Wolfgang Schwarz

Oh Dear

I just noticed that my tree prover fails on this simple formula! This is a good opportunity to rewrite the part of the script that does the proving and implement some shortcuts, and maybe some "loop detection".

Keyboard Commands in Postbote

I've added keyboard commands to Postbote: If the focus is on the frame with the mail listing, press "R" to refresh, "A" to select all mails, and "G" to quickly change the listing offset (this is for Hermann, who has 1600 mails in his mailbox...).

How To Define Theoretical Predicates: The Problem

Suppose some theory T(F) implicitly defines the predicate F. If we want to apply the Ramsey-Carnap-Lewis account of theoretical expressions, we first of all have to replace F by an individual constant f, and accordingly change every occurrance of "Fx" in T by "x has f" etc. The empirical content of the resulting theory T'(f) can then be captured by something like its Ramsey sentence f T'(f), and the definition of f by the stipulation that 'f' denote the only x such that T'(x), or nothing if there is no such (unique) x.

Implicit Definitions, Part 4: Summing Up (And a Partial Defence of Implicit Definition)

In the previous three entries, I've tried to argue that there are no genuinely implicit definitions: Whenever a new expression is introduced via an alleged implicit definition, either there is no question of definition at all, as in the case of new expressions used as bound variables in mathematics, or there is an explicit definition nearby.

This latter fact, that sometimes explicit definitions are only nearby, provides a partial vindication of implicit definitions. For example, let's assume that folk psychology implicitly defines "pain". But folk psychology itself is not equivalent to the nearby explicit definition. To get an explicit definition, we have to turn folk psychology into something like its Carnap sentence. So the theory itself could be called a genuinely implicit definition.

Implicit Definitions, Part 3: Contextual Definition

I've said that an explicit definition introduces a new expression by stipulating that it be semantically equivalent to an old expression. If there are no non-explicit definitions, this means that you can only define expressions that are in principle redundant. Aren't there counterexamples to this claim?

Consider the definition of the propositional connectives. We can explicitly define some of them with the help of others, but what if we want to define all of them from scratch? The common strategy here is to recursively provide necessary and sufficient conditions for the truth of a sentence governed by the connective: A B is true iff A is true and B is true.

Implicit Definitions, Part 2: Theoretical Terms

Scientific theories are often said to implicitly define their theoretical terms: phlogiston theory implicitly defines "phlogiston", quantum mechanics implicitly defines "spin". This is easily extended to non-scientific theories: ectoplasm theory implicitly defines "ectoplasm", folk psychology implicitly defines "pain".

The first problem from the mathematical case applies here too: Since all these theories make substantial claims about reality, their truth is not a matter of stipulation. For example, no stipulation can make phlogiston theory true. That's why, according to the standard Ramsey-Carnap-Lewis account, what defines a term (or several terms) t occurring in a theory T(t) is not really the stipulation of T(t) itself, but rather the stipulation of something like its 'Carnap sentence' x T(x) T(t). All substantial claims in T(t) are here cancelled out by the antecedent.

Implicit Definitions, part 1: Mathematics

I vaguely believe that there are no implicit definitions. So I've decided to write a couple of entries to defend this belief. The defence may well lead me to give it up, though. Anyway, here is part 1.

Explicit definitions introduce a new expression by stipulating that it be in some sense synonymous or semantically equivalent to an old expression. For ordinary purposes this can be done without the use of semantic vocabulary by stipulations of the form

Luxury Flat

This weekend, I've moved into my new flat, which has both a bath room and a fridge, and also lot's of funny records from the 1970s.

How Many Sciences is Semantics?

I often wonder to what extent different theories and approaches in philosophy of language are conflicting theories about the same matter, or rather different theories about different matters. For example, some theories try to describe the cognitive processes involved in human speaking and understanding; Others try to find systematic rules for how semantic properties (like truth value or truth conditions) of complex expressions are determined by semantic properties (like reference or intension) of their components; Others try to spell out what mental and behavioural conditions somebody must meet in order to understand an expression (or a language); Others try to find physical relations that hold between expression tokens and other things iff these other things are in some intuitive sense the semantic values of the expression tokens; Others try to discover social rules that govern linguistic behaviour; and so on. How are all these projects related to each other?

What does the Wason Selection Task test?

I'm doing a visual memory test. On the table in front of me are twelve green and fourteen red apples, and an empty basket. The lights go out, and the instructor says to me:

"Put all the green apples into the basket". (1)

I try to do what he says. When the lights go on, you, the instructor's assistant, are given a form on which you are to tick whether I've correctly or incorrectly fulfilled the task. You see twelve green and two red apples in the basket. What do you tick?