1. Inductive Argument Forms

2. Induction vs. deduction
Inductive arguments aim to make the conclusion probable, not certain, though sometimes, extremely probable.
False conclusion is logically compatible with true premises.
A strong inductive argument: one where true premises would render the conclusion highly likely.
inductive counterpart of validity

3. Induction vs. deduction
Strength of inductive argument comes in degrees.
Additional information can make it rational to retract the conclusion, without retracting the premises.

4. Statistical Syllogism

5. universal modus ponens statistical syllogism
Most
universal modus ponens
All As are Bs
x is an A
x is a B
statistical syllogism
Still a reasonable inference, but no longer deductive, no longer UMP

6. How strong is a statistical syllogism?
Depends on
proportion of As that are premised to be Bs
whatever other information you possess
rule of total evidence

7. Rule of Total Evidence
Strength of any inductive argument is determined not just by what’s internal to the argument, but by everything else you know.

8. Defeaters: considerations that tell against accepting a conclusion.
Rebutting defeaters: evidence for thinking the conclusion is false.
Undercutting defeaters: reasons for rejecting the argument that aren’t reasons for rejecting the conclusion.

9. Two arguments; one for thinking she can, one for thinking she can’t
Sheila can read music.
(CONCLUSION)
Most musicians can read music.
(PREMISE)
Sheila is a musician.
(PREMISE)
Most drummers can’t read music.
(PREMISE)
Sheila is a drummer.
(PREMISE)
Solid black indicates positive support
Two arguments; one for thinking she can, one for thinking she can’t
Dotted blue indicates defeat
in this case, rebutting defeat
What to conclude?

10. Statistical syllogism
n% of As are Bs.
x is an A.
x is a B.

11. Statistical syllogism
n% of As are Bs.
x is an A.
x is a B.
reference class

12. Statistical syllogism
n% of As are Bs.
x is an A.
x is a B.
reference class
attribute class
We’re attributing B to x, by reference to its being A.

13. Statistical syllogism
In the earlier example, Drummer is a narrower reference class than Musician:
all drummers are musicians, but not vice versa.
Use statistical syllogism only for the narrowest reference class for which you have information.
Given our evidence, we should infer that Sheila cannot read music.

14. Inductive Generalization

15. Inductive generalization
x% of observed As have been Bs.
x% of As are Bs.

16. Inductive generalization
x% of observed As have been Bs.
x% of As are Bs.
sample

17. Inductive generalization
x% of observed As have been Bs.
x% of As are Bs.
sample
population

18. Sample must be representative of the population.
no systematic difference
large and random
have variety that matches population
homogeneous population
carefully crafted (stratified) sample

19. Defeaters for Inductive Generalization

20. Biased sample serves as undercutting defeater.
Most people think dinner should start at 4 P.M.
(CONCLUSION)
Most of the people we surveyed thought dinner should start at 4 P.M.
(PREMISE)
The survey was conducted at a retirement home.
(PREMISE)
Biased sample serves as undercutting defeater.
not a reason to deny the conclusion, but a reason not to believe it on the basis of this argument
(hence the arrow attacking the other arrow, not the conclusion box)

21. Fallacies of inductive generalization
Hasty generalization
small sample
Biased statistics
unrepresentative sample
Misleading vividness
relying on anecdotes, rather than inductive generalization

22. Fallacies of inductive generalization
Argument from counterinstances
rejecting statistical generalization (“most As are Bs”) on the grounds of one or a few counterinstances (“here’s an A that’s not a B”)
note, this is a legitimate defeater for a universal generalization (“all As are Bs”)

23. Representativeness heuristic
(Unreliable) System1 heuristic for making fast judgments about probabilities, relative frequencies
Probability that something is a member of a group based on how much it resembles a stereotypical member of that group

24. Availability heuristic
Another unreliable System1 heuristic for making fast judgments about probabilities, relative frequencies
Judge how common something is on the basis of how easy it is to think of examples
but easiness is affected by vividness, recently, rarity, etc.
factors other than how common it really is

25. a.k.a. Analogical argument
Argument From Analogy
a.k.a. Analogical argument

26. Argument from analogy x resembles y in known respects. y has F.
x has F.
Dolphins and whales breathe air, give live birth, and are warm-blooded.
Dolphins lactate.
Whales (probably) lactate.

27. Strength of analogical argument
Strength of analogy (degree of similarity)
relevance of similarities
Fallacy of false analogy otherwise

28. Inference to the Best Explanation

29. Inference to the best explanation
We have such-and-such data.
Hypothesis H
would explain the data,
sufficiently well
and do so better than any rival hypothesis we can think of.
Therefore, H.

30. Best explanation? Genuinely explains Has some independent plausibility
Is simple and unified
rather than a grab-bag of independent hypotheses
Ockham’s Razor: everything else being equal, we should believe the simpler hypothesis over the more complicated one.

31. Balance of Features

32. each feature serves as independent evidence
It was a great movie.
(CONCLUSION)
The plot was engaging.
(PREMISE)
The acting was superb.
(PREMISE)
The cinematography was fantastic.
(PREMISE)
The characters were well-developed.
(PREMISE)
We argue that the movie was great by listing some “greatness-making” features the movie had.
The argument has an independent-premise (rather than a linked-premise) structure.
each feature serves as independent evidence
hence the converging, rather than bracketed, arrows

33. “Greatness-ruining” features serve as rebutting defeaters.
It was a great movie.
(CONCLUSION)
The plot was engaging.
(PREMISE)
The acting was superb.
(PREMISE)
The characters were well-developed.
(PREMISE)
The cinematography was fantastic.
(PREMISE)
The special effects were terrible.
(PREMISE)
It was 6 hours long.
(PREMISE)
“Greatness-ruining” features serve as rebutting defeaters.