(for the sake of this discussion, let’s swap out the standard ‘p’ as a variable for propositions and instead use ‘cat’)
true’(cat) iz true iff cat

I would post a link to a relevant lolcat (something of the form $PROPERTYcat iz PROPERTY) but for the life of me do not possess the patience to find such an occurrence. Right about now, I could get really excited about Google allowing variables in its searches.

ugh, need to get lolgrammar out of my meta-language.

If controversies were to arise, there would be no more need of disputation between two philosophers than between two accountants. For it would suffice to take their pencils in their hands, and say to each other, ‘Let us calculate.’

(heard in the Blackburn & Bos course on Computational Semantics–more on that course and the others when I have a chance to stop and breathe)

“At any rate the peculiar genius of the relative clause is that it creates from a sentence ‘…x…’ a complex adjective summing up what that sentence says about x. Sometimes the same effect could be got by dropping ‘x is’, as in the last example, or by other expedients; thus in the case of ‘I bought x’, ‘bought by me’ (formed by conversion and application) would serve as well as the relative clause ‘which I bought’. But often, as in the case of ‘the bell tolls for x’, the relative clause is the most concise adjective available for the purpose.”

“The ‘such that’ construction is thus more flexible than the ‘which’ construction. But what is more striking is the power and flexibility of either of these constructions as contrasted with the earlier or ‘algebraic’ ways of deriving general terms: such operations as attributive juxtaposition, application of relative terms, conversion to passive voice, derelativization (‘brother’ from ‘brother of’), and the joining of terms by ‘and’ and ‘or’. It is not obvious that any preassigned finite set of algebraic operations could suffice for the work of all relative clauses; though actually Schönfinkel’s work, which marked the inception of combinatory logic, may be said to establish an affirmative answer to that question.”

This paper claims that you can allow unrestricted impredicative quantification if you keep careful track of Frege’s sense-reference distinction, and distinguish between predicates and names of predicates. This (if it really works — I haven’t done more than skim the paper yet) would be a different method of using a predicative hierarchy to avoid the paradoxes.

Paul C. Gilmore’s An Intentional Type Theory: Motivation and Cut-Elimination

Disclaimer: I haven’t yet had the time to read the paper, so by “interesting”, I mean that I’m interested in looking at it myself :-P Mostly, this post was to serve as a later reminder for me to read it! And yes, I will indeed post comments & observations when I get around to it.

The theme relation may not qualify as a ‘natural’ category at all. What are natural categories? Any theory of lexical acquisition must make some distinction between categories that are natural and those that are not. Very roughly, the natural categories are those that humans take to be candidates for denotations of simple lexical items, spontaneously and without any explicit instruction or definition. The most famous example of a non-natural category is the property ‘grue’ discussed by Nelson Goodman in the fifties. An object is grue if it is green and has been examined before a fixed time, say December 31, 2010, or else it is blue, and has not been examined before December 31, 2010. All emeralds that have been examined so far are grue as well as green. But for some reason – and this is Goodman’s puzzle – grueness, unlike greenness, is not a category that humans come up with naturally when presented with emeralds, grass, or frogs, for example. To be sure, the concept of grueness can be grasped by human minds, but if it is, it’s on the basis of a verbal definition. The theme relation may not be quite as gruesome as grueness, but unlike the agent relation, it may still not qualify as a natural relation.

Grue just lends itself so nicely to all sorts of cute puns.  If I grue up, I’d stop being so amused by them ;-P

(The proprietor has been so kind as to make no judgments – as far as I know – about this proprietor’s ability to understand the thoughts of a philosopher.  For the record, this proprietor, too, made no assumptions about the lack of intelligence of her imp’s brother.  She assumed, actually, quite the opposite, if you really must know.)