Wolfgang Schwarz

Some tricky counterfactuals

Sometimes, a counterfactual is true even though the consequent is false in the closest world where the antecedent is true:

1) If Hurricane Katrina hadn't hit the town with 200 km/h, completely destroying our house, we would be at home now, watching TV.

Presumably, at the closest worlds where Hurricane Katrina doesn't hit the town with 200 km/h and completely destroys the house, it hits the town a little faster or slower, still completely destroying the house. Even at the closest worlds where the hurricane doesn't completely destroy the house, it destroys it almost completely, still preventing the TV event.

Influence and Backwards Causation

About half a minute ago, I've poured tea into this cup. In a few seconds, I will take a sip. What if I had taken a sip a minute earlier? I wouldn't have taken a sip of tea from an empty cup: that is impossible. So there would have been tea in the cup a minute ago. How did it get there? Maybe I would have poured it in earlier. Or maybe it would have tunnelled directly from the pot into the cup. Or maybe the tea would have just materialized out of thin air. Some of these counterfactuals do not sound very plausible, but let's assume that for the kind of counterfactuals relevant to causation, they are all equally good so that there is no fact of the matter about how the tea got into the cup at the closest world where I take the sip a minute earlier: it does so differently at different worlds that are equally close. (See Lewis, "Counterfactual Dependence and Time's Arrow" for the standards of evaluating such counterfactuals, and "Are we free to break the laws?" for the indeterminacy of divergence miracles.)

Are logical truths true?

1. Hesperus is identical to Phosophorus.
2. By modal logic, .
3. Therefore, Hesperus is necessarily identical to Phosphorus.

1. Sometimes, one is obliged to do things that are not allowed.
2. By deontic logic, .
3. Therefore, sometimes one is obliged to things that are both allowed and not allowed.

1. Necessarily, if the moon essentially consists of green cheese, then it actually consists of green cheese.
2. By provability logic, .
3. Therefore, the moon essentially consists of green cheese.

1. It is now 20 seconds past 19:00 hours.
2. It is now 30 seconds past 19:00 hours.
3. If it is now 30 seconds past 19:00 hours, it is not now 20 seconds past 19:00 hours.
4. By propositional logic, .
5. Therefore, the moon is made of green cheese.

What's wrong with these arguments? They are invalid: their premises are true, their conclusion false. In each case, the fallacy is to assume that a principle valid in some formal system is also valid when translated into English.

Truthmaking and Analytic Combinatorialism

Roughly, the principle of recombination says that anything can coexist and fail to coexist with anything else. But that's too strong: things do have essential extrinsic properties; if Kripke's origin is essential to Kripke, Kripke cannot fail to coexist with his ancestors. However, a perfect intrinsic duplicate of Kripke could fail to coexist with Kripke's ancestors. So less roughly, the principle of recombination goes somehow like this:

For any things in any possible world there is a world which contains any number of perfect intrinsic duplicates of all those things and nothing else (i.e. nothing distinct from all these duplicates).

What is a perfect intrinsic duplicate? Something that has exactly the same intrinsic properties as the original. What is an intrinsic property? A property that belongs to objects independently of what exists and goes on around them. The instantiation of an intrinsic property in some region of a world is independent of the instantiation of intrinsic properties in other regions.

Narrow Content Defined Widely

Some philosophers seem to believe that narrow content must be defined without resort to external objects, leaving only bizarre options like phenomenalism, conceptual role semantics and global descriptivism. But that's wrong. Narrow content can and should be defined by external causal relations just like wide content.

By narrow content, I mean a kind of mental content that doesn't much depend on the subject's environment. Completely narrow content is altogether intrinsic to the subject. But hardly anyone believes in completely narrow content. The question is whether there is an interesting kind of content shared between my intentional states and the states of my twin on twin earth -- and those of swampman and those of a brain in a vat.

Beta-Blogger 4

I've been working on several other websites this summer, one of which needed a blog. After struggling with Wordpress for several hours, I gave up and worked a little more on my own script instead. So here's a new version.

Monadic and Intrinsic Properties

I believe that the so-called problems of intrinsic change and accidental intrinsic properties are real problems. But I believe that their names are misleading, and that they have nothing to do with whether or not we construe properties as sets of things or as functions from worlds and times to sets of things.

Suppose we do the latter, and we also endorse counterpart theory and temporal parts theory. The property of being bent is a function that maps world-time pairs to sets of things. These things are temporal parts of world-bound individuals, ordinary fusions of particle segments, just like us, except that they are smaller along the time axis and all bent. This is a perfectly reasonable and common-sensical view, I believe (but of course I'm biased), and I don't think Lewis has any reason to reject it as turning properties into relations. There is after all a simple equivalence between being bent construed as a function and being bent construed as a Lewisian set: the set is the union of the range of the function; the function indexes all members of the set by their world and time.

Blogger upgrade

I'm updating the software behind this weblog. If everything looks broken in the next half our or so, that's the reason.

Update: OK, done. If you notice any problems, please let me know.

Non-existing properties

For many things, there is no set that contains just those things. There is no set of all sets, no set of all non-self-members, no set of all non-cats, no set of all things, no set of pairs (x,y) such that x is identical to y, no set of (x,y) with x part of y, no set of (x,y) with x member of y.

If Lewis is right and there are proper-class many possibilia, there is also no set of possible philosophers, no set of possible dragons and no set of possible red things. However, if Lewis is right and there are proper classes, there will be proper classes of all these things. But there will still not be a class of all classes, a class of all non-self-members, a class of all non-cats, etc.

First bunch of question: properties and semantic values

This is a follow-up to yesterday's entry.

Andy Egan argues that functions from worlds and times to sets of things are ideally suited as semantic values of predicates, even better than mere sets of things.

I agree, and so would Lewis. In fact, Lewis would say that functions from worlds and times are still too simple to do the job of semantic values. There are more intensional operators in our language than temporal and modal operators. Among others, there are also spatial operators and precision operators ("strictly speaking"). So our semantic values for predicates should be functions from a world, a time, a place, a precision standard and various other 'index coordinates' to sets of objects. This is more or less what Lewis assigns to common nouns in "General Semantics" (see in particular §III). Other predicates like "is green" that do not belong to any basic syntactic category get assigned more complicated semantic values: functions from functions from indices to things to functions from indices to truth values. In later papers, Lewis argues that we may need several of the world and time coordinates and, more importantly, a further mapping that accounts for context-dependence (and to deliver the kind of truth-conditions needed in his theory of linguistic conventions). Thus for predicates, we get something like a function from centered worlds to functions from functions from possibly several worlds, times, places, precision standards, etc. to functions from such worlds, times etc. to truth values. (Alternatively, if we go for the 'moderate external strategy' (Plurality) and reserve "semantic value" for 'simple, but variable semantic values' ("Index, Context and Content"), we can say that the semantic value of a predicate in a given context is the value of the function just mentioned for that context.)