Inductive Arguments

Question 1

What is Probability?

Answer 1

• For our purposes, “probability” = “degree of rational expectation.”
• Idealised: not dependent on actual psychology.
• We are interested in conditional probability – the probability that the conclusion is true, given that the premises are true

Question 2

How is an Argument inductively forceful?

Answer 2

• To say that an argument is inductively forceful is to say: the argument is not (deductively) valid, but if the premises were true, then, given the information in the premises, it would be more
  reasonable to expect the conclusion to be true than it would to expect it to be false.

Question 3

Is probability a third truth value?

Answer 3

• Probability is not a third truth value
• Probability (and therefore inductive force) is a matter of degree (unlike truth, and validity). One argument can be more or less inductively forceful than another (whereas validity is all-or-nothing)

Question 4

What is Inductive Soundness?

Answer 4

• Definition: an argument is “inductively sound” when it is inductively forceful, and the premises are actually true.
• Important note: this still doesn’t guarantee the truth of the conclusion (unlike deductive soundness).
• P1) 92% of people from China are lactose intolerant.
  P2) Xiao is from China
  C) Xiao is lactose intolerant

Question 5

What is Inductive inference?

Answer 5

• A very common strategy (especially in science), is where we extrapolate from a sample either to things outside the sample (i.e., new cases: predictions), or to the population as a whole (i.e., to figure out the general laws).
• p.124) An inductive inference is one that: (a) is not deductively valid, (b) includes a generalisation about a sample of the population in its premisses, and (c) extrapolates to the whole population or new cases in its conclusion.
  e.g. every observed goldfish has died after eating cat food, my goldfish will die after eating cat food.

Question 6

What is the problem with inductive interference?

Answer 6

• The conclusion could be false
• This is a worry for science (“The Problem of Induction”); no matter how many white swans you observe, you can’t guarantee the truth of all swans are white

Question 7

What are the Fallacy of Insufficient Statistics and the fallacy of Biased Statistics?

Answer 7

• It must be large enough (otherwise we’d commit the “Fallacy of
  Insufficient Statistics”)
  P1) None of my friends likes artichokes
  C) Nobody likes artichokes
• The sample must be representative (otherwise we’d commit the
  “Fallacy of Biased Statistics”):
  P1) All the philosophers I’ve met wear a lot of tweed.
  C) Everybody wears a lot of tweed.