1. Which of Mill’s methods does research through controlled experimentation closely resemble?

2. Which of Mill’s methods does the correlational method resemble?

4. Classical Theory of Probability ◦ (a priori theory of probability) This our oldest theory of probability. Although it is useful, its use is limited to particular conditions.

8. Relative Frequency Theory: Relative frequency theory does not require the assumption that all possible outcomes are equally probable.

9. Relative Frequency Theory: Unlike the a priori classical theory of probability, relative frequency theory depends on actual observations of frequencies of events happening in the world. This makes it applicable outside of things like gambling.

12. These results hold true only in the long run - not for individual events and series of individual events.

13. The fact that a coin has a.5 probability of coming up heads doesn’t mean that if you flip a coin four times you’ll get 2 heads.

14. Strictly speaking, neither the classical nor relative frequency methods can assign probability to individual events.  To try and do so, without drawing on additional theoretical tools, is to misapply the theory.

15. “Probabilistic instantiation” It is easy to accidentally move from a claim about a statistical generalization to a claim about a specific event in a way that is completely unwarranted.

16. From the general frequency n of outcome X occurring in the population, infer that specific event x has an n % chance of occurring.

19.  This is fallacious!  It does not follow from the fact that the probability of an arbitrarily selected individual getting cancer is.001 that Rando himself has a.001 probability of getting cancer. ◦ Once we’re talking about a specific individual, the inference doesn’t hold: Rando might have a gene that makes it super likely for him to end up with cancer, or take a drug that accidentally increases his risk, or so on. He also might have a far lower risk.

20. From your thousands of observations, you might have very good support for the claim that the frequency of cancer in a population is.001. But you need additional information to infer that a particular individual has a.001 chance of getting cancer.

21. A different way to interpret claims about probability allows for claims about individual events, though it has a cost.

22. The Subjectivist Theory understands probability claims as claims about degrees of belief, that individuals have with regard to the occurrence of an event or the truth of some proposition. We can assume that this knowledge: ◦ Is incomplete. ◦ Fluctuates daily with learning and forgetting. Thus, probabilities are subject to change.

23.  Subjectivist interpretation, in order to be useful at all, requires empirical knowledge: ◦ The more you know, the more accurately you can assign probability. ◦ However, you can be very vulnerable to error if you’re not careful!

24. NOTE: Assigning probabilities – degrees of belief – must be constrained by rationality/ coherence. This doesn’t mean seemingly irrational beliefs are barred. It means your beliefs are consistent in a particular way.

25. COHERENCE: ◦ Probability assignments are like wagers. ◦ A group of bets is coherent precisely if it does not expose the person wagering to certain loss, regardless of the outcomes of whatever events he’s betting on (and regardless of whether his betting opponent makes good choices)

26. We’ll get into this stuff more with the probability calculus, next time.