The Nature of Knowledge in Aristotle’s Posterior Analytics 1.1-1.3

In De Anima, Aristotle explores how we can be receptive to objects of thought as well as the ways in which thoughts can act as causes. In the Posterior Analytics, Aristotle explores the question of how might knowledge be grounded? There is a point of coordination between the theory outlined in Posterior Analytics and the theory outlined in De Anima in the idea that a thought can be a cause. Aristotle will argue that knowledge is grounded in simple intellectual objects that are understood as immediate propositions, some of which are definitions, and that those things are necessarily the causes of knowledge in general. Aristotle will also argue that all knowledge is from causes. From this, we can conclude that simple intellectual objects are causes of knowledge. This is the point of coordination between the De Anima and the Posterior Analytics, this idea of simple intellectual objects as causes. In the De Anima, this would be the causes of actions and in the Posterior Analytics this would be the causes of knowledge. In the Metaphysics, Aristotle sets for himself the task of producing a science which has no more primitive science behind it and which is the science of everything, the principles and causes of all beings. What makes this an impossible task is that there must be a science of demonstration behind this, a kind of epistemic science, and metaphysics will have to be posterior to this epistemic science. Aristotle says no to this. He says that he is going to produce one science, one set of principles, that encompasses both how we know things and the things that we know. If Aristotle is going to be successful in pursuing the project of the Metaphysics, he is going to need the principles of thinking and of being to be the same principles. The idea of simple intellectual objects as the causes of both acts and knowledge is the crucial claim of the Metaphysics which gets it to work.

In the Posterior Analytics I.1, Aristotle begins with the idea that all knowledge comes from prior knowledge. To Aristotle, this is obvious. An example is the case of geometric proofs. In a geometric proof, like in Euclid, you’ll end up going through a series of proofs until eventually you get down to the axioms, postulates, and definitions. There is nowhere for you to go from there. You cannot learn any of these proofs unless you know the axioms, postulates, and definitions. If you are going to learn any of these proofs, you will need to first know the prior propositions. Furthermore, you can only really be said to understand the proof if you understand the preceding material. The problem with the idea that all knowledge comes from prior knowledge is the question of where knowledge comes from. Plato’s response to this problem is outlined in the Meno wherein he responds to Meno’s Paradox by arguing for a radical metaphysics in the form of the theory of recollection. Meno’s paradox says that we cannot learn what we know and we cannot learn what we do not know, therefore it would seem that we cannot learn. Plato will respond to this by arguing that all knowledge is recollection of knowledge that already exists within the immortal soul. The claim is something like if we don’t know anything about something, we cannot learn about that thing. It seems obvious that we can learn about things we do know something about. If I have a thing, A, with several component pieces of information in it, B, C, and D. If I know B and C, but not D, and I need D to complete my understanding of A, I can look for D by seeing which of it’s component parts I know and then searching for those component parts which I don’t already know. If D’s component parts are called E, F, and G and I know E and F, but I don’t know G, I can come to know D by looking for G. In order to find G, I’ll have to repeat this process. However, if G is simple and I don’t know it, there would be no way for me to learn it and I would therefore be unable to know anything about D and A. The problem is that on the principle that I can learn things that I don’t know if I know something about them, I’m going to get an infinite regress. This is because eventually, I will hit simples where to know anything about them is to know everything about them, so if I don’t know them, I can’t know them.

Talking about how things might be complex such that I can figure out parts of them by knowing other parts is not going to help respond to Meno’s Paradox because it results in the regress problem. This is why Plato takes it as a given that we cannot know what we don’t know and that it will be the first premise, that we cannot know what we already know, that he will disagree with by arguing that we can know what we already know through a process of recollection or being reminded of prior knowledge. For Plato, containment is the only possible relation. Aristotle rejects Plato’s theory of recollection and says that we instead ought to think about how we can combine distinct pieces of knowledge into new knowledge. How can we take B and put it together with C such that we get a new thing D? Aristotle’s theory of logic is his solution to Meno’s paradox that attempts to solve it by thinking about how we go from thoughts that we already have to a new thought and the relations the thoughts need to have in order for that to be true. Aristotle develops what he calls the syllogistic. A syllogism takes us from two distinct thoughts to a new thought. An example of a syllogism is A belongs to all B and B belongs to all C, then A belongs to all C. We get a new thought, A belongs to C, on the grounds of the first two thoughts. Aristotle does not provide a substantive defense for this claim, he simply believes it would be ridiculous if it were untrue. For Aristotle, we can rely on the necessity of these simple logical relations and build up to more complex ones. He argues that all demonstration needs to be traceable down to simple syllogisms which are eventually traceable down to what he calls immediate propositions. A mediate proposition is one that has a medial term which is the cause or explanation for A’s belonging to all C. Aristotle posits primitives that are not simple. Aristotle’s distinction between mediate and immediate propositions does not imply the total simplicity of immediate things. The question of how primitives have an articulate knowable structure and yet still be simples is the deep question of the Metaphysics.

For Aristotle, knowledge consists of two different kinds of propositions: immediate ones and mediate ones. Mediate ones are syllogisms, where you understand the conclusion only by understanding the role of the mediate term in establishing it. You cannot understand all A belongs to C without understanding the whole syllogism that produces it. This leads Aristotle to the claim in the Physics that the premises are the matter of the conclusion. For Aristotle it is the form that entails the premises. Therefore, the conclusion entails the premises and makes them necessary. For Aristotle, a demonstrative syllogism is always a biconditional logically.

In Posterior Analytics I.2, Aristotle outlines what is required for demonstration. Aristotle develops the syllogistic as part of an epistemic theory, a theory of science. A syllogism is not a demonstration because what it means to be a demonstration is to produce scientific knowledge in the demonstrator. Therefore, the demonstration requires many other conditions. Aristotle provides a disorderly list of requirements for demonstration: the premises must be true, primary and indemonstrable, causes, better known than the conclusion, prior to the conclusion, antecedently known, and immediate propositions. Eventually, we have to get back to primary indemonstrable premises. We have principles and from these principles, we will get different episteme or objects of scientific knowledge. Aristotelian science will begin from first principles which are immediate propositions that we know non-demonstratively and these will lead to other demonstratively known things. We can know any given episteme even if its premises are not indemonstrable, it is just that we can trace them back eventually to indemonstrable premises. Aristotle will say that a requirement of demonstration is that primary principles are better known than conclusions. The basis of your knowing the premises that lead to the first proposition have to be better known to you. Via the requirement that primary principles need to be better known than conclusions, Aristotle will conclude that there is a faculty by which we know episteme and there will be another faculty by which we know first principles. The faculty by which we know first principles will have to be different and better than the faculty by which we know the episteme.

A basic proposition is going to be immediate. Aristotle also talks about the structure of a proposition. He says that there are enunciations, propositions that predicate on thing of another, which can be divided into demonstrative propositions and dialectical propositions.

The dialectical propositions are ones where we indifferently posit either an affirmation or negation. In an argument, a dialectical proposition would be a basic principle of a dilemma. Aristotle presents the dilemma that knowledge by demonstration must rest on something better known so either all knowledge is by demonstration, which requires circularity, or knowledge is impossible. In the course of that argument, we get a split structure where the conclusion follows from either of two demonstrations and that would be the role that a dialectical conclusion plays whereas the demonstrative ones always make a claim.

Demonstrative propositions are either going to be affirmations or negations. These two represent contradictory pairs and one of them has to be true for every proposition. Affirmations or negations can both be theses, immediate indemonstrable propositions, and theses can be either definitions or hypotheses. The distinction between a definition and a hypothesis is that Aristotle claims that a hypothesis has to do with the existence of things. Aristotle argues that there is a difference between knowing that something is the case and knowing what something is. The example given by Aristotle is that the arithmetician both states what a unit is and that a unit is. A hypothesis would say that a unit exists and a definition would tell you what a unit is. Hypothesis, if they are existential, means that the primitive thesis in a science are going to be either definitions or existential claims and it would appear that there are more possibilities than that. For example, in the case of geometry, we need postulates which are neither existential claims or definitions. So, hypothesis, as opposed to being existential claims, are claims that have truth. Hypothesis assert something as opposed to simply positing a definition. In any dialectical practice, we do not object to definitions, we object to theses which are primitive claims that have truth value. An example of a hypothesis as opposed to a definition would be parallel lines in Euclid. Parallel lines are defined such that if we have a pair of lines which form two right angles when intersecting the same line, these two lines will never meet. If you object to the definition of something like parallel lines, you cease to do geometry at all. A postulate is different in that it will not tell you how to use the term parallel, it makes a claim. For example, you can deny the Parallel Postulate and you will cease to do euclidean geometry. You will not, however, cease to do geometry. You can deny postulates, you cannot deny definitions. These two, definitions and hypotheses, form the basis of any science.

There is another kind of claim which is axioms. For Aristotle, clear cases of axioms are the law of non-contradiction, P and ~P cannot both be true (~(P^~P)), and the law of the excluded middle, P and ~P cannot both be false (Pv~P). Aristotle says that the role of axioms are the basis for any knowledge whatsoever. Aristotle argues that you need to know these axioms to know anything at all.

For Aristotle, the foundation of a science will be a set of definitions and hypotheses and demonstrations that get us to episteme. For Aristotle, no science ever has any empirical content. Aristotle is uninterested in the question of how the senses deliver knowledge to us. The reason is that sciences have no empirical content. Aristotle does not regard the question of how knowledge can be built on the senses as an intelligible one because he does not believe knowledge can be built on the senses. Aristotle is similar to Plato in this regard. Aristotle does, however, believe that knowledge ultimately comes from experience. The question of how to get into the Aristotelian scientific system is a question of experience. We get to definitions, first principles, and hypotheses by way of experience. However, this is not a justification relation. We do not justify our understanding of first principles by experience because we do not justify them at all.

In Posterior Analytics I.3, Aristotle attacks the puzzle of if all knowledge is demonstrable, then we get infinite regress or circularity. We can get an infinite regress because we’ll have to have a demonstration for whatever we say we know the knowledge on the basis of. Aristotle takes it to be obvious why knowledge based in infinite regress is impossible. The other option is that we can get circularity. If circularity were true, we would have to give up on the priority or primacy of the premises to the conclusion because some premises would be prior to themselves and the conclusion would be both prior and posterior to the premise. Aristotle points out that if you were to construct a science that is circular, it would only work for attributes that are completely coextensive and it is implausible that all properties are like this. For Aristotle, this puzzle is a proof that not all knowledge is demonstrable. He assumes that scientific demonstration is possible and that circular demonstration is not possible. In order for this to be true, there needs to be a way for us to arrive at primitive premises that isn’t demonstration. Aristotle will argue that there is a faculty of knowing better than demonstration because it has to supply us with better premises. The Posterior Analytics is ultimately an attempt to discover the structure of demonstrations to the extent that they are knowledge producing and to explain what role definitions play in a system of knowledge.