Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 4

Precise generalisations make it more difficult to divert from the topic. The quantifier ‘some’ does not mean ‘most’ or ‘all’ when making generalizations, although when stating ‘some A are B’ it is possible that all A are B.

An argument is inductively forceful if the conclusion does not necessarily follow from the premises but is still ‘probably true’. It is very likely to be true and unlikely to be false. To say that an argument is inductively forceful means that the probability of A relative to the set is greater than one-half but less than one.

The proportion indicate the part of A in the total (e.g. 7/8). Frequency refers to the number of times something occurs. The degree of rational expectation refers to the degree to which a person is entitled to believe a proposition given the evidence provided. Frequency and proportion could be used to calculate probability. Probability is a matter of degree and so is an argument being inductively forceful. The degree of indicative force of an argument is independent of the truth-values of the premises.

INDUCTIVE SOUNDNESS
An argument is inductively sound if the argument is inductively forceful and its premises are true. Another word for inductive soundness is cogency. An inductive inference refers to extrapolating from a sample of a total population of things either to something outside the sample or to a generalisation about the population as a whole. An inference is an inductive inference if it is not deductively valid, its premises include a generalisation about a sample of a given population and its conclusion extrapolates the generalisation to all or part of the total population from the sample. It frequently involves extrapolation from the past to the future. The inductive force of an argument is equal to the conditional probability of the conclusion relative to the premises.

In order to make a proper inductive inference, the sample needs to be representative of the population. An argument can be forceful and sound but the conclusion may still not be accepted. The argument is then overridden by other information one has and the argument is defeated.

CONVERSION OF INDUCTION TO DEDUCTION
An inductive argument can be converted into a deductive one by making explicit the basis for the inductive principle:

For example:

• P1: All of the observed sample of jackdaws are monogamous
  P2: If all of the observed sample of jackdaws are monogamous, then all jackdaws are monogamous
  -----------------------
  C: All jackdaws are monogamous

P2 is the added premise to make it a deductive argument. If P2 is not added it is a forceful inductive argument. People tend to make the base rate fallacy.

A PROGRAMME FOR ASSESSMENT
There is a programme for assessment of arguments:

1. Is the argument deductively valid?
2. If not, proceed to 2
3. If yes, are all the premises true?
4. If yes, the argument is deductively sound. STOP
5. If not, the argument is valid but unsound. STOP
6. Is the argument inductively forceful?
7. If not, the argument is neither valid nor inductively forceful. STOP
8. If yes, how forceful is it? Write ‘probably’ or a suitable variant, in a conclusion.
9. Are the premises true?
10. If yes, the argument is inductively sound. STOP
11. If not, the argument is neither deductively nor inductively sound. STOP