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?
In part II of Meaning and Necessity Carnap defines 'L-determinate designators' for rather specific languages (coordinate languages). I think that a more general definition is possible that pretty much meets Carnaps ideas. This more general definition simply identifies L-determinacy with what we nowadays call rigidity.
Does anyone know a good resource on probability theory with infinite
probabilty spaces (if there is such a thing)? For example, I would
like to know if the probability that an arbitrary real number lies
between 0 and 1 is defined, and if so, how the obvious awkwardness of
any answer can be explained away.
If you recently received an email from somebody called 'Wolfgang Schwarz'
mentioning wolfgang@umsu.de and containing a strange attachment, please
don't open it. It is the worm W32.Bugbear@mm. If you have opened the
attachment, this page tells you how to remove it. Also
please don't reply to the sender who is not me and completely innocent,
since the mess really spread from my old windows machine. I'm very sorry
about this.