ARISTOTLE

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Deduction, Demonstration, and Knowledge

In the Prior and Posterior Analytics, Aristotle discusses deduction and demonstration respectively. These texts belong to the logical works, which are first in the Aristotelian corpus.

• Prior Analytics I.1.24b ⊕

⊕ συλλογισμός, syllogismos, "computation, calculation." A deduction (συλλογισμός) is an argument in which, certain things having been supposed, something different from those supposed results of necessity because of their being so.

Notes on the Text

The translation of συλλογισμός as "deduction" can be misleading. We think that some deductions are valid and others are not. In this language, a συλλογισμός is a valid deduction.

⊕ • Prior Analytics I.4.25b

⊕ The reason why we must deal with deduction before we deal with demonstration is that deduction is more universal; for demonstration (ἀπόδειξις) is a kind of deduction, but not every deduction is a demonstration.

Notes on the Text

Every demonstration is a deduction, but not every deduction is a demonstration. To be a demonstration, a deduction must have several further properties.

⊕ • Posterior Analytics I.71b

⊕ "Since what is known without qualification cannot be otherwise, what is known by demonstrative knowledge will be necessary. Now knowledge is demonstrative when we possess it in virtue of having a demonstration; therefore the premises from which demonstration is inferred are necessarily true" (Posterior Analytics I.73a).

"Knowledge is a taking up (ὑπόληψις) about universals (καθόλου), things that are by necessity" (Nicomachean Ethics VI.6.1140b).

"[W]isdom is the most exact [form of] knowledge. The wise man must not only know what follows from the starting-points, but also must have the truth of the start-points. Hence, wisdom is intellect and knowledge (ἡ σοφία νοῦς καὶ ἐπιστήμη).... [It] is knowledge and intellect about what is most honorable by nature" (Nicomachean Ethics VI.7.1141b). We think we know a thing without qualification, and not in the sophistic, accidental way, whenever we think we know the cause (αἰτίαν) in virtue of which something is—that it is the cause of that very thing—and also know that this cannot be otherwise. Clearly, knowledge is something of this sort.

Notes on the Text

Aristotle restricts "knowledge" (ἐπιστήμη) to necessary truths. It grasps consequence and incompatibility among universals, both immediate and deductive.

So although 'knowledge' is the traditional translation of ἐπιστήμη, Aristotle's conception of "knowledge" is not the one reflected in the meaning of the English word.

Aristotle takes himself to describing "knowledge without qualification." This can be puzzling. To us, it can seem that something is knowledge or it is not.

What, then, is going on?

• Posterior Analytics I.71b

Whether there is any other method of knowing will be discussed later. Our contention now is that we do at any rate obtain knowledge by demonstration. By demonstration I mean a deduction that produces knowledge, in other words one which enables us to know by the mere fact that we grasp it. ⊕ Now if knowledge is such as we have assumed, knowledge must proceed from premises which are true, primary, immediate, better known than, prior to, and causative of the conclusion. On these conditions only will the first principles be properly applicable to the fact which is to be proved. Syllogism indeed will be possible without these conditions, but not demonstration; for the result will not be knowledge.

Notes on the Text

For a deduction to be a demonstration, "true, primary, immediate..." are necessary.

⊕ • Posterior Analytics I.72b

Not all knowledge is demonstrative. The knowledge of immediate premises is not by demonstration. It is evident that this must be so; for if it is necessary to know the prior premises from which the demonstration proceeds, and if the regress ends with the immediate premises, the latter must be indemonstrable. Such is our contention on this point. Indeed we hold not only that knowledge is possible, but that there is a definite starting point (ἀρχὴν) of knowledge by which we recognize definitions (ᾗ τοὺς ὅρους γνωρίζομεν).

Notes on the Text

Someone who grasps a demonstration has knowledge. He knows that the conclusion of the demonstration is true. His knowledge of the conclusion is "demonstrative."

Not all knowledge is demonstrative. Someone who grasps a demonstration has demonstrative knowledge of its conclusion. He also knows that the premises of the demonstration are true, but this knowledge need not be demonstrative. If these premises are themselves the conclusions of demonstrations, then the knowledge is demonstrative. This regress, however, must stop with knowledge that is not demonstrative. Hence not all knowledge is demonstrative.

The philosophical problem is to understand this nondemonstrative knowledge.

Aristotle provides his answer with his theory of induction.