Plato and the Forms

1. Plato and the Forms • According to Plato, common sense is wrong. We do not sense the world as it really is. • The senses present the world in a confused way. • The mind ‘sees deeper’. It sees the true natures of things. • Plato explained this with the Allegory of the Cave

2. The real things – forms – exist outside. The analogy of the cave: ordinary mortals see only the shadows of reality. The forms project their shadows onto the cave wall… …just as the forms are somehow dimly projected into real things.

3. The Forms • Reality contains forms. They are the timeless and changeless natures of things. • They contrast with particular things in the ordinary world (of appearances) which are constantly changing. • But why believe this story? How do acquire knowledge?

4. Plato, Change and Sameness The world shows signs of both stability and change, difference and plurality. A beautiful painting must be created, may be adjusted and may be destroyed: all examples of change. Two beautiful pictures may look very different yet both be beautiful. There can be many beautiful things. So, beauty can’t belong to the world open to the senses. Beauty itself cannot change or be destroyed: we could still talk and think about it in the absence of beautiful things. Beauty belongs in a different realm to the realm of appearances and it is reason that gives us access to it. The senses only reveal a world of change. But there is nevertheless something stable here: beauty itself. These beautiful things must ‘share’ it to be all called beautiful.

5. Area = πr2 We know many truths about circles But no circles we see or draw are perfect. 360o in a circle. The Imperfection Argument So, our knowledge must be of some perfect circle - the Form of the circle. Magnified section of circumference And since it can’t be sensed, it must be grasped by reason. Circle Ideal geometrical circles have unjagged circumferences with no width and are infinitely thin.

6. In the world of appearances, everything is changing. It is sunny now but it might not be later. Knowledge is of truths - if you know something, it can’t be false. The Knowledge Argument I cannot therefore know it is sunny. …and so exist in a separate realm accessible to reason. …which cannot exist in the world of appearances accessible to my senses … I can merely have theopinion or believe that it is. …the forms… Knowledge must be of changeless things…

7. There must be some explanation for why things belong in kinds. What makes something the kind of thing it is? What makes two things members of the same kind? What makes a badger a badger? What makes these two things badgers? The “one over many” argument: if x and y are badgers, there must be something – the Form of the badger – that they have in common. They both “participate in” the Form of the badger. The “One Over Many” Argument World of forms World of appearances These days, philosophers talk of universals instead of forms. Form (archetype) of the badger The Form of a badger is not present where the badgers are but exists in a different realm. The universal badger exists in each and every badger. It is quite unlike an ordinary object, as an object can be only in one place at any one time. Objects are a type of particular. But the universal exists in many places at once – it is repeated throughout its instantiations – and hence is called a universal. Participation Fundamentally, however, we’re talking about the same thing – an entity that makes a particular belong to a kind or makes it the kind of thing it is. Aristotle thought forms were immanent – located in the physical realm where their instantiations are (he would have understood them as universals) whereas Plato thought they were transcendental – located in another realm altogether.

8. Why study the forms? This is useful: we like beautiful things and we want to praise acts of goodness and punish badness. We recognise examples of beauty and goodness. But we also want to go deeper and ask what it is that we recognise. But there is also a purely philosophical angle: simply finding out the nature of the reality we inhabit. Socrates would ask, “What is beauty? Truth? Justice?” There is obviously a practical angle. People differ over what they think is right. People are sometimes uncertain. We need to remedy this. He was searching for the nature or essence or, to use Plato’s word, the formof beauty.

9. Something F in one context may not be F in another. Picture A may be beautiful in relation to picture B... ...but not in relation to picture C. Since the painting can be beautiful and not beautiful, it can't provide us with a definition of what is beautiful. Whatever beauty is, it can't fail to be beautiful. Since any thing that we find beautiful could fail to be beautiful in another context, we can't simply collect beautiful things together and hope that they will share some simple sensory property that we can identify as the property of being beautiful. The Context Argument (*) Context 1 Context 2 We have to look for the Form of the beautiful or beauty: the thing that makes beautiful things beautiful. It is the essence of beauty. But it cannot be detected by the senses, only reason. Why? Take a beautiful painting. In one context beautiful, in another not. But nothing about how the painting appears changes. So, we're looking in the wrong place if we look for beauty amongst perceptible properties.

10. In this embodied life, our knowledge of the forms is buried and must be unearthed by exercising reason – doing philosophy. Reason gives us knowledge of the Forms (universals)– the essences of things. Before we were born, our souls lived in the world of Forms. Plato and the Forms: Summary The Forms cannot be detected with the senses but only with reason. The Knowledge/Change Argument: the Forms are unchanging. Sensory experience reveals a changing world. So, the Forms are non-sensible. The Context Argument: whether a painting is beautiful or not varies with the context but its sensible features do not. So, the Forms can’t be sensible. The Imperfection Argument: No perfect circle can exist in the sensible world, only approximations. No actual circle can be infinitely thin and perfectly curved. One Over Many: If x and y are both F, then there must be something, F, that they have in common.

11. Knowledge of the forms: Meno and the Slave-boy How do we know about the form? Because we have innateideas, gained from when our souls existed in the world of forms. When we are born, our soul ‘forgets’ the ideas and they need to be recollected. Plato demonstrates this by getting Meno’s slave boy to prove a mathematical theorem. By asking a series of questions, Socrates gets the slave boy to work out the area of two squares So, if AD = DL, then AL= ? …4ft. And so the area of ALKJ is…? …8 ft2 If ABCD is a square and AD is 2 feet, then the area is… …4 ft2 No – for ABCD is 4ft2 and there are how many such squares in ALKJ? Four. So the area is…? 16ft2 Now, BDNM is composed of four parts each of which has what area? 2ft2 So, the area of BDNM is..?8ft2 This shows that the boy knew all along the relevant principles of geometry.

12. Problem: Learning or recollecting? Was Socrates asking fair questions? Or was he giving the boy the right answers disguised as questions? We might defend Plato thus. For example, it might be that you suddenly see how to calculate a percentage… Sometimes, all a teacher can do is get you to work through examples until you ‘get it’ with a flash of understanding. …or understand an argument, such as the ones we’ve looked at here.

13. Problem: Forms can’t be sensed. Common sense tells us that we should believe our eyes. …We must ask whether there’s a better explanation. But we can’t sense the forms. We believe in them as they provide the best explanation of the world we can sense. So that is how we should judge whether to believe in forms or not. We can’t sense God or numbers or atoms either.

14. Problem: Will appearance do? Socrates tells us there is a form of beauty but not of hair. So, we identify hair on the basis of (perhaps) what it is made out of, what it looks like, where it is found. But why not say the same about beautiful things? If we could, we wouldn’t need to say that there is beauty itself as a strange thing in a realm of forms. There’s no such thing as perfect hair! Socrates tells us that appearances will do. Examples of hair are just like examples of beautiful things: they differ from one another, change and can be destroyed But then how do we identify hair?

15. Question: Will ideas do? Why don’t we say that there isn’t really a perfect circle ‘out there’… Perhaps nothing! Just as people have different ideas about what is right and wrong, why not about maths and geometry? …it’s just an idea in my mind. It is an idea in your mind as well. But what about when you think of it? But what guarantees we have the same idea?

16. Question: Will ideas do? This won’t work. It is inconceivable that 2+2=5. Try making it work! Even babies have some innate mathematical skills! If 2+2=5, then 2=3? And 0=1??? If by putting 2 by 2 I get 5, I could fill the universe! …Every people that have ever thought about maths have arrived at the same ideas about numbers and shapes. Surely this shows there’s just one true set of ideas. And I could change the past by simply thinking about two people I met yesterday alongside two other people I met yesterday – I could now make a fifth person appear then!