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Brian Weatherson now says that 'the world exists' is exactly as natural as 'there is a G', where G applies to worlds that are exactly like this one. I agree. But this only makes things worse, because the class G denotes seems very natural: It contains our world and all its exact intrinsic duplicates. Is this a gruesome gerrymander? We still need a further restriction on best theories apart from naturalness.
Intuitively, some objects are more natural than others. For example, cats are more natural than mereological fusions of cats and elephants. I think that ultimately, naturalness of things should be definable in terms of naturalness of the properties the things instantiate. I'm not quite sure how exactly this is to be done, so for now I'll stick with the intuitive notion of naturalness. Intuitively natural things are spatiotemporally connected, constitute a causal unity, contrast with their surroundings, etc. The world, that is, the mereological fusion of everything that exists at any spacetime distance from us, does fairly well here: As far as I know, it is perfectly connected, causally united (indeed, causally closed) and contrasts clearly with everything outside of it (such as numbers or other worlds, if such there be). Why then does Brian Weatherson think that the world is gruesome?
I see two ways to exclude 'the world exists' as the best theory of everything. The first is the one I already mentioned: to state that a good theory must imply interesting truths a priori. The second is to stipulate that a theory must not contain individual constants. I have some sympathy with such a stipulation, though it may stipulate away haecceitism.
It is sometimes (e.g. in David Sanford, 'Fusion Confusion', Analysis 63, 2003) said that some things are not fusions of all their parts: cats and fusions of cat-parts for instance seem to differ in tensed and modal properties. It may be noteworthy that on the standard definition of 'fusion', this position is outright inconsistent: X is the fusion of Y1,Y2,... iff all of Y1,Y2,... are parts of X and no part of X is distinct from all of Y1,Y2,.... Hence if X is not the fusion of Y1,Y2,... then either one of Y1,Y2,... is not a part of X or some part of X does not overlap Y1,Y2,.... So nothing can possibly fail to be the fusion of all its parts.
In her paper 'Logical Parts', forthcoming in the december issue of Nous, L.A. Paul presents a nice theory of objects according to which things are mereologically composed of their properties. Here are a couple of potential problems.
First, the theory seems to conflict with Unrestricted Composition and incompatible properties. For suppose that P and Q are incompatible properties, like being square and being round. By Unrestricted Composition, there is a fusion of P and Q (or, if you prefer, of P and Q and Paul's red cup). This fusion has both P and Q as parts, hence, on Paul's theory, it is both P and Q. But if P and Q are incompatible, nothing can be both P and Q.
I have the vague impression that Lewis' paper 'Things qua truthmakers', and in particular the appendix by Lewis and Rosen, proves something important. But I'm not sure what it is. Maybe it's that the request for truthmakers was thoroughly misguided in the first place.
The problem is that the truthmaker principle is saisfied so eaily: Let 'w' be a name for our world that does not apply to any qualitatively different world, nor to anything inside any world. (That is, 'w' denotes our world under a rather strict counterpart relation.) Let T be any qualitative truth. Necessarily, if w exists, then T, since otherwise 'w' would be applicable to a world in which not-T, even though T holds at our world, contrary to the rule just stated. Hence w is a truthmaker for T, that is, for any truth whatsoever.
Let T be any theory. If you worry about T's overabundant ontology, there is a simple way to translate it into a theory T_i with a very sparse ontology: For every sentence S in T introduce a new primitive predicate P that applies to a world w iff S is true at w. Then replace S by 'the world is P'. A more elegant method would not introduce a new primitive predicate for every sentence, but rather use structured predicates, that are systematically built up in the way the sentence is built up. (See Quine, 'Variables explained away', and Prior, 'Egocentric Logic'). T_i is a theory that says the same as T with an ontology of just one individual - the world. The price to pay for this reduction in ontology is an overabundant ideology: Who wants all these weird predicates? Nobody.
A number of people have noticed that the problem about probability I mentioned last week is not really a problem about infinite probability spaces, but rather about possible distributions over such spaces. For instance, a Gauss distribution over the reals will yield well-defined probabilities at every interval. But in the case of the arbitrary real number, the distribution would have to be a line parallel to the x-axis, and how could the segments of the area under this line possibly add up to 1?
I'm still not sure if talk about probability really does not make sense in such cases or if it does, but we (or at least I) lack an adequate mathematical treatment. For example, are the following three conditions logically inconsistent?
1. Atom A will decay at some time in the future.
2. The probability of decay at any day is the same as at the preceeding day.
3. Future is infinite.
Just in case anyone reading this blog is also interested in Lewis exegesis, Dave Chalmers usually knows the answers to my questions: The answer to the question raised at the end of this posting, whether Lewis himself believes the deducibility claim he attributes to Jackson, is 'yes'. And about mental properties, apparently Lewis still prefered the realizer view in 1998.
Supervaluationsism and structuralism ('eliminative structuralism', not the kind of structuralism that postulates structures) almost coincide. Structuralism about something t says that any sentence 'F(t)' is to be interpreted as 'for all x (if x is a candidate for t then F(x))'. For example, arithmetical structuralism says that '2+2=4' is to be interpreted as 'for all [N,0,',+,.] (if [N,0,',+,.] satisfies the peano axioms then 0''+0''=0''''). If we translate 'x is a candidate for t' as 'x is the referent of a precisification of 't'', we get: F(t) is (super-)true iff it is true on all precisifications of 't'.
One of the many drawbacks of studying philosophy in Germany is that nobody kicks you when you spend years on your M.A. thesis. So hereby I publicly kick myself. As a consequence, this blog might become even more occupied with David Lewis than it already is.
To start this trend, here is a question about Lewis' functionalism. When a property P is multiply realizable, we cannot identify it with its realizers because then we would identify the realizers with each other, too. All we can do is locally identify P-in-k with its realizer in k, where k is a world or species or individual. Now what is P itself? In Lewis' papers on mind, he usually says that 'P' is systematically ambiguous or indeterminate, denoting the contextually salient realizer. (At least this is what I take him to say. He is not particularly explicit here.) The alternative would be to identify P with the diagonal property of being a P-realizer. The main reason why Lewis rejects this option (e.g. in 'Reduction of Mind') is that it is difficult to see how this diagonal property can occupy the causal role associated with 'P'. Difficult, but not impossible: In 'Finkish Dispositions' he proposes a solution, and consequently prefers identifying fragility not with the contextually salient realizer but rather with the diagonal property. Since then he apparently hasn't written anything more on the issue, so I would like to know if he has changed his mind on mental states (and heat, etc.) as well. (There may still be problems if the theoretical role is not entirely causal, so that even if the diagonal property can do the causal work, it might not be able to do the rest.) Or has he completely endorsed the third alternative – to simply leave the question unanswered: 'The folk well might have left this subtle ambiguity unresolved' ('Void and Object'). Can anyone help?
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