- What is wrong with what Goodman calls the 'Most Naïve' or 'Resemblance' account of representation?
- Explain the Peirce/van Fraassen 'Of-As' view of representation.
- Why does Wigner say that the effectiveness of mathematics in science is 'unreasonable'?

**The structure of a representation**. We have characterised representation as a certain kind of relationship between a source and its target.- According to Peirce, representations fall into three categories: 1)
*iconic representations*, which resemble their targets, 2)*indexical representations*, which display causal relations, and 3)*symbolic representations*, which denote their target. Try to give an example of each. - Is everything a representation of itself? Is anything a representation of itself?
- If X is a representation of Y, does it follow that Y is a representation of X? Is it ever possible to have a situation in which X and Y represent each other?
- If X is a representation of Y, and Y is a representation of Z, does it follow that X is a representation of Z? Under what circumstances (if any) might this follow?

- According to Peirce, representations fall into three categories: 1)
**The Most Naïve 'Resemblance' View**. The simplest initial view of representation is that it is a matter of resemblance.- Give an example of a representation that does not resemble its taret.
- Give an example of two things that equally resemble their target, but are not equally good representations.
- Are there any special circumstances under which the resemblance view of representation is correct? What might those circumstances be?

**The Of-As View of Representation.**The Of-As view of representation involves three components: a target, a source, and a use/aim.- How are those targets supposed to be related?
- Give an example in which two source representations have the same target, but are different, because of a differing use/aim.
- Give an example in which the same source representation can have two different targets, because of a differing use/aim.
- We described the representation relation as involving an arrow. What does that arrow represent?

**The unreasonable effectiveness of mathematics**. Mathematics provides a number of different kinds of representations that are incredibly effective at describing the world, from equations to graphs to abstract diagrams.- Do you find this unreasonable?
- Why would it be reasonable if we thought that mathematics shares an aim with science?
- Wigner thought that the aims of mathematics and science were very different. Why? Do you agree with him?
- Is mathematics really all that effective? If so, what do you think explains the effectiveness of mathematics in science?