Tuesday, June 5, 2007

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.


7 comments:

Adam said...

Sorry, that's 'Chelsey' and not 'Chelsy'.

2. GR and Truthmakers:

2.1. The Argument from Singular Terms:

(1) If the conjunction of truth-maker necessitarianism and truth-maker maximalism is true, then, if GR is true, then all modal truths have truth-makers.
(2) GR is true, and its ontological commitments extend only to individuals and set-theoretic constructions out of individuals.
(3) If (2), then, if GR is to offer an account of truth-makers for modal claims, then these truth-makers must be individuals.
(4) Individuals (or sets) will serve as the truth-makers in any GR account of truth-making. (2,3)
(5) No singular terms are apt to refer to non-actual possible individuals.
(6) (4,5) CONJ
(7) If (6), then it is not the case that GR can offer an account (in terms of individuals) for statements of de re possibility involving non-actual possible individuals.
(8) If it is not the case that GR can offer such an account, then it is not the case that, if GR is true, then all modal truths have truth-makers.
(9) It is not the case that, if GR is true, then all modal truths have truth-makers.(6-8)
(10)If (9), then it is not the case that the conjunction of truth-maker necessitarianism and truth-maker maximalism is true.
(11)It is not the case that the conjunction of truth-maker necessitarianism and truth-maker maximalism is true. (1,9 MT)

This argument does not seem overly troublesome to GR. Divers points to a way around the problem in the next chapter. If he’s right, then the GR theorist can deny premise (5), and assert that we may refer to non-actual possibilia via singular terms, thus blocking (6)-(11).

Adam said...

2.2 The Modal Argument:

(1) Claims of de dicto possibility are sometimes true.
(2) If (1), then the claim ‘It is possible that-P’ is sometimes true.
(3) If the claim ‘It is possible that-P’ is sometimes true, then, at some possible world, P.
(4) In the realm of fully unrestricted content, there is no contingent truth (GR postulate AC).
(5) If (4), then each truth is modally necessary (in the realm of unrestricted content).
(6) Each truth is modally necessary (in the realm of unrestricted content). (4,5)
(7) At some possible world, P. (1-3)
(8) Necessarily, P. (6,7)
(9) If (8), then P is a necessary condition for any claim being true, and a sufficient condition for the truth of any truth that holds of absolute necessity.
(10)If P is a necessary condition for any claim being true, and a sufficient condition for the truth of any truth that holds of absolute necessity, then it is not the case that, if GR is true, then truth-making can be cashed-out in terms of Truth-Maker Necessitarianism and Truth-Maker Maximalism.
(11)So, it is not the case that, if GR is true, then truth-making can be cashed-out in terms of Truth-Maker Necessitarianism and Truth-Maker Maximalism.(8-10)

I think this argument is sound. But why exactly is this a problem for GR, on the assumption that GR is true? Can’t GR just admit that the conjunction of truth maker necessitarianism and truth maker maximalism is too strong a requirement for truthmaking, and instead fall-back on some weaker truth making thesis (like the thesis that truth supervenes on being)? It seems like the objection is really working against the truthmaking thesis, and not against GR.

Adam said...

3. GR and Ordinary and Extraordinary Modalizing:

(1) If there exists one (and only one) class of modal claims, then the conjunction of GR Interpretation and GR Ontological Postulates is sufficient to offer explicit, uniform, non-modal analyses of the family of modal concepts.
(2) There exists a class of ‘ordinary’ modal claim that involve modalizing about individuals that exist (or co-exist) within a single region of spacetime.
(3) There exists a class of ‘extraordinary’ modal claim that involve modalizing about trans-world objects or objects that are otherwise not restricted to a single region of spacetime.
(4) (2) + (3) CONJ
(5) If (4), then it is not the case that there exists only one class of modal claim.
(6) It is not the case that there exists only one class of modal claim.(4,5)
(7) It is not the case that the conjunction of GR Interpretation and GR Ontological Postulates is sufficient to offer explicit, uniform, non-modal analyses of the family of modal concepts. (1,6)
(8) If (7), then the class of ‘ordinary’ modal claims should receive one sort of analysis, and the class of ‘extraordinary’ modal claims should receive a different sort of analysis.
(9) The class of ‘ordinary’ modal claims should receive one sort of analysis, and the class of ‘extraordinary’ modal claims should receive a different sort of analysis. (7,8)

I think that this argument is also sound. What I’m not sure about is why it would be a problem for GR to admit two classes of modal analysis. Is it a problem? If it is, which aspect of Divers’ methodology for analyzing extraordinary modal claims would be a problem for GR?

Adam said...

4. GR and Accidental Intrinsics:

(1) An ordinary individual is wholly present at more than one possible world.
(2) An ordinary individual has intrinsic properties.
(3) (1,2 CONJ)
(4) If (3), then for some intrinsic feature F, an ordinary individual will have both F and ~F.
(5) So, it is not the case that an ordinary individual is wholly present at more that one possible world.

I don’t think that, on its own, the argument from accidental intrinsics is enough to motivate GR with counterpart theory. Actualists and modal realists who believe in transworld identity/overlap will deny that the conclusion follows from (iv). An actualist might say something about how properties are always had relative to worlds (that they are relational). Though this approach doesn’t satisfy Lewis, it’s not clear to me that his refusal to countenance world-indexed properties is not one based simply on a desire to retain counterpart theory. Lewis thinks it is counterintuitive to think of properties like ‘having ten toes’ as world indexed. But is it any less counterintuitive to think that my modal properties are satisfied by my counterparts at other worlds?

Chris Tillman said...

The two arguments in the main post are not quite valid. The easiest way to fix this is to identify the claim, identify what it's supposed to imply, and link the two together with a conditional. So for instance if A is supposed to support or imply B, then we can render the argument from A to B validly as follows:

1. A
2. A --> B
3. B (1,2)

Adam said...

Here's my redo on 1a. and 1b.:


1.a The argument from Paraphrase:

(1) Things might have been otherwise than they are.
(2) If (1), then there are ways that things might have been.
(3) There are ways that things might have been. (1,2)
(4) (3) may be taken at face-value, if it is not the case that (a) taking it
as such leads to trouble, and (b) taking it another way is known not to.
(5) ~[(a)&(b)]
(6) (3) may be taken at face-value. (4,5)
(7) Taken at face-value, (3) is an existential quantification.
(8)(6) & (7)
(9) If (8), then we may say that there exist ways things might have been.
(10) There exist ways things might have been. (8,9)
(11) Everything is such that, if it is a way things might have been, then it
is a possible world.
(7) There exist possible worlds. (10,11)


1.b The Argument from Utility:

V: Universal quantifier
Ox: x is an ontological thesis.
Rx: x 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 to a greater extent than rival theories.
Tx: We have good (but not conclusive) reason to believe in the truth of (x).
g: the thesis of genuine modal realism.

Standardization:

1.Vx [(Ox & Rx)--> Tx]
2.Og
3.Rg
4.(Og & Rg) 2,3
5.Tg (1,4)

Chris Tillman said...

These should not be buried in the comments. They deserve their own post.