Wolfgang Schwarz

Why we need more intensions

Suppose we want a theory that tells us for all sentences in our language in what possible contexts their utterance is true. Call those functions from contexts to truth values "A-intensions". A systematic theory should tell us how the A-intension of complex sentences depend on their constituents. Here are some theories which are not very satisfactory in this respect.

Theory 1. Each sentence consists of a sentence radical and a fullstop. (The sentence-radical is the entire sentence without the fullstop.) All sentence radicals have the same semantic value: God. The semantic value of the fullstop maps this semantic value to a truth-value. But whether it maps God to true or false depends on the context of utterance. For instance, in a context in which it doesn't rain and the utterance of "." is preceeded by an utterance of "it rains", the value of "." maps God to false; in a context where "." is preceeded by "2+2=4", it maps God to true; and so on.

Positions on intrinsic properties and causal/nomic roles

Warning: another pointless exercise in conceptual geography.

Can intrinsic properties have their causal/nomic role essentially? It seems not. Suppose something x is P. If P essentially occupies a certain causal role, say being such that all its instances attract one another, we can infer from x's being P that either there are no other P-things in x's surrounding or x and the other things will (ceteris paribus) move towards one another. But if we can infer from x's being P what happens in x's surrounding, P cannot be intrinsic. Being intrinsic means belonging to things independently of what goes on in their neighbourhood.

CD Cases and Xmodmap

Two unrelated notes that will not interest any of my readers.

First, my LaTeX Paper CD Case Generator can now be run on the server. The Redhat LaTeX packages seem to be rather old, so new stuff doesn't work well. Maybe I'll manually install a newer tetex version sometime.

Second, I've installed the Hoary Hedgehog on the little Powerbook. The only problem, as usual, was my keyboard layout. (My keyboard is German.) Here is the .Xmodmap file I wrote to fix this, just in case anyone -- my future self, in particular -- runs into the same problem.

Suppose ZFC proves its own inconsistency

Suppose we find a proof, in ZFC, that ZFC is inconsistent. Does it follow that ZFC is inconsistent?

On the one hand, if we could infer from ZFC ~Con(ZFC) that ZFC is inconsistent, we could contrapositively infer the consistency of ZFC & Con(ZFC) from Con(ZFC); and since ZFC & Con(ZFC) obviously entails Con(ZFC), ZFC & Con(ZFC) would thereby entail its own consistency. Which it only can if it is inconsistent (Gödel's second incompleteness theorem). So it seems that we can only infer that ZFC is inconsistent from the observation that ZFC entails its own inconsistency if we presupposes that ZFC & Con(ZFC) is inconsistent.

Some Thoughts on Fundamental Structural Properties

Fundamental (or 'perfectly natural') properties are properties on whose distribution in a world all qualitative truths about that world supervene. That is, whenever two worlds are not perfect qualitative duplicates, they differ in the distribution of fundamental properties.

This is not the only job discription for fundamental properties. If it were, far too many classes of properties could play that role. For instance, all qualtiative truths trivially supervene on the distribution of all properties, or on the distribution of all intrinisic properties, or (for what it's worth) on the distribution of all extrinsic properties. (That's because no two things, whether duplicates or not, ever agree in all extrinsic properties.)

Structures all the way down

A structural property is a property that belongs to things in virtue of their constituents' properties and interrelations. For instance, the property being a methane molecule necessarily belongs to all and only things consisting of suitably connected carbon and hydrogen atoms.

There is two-way dependence: Necessarily, if something instantiates a structural property, then it has proper parts that instantiate certain other properties; conversely, if the proper parts of a thing instantiate those other properties then, necessarily, the thing itself instantiates the structural property.

Mistaken Intuitions

Some people intuit that

• the subject in a Gettier case has knowledge;
• Saul Kripke has his parents essentially;
• "Necessarily, P and Q" entails "Necessarily, P";
• whenever all Fs are Gs and all Gs are Fs, the set of Fs equals the set of Gs;
• the liar sentence is both true and not true;
• the conditional probability P(A|B) is the probability of the conditional "if B then A";
• it is rational to open only one box in Newcomb's problem;
• switching the door makes no difference in the Monty Hall problem;
• propositions are not classes;
• people are not swarms of little particles;
• a closed box containing a duck weighs less when the duck inside the box flies;
• spacetime is Euclidean;
• there is a God constantly interfering with our world.

They are wrong. All that is false.