What, in general, does it mean that something A satisfies a predicate 'F'?
Traditionally, there are three candidates:
1) 'A is F' means that A is F. That' all. Simple predications can't be analysed.
2) 'A is F' means that A instantiates the property F. Except in some special cases,
in particular the case where 'F' is 'instantiates'.
3) 'A is F' always means that A instantiates the property F.
It is not entirely obvious how to locate Lewis here. In some places, when
discussing Armstrong's request for analyses (or truthmakers) for
predication, he sounds like he favours (1): "the statement that A has F
is true because A has F. It's so because it's so. It just is." ("A world
of truthmakers", p.219 in Papers)
Brian Weatherson tells me that Lewis does mention Goodman's 'New Riddle' as
a task for natural properties in "Meaning without use: Reply to Hawthorne".
Lewis says here that we should not be scared off by "Kripkenstein's
challenge (formerly Goodman's challenge)" to find a distinction between
natural and unnatural extrapolation (p.150 in Papers in Ethics and
Social Philosophy, similar remarks can be found in the introduction to
Papers in Metaphysics and Epistemology). So the first suggestion
is very probably right.
(Reading Brian's comments it now seems to me when I argued that natural
properties can't solve the New Riddle I've been confusing it with the Old
Riddle. All the New Riddle requires is an objective distinction between
good and bad extrapolations. That induction based on good extrapolations
might nevertheless yield systematically false predictions ("not work") is the
Old Riddle.)
I think these conditions match the dot-matrix test better than the ones I
proposed earlier. They are more complicated, but closer to the matrices
and not too unnatural:
A property F is natural to the extent that the following conditions are
satisfied, where (1), (3) and (5) weigh heavier than (2), (4) and (6).
1) The Fs resemble each other intrinsically.
2) The Fs resemble each other extrinsically.
3) Anything that exactly resembles an F intrinsically is itself F.
4) Anything that exactly resembles an F extrinsically is itself F.
5) There are few intrinsic F-gaps.
6) There are few extrinsic F-gaps.
Something y is an intrinsic (extrinsic) F-gap if it isn't F and there are
Fs x and z such that y intrinsically (extrinsically) resembles both of them
more closely than x intrinsically (extrinsically) resembles z.
RL satisfies all conditions except (3), whereas R only properly satisfies
(1).
In section 6 of "Redefining 'Intrinsic'" (Philosophy and Phenomenological
Research 62, 2001), Lewis introduces an interesting test for comparative
naturalness of properties. The test is based on two-dimensional dot-matrix
pictures, where distance along the horizontal dimension measures intrinsic
dissimilarity, and distance along the vertical dimension extrinsic
dissimilarity. Roughly (p.385), a natural property demarcates a regular
region in the dot-matrix. Less roughly (p.391), two aspects of the region
are important for naturalness: spread and scatter.
Brian Weatherson has set up a weblog to track changes of online papers in philosophy, similar to my diffbot, but of course much more useful for other people.
It would actually be easy to create an even more useful tracking system, which would not only update itself automatically but also provide a flexible interface so that you could, for example, list all changes to Richard Heck's papers in the last 5 months. A possibility to search for papers on a specific topic would also be helpful. Maybe I'll think about setting up such a system when Brian gets bored with his manual updates.
My logfiles indicate that people are more interested in silly
logic puzzles than in pointless remarks on footnotes in the
metaphysical writings of David Lewis. Let's see if I can get my readership
down to zero with this one.
Besides perfectly natural properties, Lewis also needs somewhat less
natural properties in his philosophy of language and elsewhere. What
determines how natural a property is? Lewis gives three different
answers, in four different places, none of them longer than two sentences.
Sometime before christmas, Greg Restall spotted a bug in my tree prover and noticed that it didn't work with Internet Explorer on MacOS X. These problems should now be fixed. I've also started working on an implementation of proofs with identity and function symbols, but I'm not sure if I'll ever finish it.
I actually wrote the tree prover to check the results of another script, which is what I vaguely talk about in the Feedback section. This is what that other script would calculate if I'd ever get it done:
David Lewis offers a lot of work for natural properties in his semantics,
his theory of mental content, materialism, supervenience, causation, laws
of nature, etc. Strikingly missing in this list (as opposed to the list of
Anthony Quinton, "Properties and Classes") is the solution of Goodman's New
Riddle of Induction. I don't know why Lewis never mentions this. Two
suggestions:
1) He thought it was just too obvious, and he disliked repeating arguments
of other philosophers (none of the items on Quinton's list occurs on
Lewis').
Happy new year everybody. I'm still alive, and I still have questions and
comments on the metaphysics of David Lewis. This one is about Lewis'
philosophy of mathematics.
In "Mathematics is Megethology", Lewis argues
for structuralism in set theory: There is no particular relation of
membership, connecting particular things with particular classes. Instead,
there are just two sides of Reality, ordinary individuals on the one side,
proper-class many mereological atoms (called 'singletons') on the other.
Set theory is about all relations on this Reality that satisfy certain
constraints, like 'every individual stands in that relation to a singleton'.
Things are counterparts iff they are sufficiently similar to each other.
They needn't be similar intrinsically: For example, in "Individuation by
Acquaintance and by Stipulation" (§2), Lewis allows for counterparts that
are similar in standing in a particular relation of acquaintance to some
person. In fact, they needn't be similar at all: In On the Plurality of
Worlds (§4.4), Lewis accepts that, speaking unrestrictedly, everything
is an individual possibility for anything. However, in "Things qua
Truthmakers" (§5), he denies that things could be counterparts by living in
a world in which there are no unicorns. I wonder why. Lewis says that
such a respect of similarity would be too extrinsic and strike us as too
unimportant. But other eligible respects are extrinsic too, and what
strikes us as important certainly depends on the relevant context. I can
imagine theists who believe that there is a big difference between
living in a world where there is a God and living a duplicate life in a
Godless world. So in some special contexts, those of our counterparts who
live in Godless worlds might be excluded as being too different. Conversely, an atheist might exclude counterparts that live in worlds with Gods a being too different.