Induction and Deduction

Massimo Pigliucci of the Skeptical Inquirer is certainly correct in saying that “it is important for anyone interested in critical thinking and science to understand the difference between deduction and induction” (“Elementary, Dear Watson” May/June 2003). However, it has been several decades since logicians have defined that difference in terms of going from general to particulars or vice versa. His own example of deduction belies the problem. It doesn’t go from the general to the particular but from one general and one particular statement to another particular statement. All men are mortal. Socrates is a man. Therefore, Socrates is mortal. General statements aren’t needed at all in the premises of some deductive arguments. For example, “Socrates is a stonemason. Socrates is a philosopher. Therefore, at least one stonemason is a philosopher.” This is a valid deductive argument. “Rumsfeld is arrogant. Rumsfeld is Republican. Therefore, all Republicans are arrogant” is also a deductive argument, though an invalid one, going from particulars to the general.

Induction, says Pigliucci, “seeks to go from particular facts to general statements.” That is true sometimes, but not all the time. Jones was late yesterday so he’ll probably be late today is an inductive argument. I admit it is not a cogent argument, but cogency is a different matter.

The general to particular relationship isn’t rich enough to serve as a good line of demarcation between induction and deduction. Any standard logic text today will make the distinction in terms of arguments that claim their conclusions follow with necessity from their premises (deductive arguments) and those which claim their conclusions follow with some degree of probability from their premises (inductive arguments). This distinction in terms of premises either implying their conclusions with necessity or supporting their conclusions to some degree of probability is not without its problems, however. One virtue of the general/particular distinction is that there is not likely to be any ambiguity about a statement being one or the other. But there will be many cases where it won’t be clear whether an arguer is claiming a conclusion follows with necessity. There will also probably be many cases where the arguer should be claiming a conclusion follows with some degree of probability but the language might well indicate that the arguer thinks it follows with necessity. For example, many people might argue that since the sun has always risen in the east, it is necessarily the case that the sun will always rise in the east. Yet, it isn’t necessarily the case at all. It just happens to be the case and it is easy to imagine any number of things happening to the earth that could change its relationship with the sun.

By dividing arguments into those whose conclusions follow with necessity and those which don’t we end up dividing arguments into those whose conclusions are entailed by their premises and those whose conclusions go beyond the data provided by the premises. A valid deductive argument can’t have true premises and a false conclusion, but a cogent inductive argument might. This may sound peculiar, but it’s not. Even the best inductive argument cannot claim that the truth of its premises guarantees the truth of its conclusion. Even the worst valid deductive argument--that is, one with premises that are actually false--can still claim that if its premises were true, its conclusion would have to be true. No valid deductive argument can guarantee the truth of its premises unless its premises are tautologies. (In logic, a tautology is a statement that cannot possibly be false: e.g., “A rose is a rose” or “Either it will rain or it will not rain” or “If Browne is psychic and stupid, then Browne is stupid.”)

So, how does knowing the difference between induction and deduction have any bearing on critical thinking? If you understand deduction, then you should be able to understand why scientific experiments are set up the way they are. For example, if someone claims to be able to feel another person’s “energy field” by moving her hands above the patient’s body, as those who practice therapeutic touch claim, then she should be able to demonstrate that she can detect another person’s energy field when that field is beneath one of her hands, even if her vision is blocked so that she can’t see which hand is over the alleged energy field. If one can detect energy fields by feel alone then one must be able to detect energy fields without the assistance of any visual or aural feedback from the patient. Likewise, if one claims to be able to detect metal or oil by dowsing, then one ought to be able to detect metal or oil hidden from sight under controlled conditions. If one claims to be able to facilitate communication from someone who is retarded and physically unable to talk or point, then one should be able to describe correctly objects placed in the visual field of the patient even if those objects cannot be seen by the facilitator.

On the other hand, the nature of induction should, at the very least, make us humble by reminding us that no matter how great the evidence is for a belief, that belief could still be false.

See also Austin Cline, Deductive & Inductive Arguments How do they differ?

lesson 2: the concept of validity

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Last updated 14-Jan-2014