The Philosopher's Toolkit - Julian Baggini

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is invalid by replacing these variables with other terms that produce true premises but a clearly false conclusion. (Replacing terms creates what logicians call a new ‘substitution instance’ of the argument form.) If we substitute ‘cat’ for X, ‘meat eater’ for Y, and ‘the president of the United States’ for Z, we get:

      1 All cats are meat eaters.

      2 The president of the United States is a meat eater.

      3 Therefore, the president of the United States is a cat.

      The premises are true, but the conclusion clearly false. This cannot therefore be a valid argument structure. (Showing that an argument form is invalid by making substitutions that result in true premises but a false conclusion is called showing invalidity by ‘counterexample’. It’s a powerful skill well worth cultivating. See 1.7 and 3.12.)

      SEE ALSO

      1 1.2 Deduction

      2 1.4 Validity and soundness

      3 1.7 Fallacies

      READING

       * Irving M. Copi (2010). Introduction to Logic, 14th edn

       * Harry Gensler (2016). Introduction to Logic, 3rd edn

       * Patrick J. Hurley and Lori Watson (2017). A Concise Introduction to Logic, 13th edn

      Ralph Waldo Emerson (1803–82) may have written in his well‐known 1841 essay, ‘Self‐reliance’, that ‘a foolish consistency is the hobgoblin of little minds’, but of all the philosophical crimes there are, the one with which you really don’t want to get charged is inconsistency. For most purposes it’s not too much to say that consistency is the cornerstone of rationality. To do philosophy well, therefore, it’s crucial to master the idea and the practice of consistency.

      Statements are contradictory when they are opposite in ‘truth value’: when one is true the other is false, and vice versa. Statements are contrary when they can’t both be true but, unlike contradictories, can both be false. With contraries, at least one is false.

      Consistency, like contradiction and contrariety, are about comparing two or more different statements. A single sentence can, however, be self‐contradictory when it makes an assertion that is necessarily false – often by conjoining two inconsistent sentences, such as p and not‐p (1.12). You might call such a sentence self‐inconsistent. (Compare this with the idea of the paraconsistent in 3.10.)

      All this can be boiled down to a simple formulation: two or more statements are consistent when it’s logically possible for them all to be true (a) in the same sense and (b) at the same time. Two or more statements are inconsistent when it is not possible for them all to be true in the same sense and at the same time.

      Apparent and real inconsistency: the abortion example

      At its most flagrant, inconsistency is obvious. If I say, ‘All murder is wrong’ and ‘That particular murder was right’, I am clearly being inconsistent, because the second assertion is clearly contrary to the first. (One might be false, both might be false, but both can’t be true.) On a more general level, it would be a bald contradiction to assert both that ‘all murder is wrong’ and ‘not all murder is wrong’. (One must be true and the other false.)

      But sometimes inconsistency is difficult to determine. Apparent inconsistency may actually mask a deeper consistency – and vice versa.

      Many people, for example, agree that it is wrong to kill innocent human beings. And many of those same people also agree that abortion is morally acceptable. One argument against abortion is based on the claim that these two beliefs are inconsistent. That is, critics claim that it is inconsistent to hold both that ‘It is wrong to kill innocent human beings’ and that ‘It is permissible to destroy living human embryos and fetuses’.

      Exceptions to the rule?

      But is inconsistency always undesirable? Some people are tempted to say it is not. To support their case, they present examples of statements that intuitively seem perfectly acceptable yet seem to meet the definition of inconsistency. One example might be:

      It is raining, and it is not raining.

      Of course, the inconsistency might be only apparent. What one may actually be saying is not that it’s raining and not raining, but rather that it’s neither properly raining nor not raining, since there is a third possibility – perhaps that it is drizzling, or intermittently raining – and that this other, fuzzy possibility most accurately describes the current situation (3.1).

      What makes the inconsistency only apparent in this example is that the speaker is shifting the sense of the terms being employed. Another way of saying the first sentence, then, is that, ‘In one sense it is raining, but in another sense of the word it is not’. For the clauses composing this sentence to be truly inconsistent, the relevant terms being used must retain precisely the same meaning throughout. But, when you do unearth a genuine logical inconsistency, you’ve accomplished a lot, for it can be very difficult if not impossible to defend the inconsistency without rejecting rationality outright. There are poetic, religious, and philosophical contexts, however, in which this is precisely what people find it proper to do.

      Poetic, religious, or philosophical inconsistency?

      That kind of difficulty, however, may extend farther than religious contexts. Atheist existentialist philosopher Albert Camus (1913–60) maintained that there is something fundamentally ‘absurd’ (perhaps inconsistent?) about human existence. Post‐structuralist philosopher Jacques Derrida’s theory of différance raises metaphysical

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