Logic is the science of argument evaluation; it includes methods and criteria for deciding whether arguments are reliable. In this context, the term ‘argument’ has a meaning quite distinct from its everyday use as a difference of opinion: an argument is a group of statements, consisting of evidence and a conclusion. Evidence statements are called premises, and the conclusion is claimed to follow from these premises. For example, the following argument consists of three simplified statements, of which the first two are premises and the third is a conclusion:
All A are B. All B are C. Therefore, all A are C.
Deduction vs. Induction
Scientific logic has two distinctive branches: deduction and induction. Surprisingly, most scientists do not know the difference between these two types of inference. I, for example, used the word ‘deduced’ incorrectly in the title of my first major paper. Sherlock Holmes is indelibly associated with deduction, yet many of his ‘deductions’ were actually inductive interpretations based on subtle evidence.
To a first approximation, deduction is arguing from the general to the particular, whereas induction is arguing from the particular to the general [Medawer, 1969]. Often scientific induction does involve generalization from the behavior of a sample to that of a population, yet the following inductive argument goes from the general to the particular:
In spite of many previous experiments, never has a relationship between variables X and Y been observed. Therefore, this experiment is unlikely to exhibit any relationship between X and Y.
In a deductive argument, the conclusion follows necessarily from the premises. In an inductive argument, the conclusion follows probably from the premises. Consequently, totally different standards are applied to deductive and inductive arguments. Deductive arguments are judged as valid or invalid by a black-or-white standard: in a valid deductive argument, if the premises are true, then the conclusion must be true. Inductive arguments are judged as strong or weak according to the likelihood that true premises imply a correct conclusion. Statistical arguments are always inductive. The following argument is inductively strong but deductively invalid:
No one has ever lived more than 150 years. Therefore I will die before age 150.
A mnemonic aid for the difference between deduction and induction is: deduction is definite; induction is indefinite and uncertain.
Both deductive and inductive arguments are evaluated in a two-step procedure:
- Does the conclusion follow from the premises?
- Are the premises true?
The order of attacking the two questions is arbitrary; usually one considers first whichever of the two appears to be dubious. The distinction between induction and deduction lies in the evaluation of whether the conclusion follows from the premises.
