Lexicon of Arguments

 Philosophical and Scientific Issues in Dispute
 
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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.

>Conditional/Adams.
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:

Def 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.

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