Philosophy Club

A priori Knowledge and Necessary Truth

Introduction

Here's a list of some of the things that I know. There's a jacaranda tree in my backyard; I'm now wearing grey trousers; Charles Darwin wrote “Origin of the Species”; Sydney is the largest city in Australia; Charles 1 was executed in 1649. The common feature of these items of knowledge is that they are all based on sense experience, my own or someone else's. If I were asked to justify my claim to know all of these things, I would refer either to direct observation or to what I have read, learnt about, etc. So if asked “How do you know?”, I would appeal to direct or indirect sense experience. It is in this sense that these items of knowledge are “based” on sense experience. The philosophical term for this sort of knowledge is “a posteriori”. Clearly most of us have an enormous stock of a posteriori knowledge.

But now here's another list of some other things that I know. If a statement is true then its negation is false; an object with shape must also have size; there's an infinite number of prime numbers. These items of knowledge seem different from the earlier ones. For I seem to know these statements to be true without appeal to sense experience. For example, if asked “How do you know that there's an infinite number of primes numbers?”, I will appeal to the fact that it has been proved by Euclid. My justification for these items of knowledge makes no reference to sense experience. It is rather that my knowledge in these cases is the result of thought and reasoning. These items of knowledge are not based on sense experience. The term for this sort of knowledge is “a priori”. A priori knowledge, in contrast to a posteriori knowledge, is independent of experience.

It is important here to distinguish here between “a priori” and “innate” (present at birth). Obviously no-one knew at birth that there is an infinite number of primes (not even Euclid). To say that we can know a priori that there is an infinite number of primes is not to say that it can be known before experience. It is rather to say that it can be known without relying on or without appealing to experience. It is based on reason and proof rather than on perception. Our knowledge about the infinity of primes may or may not be a priori, but it is certainly not innate.

The Problem

Is a priori knowledge possible at all? If so, how? Can we discover significant truths about the world simply by thought and reasoning and without the aid of sense experience? Is all knowledge a posteriori?

Necessary Truth

One approach to this problem is to distinguish those truths which are necessary from those which are contingent. A truth is contingent if it might have been false. For example, “There are two chairs in the room where I am now sitting” is true but could have been false. It is therefore a contingent truth. By contrast, “The number 68 is even” could not be false - it could not fail to be true. It is thus a necessary truth, for it must be true.

How can this distinction between necessary and contingent truth help solve the problem of a priori knowledge? Like this: One of our main worries about a priori knowledge is that it doesn't seem to be possible to come to know what the world is like without appeal to sense experience. I know that it's raining outside now and this is a typical example of my knowledge about the world. But how could I attain such knowledge a priori? Moreover, most if not all of our knowledge seems to be a posteriori - based on sense experience. So how could I have a priori knowledge about the world at all? Perhaps like this: there are certain truths about the world which are necessary. In other words, there are certain general features of the world which must be as they are, and which couldn't be otherwise. And it is these truths which can be known a priori. We can know a priori how things must be. The way things are, as opposed to the way they must be, is known a posteriori. A posteriori knowledge is of contingent truths, whereas a priori knowledge is of necessary truths. In this way then, it is claimed, the distinction between contingent and necessary truths can explain how a priori knowledge is possible.

The adequacy of this explanation depends entirely on whether or not there are any necessary truths. Are there? Here are some suggested examples.

1. Mathematical truths eg. The number of primes is infinite; Pythagoras's Theorem; The shortest distance between any two points (on a Euclidean plane) is a straight line.
2. No two material objects can occupy the same space at the same time.
3. The past can't be changed (time travel is impossible).
4. Every statement is either true or false.
5. A whole is the sum of its parts.
6. Everything that is coloured is extended (in space).
7. Every event must have a cause.
8. Causes precede their effects (backwards causation is impossible).
9. If I know that p then I must believe that p.
10. For every mental experience their must be conscious subject which has that experience.

So the proposed explanation of the possibility of a priori knowledge can be outlined in the following way: The list (1) - (10) provides examples of necessary truths (not the only ones). Furthermore, it is suggested, each of (1) - (10) can be known to be true a priori. For instance, consider (7). The most that could be obtained from sense experience is that every event in fact has a cause. Yet our belief is stronger than that, for we believe that every event must have a cause. And the important point is that the necessity involved here can't be obtained a posteriori - by sense experience. We don't observe necessities in nature. So the fact that it is necessarily the case that every event has a cause can only be obtained a priori. Similar reasoning applies to the other examples from the list.

Some questions

1. Are examples (1) - (10) genuine examples of necessary truths? Are they knowable a priori?
2. Do the statements (1) - (10) describe the world at all? Or are they simply descriptions about use of language? For example, does the necessity of “The number of primes is infinite” derive from the meanings of the terms “prime” and “infinite”, rather than from the nature of the world?
3. Does necessary truth exist at all? For instance Aristotle thought that it was a necessary truth that the earth was at rest and at the centre of the universe. Is necessity something imposed by the human mind rather than something contained in nature?

R. Neurath