Philosophy Lexicon of Arguments

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Adams, R.
 
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Propositions Stalnaker I 34
Contradiction/Adams/Stalnaker: contradiction could be defined in terms of consistency:
A and B are contradictory, iff.
{A, B} is not consistent
And for each consistent set of propositions Γ is either
Γ U {A} or Γ U {B} is consistent.
The theory presupposes:
(W3) Each proposition has a contradiction.
Proposition/Adams/Stalnaker: this is a minimal theory of propositions. It does not impose any structure on propositions, except for what is needed for compatibility, implication, and equivalence. And to ensure that e.g. the right kind of implication is represent. E.g. implication:
Definition Implication/Proposition/Stalnaker: (here): A implies B iff. a set consisting of A and a contradiction of B is not consistent.
(W1) and (W2) ensure that our implication has the right properties.

Sta I
R. Stalnaker
Ways a World may be Oxford New York 2003


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Ed. Martin Schulz, access date 2017-03-24