Deductive and inductive arguments

In everyday speech, we say, ‘You make a valid argument’, ‘You have a valid point’, ‘That’s a sound point’, ‘That’s a good argument’, ‘That’s a strong argument’ and so on. This is rather loose-speak. In Philosophy, the notion of validity, soundness, goodness and strength have stricter definitions.

Validity is a feature of deductive arguments. A deductive argument is a form of logical reasoning where the conclusion necessarily follows from the given premises, and we call such an argument valid. We are concerned with the logical structure or form of the argument, not the contents. We are not saying that the premises are true; we are merely stipulating that if the premises were true then the conclusion necessarily follows. Thus, an argument can be valid even if the premises are in fact false.

Here is an example of a logically valid argument:

          P1:    All humans are mortal.

          P2:    Socrates is a human.

          C:     Therefore, Socrates is mortal.

If Premises 1 and 2 are true, the conclusion is necessitated.

Soundness is also a feature of deductive arguments. Here, we are concerned with the contents. If the argument is valid and if the premises are indeed true, then we have a sound argument. If the argument is invalid or at least one of the premises is false then the argument is unsound. The preceding argument is sound.

An inductive argument is a form of logical reasoning where the premises make the conclusion more probable. We do not say that an inductive argument is valid or invalid. It cannot be valid because we have defined validity as a feature that guarantees the conclusion. Instead, we say that the argument is strong (makes the conclusion much more probable) or weak (does not do much to make the conclusion more probable).

Here is an example of a strong argument:

          P1:     The Sun has risen every day for 4.5 billion years.

          C:      Therefore, the Sun will probably rise tomorrow.

Here is an example of a weak argument:

          P1:    Every week, several people win on the lottery.

          P2:    I have bought a ticket.

          C:     Therefore, I will probably win.

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