What are flaws in the Zenos proof

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Proof [1]

[799]proof, the presentation of the truth or falsehood of a judgment on grounds. The external form in which the proofs appear, or in which they can be brought, is that of the syllogism (see conclusion) or a chain of syllogisms, the axioms and definitions being the major propositions. However, when evidence is issued, these last principles are usually not gone back to, but instead the same sentences are used as a basis, which themselves require justification, but which are assumed to be valid. Thus, although it would be possible for it to derive all its theorems directly from the axioms and definitions, geometry uses, in order to avoid repetition, the propositions already proven as the basis for the B. further; in other sciences and in the demonstrations that occur in practical life, on the other hand, one must be content with deriving the proposition to be proved from some generally admitted proposition, since there is no such simple system of axioms available as in geometry. Hence the superiority of the geometrical proofs over all others, which the latter are very often devalued by the later recognition of the uncertainty or untruth of their presuppositions, which is excluded with the former. In all cases in which a dispute about the validity of a proof arises, the same usually concerns not both the correctness of the final procedure (the form of the proof) but rather that of the prerequisites of the proof (the substance of the proof). Only from this point of view is there a difference between so-called Evidence of experience and evidence of reason, in that the latter propositions of unconditional validity (judgments"a priori", see d.), while the former are based on empirical propositions, the certainty of which is always only relative. In the case of indirect B. (see apagogue), the proof of the falseness of one or more sentences is used to base the B. of the truth of another. No general rules can be given for the procedure when looking for a direct proof; [799] however, it is always a question of finding one or more middle concepts whose connection with the subject and predicate of the proposition to be proved is known, and therefore through which these themselves can be related. Very often it can at least be shown that the proposition to be demonstrated is the necessary consequence of another, whereby the B. of the former is traced back to that of the latter, which under certain circumstances can be a great relief. The main logical (i.e., formal) errors in evidence, which are almost always hidden in the rhetorical disguise of the train of thought and drawn out by reducing it to the form of naked syllogisms, are: the ignoratio elenchiconsisting in the fact that the assumptions used lead to a conclusion that differs from the assertion to be proven; the petitio principii (circulus in demonstrando), consisting in the fact that the proposition to be proved is used as a reason for proof; the hysteron proteronif assumptions are used that are more difficult to prove or understand than the proposition itself. If more or less is proven than the latter contains, at least the aim of the proof is missed (qui nimium probat, nihil probat). In addition, all inference errors (see Conclusion) also make the proofs flawed.