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From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 161. I emboldened.

  Do the inferences in this chapter occur anywhere outside the psychological laboratory? In fact, they do crop up from time to time. I was sitting at the exit of a chain store, and a young man was sitting next to me filling in a form, which I knew was to apply for a job in the store. (I’d seen it lying on the next chair when I had first sat down.) At one point, the young man got stuck, and turned to me and asked: “what’s an optimist?” I said: “Someone who always expects good things to happen.” I almost added my favorite definition of an optimist, “An optimist is anyone who believes that optimists exist,” but his accent betrayed that he was not a native speaker of English. My unspoken coda, however, has an interesting property.
  Is it true that optimists believe that optimists exist? Everyone to whom I have put this question, thinks for a moment, and then assents to the proposition. As one person said, “If you didn’t think there were any optimists, you wouldn’t be very optimistic.” I asked a class of some fifty students whether they accepted my definition. They all did. Yet, it can’t be true, and our inability to grasp its defect illustrates the problem we have in making inferences that depend on recursion—the repeated use of a general premise. Ask yourself: do you think that optimists exist? Of course, you do. I believe that there are optimists, and so do you. So, it follows from my definition that we are both optimists too. If others realize that we’re optimists (because we believe optimists exist), they are in the same position as us: they think that optimists exist—namely, us—and so they are also optimists. The definition is a mental infection. It spreads optimism among the population like a happy plague. You pass on the definition, and others succumb at once to it and become optimists. This consequence of the definition is not obvious. Unlike superhuman reasoners, we do not grasp at once the consequences of repeated uses of general propositions. We prefer to think about particular individuals, and then perhaps to use general propositions to update our models. This bias is in keeping with the fundamental principle of the model theory: models represent individuals.
  Why is the definition of optimists false? Optimists do think that optimists exist, but so do many pessimists. Hence, the definition doesn’t apply only to

p. 162

optimists. The proper definition of an optimist is: a person who expects good things to happen. And not everyone is an optimist.

What falsity? The definition includes 'anyone who believes that optimists exist', which includes pessimists.

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It's an elementary rule of definition that a definition must not define a thing by itself - if you are defining 'X' (the definiendum) then 'X' - reference to 'X' - cannot itself occur in the definition (the definiens).

'An optimist is anyone who believes that optimists exist' violates this rule since 'optimist' is to be defined and 'optimist(s)' occurs in the definition.

But the central point is that Johnson-Laird flips between definitions. He asks:

Why is the definition of optimists false? Optimists do think that optimists exist, but so do many pessimists. Hence, the definition doesn’t apply only to optimists.

But why should the proponent of the definition, 'An optimist is anyone who believes that optimists exist', accept this ? By this definition, the people Johnson-Laird calls 'pessimists' precisely are optimists because they believe that optimists exist - this is a definitional truth, given the definition, 'An optimist is anyone who believes that optimists exist'.

Johnson-Laird asssumes a different definition of 'optimist', which he doesn't defend but announces as the 'proper definition', namely that 'an optimist is: a person who expects good things to happen', in order to denote a contrasting class of persons who do not expect good things to happen (or who do expect bad things to happen) and who are therefore 'pessimists'. These people believe, or may very well believe, that there are optimists in the so-called 'proper' sense. But this doesn't show that the original definition of 'optimism', 'An optimist is anyone who believes that optimists exist' is false', since Johnson-Laird has changed the definition of 'optimism' in the course of his discussion.

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This is supposed to be a definition: An X is anyone who believes that Xs exist

Let X = “Human”. All humans, except babies, humans in a coma, and humans with strange philosophical beliefs, believe that humans exist. Let X = “golf player”. All golf players believe that golf players exist. Let X = “serial killer”. All serial killers believe that serial killers exist.

No, it’s not a definition of “optimist”.

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