[134] Now it is plain from this that neither is proof a matter upon which there is agreement; for if we suspend judgement about the sign, and proof also is a sign, ¹ we must necessarily suspend judgement about proof likewise. And in fact we shall find that the arguments propounded concerning the sign can be adapted to apply to proof as well, since it seems to be both relative and serving to reveal the conclusion, and from these properties followed nearly all the results we mentioned in the case of the sign.

[135] If,however, one ought to devote a separate discussion to proof, I shall proceed to treat of it concisely after endeavouring first to explain shortly the definition they give of proof.

Proof is, as they assert, ‟an argument which, by means of agreed premisses, reveals by way of deduction a non-evident inference.” What their statement means will be made clearer by what follows. ‟An argument is a system composed of premisses and an inference.

[136] The premisses of it are (it is said) the judgements adopted by consent for the establishment of the inference, and the inference is the judgement established by the premisses.” For example, in the argument ‟If it is day, it is light; but it is in truth day; therefore it is light,” the clause ‟therefore it is light” is a conclusion, and the rest are premisses.

[137] And of arguments some are conclusive, some inconclusive— conclusive when the hypothetical syllogism ² which begins with the combination made by the premisses of the argument and ends with its inference is valid; thus, for example, the argument just stated is conclusive since the combination of its premisses—‟it is day” and ‟if it is day, it is light” —is followed by ‟it is light” in the syllogism ‟it is day, and if it is day it is light; therefore it is light.” But arguments that are not like this are inconclusive.

[138] And of the conclusive arguments some are true, some not true—true when not only the syllogism formed by the combination of the premisses and the inference is valid, ³ as we said above, but the conclusion also and the combination of the premisses, which is the antecedent in the syllogism, is really true. And a combination is true when it has all its parts true, as in the case of ‟It is day, and if it is day, it is light;” but those of a different kind are not true.

[139] For an argument such as this—‟If it is night, it is dark; but in fact it is night; therefore it is dark”—is indeed conclusive, since the syllogism ‟it is night, and if it is night it is dark, therefore it is dark” is a valid one, but, when it is day-time, it is not true. For the antecedent combination—‟it is night, and if it is night it is dark”—is false since it contains the falsehood ‟it is night;” for the combination which contains a falsehood is false. Hence they also say that a true argument is that which deduces a true conclusion from true premisses.

[140] Of true arguments, again, some are ‟probative,” some ‟non-probative;” and the probative are those which deduce something non-evident by means of pre-evident premisses, the non-probative those not of this sort. ⁴ For example, an argument such as this— ‟If it is day it is light; but in fact it is day; therefore it is light” is not probative; for its conclusion, that ‟it is light,” is pre-evident. But an argument like this—‟If sweat pours through the surface, there are insensible pores; ⁵ but in fact sweat does pour through the surface; therefore there are insensible pores”—is a probative one, as its conclusion (‟there are therefore insensible pores”) is non-evident.

[141] And of arguments which deduce something non- evident, some conduct us through the premisses to the conclusion by way of progression only, others both by way of progression and by way of discovery as well. By progression, for instance, are those which seem to depend on belief and memory, such as the argument ‟If a god has said to you that this man will be rich, this man will be rich; but this god (assume that I point to Zeus) has said to you that this man will be rich; therefore he will be rich;” for we assent to the conclusion not so much on account of the logical force of the premisses as because of our belief in the statement of the god.

[142] But some arguments conduct us to the conclusion by way of discovery as well as of progression, like the following: ‟If sweat pours through the surface, there are insensible pores; but the first is true, therefore also the second;” for the pouring of the sweat makes discovery of the fact of the existence of pores, because of the prior assumption that moisture cannot pass through a solid body.

[143] So, then, proof ought to be an argument which is deductive and true and has a non-evident conclusion which is discovered by the potency of the premisses; and because of this, proof is defined as ‟an argument which by means of agreed premisses discovers by way of deduction a non-evident inference.” It is in these terms, then, that they are in the habit of explaining the conception of proof.