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 (or broken) on the next toss is still just 50–50. Because this factual error about probabilities remains so common and so easy to commit, it has been classified as a fallacy and given a name. It’s a fallacy, however, only in an informal way.
Now, logicians speak in these precise ways about fallacies (as ‘formal’ and ‘informal’), but remember that sometimes ordinary speech deviates from logicians’ technical usages. Sometimes any widely held though false belief is described as a ‘fallacy’. Don’t worry. As the philosopher Ludwig Wittgenstein (1889–1951) said, language is like a large city with lots of different avenues and neighbourhoods. It’s alright to adopt different usages in different parts of the city. Just keep in mind where you are.
SEE ALSO
1 1.5 Invalidity
2 3.11 Conversion, contraposition, obversion
3 4.5 Conditional/biconditional
READING
* S. Morris Engel (1974). With Good Reason: An Introduction to Informal Fallacies
* Irving M. Copi (1986). Informal Fallacies
* H. V. Hansen and R. C. Pinto (1995). Fallacies: Classical and Contemporary Readings
Scott G. Schreiber (2003). Aristotle on False Reasoning
* Julian Baggini (2006). The Duck that Won the Lottery
1.8 Refutation
Samuel Johnson was not impressed by Bishop George Berkeley’s argument that material substance does not exist. In his Life of Johnson (1791) James Boswell reported that, when discussing Berkeley’s theory with him, Johnson once kicked a stone with some force and said, ‘I refute it thus.’
Any great person is allowed one moment of idiocy to go public, and Johnson’s attempt at a refutation must be counted as just such a moment, because he wildly missed Berkeley’s point. The bishop would never have denied that one could kick a stone; he denied that stones properly understood can be conceived to be material substances. But Johnson’s refutation also failed even to be a true refutation, a concept that in philosophy has a precise meaning.
To refute an argument is to show that its reasoning is bad. If you, however, merely register your disagreement with an argument, you are not refuting it – even though in everyday speech people often talk about refuting a claim in just this way. So, how can one really refute an argument?
Refutation tools
There are two basic ways of doing this, both of which are covered in more detail elsewhere in this book. First, you can show that the argument is invalid: the conclusion does not
