|Paradoxes: are contradictions within formally correct statements or sets of statements that lead to an existence assumption, which initially seemed plausible, to be withdrawn. Paradoxes are not errors, but challenges that may lead to a re-formulation of the prerequisites and assumptions, or to a change in the language, the subject domain, and the logical system. See also Russellian paradox, contradictions, range, consistency.|
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Achilles / turtle / Carroll / Nozick: logical form: (1) If p then q - (2) p.
Problem: q is not yet accepted, but it is required that the following will also be accepted explicitly:
(3) If (if p then q) and p, then q - regress: the additional assumption (3) (s) in addition to the modus ponens) therefore is: if (1) and (2), q.
This then in turn needs an additional premise.
Solution / tradition: Problem: confusion of premises with inference principles. Then the regress not even begins. - Solution / Nozick: we need to introduce a premise that has the same shape and all inferences supplies as the other assumptions that are apparently still needed - WittgensteinVs: problems of rule-following, etc.
Philosophical Explanations Oxford 1981
The Nature of Rationality 1994