Page "Contradiction" Paragraph 18
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Post observed that, if the system were inconsistent, a deduction in it ( that is, the last formula in a sequence of formulas derived from the tautologies ) could ultimately yield S itself.
As as an assignment to variable S can come from either class K < sub > 1 </ sub > or K < sub > 2 </ sub >, the deduction violates the inheritance characteristic of tautology, i. e. the derivation must yield an ( evaluation of a formula ) that will fall into class K < sub > 1 </ sub >.
From this, Post was able to derive the following definition of inconsistency without the use of the notion of contradiction:
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