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.
Sunday, June 24, 2007
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.
Subscribe to:
Posts (Atom)
