Cold Hard Logic: Aristotle and Demonstrative Knowledge

by PDS

Aristotle’s works, as I mentioned in my last post, were not written in the form of dialogues (any dialogues he did write have apparently been lost). Instead we have works that are very dense and technical, which makes Aristotle hard to read and understand. The Posterior Analytics is no different in this regard, but since it is a relatively short work it provides us with a useful introduction to Aristotle’s philosophy and a chance to hear some of  his ideas about the nature of knowledge.

We have already heard how Plato’s defined knowledge: he said that knowledge related to that which is. Plato, moreover, thought that the objects of knowledge are the immaterial, unchanging and eternal forms (remember the form of “absolute beauty”). The objects of everyday experience do participate in the forms, according to Plato, but they themselves are only the objects of opinion, not knowledge. Building on Plato, Aristotle also thinks that knowledge must relate to what is stable and unchanging: he writes “knowledge relates to what cannot be otherwise.” But Aristotle does not shared the contention that the objects of knowledge are the forms and he also denys that we have innate knowledge in the sense Plato expresses in the Meno. The reason for this will become apparent in the next post, but first we will briefly explore another element of Aristotle’s epistemology: demonstrative knowledge.

Demonstrative or Scientific knowledge

Aristotle describes two ways of knowing. The first is pre-existing knowledge and the second is through a demonstration. Take the following argument:

1. All men are mortal

2. Socrates is a man

3. Therefore, Socrates is mortal

For Aristotle, a “demonstration” is an argument with two characteristics. First, the premises need to be true. That ‘all men are mortal’ must be a true statement and that ‘Socrates is a man’, likewise, must be knowledge (remember knowledge and truth relate to “what cannot be otherwise”). If the argument is logically valid and the premises are true then the conclusion must be true too. Both characteristics seem to be fulfilled by the argument above. The following argument, however, is invalid, but it does have true premises:

1. All men are mortal

2. Socrates is an animal

3. Therefore, Socrates is mortal

Notice that the conclusion does not follow from the premises. In contrast,take this argument:

1. All men are purple

2. Socrates is a man

3. Therefore, Socrates is purple

The argument is valid (the conclusion follows from the premises), but one the premises is clearly not true.

Aristotle calls a valid argument with true premises a “scientific syllogism” and  the conclusion “scientific knowledge”. Now the word ‘science’ obviously has a specific modern meaning, but remember for Aristotle – writing before the advent of the modern scientific disciplines – the word refers to knowledge in this broader sense.

Demonstrative knowledge, then, is knowledge gained through a logical argument. But then another question arises: how do we know whether a premise, “All men are mortal”, in this example, is true? What are the starting points for knowledge which these premises are built on? With this in mind, I will explore Aristotle ideas about sense perception, memory and the building blocks of knowledge in my next post.

Does Aristotle’s two characteristics of a demonstration seem reasonable to you? Do you agree with Plato and Aristotle that knowledge must relate to that which is or what cannot be otherwise? Why does knowledge need to relate to stable objects?