“All cats are creatures understanding French,” said Alice’s father. “And some chickens are cats.”
“Wait, I know!” said Alice, chirruping. “That means that some chickens are creatures understanding French.”1
“What you said is true, my dear,” said Alice’s father, his voice full of pride.
What Alice said was true. As true as any another truth, too. True as true can be. But it would still be a mistake for Alice, even if she ventured through the looking glass, to announce triumphantly that “It is true that some chickens are creatures understanding French!” That would be to say what is false, or rather it would be to say a nonsensical thing.
Which was Alice’s father’s specialty. Nonsense of a special sort, that is. For if you haven’t guessed, Alice’s father is Charles Dodgson, a.k.a. Lewis Carroll. Dodgson published several—
—Wait! Hold on. Skip the biography. Didn’t I just say that what Alice first said was true? How can it be that her second phrase, identical to the first, is not true?
Well, her second phrase was not identical, was it? The first time Alice spoke she said, “That means…” and it is that “that” that makes all the difference. The second time she skipped this all-important phrase. One simple word separated truth from falsity. Let’s see why.
Dodgson’s example came from his Symbolic Logic (p. 57). He said that his propositions were
so related that, if the first two were true, the third would be true. (The first two are, as it happens, not strictly true in our planet. But there is nothing to hinder them from being true in some other planet, say Mars or Jupiter—in which case the third would also be true in that planet, and its inhabitants would probably engage chickens as nursery-governesses. They would thus secure a singular contingent privilege, unknown in England, namely, that they would be able, at any time when provisions ran short, to utilise the nursery-governess for the nursery-dinner!)
This distinction is crucial, so I will repeat it. What Alice said the first time was true but only because she accepted the first two statements, the things her father said. She brought those first two phrases along with her when she said, “That means…” She left them out in the second instance, where her audience could not be expected to know that all cats, etc.
The first statement was true because of the provisos she accepted. The second statement was nonsensical, because it was not anchored, it was left floating. The audience could not say why “some chickens are creatures understanding French.” without some kind of evidence.
Those in the audience were free to supply their own evidence, of course. One person might have said to himself, “I know of no chickens who can understand French, but I’ll allow the possibility.” Given that, this person would not say Alice’s statement was exactly true, but he would also not claim that it was exactly false. A second person might have said, “Chickens don’t have lips, which are needed to speak French,” and, given that, he would say Alice was speaking a falsehood.
We have learnt two things from this example that we should never forget. We can’t speak of truth or falsity without reference to evidence, and logic is not the study of propositions but the study of connections between propositions.
A careful reader will have paused over this last sentence and say to himself, “If we can’t speak of truth or falsity without reference to evidence, does that apply to the claim that ‘we can’t speak of truth or falsity without reference to evidence’?” I am, after all, claiming it is true that “we can’t speak of truth or falsity without reference to evidence.” What evidence do I offer?
Well, in order not to go too far afield and not burden us in technicalities, I will let you yourself supply that evidence as homework. Can you think of any claim of truth (or falsity) which does not refer to evidence? If you can, then you have refuted my claim. If you cannot, my claim is not necessarily proved, of course, because just because you can’t think of a counter example doesn’t mean a counter example doesn’t exist. Nevertheless, I do make the claim.
1I was reminded of this example by reader Scott Bury.