Wednesday, April 25, 2007

3.42 Although a proposition may determine only one place in logical space, at the same time the whole of logical space must already be given by it.

(Otherwise negation, logical sum, logical product, etc. would introduce ever new elements – in coordination.)

(The logical scaffolding around a picture reaches through the whole logical space. The proposition reaches through the whole logical space.)

A set of coordinates determines only one figure, but the coordinates themselves imply a set of axes, a space or dimension (or set of dimensions) in which the figure can be. Similarly with propositions and logical space. Since logical space applies to all things, all possibilities, as such then any possibility implies it. Remember, in case this sounds controversial, that we are pretty much still dealing with definitions here, and that there might yet prove to be no cash value whatsoever to any of this.

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