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William Ockham

Summa Logicae III-2, chap. 17

On the two types of demonstration: a prioriand a posteriori

Now that we have briefly discussed the terms and propositions that are relevant todemonstration, what remains is to talk about demonstration [itself]. The first thing tonote is that given that (i), as was said above at the beginning [of this tract], ademonstration is a syllogism that produces knowledge (taking 'knowledge' for acognition that is evident and certain), where something necessary follows fromnecessary propositions, and given that (ii) there are different types of such syllogisms, itfollows that there are different types of demonstration. In light of this, it is important tosee that some demonstrations are such that their premises are absolutely prior to theconclusion; and these are called a priori or propter quid demonstrations. Other

demonstrations are such that their premises are not absolutely prior to the conclusionbut are nonetheless better known [than the conclusion] to the one who is constructingthe syllogism, with the result that it is through these premises that the one constructingthe syllogism comes to a cognition of the conclusion; and these are called quia ora

posterioridemonstrations.

For example, suppose that someone does not know that the moon is presently beingeclipsed but does know the paths and motions of the planets; if he consideres thepremises 'When the moon is in such-and-such a position, then the moon is eclipsed'and 'the moon is presently in such-and-such a position', and from these premisescomes to knowledge of the conclusion 'The moon is now being eclipsed', then such a

person has an a prioriandpropter quiddemonstration. For the premises express thecause by virtue of which things are such as they are signified to be by the conclusion.

By contrast, suppose that someone else, seeing that the moon is being eclipsed and notknowing that the earth is interposed [between the sun and the moon], argues as follows:'When the moon is eclipsed, the earth is interposed between the sun and the moon; themoon is now being eclipsed; therefore, the earth is now interposed'. Such a personwould be making an a posteriori demonstration. And he knows that the earth isinterposed, but he does not know why the earth is interposed, and so he knows that(quia) things are such-and-such, but he does not know that in virtue of which (propterquid) things are such-and-such. Still, because it is through propositions known to him

that he acquires knowledge of a necessary proposition which was unknown to him, itfollows that he has a demonstration.

Note, though, that these syllogisms are adduced only by way of example--not becausethey are realistic, but in order that students might learn from them.

From what has been said it follows that it is possible for two people to form the samesyllogism and yet for one of them to demonstrate [the conclusion] and the other not to

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demonstrate it; for the one acquires knowledge of the conclusion from the premises,and the other does not acquire knowledge of the conclusion from those same premises.For this reason, one and the same syllogism is a demonstration with respect to the oneand not a demonstration with respect to the other, since the premises produceknowledge in the one person but not in the other.

And so 'knowledge' is posited in the definition of a demonstration not only to indicate thefinal cause of demonstration, but is posited in the definition of a demonstration as apartof the definition, expressing that which is signified in an oblique case by 'demonstration'.Hence, the noun 'demonstration' not only signifies a certain type of syllogism, but alsosignifies in an oblique case the very knowledge of the conclusion that is apt to becaused by a cognition of the premises. Since this is so, the definition 'syllogism thatproduces knowledge' can be used to clarify other definitions of a demonstration--definitions that signify something that the name 'demonstration' does not signify in eitherthe nominative case or an oblique case. By way of analogy, if the phrase 'able to cuthard things' is a nominal definition of 'saw', this phrase can be used to make it clear that

a saw must be sharp and made of iron, etc. And this is the way many authors arespeaking when they say that a definition taken from the final cause can be used todemonstrate the corresponding definition taken from the material causes or from theparts of the thing defined. And this holds only when the definition taken from the finalcause is a nominal definition. But in that case such a line of reasoning will not be ademonstration properly speaking, but will instead be a sort of clarification.