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involving inconsistency (7.4). Dialetheists and others have even challenged the idea that consistency is fundamental to logic (3.10). Perhaps, then, Emerson was right, and there are contexts in which inconsistency and absurdity paradoxically make sense.

      Consistency ≠ truth

      Be this as it may, inconsistency in philosophy is generally a serious vice. Does it follow from this that consistency is philosophy’s highest virtue? Not quite. Consistency is only a minimal condition of acceptability for a philosophical position. Since it’s often the case that one can hold a consistent theory that is inconsistent with another, equally consistent theory, the internal consistency of any particular theory is no guarantee of its truth. Indeed, as French philosopher‐physicist Pierre Maurice Marie Duhem (1861–1916) and the American philosopher Willard Van Orman Quine (1908–2000) have separately maintained, it may be possible to develop two or more theories that are (1) internally consistent, yet (2) inconsistent with each other, and also (3) perfectly consistent with all the data we can possibly muster to determine the truth or falsehood of the theories (7.11).

Take as an example the so‐called problem of evil. How do we solve the puzzle that God is supposed to be good but that there is also awful suffering (an apparent evil) in the world? As it turns out, you can advance a number of theories that may solve the puzzle but remain inconsistent with one another. You can hold, for instance, that God does not exist. Or you can hold that God allows suffering for a greater good. Although each solution may be perfectly consistent with itself, they can’t both be right, as they are inconsistent with each other. One theory asserts God’s existence, and the other denies it. Establishing the consistency of a position, therefore, may advance and clarify philosophical thought, but it probably won’t settle the issue at hand. We often need to appeal to more than consistency if we are to decide between competing positions. How we do this is a complex and controversial subject of its own.

      SEE ALSO

      1 1.12 Tautologies, self‐contradictions, and the law of non‐contradiction

      2 2.1 Abduction

      3 3.10 Contradiction/contrariety

      4 7.2 Gödel and incompleteness

      5 7.6 Paradoxes

      READING

       David Hilbert (1899). Grundlagen der Geometrie

       * P.F. Strawson (1952/2011). Introduction to Logical Theory

       * Fred R. Berger (1977). Studying Deductive Logic

       * Julian Baggini and J. Stangroom (2006). Do You Think What You Think You Think?

       * Aladdin M. Yaqub (2013). Introduction to Logical Theory

1.7 Fallacies

      The notion of ‘fallacy’ will be an important instrument to draw from your toolkit, for philosophy often depends upon identifying poor reasoning, and a fallacy is nothing other than an instance of poor reasoning – a faulty inference. Since every invalid argument involves a faulty inference, a great deal of what one needs to know about fallacies has already been covered in the entry on invalidity (1.5). But while all invalid arguments are fallacious, not all fallacies involve invalid arguments. Invalid arguments are faulty because of flaws in their form or structure. Sometimes, however, reasoning goes awry for reasons not of form but of content.

When the fault lies in the form or structure of the argument, the fallacious inference is called a ‘formal’ fallacy. When it lies in the content of the argument, it is called an ‘informal’ fallacy. In the course of philosophical history, philosophers have been able to identify and name common types or species of fallacy. Oftentimes, therefore, the charge of fallacy calls upon one of these types.

      Formal fallacies

      We saw in 1.4 that one of the most interesting things about arguments is that their logical success or failure doesn’t entirely depend upon their content, or what they claim. Validity is, again, content‐blind or topic‐neutral. The success of arguments in crucial ways depends upon how they structure their content. The following argument form is valid:

      1 All Xs are Ys.

      2 All Ys are Zs.

      3 Therefore, all Xs are Zs.

      For example:

      1 All lions are cats. (true)

      2 All cats are mammals. (true)

      3 Therefore, all lions are mammals. (true)

      With this form, whenever the premises are true, the conclusion must also be true (1.4). There’s no way around it. With just a small change, however, in the way these Xs, Ys, and Zs are structured, validity evaporates, and the argument becomes invalid – which means, again, that it’s no longer always the case that if the premises are true the conclusion must also be true.

      1 All Xs are Ys.

      2 All Zs are Ys.

      3 Therefore, all Zs are Xs.

      For example, substituting in the following terms results in true premises but a false conclusion.

      1 All lions are cats. (true)

      2 All tigers are cats. (true)

      3 Therefore, all tigers are lions. (false)

This is an instance of showing invalidity by counterexample (1.5, 3.12). If this form were valid, it wouldn’t be possible to assign content to it in a way that results in true premises but a false conclusion. The form simply wouldn’t allow it. This is an important point. As we work our way through various fallacies in this book, pay attention to whether or not the fault in reasoning flows from a faulty form or something else.

      Informal fallacies

      What about fallacies that aren’t rooted in a faulty form at all but instead in characteristically misleading content? How do they go wrong? A well‐known example of an informal fallacy is the gambler’s fallacy – it’s both a dangerously persuasive and a hopelessly flawed species of inference.

      The gambler’s fallacy often occurs, for example, when someone takes a bet on the toss of a fair coin. The coin has landed heads up, say, seven times in a row. On the basis of this or a similar series of tosses, the fallacious gambler concludes that the next toss is more likely to come up tails than heads (or the reverse). What makes this an informal rather than a formal fallacy is that we can curiously present the reasoning here using a valid form of argument, even though the reasoning is bad.

      1 If I’ve already tossed seven heads in a row, the probability that the eighth toss will yield a head is less than 50–50 (that is, a tails is due).

      2 I’ve already tossed seven heads in a row.

      3 Therefore, the probability that the next toss will yield a head is less than 50–50.

      The form is perfectly valid; logicians call it modus ponens, the way of affirmation (see 3.1). Formally, modus ponens looks like this:

      1 If p, then q.

      2 p.

      3 Therefore, q.

      The flaw rendering the gambler’s argument fallacious instead lies in the content of the first premise – the first premise is simply false. The probability of the next individual toss (like that of any individual toss) is and remains 50–50 no matter what toss or tosses preceded it.

Sure, the odds of tossing eight heads in a row are very low. But if seven heads in a row have already been tossed (a rare event, too), the chances of the sequence of eight in a row being completed

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