1. Remember these terms? Analytic/ synthetic A priori/ a posteriori
Contingent/ Necessary
Inductive/ Deductive

2. Today’s Key Questions What is innatism?
Plato and Leibniz’s arguments for it
Responses to Plato and Leibniz

3. Innatism/ Rationalism/ Empiricism
In this topic, we will be using these technical terms A LOT. It’s really important that you are clear about their meaning, otherwise you will easily get lost!
Innatists argue that we can have a priori, synthetic knowledge because it exists within us innately. Since it’s already within us, we don’t need experience of the world.
Rationalists also claim that we can have real new knowledge about the world that is not based on sense experience. But rather than it being present in everyone at or before birth, we can come to know it by using our powers of reason.
Empiricists claim that all synthetic knowledge is a posteriori. Apart from analytic knowledge (which tells us nothing new), all our knowledge of the world comes from sense experience.

4. Where do we get these ideas/beliefs from? What is their source?
Belief that two plus two makes four
Idea of the colour red
Belief that parallel lines never meet
Concept of beauty
Belief that every event has a cause
Idea of god
Belief that killing innocent people is wrong

5. Innatism They are there at birth, (or perhaps even earlier).
They are a priori, which means they are acquired independent of experience.
They are universal, meaning they are known by everyone.
They are clear and distinct, self-evident, infallible, and the foundation of all our knowledge.
Innate Knowledge
 Innatists claim that we can have synthetic a priori knowledge about the world. This means we can have knowledge gained by reason, not by the senses, which is substantial and not just true by definition.
Innate Concepts This is the claim that our minds are already equipped, from birth, with certain concepts. These are called innate ideas or concepts. Different innatists argue that different concepts are innate. Some of those suggested include: God, Universals, Numbers and Shapes.

7. Plato: Mathematical knowledge is innate…
Plato argues that learning is just remembering things that we already have knowledge of, we just don’t realise it.
He uses the example of mathematical or geometrical knowledge. Socrates asks Meno’s slave boy (who has never been taught geometry) a series of questions, leading him to figure out a geometrical theorem.
Since the boy’s knowledge did not come from experience, it must have been innate.

8. Soc – if the sides are two feet long, what’s the area?
Boy – 2 x 2, which is 4 square feet

9. Soc – Imagine a square whose area is not 4, but 8 square feet
Soc – Imagine a square whose area is not 4, but 8 square feet. What would the length of its sides be?
Boy – Well, I doubled the sides of 2 to get the area of 4. So when the area is 8, the sides must be half that - 4 feet long.
Soc – OK, so you’re saying the sides are 4 feet long. If the sides are 4 feet long, what would the area be?
Boy – 4 x 4, which is 16 square feet. Oh dear!

10. Soc – So, when the sides are 2 feet long, the area is 4 square feet
Soc – So, when the sides are 2 feet long, the area is 4 square feet. When the sides are 4 feet long, the area is 16 square feet. I want to know how long the sides will be when the area is 8 square feet.
Boy – Well, 8 is between 4 and 16. So the answer must be between 2 and 4. The sides will be 3 feet long.
Soc – OK, so you’re saying the sides are 3 feet long. If the sides are 3 feet long, what would the area be?
Boy – 3 x 3, which is 9 square feet. Oh dear!
Soc – So, when the area is 8 square feet, the sides must be between 2 and 3 feet long.

11. Soc – Let’s go back to the first square
Soc – Let’s go back to the first square. If the sides are 2 feet long, what is the area?
Boy – 2 x 2, which is 4 square feet
Soc – And if I put a line like this (it’s called a diagonal), what is the area of this space?
Boy – well, you’ve cut that space in half, so it’s half of 4, which is 2 square feet.

12. Soc – And if I add these other three squares, what is their area?
Boy – they are each 4 square feet
Soc – so what is the area of the space within the diagonals?
Boy – well, each one is half of 4 square feet, which is 2. So the whole space is 2 x 4, which is 8 square feet.
Soc – Hurray! We’ve found the square with area of 8 square feet. How long are its sides?
Boy – the length of the diagonal of a square with sides of 2 feet.

13. Plato and universals
Philosophers use the term ‘universal’ to apply to properties that are shared by many different particular things. For example, we can think of lots of different beautiful things. But beauty itself is a universal.
Plato argues that sense experience only gives us concepts of particular things, not of universals. So our concepts of universals must be innate.

14. Have you ever seen a circle?
What shape is this?
Have you ever seen a circle?

15. Plato and universals
Plato argues that numbers are universals and are therefore innate. Although you may have sense experience of various instances of two things (eg. A pair of gloves), you never have sense experience of ‘two’ itself.
Similarly, our concept of ‘triangle’ or ‘circle’ may be innate. No real objects are perfectly circular. So our concept of ‘circle’ must not derive from our sense experience- it must be innate.

16. Plato and universals
Another example from Plato is the concept of being equal. Because two things we can experience can never be exactly equal, we must not get our concept of equality from experience, so it must be innate.

17. Is Plato right?
Think-pair-share

18. 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.”

19. 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.

20. Necessary Truths
What examples can you think of?

21. Leibniz’s argument for innatism
The senses only give us particular instances
A collection of instance 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.

22. 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?

23. 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.

24. 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 experience 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.

25. 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.

26. Summary What is innatism? Plato and Leibniz’s arguments for it
Responses to Plato and Leibniz