Wolfgang Schwarz

Hm.

Shelby Moore: "The specification (by definition of specification) does not allow deviations which would violate the specification."

Lewis' Account of Predication

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)

Naturalness and Projectibility II

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.)

Correction of the dot-matrix conditions

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).

The dot-matrix test for naturalness

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.

Updates of online papers in philosophy

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.

Less than perfectly natural properties

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.

Better trees, big trees

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:

Naturalness and Projectibility

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').

Immanent or Transcendent Structuralism?

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'.