Inductive Arguments Arguments n Two kinds of arguments

Inductive Arguments

Arguments n Two kinds of arguments n Deductive - conclusion doesn’t tell us more about the world than the premisses

Arguments n Two kinds of arguments n Deductive - conclusion doesn’t tell us more about the world than the premisses n Inductive – does claim to tell us more

Arguments n Two kinds of arguments n Deductive - conclusion doesn’t tell us more about the world than the premisses n n If children like ice-cream, and Bob is a child, then Bob likes ice-cream Inductive – does claim to tell us more

Arguments n Two kinds of arguments n Deductive - conclusion doesn’t tell us more about the world than the premisses n n If children like ice-cream, and Bob is a child, then Bob likes ice-cream Inductive – does claim to tell us more n All the swans I have seen are black. Therefore all swans are black

Inductive Arguments 1. A useless argument is one in which the truth of the premisses has no effect at all on the truth of the conclusion. 2. A weak argument is one in which the likelihood of the conclusion’s being true is not much affected by the truth or falsity of the premisses. 3. A moderate argument is one in which the likelihood of the conclusion being false if the premisses are true is quite low. 4. A strong argument is one in which the likelihood of the conclusion being false if the premisses are true is very low. 5. A valid argument is one in which it is just impossible for the conclusion to be false if the premisses are true.

Inductive Arguments Strong (Justified) n if the premises are true the conclusion is made much more likely to be true n n Cogent n Strong and has true premisses

(Deductively) Valid (Inductively) Justified Inductive Arguments All ravens observed in the past have been black ----------------------------The raven observed yesterday was black All ravens observed in the past have been black ----------------------------Any raven observed will be black In this argument we have a premise providing conclusive support for the conclusion (merely) strong support for the conclusion The argument is logically good since the reason is The reason is not conclusive, however it is conclusive nonetheless a strong reason and so the argument is good No further premises can undercut the argument's strength The addition of further premises can undercut the argument's strength. Add: 'The observed group is atypical' and the previously strong argument becomes weak! Validity is said to be monotonic Inductive strength is non-monotonic Valid arguments merely spell out the consequences Inductive arguments draw conclusions which go

Misconceptions Valid arguments are better than strong ones n n Not always. Getting true premises to ensure the conclusion may be impossible. All ravens are black Any raven on Pikes Peak will be black n All observed ravens have been black Any raven on Pikes Peak will be black Certainty is a virtue if obtainable, but where it is not obtainable a high degree of probability is better than none at all!

Misconceptions Valid arguments go from the general to the particular, whereas inductively strong ones go from the particular to the general n n Not always. Valid Inductively Strong John and Phil are extremists John is an extremist All ravens we have seen have been black The next raven we will see will be black

Inductive Arguments Three kinds n n Argument from Analogy Inference to Best Explanation Inductive Generalisation

Argument from Analogy We may observe a very great similitude between this earth which we inhabit, and the other planets, Saturn, Jupiter, Mars, Venus, and Mercury. (a) They all revolve around the sun, as the earth does, although at different distances and in different periods. (b) They borrow all their light from the sun, as the earth does. (c) Several of them are known to revolve round their axis like the earth, and by that means must have a like succession of day and night. (d) Some of them have moons, that serve to give them light in the absence of the sun, as our moon does to us. (e) They are all, in their motions, subject to the same law of gravitation, as the earth is. From all this similitude, it is not unreasonable to think that those planets may, like our earth, be the habitation of various orders of living creatures. There is some probability in this conclusion from analogy.

Argument from Analogy P 1 P 2 The Earth has (a), (b), (c), (d), (e) The Earth also has life P 3 (e) C Other worlds have (a), (b), (c), (d), Other worlds also have life

Argument from Analogy n Standard Form P 1 P 2 The Analogue has P 1, P 2, …, Pn The Analogue also has property P P 3 The Object has properties P 1, P 2, …, Pn C The Object also has property P

Argument from Analogy n Standard Form (inductive part) P 1 P 2 The Analogue has P 1, P 2, …, Pn The Analogue also has property P P 2* If A & B have P 1, P 2, …, Pn they have P

Argument from Analogy n Standard Form (deductive part) P 2* If A & B have P 1, P 2, …, Pn they have P P 3 The Object has properties P 1, P 2, …, Pn C The Object also has property P

Argument from Analogy Evaluating Arguments from Analogy n n Are the premisses true?

Argument from Analogy Evaluating Arguments from Analogy n n n Are the premisses true? Is the analogy strong?

Argument from Analogy Evaluating Arguments from Analogy n n n Are the premisses true? Is the analogy strong? n Are P 1, P 2, …, Pn relevant to P?

Argument from Analogy Evaluating Arguments from Analogy n n n Are the premisses true? Is the analogy strong? n n Are P 1, P 2, …, Pn relevant to P? Are there disanalogies?

Argument from Analogy Evaluating Arguments from Analogy n n n Are the premisses true? Is the analogy strong? n n n Are P 1, P 2, …, Pn relevant to P? Are there disanalogies? Is the conclusion too strong?

Abductive Arguments n Inference to Best Explanation You return home to find your door broken and some valuable items missing. This cries out for explanation. 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 mistakenly, and (4) you were robbed. Explanation 4 seems the best, so you conclude you were robbed.

Abductive Arguments n Inference to Best Explanation P 1 Phenomenon A is observed P 2 Explanation X explains A and does so better than any rival explanation C X is the case

Abductive Arguments Evaluating Inference to Best Explanation n n Is there anything that needs explaining?

Abductive Arguments Evaluating Inference to Best Explanation n Is there anything that needs explaining? What is the ‘best’ explanation? n Evaluate for Strength

Abductive Arguments Evaluating Inference to Best Explanation n Is there anything that needs explaining? What is the ‘best’ explanation? n Evaluate for Strength n Does it really explain?

Abductive Arguments Evaluating Inference to Best Explanation n Is there anything that needs explaining? What is the ‘best’ explanation? n Evaluate for Strength n n Does it really explain? Is it more widely applicable?

Abductive Arguments Evaluating Inference to Best Explanation n Is there anything that needs explaining? What is the ‘best’ explanation? n Evaluate for Strength n n n Does it really explain? Is it more widely applicable? Is it as simple as possible?

Abductive Arguments Evaluating Inference to Best Explanation n Is there anything that needs explaining? What is the ‘best’ explanation? n Evaluate for Strength n n Does it really explain? Is it more widely applicable? Is it as simple as possible? Is it conservative of prior beliefs?

Abductive Arguments Evaluating Inference to Best Explanation n Is there anything that needs explaining? What is the ‘best’ explanation? n Evaluate for Strength n n n Does it really explain? Is it more widely applicable? Is it as simple as possible? Is it conservative of prior beliefs? Have we checked all the reasonable explanations?

Enumerative Induction n A generalised conclusion about the character of some class as a whole is drawn from characteristics of a sample of the class

Enumerative Induction n A generalised conclusion about the character of some class as a whole is drawn from characteristics of a sample of the class Swan 1 is white Swan 2 is white Swan 3 is white All swans are white

Enumerative Induction Evaluating Enumerative Inductions n n True premisses?

Enumerative Induction Evaluating Enumerative Inductions n True premisses? Sample size? Biased Sample? n n n Insufficient variation Prejudice and stereotypes