Outlines of Pyrrhonism II.156-162

en · official · sha256:abf43fab63d296ca4e1b0c26467755db5143a2e5e08bddfeeb72a9add23ccb9a

Moreover, the argument that is said to be faulty through redundancy is indistinguishable from those that are probative. For, so far as concerns redundancy, even the ‟non-demonstrable” arguments so much talked of by the Stoics will be found to be inconclusive, and if they are demolished the whole of dialectic is overturned; for they are the arguments which, they say, need no proof to establish them, and themselves serve as proofs of the conclusiveness of the other arguments. And that they are redundant will be clear when we have set forth these non-probative arguments and thus confirm our statement by reasoning.

Referencing norms: Inference, Proposition, licensed_conclusion

en · official · sha256:67d1f6c31637cf2aef4cd557f4fd92823d8c80df41ad46afd9586c7ddf1330ca

Now there are, in their imaginings, many non-demonstrable arguments, but the five which they chiefly propound, and to which all the rest can, it seems, be referred, are these. The first is that which deduces the consequent from the major premiss and the antecedent, as for example ‟If it is day, it is light; but in fact it is day; therefore it is light.” The second is that which deduces the opposite of the antecedent from the major premiss and the opposite of the consequent, as for example ‟If it is day, it is light; but it is not light; therefore it is not day.”

Referencing norms: FirstIndemonstrable, FiveIndemonstrablesExhaustive, Inference, Proposition, SecondIndemonstrable, conclusion_requested, is_conditional, is_negation_of, licensed_conclusion, major_premise, minor_premise

en · official · sha256:a113b8f43db27914202dd7a426d88897b22bec6aeadd78f5fe13e9fb356262fe

The third deduces from the negation of a coupled premiss and the affirmation of one of its clauses the opposite of the other clause, as for example ‟It is not both night and day; but it is day; therefore it is not night.” The fourth deduces from a disjunctive premiss and one of its alternative clauses the opposite of the other, as for example ‟Either it is day or it is night; but it is day; therefore it is not night.” The fifth deduces from a disjunctive premiss and the opposite of one of its clauses the other clause, as for example ‟Either it is day or it is night; but it is not night; therefore it is day.”

Referencing norms: FifthIndemonstrableSextus, FiveIndemonstrablesExhaustive, FourthIndemonstrable, SextusFifthReading, ThirdIndemonstrable, is_conjunction, is_exclusive_disjunction, is_negation_of

en · official · sha256:50b0bc3d16cc9766128fef647d35e380cb0427fce3a64a3f33b5b342548e0f21

These, then, are the much talked of non-demonstrable arguments, but they all seem to me to be inconclusive through redundancy. Thus for instance, to begin with the first, either it is agreed, or else it is non-evident, that in the major premiss ‟If it is day, it is light,” the clause ‟it is light” follows from its antecedent ‟it is day.” But if this is non-evident, we shall not grant the major premiss as agreed; if, however, it is pre-evident that if the clause ‟it is day” be true, the clause ‟it is light” will necessarily be true also, then, once we have asserted that ‟it is day,” the statement ‟it is light” is also inferred, so that an argument in the form ‟It is day, therefore it is light” is sufficient, and the major premiss ‟If it is day, it is light” is redundant.

Referencing norms: FirstIndemonstrable

en · official · sha256:ddfb72643bc05139ee489b6d40d2a6d36ca8b0fa46f3e0c71bc1ddebf64f0004

And in the case of the second non-demonstrable argument we make a similar objection. For it is either possible or impossible for the antecedent to be true when the consequent is not true. But if this is possible, the major premiss will not be valid; while if it is impossible, at the moment of positing ‟Not the consequent” we posit also ‟Not the antecedent,” and the major premiss is redundant once again, the argument propounded being ‟It is not light, therefore it is not day.”

Referencing norms: SecondIndemonstrable

en · official · sha256:45ef72f5b0950b68e73bd91b8cbf00a0460f4fb0e7b11cf9f96a052d1db36f20

The same reasoning applies also to the third non-demonstrable argument. For either it is pre-evident that it is impossible for the clauses in the coupled premiss mutually to co-exist, or else it is non-evident. And if it is non-evident we shall not grant the negative of the coupled premiss; but if it is pre-evident, at the moment of positing the one clause the other is annulled, and the negative of the coupled premiss is redundant when we propound the argument in the form ‟It is day, therefore it is not night.”

Referencing norms: ThirdIndemonstrable

en · official · sha256:a319b5fc56ffb8add8f1fd6fcf14285668b267681184d82f042970af6e967f31

And we deal in like manner with the fourth non-demonstrable argument and the fifth. For either it is pre-evident or it is non-evident that in the disjunctive premiss one clause is true, the other false, in complete contradiction, as the disjunctive proclaims. And if this is non-evident, we shall not grant the disjunctive; but if it is pre-evident, if one of its clauses be affirmed it is apparent that the other is not true, and if one is negated it is pre-evident that the other is true, so that it is sufficient to frame the argument thus—‟It is day, therefore it is not night,” or ‟It is not day, therefore it is night;” and the disjunctive premiss is redundant.

Referencing norms: FifthIndemonstrableSextus, FourthIndemonstrable, SextusFifthReading, is_exclusive_disjunction