POSSIBLE WORLDS

There Is No Metaphysical Possibility

2007-09-06T12:57:00.001-07:00

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

Wormy Lumps

2007-09-05T09:20:00.000-07:00

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.

Kit Fine, "The Problem of Possibilia"

2007-08-26T18:36:00.000-07:00

I'd like to try and standardize Fine's argument against "proxy reduction."

Fine is concerned with certain sorts of (actualist) attempts to make sense of possibilist discourse. One option for the actualist is to make sense of possibilist discourse by employing “proxies,” in something like the following manner:

“With each possible x is associated another entity x’, acceptable to the actualist, and any statement Φ(a,b,…) about the possibles a,b,…is then understood in terms of a corresponding statement Φ’(a’,b’,…) about the associated entities a’,b’,…”

According to Fine the most natural way of thinking about the relationship between the entities in the first set and those in the second is in terms of the identity relation. And if that is the assumption, he argues, then the following argument can be presented against any form of actualism employing this form of proxy reduction:

Where Mx: x has the (modal) property of possibly-being-the-world
Rxy: x ‘goes proxy’ for y
w: some possible world w
r: any actualistically acceptable proxy: i.e: a maximal consistent set of propositions or states of affairs; a maximal structural property; or a ‘way a world could be.’

(1) □∀x ∀y [(x = y)-->(Fx-->Fy)]
(2) □∀x ∀y [~(Fx-->Fy)-->~(x=y)] (1) CONTRA
(3) □∀x ∀y [~(~Fx v Fy)-->~(x=y)] (2) IMPL
(4) □∀x ∀y [(Fx & ~Fy)--> ~ (x=y)] (3) DEM & DN
(5) ∀x ∀y [~(x = y)--> ~Rxy]
(6) Mw
(7) ~Mr
(8) Mw & ~Mr (5&6)
(9) ~(w=r) (4,7)
(10)~(r=w) (9)
(11) ~Rrw (5,10)

This seems to be faithful to the English argument given by Fine. I *believe* it is valid as presented. If anybody would comment and let me know if and where I am going off-course with this, it would be appreciated.

the end of last reading group

2007-08-15T13:16:00.000-07:00

Soams gives an objection to himself starting at the end of page 22.
Consider an agent A, the actual world @, and two worlds W and W*.
Suppose further that A has certain beliefs at W about W* (that is to say, were W instantiated then A would have beliefs about W*). So, W must have some defining propositions that result in belief ascriptions to A. The problem gets tricky when we try and apply knowledge ascriptions. I'll give the important sentences right here (with our modifications).
12) p is true at w*
13) A believes truely that p is true at w*
15) if (conditions for A's knowledge of S) then A knows that S
14) A knows that p is true at w*

The worry is that there may be no necessary&sufficient conditions for knowledge. If that's right, then if A is able to know S at W, then "A knows S" must be a defining proposition of W. If it were not, "A knows S" would be derivable from the defining propositions of W, and that would require conditions for knowledge. But, if "A knows S" must be a defining proposition, there are problems. Consider:

8c) A knows that: ~Saul philosophizes & it is true at @ that Saul philosophizes

If (8c) is true at W, we can infer (8b)
8b) ~ Saul philosophizes & actually Saul philosophizes
But we know apriori the truth of (8a)
8a) Saul philosophizes iff actually Saul philosophizes

So, we can know a-priori that W isn't instantiated. This is bad. Note that Soames's original strategy won't work, since if (8c) is a defining proposition of W we can take it by the indexical mode of presentation if we like. For simplicity, consider W a tiny world with only A and non-philosophical Saul, and all A does is know that (8c), and Saul does nothing.

Here's a reminder of EP1 and EP2.
EP1: A world state w is epistemically possible iff w is a way the world can coherently be conceived to be, which it cannot be known apriori not to be
EP2: A world-state w is epistemically possible iff w is a way the world can coherently be conceived to be, and one cannot know apriori that w is not a way the world could be (or have been)

The objection depends upon two principles:
1) ~E sufficient and necessary conditions for knowledge
2) EP1

If we adopt EP2 then W is still epistemically possible.

Grim & Plantinga on Cantorian arguments

2007-08-08T16:07:00.000-07:00

There's something on the back of Chelsey's folder that says we can't quantify over all the truths... that seems bad. Plantinga & Grim have a pretty lengthy discussion of it, which I'll try and outline here. First, the arguments. I'll give 3 forms of the cantorian argument, one involving sets, one involving properties, and one involving propositions. I'll give what I take to be the most brutal version of each.

sets:

1) E a set T of all truths (assume for reductio)
2) If (1) then (3)
3) T has a power set PT
4) For each member p* in PT there is a truth
5) If (4) then (6)
6) There are more truths than members of T
7) If (6) then (5)
8) T is not the set of all truths
9) If (8) then (10)
10) ~(1)

Fairly innocuous. One merely has to say that even if the truths do not form a set we can still quantify over them. Grim says that the only notion of quantification we have is in terms of sets, but assents that it's not a crucial point. There are other possible ways of quantifying. Quick support for (4): for any given t1, either "t1 is in p*" or "t1 is not in p*" is a truth.

Properties:

to avoid controversial use of "mappings" (which derive from set theory) I'll give Grim's mappings via relations:

"A relation R gives us a mapping from those things that are P1 that is one-to-one and onto those things that are P2 just in case (here we merely add a conjunct):
AxAy[[P1x & P1y & Ez(P2z & Rxz & Ryz)] -> x = y]
& Ax[P1x -> EyAz(P2z & Rxz <-> z = y)]
& Ay[P2y -> Ex(P1x & Rxy)].(3)" -Grim

I'll suplement that with an ONTO relation:
A relation R' gives a mapping from things that are P1 ONTO things that are P2 iff
Ax(P2x->Ey(P1y&yR'x))

Note that if P1 does not map ONTO P2, then P2 must have a strictly larger extension then P1

the argument:

1) E a property T which applies to all and only truths (call the things in T's extension t's)
2) If (1) then (3)
3) E a one-one relation R from t's to truths
4) E a property S0 which applies to nothing and a series of properties S1,S2,... which apply to one or more t's
5) There are at least as many truths as there are S properties (each S property has a corresponding truth)
6) (3)&(5)
7) If (6) then (8)
8) There are at least as many t's as there are S properties
9) if (8) then (10)
10) There is a relation from the t's ONTO the S properties
11) for any relation R' from the t's onto S properties, E an S property (D) which is the property of being a t such that tR'S* and ~S*t
12) if (11) then (13)
13) ~(10)
14) (10)&~(10)
15) ~(1)

propositions:

Consider a proposition P which is about all propositions. Call the propositions which P is about p's.

1) E a proposition P which is about all propositions.
2) if (1) then (3)
3) E a one-one relations between the p's and all the propositions
4) E a proposition not about any proposition, and some propositions S1,S2,... about one or more p's
5) if (4)&(3) then (6)
6) there are at least as many p's as S's
7) if (6) then (8)
8) there is a relation from p's ONTO the S's
9) for any relation R' from p's ONTO S's, there is an S that is about those p's such that pR'x -> x is not about p
10) if (9) then (11)
11) ~(8)
12) (8)&~(8)
13) ~(1)

That's 3 cantorian arguments. The first is to the effect that there is no set of all truths. The second concluded that there is no property had by all truths. The third, that there is no proposition which is about all propositions. In the second two arguments, all set-theoretic notions have been put in terms of properties and relations. Thus, showing that even if the problems lie in set theory, they carry over to common philosophical notions that we'd want to keep around. That in itself busts Plantinga's first rebuttle, but fear not, he doesn't fail us.

Plantinga's first strategy is to deny the "diagonal premise" in each argument (except the first, which lacks one). The diagonal premises are these:
in the first argument:
11) for any relation R' from the t's onto S properties, E an S property (D) which is the property of being a t such that tR'S* -> ~S*t
in the second argument:
9) for any relation R' from p's ONTO S's, there is an S that is about those p's such that pR'x -> x is not about p
These are perhaps the easies to deny on face value. After all, they involve a rather cryptic property (or proposition), and when we deny that there is such it seems like we're denying a rather obtuse philosophical entity. Not so says Grim. Grim asserts that each diagonal premise is built from fundamental principles, and to deny the diagonal entities one would have to deny one of the principles that allowed them to be built. For instance, from what I can tell, all that's needed for the diagonal premise in the property case would be a principle like (P1):
P1) For any set of conditions, there is a property whose extension is those entities which satisfy those conditions
I doubt one would want to give up (P1). Granted lots of properties generated by such a principle will have an empty extension, but that's allowed for in the argument.
Plantinga notes that each premise is less disasterous to reject than the conclusion. Therefore, reject a premise, any premise... we NEED to! To bolster this point, he notes that the conclusion is impossible to state. Take the conclusion of the proposition argument:
CP) there is no proposition about all propositions
That's about all propositions!!!! We don't merely get a bad conclusion out of these arguments, we get lunacy! Therefore, reject a premise for the love of Bhudda! In addition, many of the premises are themselves illegally universal by the conclusion. So if we accept the conclusion we have to reject premises ANYWAY. So just reject the premises, keep the conclusion, and count our losses.
I agree with Plantinga here. We can either toss out everything, or toss out (P1) and it's mates. That's contradiction baby. But perhaps something can be salvaged if we have a suitable replacement for (P1). I suggest something like (P2):
(P2) For any set of conditions which is not illegally self-referential, there is a property whose extension is those entities which satisfy those conditions
I know not what is involved in legal self-reference, but it does seem like (D) is self-referential in a strange way. Consider this property:
Q) Ax, Qx iff ~Qx
Is that a genuine property? Or is it illegally self-refferential? This is the liar paradox all over again. So if we declare liar paradoxes illegal for generating properties, would (D) be illegal? How would this work for the diagonal premise in the proposition argument?

I need to mull this over now, but hopefully with this explication of the debate everyone can share in the frustration!

a time argument

2007-08-03T14:11:00.000-07:00

Here's an argument that was recently presented to me...

Assume 4 dimensionalism. Consider the time-worm Dyck. Let A be the individual corresponding to Dyck from conception to death. Let B be the individual corresponding to Dyck from conception to 5 minutes before his death. Here's the argument:

1) []~(A=B)
2) Dyck could have died 5 minutes before he actually died
3) if (2) then (4)
4) <>(A and B share all their parts)
5) If (4) then (6)
6) <>(A=B)
7) ~[]~(A=B)
8) (1)&(7) contradiction

I'm not sure I understand the argument quite right, because it seems like one could easily deny (5) (if they're any sort of hecceatist). Also it seems like you could run a spatial argument in a similar way. Let A be Dyck, and B be the parts of Dyck vital to survival. Let (2) be "everything not vital to Dyck's survival could have been amputated". Anyway, I'm confused as to how this is supposed to work, I'm sure I don't have the best formulation of the argument.

Objection from Spatiotemporal Analogy

2007-07-31T22:31:00.000-07:00

I'm thinking of doing something or other with this objection, so if anyone has anything to add please do!

as always:
<> is the possibility daimond
[] is the necessity box
A is the universal quantifier
E is the existential quantifier

Let (ST) be a second order predicate that has all and only spatiotemporal relations in its extension. Given that there are multiple spatiotemporal relations, a natural definition of worldmateism is as follows:

defn': Two things x and y are worldmates iff ER((ST)R&xRy)

Too avoid sticky issues, lets assume all worlds discussed are chaotic (no causal relations involved). This isn't cheating since causal relations aren't necessary for spatiotemporal relations.

The complaint is that Lewis now owes us some necessary and sufficient conditions for being a spatiotemporal relation. I'll argue that he can't, in principle give one.
Consider two relations that must count as spatiotemporal relations: being spacially related, and being temporally related. These can be conceptually divided. Moreso, being related to something in a world by either means is sufficient for being in that world. For isntance, if there's two spacially isolated worlds, but each moment in time in one is the very same moment in time in the other, they would be one world on Lewis's view. Indeed, he gives these kind of compromises when he argues that the impossibility of island universes is not so bad.

So if we propose any necessary conditions for being a spatiotemporal relation, both space and time must have them. Maybe some philosophers of time will help sort this out. What I will argue is that all the features that space and time have in common do not jointly make sufficient conditions for being a spatiotemporal relation. If the sum of all necessary conditions do not make for sufficient conditions, there is not set of necessary&sufficient conditions. If a condition is added so the the set is sufficient for being spatiotemporal, the resulting set would not be necessary since either space or time (or both) does not have that condition. Thus, necessary and sufficient conditions can not be given, and Lewis's fallback definition of worldmate gainst the status of "bogus".

So, space and time are conceptually different. One may say qualitatively different. By this I mean there's no basic unexpressable quality they have in common (there's no way to describe time to a timeless person in terms of space, or space to an intelligent volumeless spirit in terms of time). Barring that, there are a few similarities that may be candidates for necessary conditions of spatiotemporallness.
note: when "R" contains no ' after it, it denotes a general relation "sharing a space" if you will. R', R'' denote specific relations within the general one ex. "being 3 feet to the left of", "being 5 seconds after".
1) conditional reflexivity: Ax(Ey(xRy)->xRx)
2) symetry: AxAy(xRy->yRx)
3) transitivity: AxAyAz((xRy&yRz)->xRz)
4) occupancy: Ax(Ey(xR'y&xR''y&xR'''y...)->Az((~z=x)->~(zR'y&zR''y...)))
5) absolutism: AR'ExEy(xR'y)
6) capacity: Ax(Ey(xRy)->Px)

I assume the first 3 are self explanitory. Occupancy simply states that if one "point" in the "world" is properly situated, no other point can share that space. That is to say, if a world has n many spatiotemporal relation, and x bears a specific relation to y with respect to each of them, no z may bear the exact same relations to y. Absolutism would state that for any specific spatiotemporal relation (ex. being 3 cm to the left of), you'll find a couple points that meet it. Capacity requires some explanation. I'll define Px as "x can be assigned a value". I mean this only to say some points can be considered "occupied" while others can be considered "unoccupied". I wanted to leave it open whether a point could be more or less occupied on a scale. I figure, those are the important similarities between space&time (although there are more I'm sure). Which of those merit being necessary conditions for being a spatiotemporal relation? Well, for arguments sake let's suppose all of them are (that will only make my conclusion stronger). Now I simply need to ask, is there any relations that satisfies these which is not a spatiotemporal relation? Of course there is! There's lots! Consider the relation (xRy iff x and y both hold world records). Say x holds a world record if for some value, x holds more of that value than anything else. The universe would probably get the world record for biggest individual, perhaps Carl Friedrich Gauss would hold the world record for greatest mathematical ability. To produce the sub-relations R', R'' etc. you could just arrange an arbitrary ordering of the world record holders, and xR'y iff y succeeds x in the ordering.

So, finaly, I can set up an argument:

1) Space and time must both meet all necessary conditions for being a spatiotemporal relation
2) If (1) then (3)
3) If there are necessary&sufficient conditions for being a spatiotemporal relation, space and time must have them as well
4) ~(space and time jointly have sufficient conditions for being a spatiotemporal relation)
5) if (4) then (6)
6) ~(consequent of 3)
7) ~(there are necessary & sufficient conditions for being a spatiotemporal relation)

if (7) is right, Lewis can't say much about what constitutes a world aside from "gather the stuff I want to be worldmates together, and call that a world". We need more than that!!!

8) if(7) then (9)
9) ~(there are necessary&sufficient conditions for two things being worldmates)

it's 4:30 AM, so I'll add some sarcasm here

10) if (9) then (11)
11) only magic can bind worldmates together! (that's kind of a sweet thought)

I wanted to argue that Lewis get the wrong result as far as saying what's a world-mate of what, but I've argued that he doesn't get any result. Well, I'll stop here. Please comment, especially time folks.

Assignment Part 3

2007-07-28T11:46:00.000-07:00

Sorry I know this is long, and repeats a number of things, but I wanted to address both Dan and Adam's comments point by point.

Both Dan and Adam noted that my reconstruction of Salmon's irrelevance objection, as it is presented in Divers (8.1), was invalid. Which I do agree with. So first, I reconstructed the argument, which appears as follows:

Irrelevance objection from Salmon (via Divers) made valid:

If an ordinary possibility sentence of modal English is about a counterpart (i.e. facts about an individual y having a certain feature F, at possible world, w), then that counterpart is relevant to the truth of a sentence of ordinary modal English which is about an individual x, which shares the same feature F, as y, at another world.
Nothing is a counterpart of anything else in its world (P5).
Anything in a world is a counterpart of itself (P6).
(2) & (3)
If (4), then the relevant modal truth about an individual, x, is its own counterpart in its own world (i.e. not another counterpart, y, having a certain feature F, at possible world, w).
So, the relevant modal truth about an individual, x, is its own counterpart in its own world (i.e. not another counterpart, y, having a certain feature F, at possible world, w).
Therefore, it is not the case that an ordinary possibility sentence of modal English is about a counterpart (i.e. facts about an individual y having a certain feature F, at possible world, w).

I'll first deal with Dan's, then Adam's objections to my reconstruction of the irrelevance argument presented above, then rewrite the above argument to better reflect their suggestions.
Dan on Chelsey, on Divers, on Salmon:

As Dan notes in his evaluation, there are two significant changes that he would make to the irrelevance argument which he reconstructs as follows:

If ordinary possibility sentences of modal English are about counterparts (i.e. facts about an individual y having a certain feature F, at possible world W) then entailment relations that hold in CT will hold in ordinary modal English.
(P5)
(P6)
(2)&(3)
If (4) then there is some entailment relation that holds in CT but not in ordinary modal English.
There is some entailment relation that holds in CT but not in ordinary modal English.
It is not the case that ordinary modal sentences are about counterparts.

First, Dan argues that Salmon would not accept premise (5) and (6) in the above argument. There are two ways this can be taken, either Dan thinks that I am being unfaithful in reconstructing the argument presented in Divers, or my reconstruction is faithful to Divers but Divers is unfaithful to Salmon. In either case he thinks (5) and (6) should be changed in order to deliver a better argument. His justification for this is as follows:

“I do not think that Salmon would accept premise (5). Salmon’s argument involves a dis-analogy between the semantics of GR and that of English. That is, he asserts that “there may have been a Humphrey counterpart who won” entails “Humphrey might have won” in GR, but it does not in English. This lack of analogy is meant to support the claim that concerns about our counterparts are different from, and irrelevant to, concerns about our modal properties. Salmon would agree that premise (5) holds for certain individuals & propositions meant to produce counter-examples, but I do not think he would have it be a fully general rule. He would reject (6) on the same grounds.”

Second, Dan suggests that (2) to (5) are superfluous:

“Indeed, the argument may be better without them. (P5) and (P6) need not be true for the argument to go through, they merely need to be true according to GR. If we hold them true simpliciter, then the argument entails things about counterparts. However, it’s best if an argument against counter part theory does not entail things about counterparts. So, simply put, the argument can be reconstructed like so:

9. If ordinary possibility sentences of modal English are about counterparts (i.e. facts about an individual y having a certain feature F, at possible world W) then entailment relations that hold in GR will hold in ordinary modal English.

10. There is some entailment relation that holds in GR but not in ordinary modal English

11. It is not the case that ordinary modal sentences are about counterparts.”

Here, Dan makes two particular points about the argument's construction which I will address in turn.

First, I think Dan is jumping the gun a bit with Salmon's argument. As it is presented in Divers, it is meant as an irrelevance objection, that is, counterparts are irrelevant to the truth of an ordinary possibility sentence of modal English. In other words, that counterparts are irrelevant, for certain purposes. As it is presented, it is not an argument against counterparts, it is simply to show that they suck in a particular way. So, incorporating counterparts by way of premises (2) to (5), that is to hold them true simpliciter is required. This may just be a preference on my part, but I think stripping Salmon's argument of premises (2) to (5) is to eliminate one of the awesome characteristics that it has as an argument type. Essentially what Salmon's irrelevance argument is saying to the genuine realist is this, okay fine I'll accept your counterpart theory, and even better I'll accept the identity fixing postulates that you give which accompany it, but even when I play your game by your rules, counterparts are still useless at doing what it is that you want them to do. To Dan's credit, I do believe that he is correct, in that this argument lends to the further argument against CT and GR. In which case, it would be best if the argument does not entail things about counterparts, but that would be an additional argument, which would require additional premises, and not that present in Divers as Salmon's irrelevance objection.

The second point is that for the reconstruction, (8) to (10), that Dan offers, he has essentially chosen to eliminate the premises (2) to (5) because they are plainly superfluous. But as he notes later, the justification for (9) will require invoking the postulates (P5) and (P6) when asserting which entailment relations hold under GR. So, I suppose (and Chris your input on this particular point would be appreciated), should the postulates (P5) and (P6) be written as explicit premises within the argument's reconstruction, or taken as the implicit justification for premise (9)? In either case they are still being used, as it were, by and in the argument. Personally, I would prefer to keep them as explicit premises. It seems only fair to have them as individual premises, so that if an objector to the argument wishes to deny either (for what it is worth denying either postulate, in the hopes of denying the conclusion, seems like an untenable and misguided way to object to this argument) they can do so.

Adam on Chelsey, on Divers, on Salmon:

Adam makes one main recommendation for the reconstruction of my Divers on Salmon (other then making it valid). He thinks a more faithful reconstruction would look something like this:

C: The non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English correctly represent our pre-theoretical modal intuitions.
R: The non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English are relevant to the modal truth of the individuals they are about.
M: An (object language) sentence of modal English about a counterpart of an individual a is intuitively weaker than a sentence of modal English about a itself.
U: The (CT) truth-conditions specified for a modal English sentence about a counterpart of an individual a logically entail the (CT) truth-conditions specified for a modal English sentence about a itself.

~C → ~R
M
M → (U → ~C)
(U → ~C) (2,3)
U
~C (4,5)
~R (1,6)

Adam argues that the conclusion, that it is therefore not the case that an ordinary possibility sentence of modal English is about a counterpart, in my reconstruction is unfaithful to that presented in Divers. In Adam's reconstruction the conclusion states that, it is not the case that the non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English are relevant to the modal truth of the individuals they are about. I both agree and disagree with Adam on this point (as is my usual m.o.). I agree that my previous reformulation does not quite capture faithfully the conclusion intended by the irrelevance argument. The problem does not lie with English not being about couterparts, which is the conclusion that my reconstruction delivers. But, I disagree that his reformulation is any better. For the argument to be faithful to one presented in Divers, it must be the case that the individuals (or counterparts) are doing the work. That is, that the roles expressed in the conclusion of his reconstruction need to be reversed and reformulated as such:

7. It is not the case that the modal truth of the individuals are relevant to the non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English, in which they are about.

Adam also suggests that the argument can be shortened to the following:

P: An ordinary sentence of modal English is about a counterpart.
Q: A counterpart is relevant to the truth of an ordinary modal English sentence.
R: Nothing is a counterpart of anything else in this world.
S: Anything in a world is a counterpart of itself.

I believe this could be shortened to the following and still remain valid:

R
S
(R&S)
(R&S) →~Q
~Q →~P
~P (1-3 HS)

I must admit, I'm a little confused here. Premises (1) to (3) cannot derive the conclusion in (6) using hypothetical syllogism. (4) and (5) can because they are conditionals. But, then the conclusion in (6) would read ~P → (R&S). Which is not the conclusion that is needed for the irrelevance argument. If I am mistaken here please let me know.

The other points that are brought up by Adam pertain to the fact that the argument as it is presented in Divers is not faithful to Salmon. I think he is correct in this analysis. Unfortunately, for the present purposes of this assignment I am unsure where my loyalties are supposed to lay. Am I supposed to reconstruct the argument as faithfully to Divers' text, or should I be going to the original source and be faithful to that presented by Salmon?

Sticking with the Divers text and taking the previously mentioned, new and hopefully more faithful conclusion, the irrelevance argument can be reformulated once again as follows:

Irrelevance objection from Salmon (via Divers) made valid:

If the modal truth of a counterpart (i.e. facts about an individual y having a certain feature F, at possible world, w) are relevant to the non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English, in which they are about, then that counterpart is relevant to the truth of a sentence of ordinary modal English which is about an individual x, which shares the same feature F, as y, at another world.
Nothing is a counterpart of anything else in its world (P5).
Anything in a world is a counterpart of itself (P6).
(2) & (3)
If (4), then it is not the case that that counterpart is relevant to the truth of a sentence of ordinary modal English which is about an individual x, which shares the same feature F, as y, at another world. (i.e. not another counterpart, y, having a certain feature F, at possible world, w).
So, it is not the case that that counterpart is relevant to the truth of a sentence of ordinary modal English which is about an individual x, which shares the same feature F, as y, at another world. (i.e. not another counterpart, y, having a certain feature F, at possible world, w).
Therefore, it is not the case that the modal truth of a counterpart (i.e. facts about an individual y having a certain feature F, at possible world, w) are relevant to the non-modal (metalinguistic) truth-conditions specified by (CT) for ordinary (object language) sentences of modal English, in which they are about.

Sorry for the wordiness, but hopefully it's v.f.a. (valid, faithful and awesome).

Assignment Part 1

2007-07-28T10:15:00.000-07:00

I'm going to post what I originally submitted (invalid warts and all) for the first part of the assignment here (sorry if it looks messy... blogger did not like the formatting from the word doc.), along with your recommendations as comments to this post. I hope y'all don't mind, but it does seem easier to blog these works in progress then e-mailing things back and forth.

So here is the first part:

“Lewis proposes that a world w may represent de re of an individual x (even when x is not part of w) that x has a certain feature F by w having as a part an individual y that is a suitable simulacrum – a counterpart – of x and which is F.” (Divers 122) So, if the facts about counterparts are relevant, then they are relevant to the modal truth about an individual.

Irrelevance objection from Salmon:

If an ordinary possibility sentence of modal English is about a counterpart (i.e. facts about an individual y having a certain feature F, at possible world, w), then that counterpart is relevant to the truth of a sentence of ordinary modal English which is about an individual x, which shares the same feature F, as y, at another world. [P → Q]
(P5) [R]
(P6) [S]
(2) & (3) [R & S (2), (3) CONJ]
If (2) & (3), then the relevant modal truth about an individual, x, is its own counterpart in its own world (i.e. not another counterpart, y, having a certain feature F, at possible world, w)[(R&S) → ~Q]
So, the relevant modal truth about an individual, x, is its own counterpart in its own world (i.e. not another counterpart, y, having a certain feature F, at possible world, w). [~Q (5), (4) MP]
Therefore, that counterpart is not relevant (irrelevant) to the modal truth about an individual, x. [~P (1), (6) MT]

Justifications:

(1) According to the counterpart-theoretic specifications for truth-conditions (CT-P) x is possibly F, just in case there is a world in which x has a (relevant) counterpart which is F. It is the counterpart’s connection in the left side of the conditional that figures in (i.e. is relevant) to part of the left side’s truth conditions, which is about the individual.
(2) Postulate (P5) of CT stipulates that: “nothing is a counterpart of anything else in this world” (Divers 124)
(3) Postulate (P6) of CT stipulates that: “anything in a world is a counterpart of itself” (Divers 124)
(4) Conjunction of premises (2) and (3).
(5) Because premises (2) and (3) fix identity as an intra-world counterpart relation, then the relevant modal truth about an individual, x, is its own counterpart in its own world. As Divers’ puts it loosely, x = y. So, the separation, and thereby the relevancy of y’s identity to that of x, is mute. This can be seen when considering the sentence examples of ordinary modal English (e.g. (1) and (2)) and their respective translations (e.g. (1*) and (2*)) in Divers pages 125-126.
Where the sentence:

(1) Humphrey might have won.

and, its translation:

(1*) ∃w[∃x[Pxw & Cxh & Vx]]

Is considered with respect to the sentence involving Humphrey’s counterpart:

(2) There might have been a Humphrey counterpart who won.

and, its translation:

(2*) ∃w[∃x[∃y[Pxw & Pyw &amp; Cyh & Cxy & Vx]]]

When the postulates (P5) and (P6) are taken into consideration, then as mentioned the identity of x = y, become fixed, and thus gives:

(1*) ∃w[∃x[Ixw & Cxh & Vx]]

as a valid translation for (2*). Notice that this translation is the same as that given to the sentence of (1) above.
(7) Which gives the conclusion, that the counterpart, y, is irrelevant to the truth of a sentence about an individual, x.

Argument Against Salmon's Objection (i.e. denying (P5) of CT):

If (P5) & (P6), then the relevant modal truth about an individual, x, is its own counterpart in its own world.
If (P5), then, if (P6), then the relevant modal truth about an individual, x, is its own counterpart in its own world.
But, it is not the case that if (P6), then the relevant modal truth about an individual, x, is its own counterpart in its own world.
So, it is not the case that (P5)

Justifications:
(1) See premises (2)-(5) of Salmon's objection above for justifications.
(2) Exportation from premise (1).
(3) It cannot be the case that (P6) alone gives the relevant modal truth about an individual, x, as being its own counterpart in its own world. The identity fixing axioms (P5) and (P6), can only do this in conjunction, not on their own.
(4) Therefore it is not the case that (P5). Which means that the argument from Salmon above starting with premise (4) cannot follow through.

Comment on "Counterparts and Actuality"

2007-07-27T14:29:00.000-07:00

This paper was posted a while back, here's the link:
http://www.princeton.edu/%7Efara/papers/counterparts.pdf
for this post:
<> is the possibility daimond
[] is the necessity box
A is the universal quantifier
E is the existential quantifier

Williamson and Fara argue that any modal theory needs an actuality operator to handle sentences like this:

(4) it might have been that everyone who is in fact rich was poor

Without an actuality operator, CT would translate it as follows:
(4*) <>Ax(Rx -> Px)
or
(4**) Ax(Rx -> <>Px)

(4*) says that possibly all rich people are poor. That's not a good translation of (4) because (4*) excludes the possibility of some people who are in fact poor being rich while (4) does not. (4**) is not a good translation because it asserts that each individual who is rich may have been poor. This is different from asserting that it could've been the case that they're all poor.

Williamson and Fara introduce the actuality operator to solve this problem:
for any sentence S:
ACT S is true at a world iff S is true at the actual world

This provides a correct translation of (4):
(4A) <>Ax(ACT(Rx) -> Px)

The problems arise when the question is raised of how this should be implemented into counterpart theory. W&F propose a few formulations:
(L1) ACT S(a)w is Ex(Ix@&Cxa&S@(x))
(L2) ACT S(a)w is Ax[(S@(x">Ix@&Cxa)->S@(x)]
These fail because they validate known contradictions. For instance, L1 translates
(12) <>Ex(ACT Fx iff ACT~Fx)
into
(13) ExEw(Ixw&[Ey(Iy@&Cyx&Fy)iffEy(Iy@&Cyx&~Fy)]).
(12) is inconsistent while (13) can be satisfied in certain models of CT. Bad translation. To see how (13) is satisfiable, just picture a situation in which one has more than one actual world counterpart. (L2) and the rest of W&F's proposals have the same drawback. They find, for each one, some logical contradiction that is translated into a satisfiable sentence.
W&F are very thorough, and ultimately correct (I think) about the formulations of the CT actuality operator they come up with.
My confusion is what stops CT from adopting a more neutral ACT operator that doesn't invoke counterparts? Consider:
(AD) ACT S(a)w iff Ex(Ix@&x=a&S(x))
(L1) & (L2) as well as the other suggestions in the paper try and make it so you can speak of non-actual individuals (that are counterparts of actual individuals) and say true things of how they actually are. Consider the hypothetical Humphrey at world w that didn't win. With the actuality operator (L1) you could truely say of him that he actually lost. That is:
(H) Humphrey(w) actually lost
This would come out false on (AD) translation:
(HAD) Ex(Ix@&x=h&L(x))
This may be seen as a drawback of (AD), but I don't see it as such. It's perfectly reasonable to say that the non-actual winner Humphrey actually won. That is to say, evaluated at this world, the proposition about non-actual Humpthrey to the effect that he won is true. Another worry may be that (H2) would get the wrong result.
(H2) Necessarily Humphrey actually lost.
(HAD) would translate that to:
(H2*) AwAx((Cxh&Ixw)->Ey(Iy@&y=x&L(y))
But (H2*) is false. So we get the right result again. This fits for Lewis's indexical account of "Actually". What about such sentences evaluated at other worlds? Surely at world w, all ordinary sentences involving the actuality operator shouldn't come at false! To this I'd answer that when evaluating a sentence at another world, substitute that world in for @. That's not ad-hoc, after all according to CT according to that world w IS the actual world.
I haven't checked (AD) thoroughly, but I believe the problems involving the other trials for an actuality operator were problems in invoking the counterpart relation. (AD) does not.

New Readings

2007-07-27T12:42:00.000-07:00

For the next meeting please read Scott Soames's "Actually". There should be enough overlap with views discussed in Divers for you to formulate objections to and questions about Soames's view. So please bring objections to and questions about Soames's view to the next meeting.

After Soames, I had previously proposed we read a paper by Kit Fine. But there's a brand new paper by Otavio Bueno and Edward Zalta, "A Defense of Actualist Realism", that is a direct response to Divers. So I think we should look at it before looking at Fine (and before we forget too much of Divers).

Then I think we should read Kit Fine's "The Problem of Possibilia".

Homework 3

2007-07-27T12:20:00.000-07:00

Here's the revised argument against GR. I've re-ordered the premises as to make it a valid IP. I've also added a new premise and new conclusion so that the addition of 013 makes it possible to object to a premise. A quick note about Adam's criticism. He claimed that the definition given of an alien natural property can be generalized as a definition for what it means for a natural property to be alien of a world. This is true. And if we were to generalize the definition, his criticism would be correct. However, for the purposes here I need not, and did not make this definition general. Given that "alien natural property" as defined here is Adam's "@ alien natural property", that criticism is avoided and no revision is required. However the criticism is relevant to the response I gave. I did invoke Adam's generalized definition when stating the principle 013. I didn't define what it means for a property to be "alien to a world". For the purposes of stating 013, let the definition be the same, except replace @ with w*.

Def’n:“An alien natural property is a natural property that is not instantiated by any individual in @, and is not analyzable as a conjunctive or structural property built up from constituents that are all instantiated by parts of @”Divers p.115 quoting Lewis (1986a: 91)Let’s assume that Lewis can give a good account of natural properties, since if he can’t that is an objection in and of itself. The objection can proceed as follows:
1) It’s possible for alien natural properties to be instantiated
2) If (4) then (5)
3) If (5) then (6)
4) Postulates O1 – O12 exhaustively represent reality (as required by GR to give a complete analysis of modal concepts). (assume for reductio)
5) No individuals (speaking un-restrictedly) instantiate alien natural properties
6) ~(1)
7) (1)&(6)
8) ~(4)
9) if (8) then (10)
10) GR does not give a complete account of modal concepts

In support of (1), we intuitively think it’s possible that there are ways things could have been that are different than ways things are on a fundamental level. That is, things could have been so different that Humean recombination cannot account for that difference. For instance, things could have been massless, colourless, shapeless, but still had properties we can’t conceive of. Alternately, the universe could have been Newtonian.In support of (2), postulates O1 – O12 postulate the actual world, and us. It then uses postulates O8-O10 and O12 to generate the rest of the worlds. Any individuals generated in this manner can’t be fundamentally different from actual individuals in the way previously described.In support of (3), according to GR P is possible iff P at some world. If no individual at any world instantiates natural property A, then A is impossible by the lights of GR. In support of (9), if the ontological componend of GR does not include all things we think are possible, then by CT not all things we think are possible are possible. If by GR's lights some pre-theoretic possibilities are impossible, then GR is does not give a complete account of possibility.
The most assailable principle is (9). A proponent of GR may argue that while 01-012 are inadequate it may be supplemented, and promise a suitable addition to the postulates O13 - On that may account for alien natural properties. Here’s a possible O13 that may account for alien properties:
O13: For any world w and for any number n, there exists a world w* such that w* has n number of instantiated natural properties that are alien to w AND w* has parts that instantiate every natural property in w.
O13 will guarantee that there is a plenitude of alien natural properties that are instantiated in other worlds. It’s also more defensible in the face of the argument in divers on p 118. That objection tries to set up a model which satisfies (GR) + (OAN), and then set up another model that also satisfies (GR) + (OAN) but fails to include all of the alien natural properties of the first model (thus saying GR + OAN is apt to lose out on some). That is more difficult with (GR) + (O13). Should you generate a w* with respect of @, such that it excludes some number of alien natural properties, O13 posits another world w** with properties alien to both w* and @ that may include them after all. O13 will posit a world that includes n alien natural properties as well as all the natural properties of @. It will in turn posit a world with all of those natural properties as well as other natural properties not yet accounted for, and iterate. Recombination (O12) guarantees that there are worlds with only alien properties, and different combinations of those properties. Note also that alien properties that only come in pairs (or triplets, or quadruplets etc.) can be generated using O13. While it’s still true that no particular alien property is guaranteed to be accounted for, none are explicitly un-accounted for. The drawback is that by O13, it’s impossible for a world to instantiate all of the natural properties. O12 would like there to be such a world, but the qualification “if there is a spacetime big enough to hold them all” would have to be used to say that this is an exception.Should that fail, the next most assailable principle is (3). One would need a good account of natural properties to ensure that O1-O12 don’t in fact capture them all. In other words, this objection may be a little premature

Homework V.3

2007-07-26T10:10:00.001-07:00

First of all, sorry to Dan for bumping down his new and excellent post. Here's my homework for the week:

Here is a revised version of the objection from alien natural properties. I believe I’ve incorporated the changes suggested by Dan and Chelsey (with respect to the original version of the objection I had presented). Here goes:

(1) There is at least one world in which there is an individual that instantiates an α-alien natural property.
(2) If there is at least one world in which there is an individual that instantiates an α-alien natural property, then there is an infinite sequence of α-alien instantiable natural properties.
(3) If there is an infinite sequence of α-alien instantiable natural properties, then it is not the case that the GR analysis of the modal concepts is complete.
(4) If it is not the case that the GR analysis of the modal concepts is complete, then it is not the case that the ontological component of GR (postulates O1-O11 and the principle of recombination) provides an accurate analysis of the modal concepts.
(5) It is not the case that the ontological component of GR (postulates O1-O11 and the principle of recombination) provides an accurate analysis of the modal concepts.(1-4)*

Divers provides a justification of the move from (1) above to the conditional in (2) with the following sub-argument. Let ‘L1’ designate the exhaustive list of actually instantiated natural properties.

(1a) L1 is the list of all the actually instantiated natural properties.

We have it pre-theoretically that, whatever natural properties are included in L1, it could have been the case that L1 contained one more natural property. In other words, (2a) and (3a):

(2a)(1a)-->by ‘alienation’ and recombination there exists a world W1 such that the individuals in W1 instantiate all the properties in L1, plus some natural property X1 not contained in L1. Call this list L2.
(3a)By ‘alienation’ and recombination there exists a world W1 such that the individuals in W1 instantiate all the properties in L1, plus some natural property X1 not contained in L1. Call this list L2.

The move from (1a)-(3a) above establishes (1) in the main argument. Next, since the (individuals in) the actual world could have instantiated L2 (instead of L1), we have:

(4a)(3a)-->the actual world could have instantiated all the properties in L2.
(5a)The actual world could have instantiated all the properties in L2.

However, if the actual world could have instantiated L2, then it is also the case that the actual world could have instantiated some new list of natural properties, distinct from (L1 and L2). In other words, reiteration of the move in (2a) will generate an infinite sequence of worlds containing more and more alien natural properties:

(6a)(5a)-->successive applications of alienation + the principle of recombination will generate an infinite sequence of worlds containing more and more alien natural properties.
(7a)Successive applications of alienation + the principle of recombination will generate an infinite sequence of worlds containing more and more alien natural properties.

And, if that’s right, then there exist infinitely many instantiable alien natural properties:

(8a)(7a)-->(9a)
(9a)There are infinitely many instantiable alien natural properties.

To justify (3) Divers argues that (i) the ontological postulates of GR are unable to generate a set of worlds such that an infinite sequence of α-alien natural properties are instantiated among individuals existing at those worlds and (ii) that completeness requires GR to provide a world to match all of the possibilities we intuitively think there are. And finally, Divers justifies (4) by arguing that, since completeness is one criterion of extensional accuracy, it follows that if GR does not deliver completeness, then it does not deliver an accurate analysis of the modal concepts.

I proposed that we conceive of the natural properties as tropes. This suggestion did not receive a response, so I will just restate it briefly. Please note that I don’t necessarily think this is a satisfying response to the problem, only that it seems perfectly consistent with what Lewis says on the topic of natural properties. For Lewis says the following:

I noted that one way to characterize natural properties was to help ourselves to Armstrong’s theory of universals. But in ‘Against Structural Universals’ I note that one part of that theory gives us trouble: the part about structural universals. Those are universals built up somehow- the problem is how?- out of simpler universals. I note that a similar theory of structural tropes-particular property instances- has no parallel problem; and, further, that accepting a sparse theory of tropes would be another good way to give ourselves the distinction between natural and gerrymandered properties.**

So: Lewis thinks that it is plausible to suppose that the natural properties are tropes. I suggested that the standard metaphysical account of the nature of tropes leads to the following two principles:

(T1)∀x {[Wx-->∃y (Ty & Iyx)] & ∀z (Tz & Izx)--> z = y}
(T2)∀x {[Wx -->∃y (Ty & Iyx)] & ∀z [(Wz & z ≠x)-->~Iyz]}

(where Wx is ‘x is a possible world’, Tx is ‘x is a class of natural-quality tropes’ and Ixy is ‘x is instantiated by y’).

And, if this is right, then the argument given by Divers in support of (2) is blocked, since the conditional in (2a) would be false. I think it would go something like this:

(1t) All and only the perfectly natural properties are tropes.
(2t) (1t)--> ~[(1a)-->(3a)]
(3t) ~[(1a)-->(3a)] (1t,2t)
(4t) ~(1a) v ~(3a) (3t)
(5t) ~ ~ (1a)
(6t) ~ (3a) (4t, 5t)

(5t) seems right if we think it is plausible to suppose that there is some sort of ideal list of the natural properties that are actually instantiated. So it seems like the above is one argument Lewis could give on behalf of GR. It doesn’t seem to be a happy one, but it would work. The view would appear to be one according to which extreme modal haecceitism is true, since this is a consequence of identifying the natural properties with tropes.

Alien Hecceatism

2007-07-25T20:28:00.001-07:00

I'd just like to recap here the debate that took place in class on teus between Chris & me. The spark was the following argument against linguistic ersatzism:
Consider and alien individual a, and another alien individual b. Consider two worlds that are qualitatively identical, but in w2 a is qualitatively identical to b in w1, and vice versa. The argument can proceed as follows:
1d) Our language (L) cannot distinguish between w1 and w2
2d) w1 and w2 represent to distinct possibilities
3d) (1)&(2)
4d) if (3) then (5)
5d) Linguistic ersatzism conflates some possibilities that should be distinct

After some deliberation, it was noted that a & b must be unnamable, else (1) does not hold.
I (with waving hands) wanted to deny (2). Chris gave a motivation for why (2) should be accepted:
(1) The property of being nameable is ontologically insignificant
(2) Were a and b nameable, then (2d) would hold
(3) (1)&(2)
(4) if (3) then (5)
(5) (2d)

I countered with this:

(6) If a is nameable then a is describable in terms of actual things
(7) being describably in terms of actual things is ontologically significant
(8) (6)&(7)
(9) if (8) then ~(1)
(10) ~(1)

Leaving aside the obvious issue of spelling out what it is to be describably in terms of actual things, or what ontological difference that's supposed to make, let's move on. Let's call things describable in terms of actuals "impure hypotheticals" and things not describable in terms of actuals "pure hypotheticals". So the handsom man resulting from the sperm that Adam came from and the egg that Chelsea came from (call him Chadam) would be an impure hypothetical. Gandalf the White from Tolken's fantasy would be a pure hypothetical. So my position could be called anti-hecceatism about pure hypotheticals.
Chris then posed a different argument:
Consider a purely descriptive world W that is complete in the appropriate ways and conforms to tolken's Lord of the Rings universe. Chris's argument could run like so:
(11) anti-hecceatism about pure hypotheticals
(12) if (1) then (3)
(13) W would be one possibility
(14) if (13) then (15)
(15) W is necessarily exactly one possibility
(16) Necessarily if W were actual W would be many possibilities
(17) if (15) then (18)
(18) necessarily W is not many possibilities
(19) Necessarily W is not actual (16, 18, necessary MT)

(19) is very bad if we want W to be a real possibility. I responded by denying (12). W is not one possibility because any actual individuals could play the individual roles in W, making for distinct possibilities. For instance, Chris could be qualitatively identical to Gandalf in W, or Chelsea could be.

I think I captured most of the main arguments for this issue. A couple motivations for anti-hecceatism about pure hypotheticals:
A) It seems like there's a difference between Chadam and Gandalf (just an intuition)
B) All accidental properties belonging to a pure hypothetical are stipulative. This is not true for impure hypotheticals (for instance, I need not stipulate that Chadam is male). This may support the intuition that there is little more to pure hypotheticals than their stipulated properties.

The Reasoner

2007-07-20T16:49:00.000-07:00

The Reasoner contains new, short articles of philosophical interest. Several in the new issue are relevant to modality.

Cantorian Arguments

2007-07-16T12:55:00.000-07:00

Divers is pretty slim on how Cantorian arguments are supposed to work. I thought this exchange between Grim and Plantinga might be helpful.

Propositions and Sets

2007-07-05T17:58:00.001-07:00

Today we mentioned some reasons for thinking that propositions are not reducible to set-like entities. The objection explicitly considered by Divers is one from Plantinga:

1. Some propositions have truth values and no sets have truth values.
2. If (1), then some propositions are not sets. (by Leibniz's Law)
3. If some propositions are not sets, then not all propositions are sets.
4. If not all propositions are sets, then propositions are not reducible to sets.
5. So if (1), then propositions are not reducible to sets. (2-4)
6. So propositions are not reducible to sets. (1,5)

Plantinga contends that (1) is obvious. Divers thinks it is not obvious. Let's concede the point to Divers unless someone can come up with another way to support (1).

Another objection, from Jeff King's SEP entry on structured propositions, is as follows:

7. If some sets are propositions, then some sets have truth values (modal properties, etc) and others do not.
8. If some sets have truth values and others do not, then there is an explanation of why this is the case.
9. So if some sets are propositions, then there is an explanation of why some sets have truth values and others do not. (7,8)
10. There is no explanation of why some sets have truth values and others do not.
11. So it's not the case that some sets are propositions. (7,10)

I think someone like Lewis can resist (10) with some plausibility. Here's a view that Lewis and some of his opponents, like Salmon and Soames, both seem to hold:

Propositions are pieces of information semantically encoded by well-formed declarative sentences. They are truth-apt objects of cognitive attitudes (like belief, etc).

This characterization serves to specify the role of propositions. Something is a proposition iff it's the best candidate for that role. If that turns out to be shoes or fish or whatever, then propositions may be identified with shoes, fish, whatever. Now Lewis holds that certain sets occupy this role. (For what it's worth, Salmon and Soames give their theories of propositions in set-theoretic terms but are not explicit about whether the set-theoretic entities are supposed to be propositions or if they merely represent them.) If he's right about that, then it seems he has a not implausible explanation of why (e.g.) some sets are true and others have no truth value. There's more that can be said about this objection, but I'll leave it at that for now.

King's second objection is a version of the Benacerraf problem. (Link requires JSTOR access.) It requires a bit of set-up. Consider sentence *:

* Brendan loves Adam

Suppose we held that propositions were ordered n-tuples. Consider the following ordered triples:

(i) bLa
(ii) aLb
(iii) Lab
(iv) Lba
(v) abL
(vi) baL

Furthermore, there are many ways to construct ordered n-tuples. For each way, there is a non-equivalent set that corresponds to each of (i)-(vi). Let's suppose there are only seven ways. Then there are 42 sets: each of (i)-(vi) constructed in each of the seven ways. Here's the objection:

12. If propositions are sets, then there is a unique most eligible candidate among the sets for being the proposition expressed by * in English.
13. There are (at least) 42 sets that are equally eligible candidates for being the proposition expressed by * in English.
14. If there are (at least) 42 sets that are equally eligible candidates for being the proposition expressed by * in English, then there is no unique most eligible candidate among the sets for being the proposition expressed by * in English.
15. So there is no unique most eligible candidate among the sets for being the proposition expressed by * in English. (13,14)
16. So it's not the case that propositions are sets. (12,15)

Carl offered a reason for denying (1): given a multiplicity of equally eligible candidates, a proponent of the "propositions are sets" view could hold that it's indeterminate which of the 42 sets is the proposition that Brendan loves Adam. One could add that picking any of the 42 to represent the information that Brendan loves Adam is harmless as long as one makes the appropriately uniform choices for representing other propositions. One could also hold that it's appropriate to talk about the proposition that Brendan loves Adam iff according to any legitimate way of eliminating the indeterminacy, there is only one candidate for the proposition.

Some thoughts:

A. The sharpenings would have to be done with care. Suppose one pursued the same tack for numbers. There may be admissible sharpenings for propositions according to which S is a proposition and admissible sharpenings for numbers according to which S is a number; 0, for instance. Then 0 would have a truth value and it would be possible to believe 0. That's no good. But it seems like it could be prevented by adding the relevant constraints on admissible sharpenings.

B. I worry on the indeterminacy proposal that it would be true that, were we to have decided on a different sharpening, then the proposition expressed by 'Brendan loves Adam' would have been the proposition expressed by 'Adam loves Brendan' (while all the facts about the English sentences 'Brendan loves Adam' and 'Adam loves Brendan' remain fixed). The counterfactual strikes me as false. There are probably ways around this too: there are similar views about vagueness according to which there are several admissible sharpenings for 'red' and 'orange' and some things that are red under one sharpening are orange on another, but under no sharpening are some things both red and orange. But note a lack of parallel: all of the set-theoretic candidates for being the proposition that Brendan loves Adam are the set-theoretic candidates for the proposition that Adam loves Brendan. In spite of the disanalogy, I confess that the objection does not strike me as especially serious.

C. It would be self-refuting for me to believe that there are no beliefs. On one usage of 'belief', the word refers to the objects of belief. On this understanding, 'I believe there are no beliefs' expresses a proposition that entails that I bear a relation to the proposition that there are no propositions. Contrast this with my (pretend) belief that there are no sets. This does not seem similarly self-refuting. But it would be on the "propositions are sets" view. This is the basis for a Leibniz's Law objection, but I think it's better than Plantinga's because it does not rest on the contention that it's just obvious that sets don't have truth-values. Divers will cry "hyperintensionality" here, but I don't buy it. The two beliefs really strike me as different in the way described.

D. There are cardinality problems for the view that propositions are sets. There are several ways to state these. Here's one. The proposition that absolutely everything is self-identical is (logically) true. But there is no ordered pair with absolutely everything as one member and the property of being self-identical as the other. That is because there is no set that has as a proper subset absolutely everything. That is because if sets are things, there are too many things for all of them to be a subset (even an improper subset) of a set. (Given any set, the set of all of its subsets has a strictly greater cardinality. So any candidate for being a set that has absolutely everything as a subset is such that there's a "bigger" set: the set of all of its subsets.) Furthermore, if there were a proposition that absolutely everything is self-identical, and it was a set, then it would be a proper subset of itself (since it, too, is one of absolutely everything). This violates standard axioms of set theory ("well-foundedness"). Upshot: if the "propositions are sets" view is true, then there is no proposition that absolutely everything is self-identical. So if propositions are sets, then some logical truth is not true.

I take the last sort of problem to be the most serious. But note it will not do to rest with the claim that propositions are not sets. A positive theory is needed. And part of the burden of the proponent of the positive theory is to show that propositions don't run into cardinality problems anyway. More work is called for.

At any rate, my main purpose in posting this was to recap some of the discussion and elicit further thoughts on the thesis that all propositions are sets.

Reducing Modality

2007-07-04T12:49:00.000-07:00

For "Reduction is Good" see Sider's "Reductive Theories of Modality". (For his in-progress attempt at a non-Lewisian reductive theory see here. See also his "The Ersatz Pluriverse" for a detailed formulation of the sort of AR view I was sketching last time.)

For "Reduction is Bad" see Plantinga's "Two Concepts of Modality: Modal Realism and Modal Reductionism" (JSTOR access required.)

Objection from Alien Properties

2007-07-02T23:31:00.000-07:00

Def’n:
“An alien natural property is a natural property that is not instantiated by any individual in @, and is not analyzable as a conjunctive or structural property built up from constituents that are all instantiated by parts of @”
Divers p.115 quoting Lewis (1986a: 91)
Let’s assume that Lewis can give a good account of natural properties, since if he can’t that is an objection in and of itself. The objection can proceed as follows:
1) It’s possible for alien natural properties to be instantiated
2) Postulates O1 – O12 exhaustively and exclusively represent reality.
3) If (2) then (4)
4) No individuals (speaking un-restrictedly) instantiate alien natural properties
5) If (4) then (6)
6) ~(1)
7) (1)&(6)
8) ~(2)

In support of (1), we intuitively think it’s possible that there are ways things could have been that are different than ways things are on a fundamental level. That is, things could have been so different that Humean recombination cannot account for that difference. For instance, things could have been massless, colourless, shapeless, but still had properties we can’t conceive of. Alternately, the universe could have been Newtonian.
In support of (3), postulates O1 – O12 postulate the actual world, and us. It then uses postulates O8-O10 and O12 to generate the rest of the worlds. Any individuals generated in this manner can’t be fundamentally different from actual individuals in the way previously described.
In support of (5), according to GR P is possible iff P at some world. If no individual at any world instantiates natural property A, then A is impossible by the lights of GR.
The most assailable principle is (2). A proponent of GR may agree with the conclusion, and promise a suitable addition to the postulates O13 - On that may account for alien natural properties. Here’s a possible O13 that may account for alien properties:

O13: For any world w and for any number n, there exists a world w* such that w* has n number of instantiated natural properties that are alien to w AND w* has parts that instantiate every natural property in w.

O13 will guarantee that there are a plenitude of alien natural properties that are instantiated in other worlds. It’s also more defensible in the face of the argument in divers on p 118. That objection tries to set up a model which satisfies (GR) + (OAN), and then set up another model that also satisfies (GR) + (OAN) but fails to include all of the alien natural properties of the first model (thus saying GR + OAN is apt to lose out on some). That is more difficult with (GR) + (O13). Should you generate a w* with respect of @, such that it excludes some number of alien natural properties, O13 posits another world w** with properties alien to both w* and @ that may include them after all. O13 will posit a world that includes n alien natural properties as well as all the natural properties of @. It will in turn posit a world with all of those natural properties as well as other natural properties not yet accounted for, and iterate. Recombination (O12) guarantees that there are worlds with only alien properties, and different combinations of those properties. Note also that alien properties that only come in pairs (or triplets, or quadruplets etc.) can be generated using O13. While it’s still true that no particular alien property is guaranteed to be accounted for, none are explicitly un-accounted for. The drawback is that by O13, it’s impossible for a world to instantiate all of the natural properties. O12 would like there to be such a world, but the qualification “if there is a spacetime big enough to hold them all” would have to be used to say that this is an exception.
Should that fail, the next most assailable principle is (3). One would need a good account of natural properties to ensure that O1-O12 don’t in fact capture them all. In other words, this objection may be a little premature.

Lewis and Meinong

2007-06-30T19:19:00.001-07:00

Is Lewis a Meinongian? Bernard Linsky and Edward Zalta answer: 'Yes and no'.

Modal Parts, Temporal Parts

2007-06-24T15:09:00.000-07:00

Suppose other times/worlds exist as real, concrete or abstract entities. Suppose also that any things compose a thing. Finally, suppose that it's not the case that anything is located at two times/worlds by being wholly located at each (this is intended as a denial of trans-time/world identity). The resultant ontology is lavish: there exist all manner of fusions with temporal and modal parts. But which is you?

Given that we are rejecting transtime/world identity, and given that there are non-present/actual modal facts about you, it seems there are two main ways we can accomodate these sorts of truths. One way would be to say you have different (proper) parts at different times/worlds. Another would be to say that you have counterparts at different times/worlds. (Note that the differences between these views are semantic rather than ontological: there is no language-independent entity that exists according to one of the views and not the other.) Lewis holds that you have different parts at different times but different counterparts at different worlds. This is a mixed view. Other combinations are possible. Which combination is best?

Carl was asking last time what problems there are for a view according to which objects about which there are non-actual modal truths are modally extended by having different proper parts at different worlds. We discussed some of the objections from Lewis in Plurality but there is only one paper I am aware of that considers the issue in detail. It is a long manuscript from Brian Weatherson: "Stages, Worms, Slices and Lumps". (Weatherson critically evaluates Lewis's objections in section 7 of his paper.)

I wanted to post this to draw your attention to Weatherson's paper, but reading that is not a prerequisite for airing any thoughts on the main topic of the post.

Links

2007-06-22T10:02:00.000-07:00

A couple of links from around the philosophy blogosphere that are relevant to our lives:

Modal and Temporal Irrelevance discusses a version of the "Lewis's view is irrelevant to modality even if he's right about there being other worlds" and considers a parallel argument the presentist might lodge against the eternalist.

Lewis on Natural Properties part 1 and 2 contain detailed discussion of, well, Lewis on natural properties.

Does Lewis Reject K? considers whether Lewis rejects K ([](A --> B) --> ([]A --> []B)), the fundamental axiom of all standard models of modal logic.

And finally, a couple of papers:

"Are Shapes Intrinsic?"

" Haecceitism, Anti-Haecceitism and Possible Worlds: A Case Study"

Hypergunk!

2007-06-21T16:15:00.000-07:00

A few definitions of Hypergunk were given in Nolan's paper. Two on page 6:

(S) Something is Hypergunk iff it is atomless, and for every set containing only its parts, there is a strictly larger set containing only its parts

(P) Something is Hypergunk iff it is atomless, and whenever there are some of its parts, there are some others of its parts such that there are more of the second than there are of the first

The second is a paraphrase of the first meant to eliminate set-theory talk, for fear that plural quantification can only go as far as set-theory. He mentions breifly that if plural quantification over more than set many objects is possible then (P) is inconsistent.

However, I think there's something I don't understand here. He glosses over that argument pretty quickly. Assuming one can quantify over more than set many things, he argues against (P).

1) We can quantify over more than set many things

2) if (1) then (3)

3) We can refer to ALL of x's parts (where x is a piece of hypergunk)

4) (P)

5) (3)&(4)

6) If (5) then (7)

7) There are some parts of x such that there are more of these than ALL of x's parts

Reductio, ~(P) voila. Hence, if we can quantify over more than set many things we should stick to (S). That way, we can speak of all of x's parts, we just can't speak of the set of all of x's parts. If we can't quantify over more than set many things, we can't speak of all of x's parts at all (it seems). That would have bad consequences, so let's assume we can.

I'm not going to argue that the concept of hypergunk is incoherent, rather that it has a couple veeery strange properties. Consider thesis (H).

(H) Every piece of hypergunk has a proper part which is itself hypergunk

Not going to prove this here, but intuitively this is very plausible. A quick reductio. Assume not for hypergunk chunk x. Each part of x has a largest set of parts. For any two sets, the union of those sets forms a set. Union up all the largest sets and you have a set of all of x's parts. That makes x set-sized, but x can't be set-sized (I'm pretty sure this goes through, but I have to brush up on my set-theory).

Now suppose you have a finite chunk of something (matter - finite mass, time - finite seconds, whatever you like). This cannot be the fusion of only hypergunk parts. Consider thesis (M).

(M) No amount of massless (I'll use mass for simplicity, take any unit you like) hypergunk can form an object with finite mass.

This I'll need to prove.

1) suppose for reductio: It takes cardinality C many pieces of massless hypergunk to form a piece of hypergunk X with finite mass.

2) Each part of X has at least C many parts.

3) Each part of X is massless.

4) if (2) then (5)

5) ~(3)

6) (3)&~(3)

Notice this argument won't work for regular gunk. Not matter how divisible regular gunk is, the buck stops somewhere. If a piece of regular gunk has cardinality aleph67 many parts, you can just say aleph67 pieces of massless gunk form a piece of gunk with finite mass. It's hard to see how massless things can constitute a thing with mass anyway, but we do this all the time. A line has length, and can be seen as a union of points. Yet, no point has a length. And it's also intelligble to say that continuum many points can form a line with a finite length. Moreso, it seems like we need to do something like this if we're to say something is infinitely divisible in any sense. If every point in a line had length, and there were continuum many points, the line would be infinitely long.

So, if there's hypergunk around, it's either devoid of any qualitative unit of measurement, or it has that measurement to infinity. If it does have a finite amount of some measurement, that is in virtue of some part that is not hypergunk. It seems like a bad thing for hypergunk, although I'm not sure exactly how damaging it is (or helpful for GR and AR). It's a kind of out-there sketch.

Accidental Intrinsics

2007-06-20T12:36:00.000-07:00

Last meeting we spent a good deal of time talking about accidental intrinsics. In particular, there was concern over whether the argument applied only to concrete realists. I'm going to try to sort out some of the issues here.

First: What is it for a property to be intrinsic? Here is a loose gloss that I think will be sufficient for our purposes: F is intrinsic iff whether an object is F depends solely on that object itself, independent of anything else.

Confession: I don't think the argument from accidental (or temporary) intrinsics really has anything special to do with intrinsicness. It seems the problem, insofar as there is one, is a problem that can be run using any accidental (temporary) properties. By property I mean a feature of a single thing--the sort of feature that is expressed by a one-place predicate.

This is because the argument, as I understand it, trades on certain sorts of inferences. So, for example, forget whether being a person is intrinsic. But note that whether someone is a person does not have anything to do with whether they are in (e.g.) Winnipeg. So consider the following:

(a) Adam is a person in Winnipeg.

(a) is logically equivalent to (b):

(b) Adam is a person and Adam is in Winnipeg.

Both (a) and (b) imply (c):

(c) Adam is a person.

This sort of logical relationship shows that is a person is not a relation to being in Winnipeg. Let's call these sorts of inferences 'Term-eliminating inferences' (TEI) (the inference eliminates the term 'Winnipeg'). The TEI from (a) to (c) is valid. But TEI is not valid when we try it out on real relations. So consider (d):

(d) Adam is three feet from Dan.

(d) does not imply (e):

(e) Adam is three feet from.

This shows that being three feet from is a real relation and is not a one-place property.

Now what I think is that it is (partly) the licensing of TEIs that is really important to Lewis's argument. I think his reasons for choosing intrinsic properties are two-fold: first they seem to license TEIs. Second, if they are intrinsic, they are not really relations between independent things. But notice that one could run the argument(s) with any property that has these features. Intrinsic properties just happen to combine them handily.

Now let's consider one way of running the argument from temporary intrinsics. Suppose that at t Adam is bent and at t* Adam is straight. We can represent these claims semi-formally as follows:

(f) Bat
(g) Sat*

Given that 'B' and 'S' represent intrinsic properties (and not relations), we can validly infer (h) via a TEI on both and conjunction:

(h) Ba & Sa

Given that (f) and (g) are true, and they validly imply (h), it follows that (h) is true. But (h) cannot be true; nothing (not even Adam) can be both bent and straight. (Note that my earlier example 'Adam is a person in Winnipeg' was carefully chosen: the "in Winnipeg" part is superfluous. In an exactly analogous way, according to the objection, the "at t/t*" part is superfluous given that the relevant properties are intrinsic. This is why the TEI is licensed here.)

Now for the parallel argument from accidental intrinsics. Adam has 5 digits on his left hand but he could have had 6. Let's represent these claims as follows:

(i) 5aw
(j) 6aw*

By TEI and conjunction, we infer:

(k) 5a & 6a

On the assumption that (i) and (j) are true, and the inference is valid, (k) must be true as well. But (k) cannot be true; nothing (not even Adam) can be both 5- and 6- digited on his left hand.

Note that nothing was assumed about the nature of w or w*. All that is required is that (i) and (j) are true. This, presumably, just requires of 'w' and 'w*' that they refer. It does not matter what they refer to.

A worry: The argument from temporary intrinsics does not work on presentists. Since actualism is the modal analogue of presentism, doesn't the argument from accidental intrinsics fail against the actualist for exactly the same reasons?

Reply: I don't think all presentists automatically escape the argument from temporary intrinsics. And those that don't automatically escape are the ones that are the real temporal analogues of actualist realism. Let me explain. The most straightforward way out for the presentist is to deny that (at least) one of (f) or (g) is true. If 't' or 't*' does not refer to the present time, then, on this view, it does not refer. So at least one of (f) or (g) is false. Thus the argument for (h) is unsound. But here's another view that deserves the name 'presentism':

Non-present times exist, but they exist presently. They are abstract objects that represent things as being different than they (now) are. Only one of these ways the world was, is, or will be is instantiated, and all of the others are uninstantiated.

This view, I think, does not automatically avoid the objection from temporary intrinsics. And it is the real analogue of abstract realism about modality.

Another worry: Consider the following bit of literature, L:

Once upon a time, Adam has straight hair. The end.

It certainly does not follow from Adam's having straight hair in L and having curly hair in reality (R) that Adam has straight hair and Adam has curly hair. But an actualist realist thinks that ways things could be but aren't is relevantly analogous to ways things are according to certain stories, like L. So actualist realists are automatically invulnerable to the argument from accidental intrinsics.

Reply: Bottom line: worldly actualist realism is not relevantly analogous to the view sketched above. The imagined objector is right that we should not regiment the claim that according to L, Adam has straight hair and according to R, Adam has curly hair as follows:

(l) Sal
(m) Car

Rather, we should think of "according to L" as a sentential operator that is not reducible to a quantifier over "stories" (indulge me in thinking of Reality as one of the "stories", but an ontologically special one). So (l) and (m) should be regimented as follows:

(n) L(Sa)
(o) R(Ca)

On this view, (n) and (o) do not entail (l) and (m). Furthermore, (n) does not entail (p) but (o) does entail (q):

(p) Sa
(q) Ca

So one cannot validly infer (p) and (q) even if the relevant properties are intrinsic.

Note that this "irreducible operator view" is exactly analogous to the view of presentists who immediately avoid the argument from temporary intrinsics. They hold that "WAS", "WILL", "NOW" operators are not reducible to quantification over times. So they hold that the logical form of 'Adam was bent' and 'Adam is straight' are (r) and (s), respectively:

(r) WAS(Ba)
(s) NOW(Sa)

And just like on the "stories" operator view, (r) does not entail (t) but (s) does entail (u):

(t) Ba
(u) Sa

So one cannot validly infer the conjunction of (t) and (u) from the truth of (r) and (s) on this view.

Now, on the modal analogue of this view, the logical form of 'Adam could have had 6 digits on his left hand' and 'Adam has 5 digits on his left hand' are, respectively:

(v) POSSIBLY(6a)
(w) ACTUALLY(5a)

where the operators 'POSSIBLY' and 'ACTUALLY' are not reducible to quantifiers over worlds. On this view, (v) does not entail (x) but (w) does entail (y):

(x) 6a
(y) 5a

Thus, as on the other views, one cannot, on this view, validly infer the conjunction of (x) and (y) from the true (v) and (w). But it is absolutely crucial to this response that the operators are not reducible to quantifiers over worlds. If they were, then (v) and (w) would imply (i) and (j):

(i) 5aw
(j) 6aw*

and we would be right back where we started.

So what's wrong with this sort of actualist realism? Perhaps nothing. (Barring the obvious point that any philosophical view whatsoever has some sort of problem.) I'm even inclined to think that it is correct (though not because of the argument from accidental intrinsics). But note that this view is not a version of what Divers calls worldly actualist realism. That is, the view cannot accept claims like (P) and (N):

(P) <>P iff there is a world at which P
(N) []P iff at all worlds, P

(More carefully, this sort of actualist realist cannot accept a reduction of modal operators to quantification over worlds.)

Thus, I conclude, worldly actualist realists do not "automatically" escape the argument from accidental intrinsics the way some presentists do. So I also conclude that the problem, insofar as it is a problem, is not only a problem for the concrete realist.

(To be clear: I am not trying to suggest that the argument is fatal to any view. I've only tried to show how one does not automatically escape it by being some sort of abstract realist.)

Recent Work on Counterpart Theory

2007-06-18T20:12:00.000-07:00

Here are a few recent papers on counterpart theory:

In "Counterparts and Actuality", Michael Fara and Timothy Williamson argue that adding an actuality operator to CT is obligatory but it ruins the counterpart theorist's day.

In "The End of Counterpart Theory" Trenton Merricks argues that non-Lewisians who are counterpart theorists are in serious trouble. (This paper is unfortunately not available online but should be available via campus computing resources.)

In "Beyond the Humphrey Objection" Ted Sider responds to objections from Merricks and Fara and Williamson (as well as Kripke). This is an in-progress defense of counterpart theory from some of the most serious damaging recent objections.

Finally, I earlier linked to Delia Graff Fara's paper from the Second Online Philosophy Conference "Counterparts Within Actuality" (along with comments by Sider and Melia (the co-author of "Lewis's view is either not reductive or incomplete" argument from Divers chapter 7)). Counterpart theorists' days are again ruined.

(Most of this has fairly technical moments but mastery of the above material plus chapter 8 will make you up-to-the-minute on the philosophical debates over counterpart theory. As always, feel free to post questions/comments.)

Hypergunk and Modality

2007-06-18T11:22:00.000-07:00

Something is hypergunk iff it is atomless (every proper part of it has proper parts) and for every set S containing only parts of it there is another set S* containing only parts of it which has a subset whose members are equinumerous with the members of S, but S* itself is not equinumerous with S.

Put more simply but less carefully, for any set of parts of hypergunk there is another set of parts of hypergunk such that the second set has a strictly greater cardinality than the first.

The possibility of hypergunk makes all sorts of trouble for views like Lewis's, and others as well. (Want to hold that worlds are maximal sets of propositions? There are no such sets if hypergunk is possible.) Or so argues Daniel Nolan in his "Classes, Worlds and Hypergunk".

If hypergunk is possible, then there are possibly more than set-many individuals. This is because there is no set that has as members all the parts of hypergunk. For suppose there were such a set and its cardinality were c (for reductio). Then by the definition of hypergunk, there is another set with a cardinality c* such that c* > c. But since it's not the case that c > c, our assumption that there is a set that has as members all the parts of hypergunk is false. So there is no such set.

Some immediate implications for Lewis's view:

There are worlds that do not correspond to any set of individuals
There is no set of all worlds
There are no necessary truths
There are no truths about some worlds
There are no truths about some individuals

The paper also discusses several other interesting cardinality issues related to modality. It's highly recommended. Feel free to post questions, comments, or objections in the comments section of this post.

(Former Priestly seminarians may also be interested in these papers by Nolan.)

Ode to My Counter-Part

2007-06-15T15:12:00.001-07:00

(or "Come Share my Space-Time")

Isolated,
And yet still there,
The counter-part of me.

I love the way,
You open up,
Such possibility.

And even though,
You can't be seen,
By actualities.

I sure can still,
Know that you're mine,
Like knowing one two three.

I'm now in force,
To find a name,
That can refer to thee.

I have but one,
Solo account:
The one who's just like me.

I wonder if,
You can bear,
Impossibility.

Cause if you can,
Meinong says you,
Can still relate to me.

So here you have,
For this dear blog,
Some modal poetry.

Thank goodnes for,
The poets who,
Can do philosophy.

thought I'd give y'all a sample after last philosophy club. I seem to remember some kids tale about a philosopher/poet who didn't do any useful work in his villaige or something.... Hope you guys got a kick out of it.

a lewisian response to salmon

2007-06-12T23:26:00.000-07:00

for the purposes of this post, let:
<> be the possibility daimond
[] be the necessity box
E be the existential quantifier
A be the universal quantifier

Let me run over Salmon's pen argument again. Suppose it's metaphysically possible for the pen to have originated from 5 blobs of material different than it actually did. We have the actual world @, world w1 at which the pen is from 4 blobs of material different, and w2 at which the pen is 4 blobs different than at w2. Salmon argues as follows:

1) w3 is an impossible world which legitimately exists
2) therefore Ex(x is an impossible world which legitimately exists)

Thus impossible worlds. Relative possibility always sort of bugged me. What's possility if not possibility simpliciter? What does possibly possible mean? Something like it could be possible? Well, the pen argument makes things a little clearer (at least it lit something up in my head).
Take Nathan Salmon. It's impossible for him to be a visa credit-card account. However, it's not impossible for anything to be a visa credit-card account(assuming we're realists about such things). This is possibility/impossibility relative to an object. Now imagine a world with no banks, no credit cards, nothing that could conceivably be a credit card account. It would be true that (N).
(N) ~Ex<>(x is a credit card account)
Unless you believe the barcan formula to be valid, this would not imply (N*)
(N*) ~<>Ex(x is a credit card account)
If (N*) were true, then credic card accounts would be truely impossible objects. As it stands they're only relative impossible objects. Everything's pretty simple so far.
Let @ be a proper name designating the actual world. Let 2x and 3x be complex predicates representing the maximal ways world 2 and world 3 are. Now (W) is true.
(W) ~<>3@
But (W) is silent with respect to (3).
(3) ~<>Ex3x
In fact, (3) is obviously false, since w2 can possibly be the way w3 is. Now, a truely impossible world would fit into be predicated by (I).
(I) Ix iff ~<>ExIx
That is, something is impossible if it's not possible for anything that exists to be that way.

So, as far as Lewis goes, he can respond to Salmon using this machinery. He can claim that he only rejects impossible worlds that satisfy Ix (someday I'll try rephrasing this so I don't quantify over impossibelia). This isn't the logical metaphysical distinction, this is the relative possibility, absolute possibility distinction. He admits the existence of W3, though he may make such moves and denying W3 is a counter-part of @ (this would be denying that @ is possibly the way w3 is).

So what about Salmon's pen? It still has the modal property of not being able to have come from 5 blobs different material. It also has the counter-factual modal property that if it had come from 4 blobs different material, it could have come from 8 blobs different material(as the material it actually came from).

That's my rant. Anyone well-versed in Salmon want to respond? Personally, I'm worried that (I) is trivially un-satisfiable (Lewis might be ok with that), although I'm unsure of how else to represent impossibility simpliciter.

Lewis and probability

2007-06-11T15:41:00.000-07:00

In addition to modal properties like possibility and necessity, we also have a notion of likely and un-likely. GMR doesn't give an account of likelyhood (as far as I've seen). This could be a problem:
1) There are as many worlds that realize "unlikely" scenarios as there are worlds that realize "likely" scenarios.
2) It's just as likely we're in an "unlikely world" as a "likely world".
3) (1)&(2)
4) If (3) then (5)
5) "Unlikely" events have just as much chance of occurring as "likely" events.
Now, when I say "unlikely", let your imagination do what it will. Gravity starts acting in reverse tommorow, everything that's blue suddenly turns red and vice versa etc. According to the recombination principle, there are just as many worlds out there in which gravity reverses "tommorow" as there are worlds in which it does not. My claim isn't that there's a bit of a chance we're in one of those worlds, our chances are 1 in 2, and that's just for one skeptical notion!
How is this different from ordinary skeptical concerns? Well, if you come up with an inductive argument (best explanation, un-observed to observed induction etc.) to fend off skeptical doubts, they don't work here. What argument do we have that the actual world is of the special few that maintain order next to the many more possible worlds that have only maintained order up until today? If possible worlds were merely propositions, possible states of affairs(in an abstract sense), or ways the world could have been, favouritism toward the actual world is warranted for any number of reasons. Lewis however sets all worlds on a par.
Responses:
1) probability is an epistemological concern. I agree with this to a certain extent. But even so, holding lewis's theory puts on in an epistemological position of skepticism.
2) There may be more "likely worlds" than "unlikely worlds" if there are many indiscernable "likely worlds". This is sort of ad-hoc, and it screws up Divers's response to the impossibility of singular reference to non-actuals.
3) skepticism. I will not chose skepticism over GMR!
4) You haven't shown a that there's a higher cardinality of "unlikely worlds". This is true. But at best this response gives us 1/2 a chance of being in an "unlikely world". Also, it's entirely plausible that there are a finite number of "likely worlds". If you're a determinist, there's only one.

This is entirely off-topic I know, but does anyone have any ideas about this? Am I way off base somehow?

How many impossible worlds are there?

2007-06-09T14:20:00.000-07:00

First off, how many possible worlds are there? Well, consider the set of all atomic propositions p1,p2,…. If we accept bivalence (let’s do that for the sake of argument) each of those propositions will have a truth value at each possible world w. Suppose we represent the “valuation” of a world as the set of all propositions that are true at that world. So the “valuation” of a world w* might be {p1,p56,p109}. I’ll assume each possible world has a unique valuation, and every valuation corresponds to a unique world. Now it looks like the set of all valuations would consist of the set of all subsets of the set of all propositions, or, the power set of all propositions. For my purposes here, I’ll assume that the set of propositions is countably infinite. So that cardinality would be aleph0. So it looks like the cardinality of the possible worlds is aleph1 (the cardinality of the real numbers).

When considering the impossible worlds it will be handy to adjust the valuations a bit. Let each valuation be the set of all propositions, except if a proposition p* is false at world w*, take p* out of the valuation for w* and replace it with ~p*. So a valuation may look something like this: {p1,~p2,p3,p4,~p5,…}. You can make a one-one mapping from the previous notion of valuation onto this new one, so it doesn’t screw up any cardinality issues I’m working with. Now consider the impossible worlds. They are free to have as a subset of their valuation {p*,~p*}. If we accept that there are gappy impossible worlds, then the valuation is free to leave p* out altogether (I’m assuming impossible worlds are not closed under entailment, badness would result). I’ll use “(p)” to represent p not having a truth value and “

” to represent p as having both truth values. So a valuation for an impossible world might look like {p1,(p2),,~p4,…}. This can also be represented as a string of integers from 0 to 3. The first digit corresponding to p1, 0 being true, 1 being false, 2 being in contradiction and 3 being absent. So the set previously mentioned would be 0321… . Possible world valuations would be the same, except with only two digits, 0 and 1.

So we have two sets of non-terminating strings of integers, one using only 0 and 1, the other using only 0-3. This was a surprising result for me, since this corresponds to the base 2 real numbers, and the base 4 real numbers. Thus they have the same cardinality. I won’t go through the whole proof, but in short: You can make a one-one mapping from the base 2 natural numbers to the base 4 natural numbers (anyone who’s taken comp-sci will know how to do this). The real numbers are obtained by taking the power set of the natural numbers (do this in a way similar to the one I used to generate the possible worlds above). If you take the power set of one set, and the power set of another, and the original sets had the same cardinality, I’d venture a guess that the resulting sets also have the same cardinality.
Why is this relevant? For one, I started out trying to prove that there were a great many more impossible worlds than possible worlds, thinking that would make trouble for Lewis if he added them. But, I got the opposite result. The result being, the addition of impossible worlds doesn’t add that much more to your ontology (in terms of the mere quantity of postulated entities). If adding them makes your ontology profligate it would be because of the nature of the impossible worlds themselves. Also, it’s handy to know that any cardinality issue that pertains to the possible worlds will carry over to the impossible worlds.
This is all, of course, in terms of logical impossibility. Metaphysical possibility would be much harder to capture, since what is and is not metaphysically impossible is still on the table (as far as I understand).

assignment

2007-06-05T16:57:00.000-07:00

Argument from paraphrase:

1) Things might have been otherwise than they are
2) (1) can be paraphrased as “there are ways things might have been”
3) (1)&(2)
4) If (3) then (5)
5) There are ways things might have been
6) (5) is an existential claim
7) (5)&(6)
8) If (7) then (9)
9) There exist entities called “ways things might have been”

Lewis says these are the same as possible worlds.

Argument from utility:

10) When faced with competing theories, all else being equal, the one with greatest net utility is probably true.
11) GMR has more net utility than AR
12) (10)&(11)
13) If (12) then (14)
14) If (MR) then (GR)

These two arguments can be seen as working in conjunction. The paraphrase argument argues for MR, and utility takes one from MR to GR. As far as I can tell, premise 6 begs the question against anti-realists. They would attempt to give a reading of (5) without any existential commitments. One could say it’s not clear from ordinary language use that (5) is an existential claim because it could be paraphrased into (1).
As far as the argument from utility goes, (10) is un-argued for. A fictionalist, for example, would try to suck any utility out of a theory without committing to its truth in any way. As well, it’s not unreasonable to use theories known to be false if that yields certain pragmatic purposes. It would seem utility is not quite to related to truth as Lewis would have it.

Arguments against truthmakers:

1) de dicto impossibility claims have no clear truth-makers in GR
2) if (1) then (3)
3) GR does not provide truth makers for every claim

1) If (p is true iff a exists) then (a is a truth-maker for p)
2) If something exists at some world it necessarily exists at some world
3) If (2) then (4)
4) True unrestricted possibility claims are necessarily true
5) (2)&(4)
6) If (5) then (7)
7) For any object a and unrestricted possibility claim p, p is true iff a exists
8) For any object a and unrestricted possibility claim p, a is a truth-maker for p
9) If (8) then (10)
10) GR does not provide adequate truth makers for unrestricted possibility claims

If I understand the concept of truthmakers right, I’d deny premise (1) in this argument. It’s coherent to think that even if p is true iff a exists, a is not a truth-maker for p. Some other quality must be present, the being true in virtue of the existence of a. I don’t think it’s such a mysterious concept either. For instance “it’s possible there are unicorns” could be represented thusly:
ExEy(Ux&Wy&Pxy)
It’s clear that this is necessary under GR and is thus true whenever any other necessary proposition is true. However it’s true in virtue of those objects that satisfy that description. To pull this off Lewis may have to grant that propositions are more than just sets of possible worlds. However, he does grant that propositions can be defined in more fine-grained terms if need be.

Argument for special treatment:

1) Modal operators allow quantifiers to range over worlds that were otherwise restricted; they do this in precise ways.
2) If (1) then (3)
3) Modal operators are redundant if there is no implicit restriction on the appropriate quantifier
4) If (3) then (5)
5) Certain modal sentences require different treatment than others
I’d deny premise 1 of this argument. I don’t think this captures all the uses of modal operators in ordinary language. For instance, there should be a difference in meaning between “there is a plurality of worlds” and “there is necessarily a plurality of worlds”. One would express a brute fact while the other should express a necessary one. While Lewis holds that it is in fact necessary that there is a plurality of worlds, his semantics should allow for this distinction.

1) Individuals are part of all possible worlds that would otherwise require a counter-part of that individual(suppose for reductio)
2) Individuals have contingent intrinsic properties
3) If (2) then (4)
4) Some individual a has contingent intrinsic property F
5) (1)&(4)
6) if (5) then (7)
7) at some world w, a is a part of w and ~Fa
8) if (7) then (9)
9) ~Fa
10) If (4) then (11)
11) Fa
12) (9)&(11)
13) Individuals are not directly represented in all possible worlds that would otherwise require a counter-part of that individual
14) If (13) then (16)
15) Every individual that is part of any world is part of exactly one world
I’m not exactly sure what was meant by “intrinsic property” (is it something like ‘essential proptery’?). However, this is the best I could formulate the argument. The most assailable premise would probably be (8). If a theory like that of modal parts were accepted, unqualified “~Fa” wouldn’t result from ~Fa being true at a world.

2007-06-05T08:25:00.000-07:00

I'm going to do like Chelsy did: post 1.a and 1.b on the main page and then the remainder as a comment on the original. Here goes:

1.a. Argument from Paraphrase.

(1) Things might have been otherwise than they are.
(2) If things might have been otherwise than they are, then there are ways that things might have been.
(3) There are ways that things might have been. (1,2)
(4) If we take (3) at face value, then we may say that there exist entities of a certain description; namely, ways things might have been.
(5) There exist ways things might have been. (3,4)
(6) Everything is such that, if it is a way things might have been, then it is a possible world.
(7) Possible worlds exist. (5,6)

1.b. Argument from Philosophical Utility

(1) If an ontological thesis (OT) offers us a way to (a) reduce the diversity of notions we must accept as primitive, and (b) improve the unity and economy of our total theory, then we have good (but not conclusive) reason to believe in the truth of OT.
(2) Genuine modal realism (GR) is an ontological thesis.
(3) A GR commitment to possibilia (i.e. possible worlds and possible individuals) allows us to reduce the diversity of our primitive notions, thereby improving the unity and economy of our total theory.
(4) GR is an ontological thesis, and its commitment to possibilia allows us to meet criteria (a) and (b). (2,3)
(5) We have good (but not conclusive) reasons to believe in a GR commitment to possibilia. (1,4)

Bricker would deny (1). Instead, he uses the nature of intentionality to motivate GR. According to Bricker, possibilia provide (i) the objects that our intentional states are about, and (ii) provide the requisite domain of objects for our modal operators to range over. Bricker’s argument for GR goes something like this:

(1) All narrow psychological states (like belief) are genuinely relational.
(2) If a narrow psychological state S is genuinely relational, then there must exist entities x, y such that x and y are the relata of S.
(3) All narrow psychological states are such that their relata exist. (1,2)
(4) The relata of an intentional relation may be actual or merely possible.
(5) The relata of all narrow psychological states exist, and may be actual or merely possible. (3,4)
(6) If (5), then possibilia (possible worlds and possible individuals) exist.
(7) Possibilia exist. (5,6)
(8) Whatever is possible is true in some possible world.
(9) If (8), then the realm of possibilia is plenitudinous.
(10)The realm of possibilia is plenitudinous. (8,9)
(11) The realm of possibilia exists, and is plenitudinous. (7,10)

So, Bricker thinks we need GR to account for intentionality. Lewis, on the other hand, appears to think that an account of intentionality is one, but only one, of several reasons to adopt GR (others include modality, counterfactuals, properties and propositions, etc). But if this is right, then Bricker would need some independent reason to think that intentionality is somehow more fundamental (in terms of order of explanation) than say, counterfactuals or properties. Lewis appears to think that they are all on a par. I’m not sure who is right.

1

2007-06-05T06:34:00.000-07:00

I guess no one else is posting their responses up for the assignment? (common little lemmings you know you can fly!...) Well perhaps someone needs to leap first. So, I'll post what I have for the first question up, and the rest of the questions as comments to the already placed posts. If anyone thinks I'm plainly wrong, have made things to convoluted, etc. LET ME KNOW. If people don't let others know where they go wrong, or where to make some revisions to their arguments, then ya' can't improve. So, on to question:

1.
a. Argument from Paraphrase:

(1) I believe permissible paraphrases of ordinary language.

(2) I believe permissible paraphrases of ordinary language of what I believe.

(3) Ordinary language permits the paraphrase: there are many ways that things could have been, besides the way they actually are.

(4) (3) is a sentence of existential quantification; that there are entities of a certain description (“ways things might have been”).

(5) So, I believe that there are entities of a certain description (“ways things might have been”).

Hopefully this is a valid re-construction of the argument. The truth of the conclusion follows from the truth of the premises in virtue of the argument's form, so all good. But, premise (4) seems glaringly false, therefore making the argument unsound. I don't think (4) is on the face of it paraphrased properly as a sentence of existential quantification from (3). Unfortunately it is difficult to pinpoint why, but I'll give it a shot.

In (3) the phrase “there are many ways that things could have been” the emphasis is placed strictly on the ways. It is about the ways things are, or could be. In (4) the phrase “there are entities of a certain description (“ways things might have been”)”, there is a doubling of things emphasis. (4) could be rephrased as: “there are things of a certain description (“ways things might have been”). In a sense there in a conjunction of emphasis in this phrase. First, there are things of a certain description, and second, there are ways these things might have been. So, (4) is not a strict paraphrase of (3). It is something extra, plus a paraphrase of (3). Where the something extra is the thing, not just the way it is or could be.

b. Argument from Philosophical Utility:

(1) If an ontological hypothesis (GR) has sufficient and greater net utility than its rivals, then GR has eminent utility.

(2) The ontological hypothesis (GR) has sufficient and greater net utility than its rivals.

(3) So, GR has eminent utility.

(4) If an ontological hypothesis (GR) has eminent utility, then that gives us good reason to believe that GR is true.

(5) So, we have good reason to believe that GR is true.

This also seems to be a valid re-construction. (2) and therefore (3), seem false or rather, yet to be proven. Or as Bricker would say “wishful thinking” in possibilia. For Bricker, possibilia provide both the requisite objects that intentional states are about, and the requisite domains over which modal operators range. So Bricker takes “the existence in possibilia to be a prerequisite”. Now, taking what Lewis says in Counterfactuals, it seems that his criteria in favour for the sufficient and greater utility of GR (or eminent utility), is that it's possibilia, or sentences concerning, “should be taken at their face value unless (1) taking them at face value is known to lead to trouble and (2) taking them some other way is known not to.” In a sense, I think Lewis is making a stronger claim than Bricker. Namely that: The ontological hypothesis (GR), that possibilia exist, is true iff GR has sufficient and greater net utility than its rivals, i.e. taking them at face value is not known to lead to trouble and not taking them some other way is known not to.

I realize this is a messy biconditional, but, that is what Lewis seems to want for (2). Unfortunately, I cannot see a way in which the right-hand of the biconditional can be satisfied, unless an appeal to wishful thinking is made just as Bricker (though I should mention that I don't agree with his motivations for realism either), states. And perhaps this is more of a reflection on myself, but, I do not defer to the glass being half full of utility juice, unlike Lewis.

GR and Truth-Makers

2007-06-03T23:38:00.000-07:00

Hi folks. I had a couple of questions regarding question 2 of our homework assignment. I count three arguments. The first is that GR cannot give an account of truth-makers for every modal claim; specifically, for de re modal claims about non-actual possible individuals. (52-53)

The second is the modal objection/problem of non-contingency on 54-55. The third is the claim that, given certain background assumptions, GR cannot provide an account of the relation between truth and truth-maker that captures what Divers calls "correct matching."(56)

The first two seem important for the homework question. The third one....not so much. Does this seem right to you guys? Does anyone identify additional relevant arguments?

Thanks

a couple thoughts

2007-05-26T13:57:00.000-07:00

Just a few thoughts I thought I'd air here.

Is GMR contingently true? So far I've seen nothing that would indicate that if there are a plurality of concrete worlds there are necessarily a plurality of concrete worlds. Consider a Lewisian universe in which all worlds with green rabbits aren't there. That seems just as metaphysically possible as the universe in which all Lewisian worlds are there. If that's true, any given Lewisian world is a contingent entity (the fact that he lacks the vocabulary to describe what that would mean irregardless). In other words, most actualist possible worlds exist in virtue of the world possibly being a certain way (and thus all possibilities are necessarily represented). Lewisian worlds don't have this to fall back on.

utterly contingent.... disgusting!

Also, I had a couple chats with the reductionists of the class about the epistemology of modality. The question had come up, "how can we know about possibilities". This could be directed to either realist theory.
Well, I'll attempt an empiricist approach to this problem. We can observe actual properties and relations and conceptually divide them from their instances. We can also notice scientific trends, or natural laws. If we can conceive of a few properties and relations combined, and notice that nothing in our natural laws prohibits this combination, voila! We've conceived of a possibility. Of course hard determinists will have to be more strict about the laws they employ, and give a story about a causal history. But that's ok, we don't need to be hard determanists (at least no present natural law entails HD).
If we grant Lewis that all possibilities are realized in a concrete world, then voila! We know stuff about other concrete worlds. However, if all these worlds are contingent, we have less cause to grant then to Lewis.

Accidental Intrinsics and Counterpart Theory

2007-05-24T10:07:00.000-07:00

In an endnote, Divers presents an argument from Lewis for counterpart-theoretic accounts of de re modality. Since not everyone has the endnote and since the sort of argument Divers mentions from Lewis is oft-discussed in metaphysics, I thought I would reproduce it here:

"Why does a world represent Carnap vicariously, by means of a counterpart of Carnap rather than by means of Carnap himself? This is a complex question that speaks to issues at many levels. The immediate answer is two-fold: (i) in GR worlds represent individuals by having individuals as parts; and (ii) every individual that is part of any world is part of exactly one wold, so when many worlds each represent possibilities of Carnap, it cannot be as a result of Carnap being part of each world. GR cleaves to (i) since tehreby representation can be accounted for directly by one of the conceptual primitives of the theory, viz. parthood (see (4.2)). GR cleaves to (ii) because, given (i), an adequate account of the modal phenomenon of accidental intrinsics forces one's hand. (Lewis 1986a: 198-209). Swiftly, having a certain number of fingers is an intrinsic property of Carnap. But how can the individual Carnap have ten fingers at w and have only nine fingers at v, if Carnap having a certain number of fingers at a world is (a) a matter of one individual (Carnap) being part of a world and (b) the one individual having different numbers of fingers at different worlds? It seems that something has to give, and Lewis holds that it should be tolerance of individuals that are wholly present in more than one world. Consequently, de re representation of individuals is achieved vicariously, by counterparts, rather than directly." - Divers pp. 306 n. 4, Possible Worlds.

A Famous Argument from Lewis for GR

2007-05-24T09:13:00.000-07:00

Divers cites two sorts of justification given by Lewis for GR. One he calls "The Argument from Paraphrase". Here is the passage that Divers cites:

"If an argument is wanted, it is this. It is uncontroversially true that things might have been otherwise than they are. I believe and so do you that things could have been different in countless ways. But what does that mean? Ordinary language permits the paraphrase: there are many ways that things could have been, besides the way they actually are. On the face of it, this sentence is an existential quantification. It says that there exist many entities of a certain description, to wit "ways things might have been". I believe things could have been different in countless ways; I believe permissible paraphrases of what I believe; taking the paraphrase at its face value, I therefore believe in the existence of entities that might be called "ways things might have been". I prefer to call them "possible worlds"." - David Lewis, pp. 84, Counterfactuals, Oxford: Blackwell.

"I do not make it as an inviolable principle to take seeming existential quantifications of ordinary language at face value. But I do recognize a presumption in favor of taking sentences at their face value unless (1) taking them at face value is known to lead to trouble and (2) taking them some other way is known not to." - David Lewis, pp. 90, Counterfactuals, Oxford: Blackwell.

Truthmakers

2007-05-24T08:54:00.001-07:00

Divers spends a good deal of Chapter 4 evaluating the claim that GR provides truthmakers for modal claims (utterances? sentences? propositions?). I thought it would be helpful to say a bit more about what truthmakers are supposed to be. Here's Armstrong on truthmakers:

"The idea of a truthmaker for a particular truth, then, is just some existent, some portion of reality, in virtue of which that truth is true. The relation, I think, is a cross-categorical one, one term being an entity or entities in the world, the other being a truth. (I hold that truths are true propositions, but will leave this matter aside . . . ) To demand truthmakers for particular truths is to accept a realist theory for these truths. There is something that exists in reality, independent of the proposition in question, which makes the truth true. The 'making' here is, of course, not the causal sense of 'making'. The best formulation of what this making is seems to be given by the phrase 'in virtue of'. It is in virtue of that independent reality that the proposition is true. What makes the proposition a truth is how it stands to this reality."

"Two questions immediately arise. First, do truthmakers actually necessitate their truths, or is the relation weaker than that, at least in some cases? Second, do all truths have truthmakers, or are there some areas of truth that are truthmaker-free, modal truths, for instance? My answers to these questions are, first, that the relation is necessitation, absolute necessitation, and, second, that every truth has a truthmaker. I will call these positions respectively 'Truthmaker Necessitarianism' and 'Truthmaker Maximalism'."- D. M. Armstrong, pp. 5, Truth and Truthmakers, 2004, Cambridge University Press.

Paradox of Analysis and Reduction

2007-05-22T18:00:00.001-07:00

Lots of interesting issues came up today. One of them concerned what, exactly, we're trying to do when we attempt to give a philosophical analysis. Jeff King has a good discussion of that issue here. Another issue concerned reduction. One idea we discussed was that a reductive account of something gives some sort of account in terms of a more fundamental ontological level. This presupposes that there are distinct ontological levels and some are more fundamental than others in the sense that more fundamental levels are more real than less fundamental levels. Ned Markosian discusses that presupposition here.

Re-characterizing realism

2007-05-18T21:29:00.000-07:00

Let’s call any sentence in which a modal word such as “possible”, “necessary”, “impossible”, “can”, “cannot” etc. plays a decisive role in determining the truth of that sentence a “modal sentence”.
A modal realist(MR) would subscribe to the following:
a) There are modal sentences.
b) The truth values of some modal sentences are fixed by the behavior of something(s) that is not both actual and concrete. (call these things m-entities)
c) M-entities exist.

A genuine modal realist (GMR) would add the following:
d) Some m-entities are concrete

An abstract modal realist (AMR) would add the following:
e) No M-entities are concrete.

Note that (d) -> (f)
(f) Some m-entities are non-actual

And that (e) is compatible with (g)
(g) All m-entities are actual

Note that (d)-> ~(e) and (e) -> ~(d), thus GM and AM are exclusive. Note also that ~(d) -> (e) and ~(e) -> (d), thus GM and AM are exhaustive.

A couple things are worth noting here. If we're speaking of possible worlds (for example), the m-entities would be all merely possible worlds. I'm not trying to parse out what different theories think of the actual concrete world (and actual concrete objects), since that is trivial (I hope) and would make the characterization needlessly confusing.
It may seem that (b) makes (c) redundant, but I threw (c) in to exclude noneism.
The versions of abstract realism he mentions in the book still fall under AMR under my characterization. In addition, Soames would count as an AMR under my characterization.
A fault of this characterization is the extremely vague notion of a "modal sentence" I employed. I'm still kind of fuzzy on the whole relationship between everyday english usage and the more strict philosophical talk. If only english had boxes and daimonds!

OPC2

2007-05-18T14:17:00.000-07:00

The 2nd Online Philosophy Conference is here. There is only one metaphysics paper in the first week and it's by Delia Graff Fara with comments from Ted Sider and Joseph Melia. The discussion gets technical, but the basic problem she raises for Lewis is not terribly hard to grasp.

Characterizing the Positions

2007-05-17T09:22:00.000-07:00

There are several things I don't like about the way things proceed in chapter 2. A major problem I have is that views that seem intuitively relevant to the sort of debate that Divers wants to consider are rendered irrelevant to the debate given the way things are set up in chapter 2. A good example of a position that is defined away by Divers is presented in the first ten pages of Scott Soames's "Actually".

Necessity, Contingency, and Essence

2007-05-15T20:59:00.000-07:00

Today I gave a brief consideration that could be turned into an argument against the following thesis from Divers (which Divers was just presenting, not defending):

(1) x is essentially F iff for all metaphysically possible worlds w, if x exists in w then x is F in w.

Here is a case (this is from Kit Fine's "Essence and Modality"): the essential properties of an object, in the Aristotelian sense, stem from the nature or identity of that object. Intuitively, it is no part of the nature of Sparky that he is a member of a set. But if he exists at w, then he is a member of a set at w. So by (1), being a member of a set is an essential feature of Sparky. So (1) is false. (I hope it's obvious how to make this argument valid.)

If this is right, then the right-to-left direction of (1) fails, but (2) may still be plausible:

(2) If x is essentially F, then for all metaphysically possible worlds w, x is F in w.

Carl suggested that Ben rejects (1) because of the "existence restriction" in the right-hand side. I take it that Ben instead endorses (3) (?):

(3) x is essentially F iff for all metaphysically possible worlds w, x is F in w.

(I assume Ben holds that objects can have properties at worlds where they are absent? (Homework: State the assumption I am attributing to Ben in a way that does not imply the truth of that assumption.))

So if one accepted both Fine's argument and Ben's point, the (partial) account would be (4):

(4) If x is essentally F, then for all metaphysically possible worlds w, x is F in w.

Joe Salerno at Knowability argues here that there are contingent essential properties. So his view is that (5) is correct:

(5) x is essentially F iff if nothing were F, then x would not exist.

This account has several interesting features. One of them is that the right-hand-side counterfactual conditional is, on his view, not vacuously true if the antecedent is impossible. Any thoughts on which, if any of these accounts, is correct, or on what, if anything, can be added to (2) or (4) to yield a more complete account?