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Tuesday, August 03, 2010

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I understood from my introduction to logic, which I endured at the insistence of Peter Lupu, that it is precisely sets of propositions which are consistent or inconsistent. Isn't that so?

It seems to me that consistency/inconsistency is a relation, and that

1. The propositions p, q, r are inconsistent.

is an elliptical sentence which fully spelled out should read

1*. The propositions p, q, r are inconsistent with one another.


Then the notion of (self)-inconsistency would be sort of parasitic on that primary notion.

2. The conjunctive proposition p & q & r is (self)-inconsistent.

can be read as

2*. The conjunctive proposition p & q & r is inconsistent with itself.

Or is there a problem with a proposition having a relation with itself?

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