1. On your whiteboard (1):
1. What is innate knowledge? 2. What were Plato’s arguments for innate knowledge? 3. Was he right? Explain your answer

2. On your whiteboard (2):
Explain these terms: analytic / synthetic a priori / a posteriori necessary / contingent

3. Leibniz
“The senses never give us anything but instances, i.e. particular or singular truths. But however many instances confirm a general truth, they aren’t enough to establish its universal necessity; for it needn’t be the case that what has happened always will – let alone that it must- happen in the same way.”

4. Leibniz
The sun may have risen every morning we’ve experienced, but that doesn’t mean that it will tomorrow. Our next sense experience could be different from our previous ones. But, there seem to be some truths that we know will always be true. Whatever our sense experience was, there couldn’t possibly be a time when doesn’t = 5. Another of Leibniz’s examples is “It is impossible for the same thing to both be and not be”.

5. Necessary Truths
What examples can you think of?

6. Leibniz’s argument for innatism
The senses only give us particular instances
A collection of instances can never show the necessity of a truth
We can grasp and prove many necessary truths (such as maths)
IC. Therefore the necessary truths that we grasp with our mind do not derive from the senses.
MC. Therefore necessary truths must be innate.

7. With your partner:
Are any of these examples convincing in showing that we can have innate a priori knowledge of the world?
Why/ why not?

8. Response 1 - “Innate knowledge” is actually a posteriori
 The empiricist could respond to suggestions of innate knowledge by claiming that these examples are gained not by reason, but by sense experience.
For instance, the slave boy was basing his knowledge on his experience of squares.  
Some philosophers, such as Mill, have argued that all mathematical knowledge is actually based on experience. For instance, I know that = 5 because I have seen 2 things and 3 things, and when I put them together I have seen that they make 5.
Mill claims that there is no a priori knowledge. All knowledge is a posteriori.
If sense experience is required to know these propositions, then they are not innate.

9. Response 1 - “Innate knowledge” is actually a posteriori
The empiricist can respond to Plato by claiming that our concepts of universals really are based on sense experience. For example, by experiencing lots of beautiful things, we can form the concept of the beauty by working out what these things have in common. And we have the concept of two by experiencing two things. Although this may seem plausible for the case of small numbers like two, I can have the concept of the number 8,346,231 without ever having seen a collection of that many things!
Similarly, the empiricist may convince you that you have derived the concept of circle from your experiences of circular things. But Descartes responds to this by pointing out that he can form a concept of a thousand-sided shape, even though he has never experienced one, and he can’t even imagine one.

10. Response 2 - “Innate knowledge” is actually analytic
Another way the empiricist can respond is to claim that these proposed “innate” propositions are only analytically true. They are true just because of the meanings of the words, so they tell us nothing new about the world.
For Leibniz’s example of “the same thing can’t both be and not be”, again if you understand all the words in this sentence, then you know that the claim is true. This truth isn’t something separate from the definitions in the sentence.
If these truths are not synthetic but analytic, then the innatist has failed to prove that there is innate synthetic knowledge.

11. With your partner: What do you think of innatism now?
Justify your position.

12. Summary: Homework: What is innatism?
Plato and Leibniz’s arguments for it
Responses to Plato and Leibniz
Read Locke’s arguments against innatism. Be ready to discuss and evaluate them next lesson.