[193] So then it is also superfluous, perhaps, to discuss in detail the much vaunted ‟syllogisms,” since, for one thing, they are included in the refutation of the existence of ‟proof” (for it is plain that if this is non-existent there is no place either for probative argument), and for another, we have implicitly contradicted them in our previous statements, when in discussing redundancy ¹ we mentioned a certain method by which it is possible to show that all the probative arguments of the Stoics and the Peripatetics are really inconclusive.

[194] Yet perhaps it will not be amiss to go further ² and deal with them separately, especially since these thinkers pride themselves upon them. Now there is much that one can say by way of suggesting their unreality, but in an outline sketch it is sufficient to treat of them by the method which follows. And I will deal at present with the axiomatic ³ arguments; for if these are destroyed all the rest of the arguments are overthrown as well, since it is from these that they derive the proof of their deductions.

[195] Well then, the premiss ‟Every man is an animal” is established by induction from the particular instances; for from the fact that Socrates, who is a man, is also an animal, and Plato likewise, and Dion and each one of the particular instances, ⁴ they think it possible to assert that every man is an animal; so that if even a single one of the particulars should apparently conflict with the rest the universal premiss is not valid; thus, for example, when most animals move the lower jaw, and only the crocodile the upper, the premiss ⁵ ‟Every animal moves the lower jaw” is not true.

[196] So whenever they argue ‟Every man is an animal, and Socrates is a man, therefore Socrates is an animal,” proposing to deduce from the universal proposition ‟Every man is an animal” the particular proposition ‟Socrates therefore is an animal,” which in fact goes (as we have mentioned) to establish by way of induction the universal proposition, they fall into the error of circular reasoning, since they are establishing the universal proposition inductively by means of each of the particulars and deducing the particular proposition from the universal syllogistically.

[197] So likewise in the case of such an argument as ‟Socrates is a man, but no man is four-footed, therefore Socrates is not four- footed,” by proposing to establish the premiss ‟No man is four-footed” by induction from the particular instances while wishing to deduce each several particular from the premiss ‟No man is four-footed,” they become involved in the perplexity of the circular fallacy.

[198] And a similar criticism may be passed upon the rest of the ‟axiomatic” arguments, as they are called by the Peripatetics; and also upon arguments in the form ‟If it is day, it is light.” For the proposition ‟If it is day, it is light ” is capable, they say, of proving that ‟it is light,” and the clause ‟it is light” in conjunction with ‟it is day” serves to establish the proposition ‟If it is day, it is light.” For the hypothetical premiss stated above would not have been considered valid unless the constant co- existence of ‟it is light” with ‟it is day” had already been observed.

[199] If, then, one has to apprehend beforehand that when there is day there certainly is light also, in order to construct the hypothetical premiss ‟If it is day, it is light,” while by means of this premiss we deduce that when it is day it is light, the co-existence of the being of day and of night being proved (so far as depends on the axiomatic argument before us) by the premiss ‟If it is day, it is light,” and that premiss in turn being established by the co-existence of the facts aforesaid, —in this case also the fallacy of circular reasoning overthrows the substance of the argument.

[200] So likewise with an argument in the form ‟If it is day, it is light; but it is not light; therefore it is not day.” For from the fact that we do not observe day without light the hypothetical premiss ‟If it is day, it is light” might be considered to be valid; just as if, should day, let us suppose, at some time appear, without the appearance of light, the premiss would be said to be false; but, so far as concerns the axiomatic argument aforesaid, the non- existence of day when light is non-existent is proved by the premiss ‟If it is day, it is light,” so that each of these statements needs for its confirmation the secure grasp of the other in order thereby to become credible by means of circular reasoning.

[201] Moreover, from the fact that some things are unable to co-exist—take, for instance, if you like, day and night—both the conjunctive ⁶ negation ‟Not day exists and night exists” and the disjunctive ‟Either day exists or night exists” might be considered to be valid. But they consider that their non-co-existence is established both by the negative of the conjunctive and by the disjunctive, arguing ‟Not day exists and night exists; but in fact night exists; day therefore exists not;” and ‟Either it is day or it is night; but in fact it is night; therefore it is not day,” or ‟it is not night, therefore it is day.”

[202] Whence we argue again that if for establishing the disjunctive proposition and the negative of the conjunctive we require to apprehend beforehand the fact that the judgements they contain are incapable of co-existence, while they believe that they are deducing this incapacity for co-existence by means of both the disjunctive and the negative conjunctive, we involve ourselves in circular reasoning, seeing that we are unable either to give credence to the aforesaid premisses without having apprehended the incapacity for co-existence of the judgements they contain, or to affirm positively that incapacity before concluding the syllogisms based on these premisses.

[203] Consequently,as we possess no principle on which to ground belief owing to the circular style of the argument, we shall declare that, so far as depends on these statements, neither the third nor the fourth nor the fifth of the ‟axiomatic” syllogisms ⁷ possesses valid substance.

For the present, then, it will suffice to have said thus much concerning syllogisms.