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Re: FUTURE LOGIC - Comments & Queries

Hi JD,

Do these relations hold for ALL the forms of proposition which are covered in the book? (categorical, modal, conditional, etc).

THE LISTED OPPOSITIONS (CONTRADICTION, CONTRARIETY, ETC.) ARE OBVIOUSLY APPLICABLE TO ANY PAIR OF PROPOSITIONS OF ANY SORT, IN THIS BOOK OR ANY OTHER. THEY ARE JUST EXTENSIONS OF THE THREE LAWS OF THOUGHT.

I notice that the unconnectedness relation has no column in which a pair of propositions is not possible. Would it be true to say that in general, the "strength" of a relation is correlated (positively) with the number of impossible combinations? So the strongest relations are implicance and contradiction, each having two "no's", and the weakest is unconnectedness, which has none.

YES, THAT IS CORRECT. THE MORE COMBINATIONS ARE IMPOSSIBLE, OBVIOUSLY THE STRONGER THE 'OPPOSITION' RELATION BETWEEN THEM.

JD, keep in mind that the named oppositions refer to PAIRS of propositions. When dealing with sets of 3, 4, 5, 6, etc. propositions, the different possibilities of 'impossible' and 'possible' rows are ALSO 'oppositions', except that we have not given them any specific names because that would require a never-ending vocabulary! Instead we resort to descriptive sentences like "one of them must be true" or "all but one of them must be false" etc. All this, to repeat, is merely application of the laws of thought.