Some Remarks on Logical Form: Difference between revisions

I have said elsewhere that a proposition "reaches up to reality", and by this I meant that the forms of the entities are contained in the form of the proposition which is about these entities. For the sentence, together with the mode of projection which projects reality into the sentence, determines the logical form of the entities, just as in our simile a picture on plane II, together with its mode of projection, determines the shape of the figure on plane I. This remark, I believe, gives us the key for the explanation of the mutual exclusion of R P T and B P T. For if the proposition contains the form of an entity which it is about, then it is possible that two propositions should collide in this very form. The propositions, "Brown now sits in this chair" and "Jones now sits in this chair" each, in a sense, try to set their subject term on the chair. But the logical product of these propositions will put them both there at once, and this leads to a collision, a mutual exclusion of these terms. How does this exclusion represent itself in symbolism? We can write the logical product of the two propositions, ''p'' and ''q'', in this way:—(170)

What happens if these two propositions are R P T and B P T? In this case the top line "T T T" must disappear, as it represents an impossible combination. The true possibilities here are—

That is to say, there ''is'' no logical product of R P T and B P T in the first sense, and herein lies the exclusion as opposed to a contradiction. The contradiction, if it existed, would have to be written—

but this is nonsense, as the top line, "T T F," gives the proposition all greater logical multiplicity than that of the actual possibilities. It is, of course, a deficiency of our (171) notation that it does not prevent the formation of such nonsensical constructions, and a perfect notation will have to exclude such structures by definite rules of syntax. These will have to tell us that in the case of certain kinds of atomic propositions described in terms of definite symbolic features certain combinations of the T's and F's must be left out. Such rules, however, cannot be laid down until we have actually reached the ultimate analysis of the phenomena in question. This, as we all know, has not yet been achieved.