's knowledge, but relative to their knowledge 201 year ago, it was correct.
Similarly, we can safely assume that many of our current claims about possible states of affairs will be false relative to some future level of knowledge. However, today they are perfectly assertable/true/acceptable. Frankly, I'd think in this view, possibility claims are only ever assertable, never true (although 'true' is an easy shorthand, just like how scientific theories and the existence of their entities are 'true').
Robust views of possibility are not needed to explain why we make statements about possibility. Possibility statements are certainly useful, given our lack of knowledge, need for personal accountability, and sometimes just unwillingness to perform the required calculation, so I wouldn't suggest we stop using them.
Possibility is thus either epistemic or instrumental and therefore isn't required in our metaphysics.
Kripke's claim: no.
Explain.
- Jason Christie
Thursday, September 6, 2007
Wednesday, September 5, 2007
Wormy Lumps
Two of Lewis' Five Objections:
Trans-World Glue
(found on pages 49-50 in Weatherson's “Stages, Worms, Slices and Lumps”, and 218 of Lewis' Possible Worlds)
“The general worry here is determining which stages are part of a particular worm and/or lump. That is, the worry is about how the worm or lump is held together. There are two ways in which this seems more problematic for lumps than for worm. First, the various parts of a worm are held together by a causal dependence of some parts on others. But since worlds are causally isolated, this cannot be the way that worms are held together. Secondly, to the extent that we need a similarity relation on top of the causal relation for worms, it is the similarity of one part to the nearby parts. Because there is no one-dimensional ordering of modal space matching the ordering of temporal space, the relevant similarities will have to be “a matter of direct similarity between stages.” (Lewis 1986a: 218).” (49)
Run-down of the above argument in two pieces:
A.)
(1)If the worm / lump theory is true, then the various parts of a worm are held together by a causal dependence of some parts on others.
(2)If the various parts of a worm are held together by a causal dependence of some parts on others, then worlds must not be causally isolated.
(3)So, if the worm / lump theory is true, then worlds must not be causally isolated.
(4)Worlds are causally isolated.
(5)Therefore, the worm / lump theory is not true.
(1) p → q premise (1)
(2) q → ~r premise (2)
(3) p → ~r sub-conclusion (1)-(2) HS
(4) ~~r → ~p (3) CONTRA
(5) r → ~p (4) DN
(6) r premise (4)
(7) ~p conclusion (5)-(6) MP
(N.B. Yes, I know there are two extra steps in the inference argument when reconstructed. I put in contraposition and double negation in there as extra steps to make everything explicit.)
B.)
(1)If the worm / lump theory is true, then the various parts of a worm are held together by both a causal dependence of some parts on others and a direct similarity relation between the stages or worms.
(2)If the various parts of a worm are held together by both a causal dependence of some parts on others and a direct similarity relation between the stages or worms, then there is a one-dimensional ordering of modal space matching the ordering of temporal space.
(3)So, if the worm / lump theory is true, then there is a one-dimensional ordering of modal space matching the ordering of temporal space.
(4)There is no one-dimensional ordering of modal space matching the ordering of temporal space.
(5)So, the worm / lump theory is not true.
(1) p → (q & r) premise (1)
(2) (q & r) → s premise (2)
(3) p → s (1)-(2) HS
(4) ~s premise (4)
(5) ~p (3)-(4) MT
Now here is the Lewis version of the argument from Possible Worlds:
“(1) The temporal parts of an ordinary thing that perdures through time are united as much by relations of causal dependence as by qualitative similarity. In fact, both work together: the reason the thing changes only gradually, for the most part, is that the way it is at any time depends causally on the way it was at the time just before, and this dependence is by and large conservative. However, there can be no trans-world causation to unite counterparts. Their unification into trans-world individual can only be by similarity.
(2) To the extent that unification by similarity does enter into perdurance through time, what matters is not so much the long-range similarity between separated stages, but rather the linkage of separated stages by many steps of short-range similarity between close stages in a one-dimensional ordering. Change is mostly gradual, but not much limited overall. There is no such one-dimensional ordering given in the modal case. So any path is as good as any other; and what's more, in logical space anything that can happen does. So linkage by a chain of short steps is too easy: it will take us more or less from anywhere to anywhere. Therefore it must be disregarded; the unification of trans-world individuals must be a matter of direct similarity between stages.”( L 218)
Here's my difficulty. After the first couple of readings of Weatherson it seemed that his rendition of Lewis' argument was reasonably faithful to Lewis. But, now after reading it over again a few times, I'm not so sure it is. The reason being is that the argument presented causes problems for any wormy theory, which is Lewis' theory as well. Which means Lewis has a hard time denying any of the premises above, as they are writen. Bad. Lewis forwards these as arguments that cause greater difficulties for lumps, then for worm theories such as his own. Something needs to be added that will capture the difference between Weatherson's lumps and Lewis' worm. Hopefully, I'm not completely wrong here, but the something should be that Lewis can chose between the counterpart or mereological components of his view. Whereas Weatherson doesn't accept counterparts (it's just the lump, even if the lump includes what Lewis would refer to as a counterpart of x), so he cannot divide as finely as Lewis can in his response. Which as far as I can tell is what is needed for Lewis to show that there are greater difficulties for the lump view as opposed to the worm view.
Anyhow tell me what ya' think. And yeah, tell me what needs to be clarified and further explicated.
Trans-World Glue
(found on pages 49-50 in Weatherson's “Stages, Worms, Slices and Lumps”, and 218 of Lewis' Possible Worlds)
“The general worry here is determining which stages are part of a particular worm and/or lump. That is, the worry is about how the worm or lump is held together. There are two ways in which this seems more problematic for lumps than for worm. First, the various parts of a worm are held together by a causal dependence of some parts on others. But since worlds are causally isolated, this cannot be the way that worms are held together. Secondly, to the extent that we need a similarity relation on top of the causal relation for worms, it is the similarity of one part to the nearby parts. Because there is no one-dimensional ordering of modal space matching the ordering of temporal space, the relevant similarities will have to be “a matter of direct similarity between stages.” (Lewis 1986a: 218).” (49)
Run-down of the above argument in two pieces:
A.)
(1)If the worm / lump theory is true, then the various parts of a worm are held together by a causal dependence of some parts on others.
(2)If the various parts of a worm are held together by a causal dependence of some parts on others, then worlds must not be causally isolated.
(3)So, if the worm / lump theory is true, then worlds must not be causally isolated.
(4)Worlds are causally isolated.
(5)Therefore, the worm / lump theory is not true.
(1) p → q premise (1)
(2) q → ~r premise (2)
(3) p → ~r sub-conclusion (1)-(2) HS
(4) ~~r → ~p (3) CONTRA
(5) r → ~p (4) DN
(6) r premise (4)
(7) ~p conclusion (5)-(6) MP
(N.B. Yes, I know there are two extra steps in the inference argument when reconstructed. I put in contraposition and double negation in there as extra steps to make everything explicit.)
B.)
(1)If the worm / lump theory is true, then the various parts of a worm are held together by both a causal dependence of some parts on others and a direct similarity relation between the stages or worms.
(2)If the various parts of a worm are held together by both a causal dependence of some parts on others and a direct similarity relation between the stages or worms, then there is a one-dimensional ordering of modal space matching the ordering of temporal space.
(3)So, if the worm / lump theory is true, then there is a one-dimensional ordering of modal space matching the ordering of temporal space.
(4)There is no one-dimensional ordering of modal space matching the ordering of temporal space.
(5)So, the worm / lump theory is not true.
(1) p → (q & r) premise (1)
(2) (q & r) → s premise (2)
(3) p → s (1)-(2) HS
(4) ~s premise (4)
(5) ~p (3)-(4) MT
Now here is the Lewis version of the argument from Possible Worlds:
“(1) The temporal parts of an ordinary thing that perdures through time are united as much by relations of causal dependence as by qualitative similarity. In fact, both work together: the reason the thing changes only gradually, for the most part, is that the way it is at any time depends causally on the way it was at the time just before, and this dependence is by and large conservative. However, there can be no trans-world causation to unite counterparts. Their unification into trans-world individual can only be by similarity.
(2) To the extent that unification by similarity does enter into perdurance through time, what matters is not so much the long-range similarity between separated stages, but rather the linkage of separated stages by many steps of short-range similarity between close stages in a one-dimensional ordering. Change is mostly gradual, but not much limited overall. There is no such one-dimensional ordering given in the modal case. So any path is as good as any other; and what's more, in logical space anything that can happen does. So linkage by a chain of short steps is too easy: it will take us more or less from anywhere to anywhere. Therefore it must be disregarded; the unification of trans-world individuals must be a matter of direct similarity between stages.”( L 218)
Here's my difficulty. After the first couple of readings of Weatherson it seemed that his rendition of Lewis' argument was reasonably faithful to Lewis. But, now after reading it over again a few times, I'm not so sure it is. The reason being is that the argument presented causes problems for any wormy theory, which is Lewis' theory as well. Which means Lewis has a hard time denying any of the premises above, as they are writen. Bad. Lewis forwards these as arguments that cause greater difficulties for lumps, then for worm theories such as his own. Something needs to be added that will capture the difference between Weatherson's lumps and Lewis' worm. Hopefully, I'm not completely wrong here, but the something should be that Lewis can chose between the counterpart or mereological components of his view. Whereas Weatherson doesn't accept counterparts (it's just the lump, even if the lump includes what Lewis would refer to as a counterpart of x), so he cannot divide as finely as Lewis can in his response. Which as far as I can tell is what is needed for Lewis to show that there are greater difficulties for the lump view as opposed to the worm view.
Anyhow tell me what ya' think. And yeah, tell me what needs to be clarified and further explicated.
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