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Gap/Dummett: a gap does not occur in material conditional - but probably with bets that leave it unclear whether the antecedent is satisfied at all.
Statements/truth/Dummett: assuming simple language without counterfactual conditionals: then two types of conditionals are possible:
1) conditional statement
a) if the antecedent is fulfilled, then like categorical statement
b) if antecedent is not fulfilled: No statement!
2) as material conditional it is true if antecedent is false.
E.g. Indigenous people: then the behavior does not show which of the two statements is correct - then empty distinction - Conclusion: every sit in which nothing can be conceived as being false is one of being true -> gap - analogy: Command: suspension of the test: no disobedience - conditional: no abuse possible. - The speaker implies that he precludes that the antecedent is true and the consequent is wrong - otherwise: > atomic sentence.
Ursprünge der analytischen Philosophie Frankfurt 1992
Wahrheit Stuttgart 1982