Saturday, June 30, 2007
Sunday, June 24, 2007
Modal Parts, Temporal Parts
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.
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.
Friday, June 22, 2007
Links
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"
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"
Thursday, June 21, 2007
Hypergunk!
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
(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.
Wednesday, June 20, 2007
Accidental Intrinsics
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':
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:
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.)
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.)
Monday, June 18, 2007
Recent Work on Counterpart Theory
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.)
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
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:
(Former Priestly seminarians may also be interested in these papers by Nolan.)
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
(Former Priestly seminarians may also be interested in these papers by Nolan.)
Friday, June 15, 2007
Ode to My Counter-Part
(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.
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.
Tuesday, June 12, 2007
a lewisian response to salmon
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.
<> 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.
Monday, June 11, 2007
Lewis and probability
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?
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?
Saturday, June 9, 2007
How many impossible worlds are there?
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 “
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),
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).
Tuesday, June 5, 2007
assignment
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.
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.
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.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
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.
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.
Sunday, June 3, 2007
GR and Truth-Makers
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
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
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