William M. Briggs

Statistician to the Stars!

Sloppy Language About What’s True: Part I

“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. Charles Dodgson

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.

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1I was reminded of this example by reader Scott Bury.

14 Comments

  1. Alice was Alice Liddle the daugter of the Dean of Christ Church, Oxford.

  2. I am, after all, claiming it is true that “we can’t speak of truth or falsity without reference to evidence.”

    CONSIDER: “God exists.” (and to simplify, consider that “God” to be one of the “Christian” gods).

    No “evidence” for that. In fact, much of what is hailed as “evidence” has some serious flaws.

    HOWEVER, to even address that, one must necessarily first define WHICH CHRISTIAN GOD? — as there are several, though people work very hard to see it not that way. Which is to say that most work hard on not seeing what is very apparent to anyone paying any attention.

    Shortly after Martin Luther split up what had been a going monopoly, there was (outside of the R. Catholich Church) the view that there was the One God that pre-destined certain people to salvation, others would not be “saved” (though nobody knew where they stood). This was a view held by a sizeable proportion of the first immigrants to the New World.

    Others, today, believe that God saves those who merely believe someone really existed.

    Others disagree–that good behavior is still mandated. And that behavior better not include homosexuality, which is verboten…though Episcopalians might have it either way, depending (for example).

    Some say God has inspired authors to present literal writings — as a result things like evolution and billion-year old Earth cannot possibly be true (e.g. http://www.answersingenesis.org). Others have precisely the opposite viewpoint–reading the same source material and finding the opposite (e.g. http://www.reasons.org).
    — Consider how the same source material documents lead to such diametrically opposed conclusions as how credible they are as “evidence.”

    Others say God never got into the science to that depth (arguably, the R. Catholic church has straddled both postions with Galileo…later backpeddling & accepting things like evolution, in general).

    Our standards for “Christian”-based behavior have likewise evolved radically:
    Jamestown, VA in its early days made this a core value: http://www.virtualjamestown.org/rlaws1.html
    So did England, etc.–prompting the Pilgrims to emigrate as the religion of the “Prince of Peace” was, in practice, incredibly violent & unforgiving: http://www.loc.gov/exhibits/religion/rel01.html
    And still is: http://www.bbc.co.uk/news/world-middle-east-16347418 & http://www.guardian.co.uk/world/2004/sep/28/israel.religion
    And still even the most devout are inspired to maintain petty feuds that put the most sacred landmark’s existance at risk: http://www.loweringthebar.net/2009/03/brawl-at-the-sepulchre.html

    Such a list can go on & on….the inescapable point is that we truly make God in our image, to serve whatever particular selfish ends we hold (recall Jeramiah Wright’s “God Damn America! …. it’s in the bible” remarks, etc.)…and have done so so very well that so many mutually incompatible versions exist one can have pretty much whatever one wants…and stay free to change one’s mind along the way. THAT IS EVIDENCE–EVIDENCE OF JUST HOW (such as it is) INFLUENTIAL THIS GOD IS (i.e. in the absence of direct objective evidence one can use indirect indicators, patterns, etc. — like juding a tree by its fruits…basically the same).

    But, there is no “evidence” for God. Which is why it is called “faith” — and, in the USA moreso than anywhere else on the planet, “faith” as indicated by “Christianity” (whatever that means to whoever is using the term at a given moment) has achieved a diversity religious historians (e.g. Bart Ehrman, etc.) have noted has become comparable to that observed in the first century.

  3. I dropped mathmatical logic somewhere after we discussed that “There is something rotten in the state of Denmark” was equivelant to “Not everything in Denmark is not rotten.” Where is the poetry?

  4. Briggs

    20 January 2012 at 3:57 pm

    Ken,

    You have become side-tracked. If the proposition you question is “God exists”, then if that is true, it is true based on evidence. There are many offers of this evidence. But if it is false, it is false based on evidence. There are offers of evidence here, too.

    Let us not concern ourselves (here) with whether either set of evidence is conclusive. We only must demonstrate, for my claim to be true, that such evidence exists.

    Which we have.

    Your comments, therefore, are no counter-example.

  5. Answer = no.

    Spent a pleasant month as an undergrad with cognito ergo sum, soft determinism,
    hard determinism, etc. and as expected got nowhere.

    But then – on any given Wednesday I am apt to decide I don’t really believe in electrons
    anymore.

  6. Bill S.,

    Electrons will be hard to disbelieve when they gather in early Nov. Depends on their choice, I guess.

  7. @Doug M,

    True, some would even say ‘Alice Liddell’, daughter of Henry.

  8. So far so good, mr Briggs. I’ll give you a 20/20, specially on the cautious wordings. IOW, spoken like a real relativist ;). Let’s see if you fall on self-made traps of your own device later on ;).

  9. How about non-Euclidean Geometry?

    Using proof by contradiction, mathematicians were trying to prove that the parallel postulate was true. Rather that proving what they set out to prove, they developed a whole new “truth.” A truth that did not fit the evidence of the time.

    After the fact, we found the applications for this new “truth.”

  10. Briggs

    21 January 2012 at 10:28 am

    Luis,

    You won’t be happy! I’ll be proving that relativism fails.

  11. Briggs

    21 January 2012 at 10:30 am

    Doug M,

    Doesn’t work. You still have a chain of argument, i.e. evidence, that leads to the conclusion “non-Euclidean Geometry” is true or false.

    Remember, all, we’re not after a certain proposition that is true or is false. We want to show how we know these propositions.

  12. Many French are chicken.
    so many chickens are French.
    All French speak French so it seems
    some chickens speak French.
    cats don’t get a word in Frenchways.

  13. It seems self-evident that you can’t make a moue with a beak. Do cows speak French?

  14. Alice’s first claim is of the form “(if A and B) then C”, with implied bracketed part, and may be valid logic, but you can argue that “validity” is a different category to a “true” statement about the real world, and conclude her statement is not true in the usual sense of truth.

    From a single example suggesting certain specific evidence is sufficient to make one statement true, you conclude that evidence is necessary for all statements. That seems rather weak justification for your belief. To put it on firmer ground you will need to explore the nature of evidence. Whether evidence is required depends on what you mean by “reference” to evidence. For a true but non-evidence-referring claim, how about “This statement is in a language you understand or have had translated”?

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