Analysing arguments: premises, conclusions, validity and soundness

What this dot point is asking

This dot point asks you to take a piece of reasoning apart, label its parts, and judge how good it is. This is criterion 2 of the TASC course: using logic to develop and analyse arguments.

Premises and conclusions

An argument has two kinds of statement. The conclusion is the claim the arguer wants you to accept. The premises are the reasons given for it. Indicator words help you locate each part. Words like because, since and for usually introduce premises, while therefore, thus, hence and so usually introduce conclusions. Putting an argument into standard form, with each premise numbered and the conclusion last, makes its structure visible.

Deductive and inductive reasoning

Philosophers distinguish two broad kinds of inference. In a deductive argument the premises are meant to guarantee the conclusion. In an inductive argument the premises are meant only to make the conclusion probable. The classic deductive example comes from Aristotle, who founded formal logic with the syllogism:

• Premise 1: All humans are mortal.
• Premise 2: Socrates is a human.
• Conclusion: Therefore Socrates is mortal.

An inductive example reasons from observed cases to a general rule, as when David Hume noted that we expect the sun to rise tomorrow because it has always done so. Hume warned that no number of past observations can logically guarantee a future result, which is the famous problem of induction.

Validity

Validity is a property of deductive arguments only, and it concerns structure rather than truth. An argument is valid when it is impossible for all the premises to be true and the conclusion false at the same time. Crucially, an argument can be valid even when its premises are false. Consider:

• Premise 1: All fish can fly.
• Premise 2: Sharks are fish.
• Conclusion: Therefore sharks can fly.

This is valid, because if the premises were true the conclusion would have to follow, yet it is obviously not a good argument because premise 1 is false. Validity alone does not give us truth.

Soundness

A sound argument is a deductive argument that is both valid and has all true premises. Because a sound argument is valid, its conclusion cannot be false. The Socrates syllogism above is sound: it is valid in form, and both premises are genuinely true, so the conclusion is guaranteed. When you evaluate a deductive argument you therefore ask two separate questions. First, is the structure valid? Second, are the premises true? Only when both answers are yes is the argument sound.

Strength and cogency for inductive arguments

Inductive arguments are not described as valid or sound. Instead we call them strong or weak depending on how probable the premises make the conclusion, and cogent when a strong argument also has true premises. A survey of a large, representative sample gives a strong inductive argument; a survey of three friends gives a weak one. Keeping deductive and inductive vocabulary separate is a common marker of clear thinking in the exam.

Evaluating arguments well

A strong analytical answer does three things. It reconstructs the argument charitably in standard form, it tests the structure for validity, and it scrutinises each premise for truth. If the argument fails, you should say precisely where: is the inference invalid, or is a premise false? This precision is what distinguishes a philosophical evaluation from a mere disagreement.