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Whether or not they are actually true, suppose or pretend that the premises were all true; then in that situation -aside from how things really are - could the conclusion conceivably be false? If it could not be, then the argument is valid. If it could, then the argument is invalid.

The systematic study of validity is the concern of logic. Logicians are concerned to devise perfectly reliable procedures for detecting validity, or the lack of it, even in the case of extremely complex arguments such as those occurring in mathematical proofs. Since the validity of an argument is independent of the truth-values of its premises, logic has a unique status amongst the sciences; for other sciences are concerned to find out the truth-values of particular propositions about its characteristic subject matter. Ichthyology, for example, seeks to know which propositions about fish are true, and which false. The logician has no particular concern with fish, nor with the truth as regards anything else in particular. Logic has no concern with particular truths. In a sense, the logician does not have to know anything. The logician is concerned only with relations between propositions, not with their truth-values. These are the sorts of relations displayed between premises and conclusion in valid arguments such as 1-5. There are sophisticated technical procedures involving special symbols for exploring these relationships in a systematic, detailed way. Such is the concern of what is known as 'formal logic', 'mathematical logic' or 'symbolic logic'. Courses on the subject are taught in philosophy, mathematics, linguistics and computer science.

In critical thinking we are doing what you might call practical logic. We want to learn to identify the reasoning in commonly encountered attempts to persuade us, and to assess it as good or bad. For this, we need the concept of validity, but we do not need elaborate technical procedures for detecting validity. The reason is that the logic of the vast majority of arguments in everyday life is rarely of any great complexity. Once we know exactly what the argument is, whether or not it is valid can, almost always, simply be seen by applying the definition given above. Most of the work goes into the reconstruction. And as we have seen - and will see in more detail later - we cannot profitably reconstruct an argument without knowing what makes a good argument, hence not without grasping the concept of validity.

Logic: deductive validity

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