Plato 3

Where does certain knowledge come from ?

Some things seem capable of proof.

Let me try and prove something. If you have read and followed the details of the Meno you won't need me to - but perhaps forgive those who haven't.

I want to try and prove something very simple, but to really prove it. I want to prove that the two angles marked must be the same.

I am positing that there are two parallel straight lines here and another straight line crossing both of them. I want to prove that the two angles I have marked X must then be equal.

It isn't quite what Socrates tried to get the boy to agree, but it's a bit long to go through that in a lecture and this will serve the same purpose.

Here is the proof. Watch very carefully.

Start with the following triangle:

Take a copy of it:

Turn this one around:

Now join up the two triangles along their longest line:

Look! The two angles are the same!

And the two lines AB and CD are the same length (because one is a copy of the other).

So we have the case of one line crossing two parallel lines.

QED

Is this an example of a priori knowledge? Are there others?

A priori knowledge is knowledge you have independently of any experience. It is contestable whether there can be such. Plenty of people say: everything you know has to come from what you are told, or what you find out by looking - by observing, by experimenting. These are people who deny the possibility of a priori knowledge.

Those who believe there is such a thing, that there are things we know independently of what we find out through observation etc. have in mind a variety of examples.

Here are some candidates I prepared earlier: possible examples.

A real ragbag.

Theories about the possibility of a priori knowledge.

1. Plato

Plato's theory is that we do have a priori knowledge and that we bring it with us from an earlier existence...

SOCRATES: Then he who does not know [the slave boy before Socrates has brought his 'knowledge' to the surface] may still have true notions of that which he does not know?

MENO: He has.

SOCRATES: And at present these notions have just been stirred up in him, as in a dream; but if he were frequently asked the same questions, in different forms, he would know as well as any one at last?

MENO: I dare say.

SOCRATES: Without any one teaching him he will recover his knowledge for himself, if he is only asked questions?

MENO: Yes.

SOCRATES: And this spontaneous recovery of knowledge in him is recollection?

MENO: True.

SOCRATES: And this knowledge which he now has must he not either have acquired or always possessed?

MENO: Yes.

...

And I am certain that no one ever did teach him.

SOCRATES: And yet he has the knowledge?

MENO: The fact, Socrates, is undeniable.

SOCRATES: But if he did not acquire the knowledge in this life, then he must have had and learned it at some other time?

MENO: Clearly he must.

Plato, Meno, 85c

What other theories are there?

2. A priori knowledge consists of analytic truths

Hume's is one version.

How did Hume think of mathematics?

He thought of it as a matter of the relation between ideas.

Let me explain in terms not of maths itself but of what we might call logical truths - truths which seem even more obviously to flow from relations between ideas.

Take the idea of a brother. Hume would say:

This is the idea of a male joined to the idea of a sibling.

The idea of a male is contained in the idea of a brother, so when we assert that a brother is male this is true, but true in virtue of the second idea simply being a component of the first idea.

Brothers are male

[Male + sibling] includes [male]

Male = male

So in saying 'brothers are male' we are asserting something that is necessary. The relation between brothers and maleness is a necessary one. Brothers must be male.

3. We can work out that experience is possible only if we possesses certain concepts, and we can work out what these these concepts must be.

For example, could we have any experience if we didn't have the concept of time?

Or could we imagine what such experience would be like?

Could you argue that you can't have experience unless you think of one sensation following another? (and to think of one sensation following another you have to have the concept of time?)

What about space.

Could we have experience at all if we didn't have the concept of space?

Is it possible to imagine what experience would be like if we didn't have the concept of space?

These are the type of questions pursued by Kant.

There is a priori knowledge. It takes the form of truths about what concepts are presupposed by our having experience.

4. There are some truths (eg mathematical truths, logical truths) to which our reason gives us partial access.

5. Mathematical and logical truths are empirical generalisations - there is no a priori knowledge.

Is this another thing you can prove?