Monday, July 26, 2010

The Proposition

"The proposition" is a concept which has for a long time been growing, by stealth, more important in my scheme of things.

For most of that time, I have regarded the nature of the proposition as being determined only relative to a particular description of the semantics of a particular language, and hence as belonging to semantics rather than to metaphysics.

What I now dimly perceive is that the nature of the proposition probably does become an important problem in metaphysics as soon as you try to come up with something less language specific, and that there are many good reasons for attempting to do that.

An easy way for me to motivate that process, is just from the pragmatics of formalisation, in which there is a problem, shared with software engineering, of maximising re-use.
In the development of formal theories what one wants to make maximum use of is theorems, what one wants to avoid is having to prove essentially the same result many times over.
This is what polymorphism (and Russell's typical ambiguity) is about, it is what good modular structure is about, it is the principle reason why I think about non-well-founded foundation systems, and it is a central influence on the structure of X-Logic.

There are more connections between my other ideas and the concept of proposition, and now that I am become more aware of how important the notion of proposition might become for me, I shall make a place to discuss it.
This will be a broadening of a skeletal document which I started when I briefly paid some attention to Harvey Friedman's concept calculus.
I can broaden that document to deal more generally with propositions and still have a place in there for some discussion of Harvey's ideas.

RBJ

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