1. Laws of Nature

2. Aristotle’s Explanations
Aristotle’s structure of knowledge consisted of explanations such as:
Statue is Bronze Bronze is Brown Statue is Brown
Inductions gave us fundamental middle terms for these explanations

3. Aristotle’s Explanations
Aristotle thought there were 4 types of explanation depending on the type of ‘cause’
Formal (statue has legs … it’s the image of a man)
Material (it’s brown … it’s bronze)
Final (it was made … it honours Pericles)
Effective (it looks like a man … it’s from a mould)
We thought that only this sort of cause was interesting to science

4. Aristotle’s Explanations
Aristotle’s example of an efficient cause
Why is the child ugly?
Because the father is ugly
The father is ugly An ugly father will have an ugly child The child is ugly
The middle premiss looks like a ‘law of nature’

5. Aristotle’s Explanations
Laws of Nature
An ugly father will have an ugly child
A hockey stick dipped into water will appear to bend
A dropped cannonball will accelerate as it falls
One billiard ball hitting another will make it move
These are causal relations
Identified by induction on particular observations?

6. Hume on Causes
What’s the relationship between those two billiard balls?
Event 1: BB1 strikes BB2
Event 2: BB2 moves away from BB1
Event 1 follows Event 2
We say Event 1 causes Event 2
There is some power in E1 that brings about E2
There is some necessary link between E1 and E2

7. Hume on Causes Why do we say there is such a necessary link?
Because we have seen those sorts of events many times
They have always been in that time order
There has always been that sort of immediacy
We conclude by induction that
Any object striking another is followed by the other moving away

8. Hume on Causes
This does not give us the idea of a ‘necessary’ link or a ‘power’
We only see a ‘constant conjunction’ of events
That is all that causal talk can really refer to
The idea of ‘necessity’ and ‘power’ is a trick of the mind
It arises from the constant movement from ideas of one event to ideas of the other
It’s a track worn in the mind by repetition

9. Trouble with Hume on Causes
Is there no difference between ‘accidental’ constant conjunctions and ‘causal’ relationships?
When I leave the lights on in my car the battery goes flat
When I invite people to a BBQ it rains
The first tells me something about the world; the second really doesn’t
What makes the first a Law of Nature and the second not?

10. Mackie on Inductive Support
Instances of accidental uniformities don’t give inductive support for a possible regularity, whereas instances of a Law of Nature do
That certainly seems to capture our attitude to them
We do think that given previous battery examples we can conclude that it will also go flat next time we leave things on
We don’t really think that previous BBQ examples justify concluding that next time it will also rain

11. Mackie on Inductive Support
Instances of accidental uniformities don’t give inductive support for a possible regularity, whereas instances of a Law of Nature do
That certainly seems to capture our attitude to them
But this doesn’t explain how we have these intuitions or justify them
C.f. Goodman’s solution to his New Problem of Induction:
The predicates for which induction works are projectible
Projectible predicates are the ones for which induction works

12. The System Solution
Look at Science as a system of deductions which aims to express all the truths about the world
There are two virtues:
Simplicity: Science could minimise the axioms and derive as much as possible by deduction
Strength: Science could just include all true statements (including what we think of as accidents)
Try to find the system that is optimal with respect to strength and simplicity

13. The System Solution
Laws of Nature are all and only the general statements that appear in all the best systems
Thus battery draining is derivable from generalities about electrons, currents, etc. in all the best systems
BBQ rainouts are not derivable from axioms that appear in all the best systems

14. The System Solution Are these really significant virtues?
Simplicity: are law of natures dependent upon our intellectual capacities?
Do aliens with minds not made like ours live in a universe with different laws of nature?

15. Against Hume
Hume showed that we couldn’t derive our concept of cause by induction.
And therefore not from observation at all
And therefore it’s an unsupported concept

16. Against Hume Two problems
1. Hume is interested in a psychological theory of how concepts can arise. We’re not.
If we can accept that we have a concept of necessity then the problem is not how to generate it, but how to apply it to statements of regularities
We do have a concept of necessity for maths, ethics, habits, etc.

17. Against Hume Two problems
2. Hume is theoretically committed to enumerative induction. We’re not.
We can appeal to an Inference to Best Explanation
Phenomenon C is observed
A explains C and does so better than any rival explanation A
This is clearly an inductive argument, and a common one

18. Against Hume
You return home to find your door broken and some valuable items missing.
Possible explanations include:
1. A meteorite struck your door and vaporised your valuables.
2. Friends are playing a joke on you.
3. A police Tactical Response Group entered your house
4. You were robbed.
Explanation 4 seems the best, so you conclude
You were robbed.

19. Against Hume Object A striking object B is followed by B moving off
Object C striking object D is followed by D moving off …
Object Y striking object Z is followed by Z moving off
These observations could be explained if the event of an object of a certain type striking another object of that type was necessarily connected to the event of the second object moving off.
This is the best explanation on offer for those observations
The event of an object of a certain type striking another object of that type is necessarily connected to the event of the second object moving off.

20. Against Hume
On the other hand just saying causation is this sort of necessary connection doesn’t really get us very far
What is this necessity?
We still don’t have an explanation for causation
And therefore we still don’t have a good criterion for identifying laws of nature