The Self-Confidence Argument for Anarchism Re-visited: Premise 5 and Marco Polo

Back in December, I posted about an original argument against the legitimacy of the state, which I called The Self-Confidence Argument for Philosophical Anarchism. Here’s the argument, again:

  1. This argument is a valid deductive argument. (Premise.)
  2. If this argument is a valid deductive argument and all of its premises are true, then its conclusion is true. (Premise.)
  3. Its conclusion is No state could possibly have legitimate political authority. (Premise.)
  4. If No state could possibly have legitimate political authority is true, then no state could possibly have legitimate political authority. (Premise.)
  5. All of this argument’s premises are true. (Premise.)
  6. This is a valid deductive argument and all of its premises are true. (Conj. 1, 5)
  7. Its conclusion is true. (MP 2, 6)
  8. No state could possibly have legitimate political authority is true. (Subst. 3, 7)
  9. ∴ No state could possibly have legitimate political authority. (MP 5, 8)

Q.E.D., and smash the state.

The problem, of course, is that if this argument is sound, then it seems like you could construct another argument that must also sound, simply by substituting Some states have legitimate political authority everywhere in lines 3, 4, 8 and 9 that No state could possibly have legitimate political authority. And then you’d get an apparently perfectly sound Self-Confidence Argument for the State. It’s easy enough to figure out that there has to be something wrong with at least one of those arguments. Their conclusions directly contradict each other, and so couldn’t both be true. But they are formally completely identical; so presumably whatever is wrong with one argument would also be wrong with the other one. But if so, what’s wrong with them? Are they invalid? If so, how? Whichever argument you choose to look at, the argument has only four inferential steps, and all of them use elementary valid rules of inference or rules of replacement. Since each inferential step in the argument is valid, the argument as a whole must be valid. This also, incidentally, provides us with a reason to conclude that premise 1 is true in both. Premise 2 seems true by definition, under any standard definition of deductive validity. Premise 3 is a simple empirical observation. If you’re not sure it’s true, you can just look down the page to line 9 and find out. Premise 4 is a completely uncontroversial application of standard disquotation rules for true sentences. That seems to leave Premise (5). And premise (5) may seem over-confident, perhaps even boastful. But what it says is that just all the premises of the argument are true; so if it’s false, then which premise of the argument are you willing to deny? Whichever one you pick, what is it that makes that premise false? On what (non-question-begging) grounds would you say that it is false?

On my first post, a commenter named Lexi made the following observation, in order to suggest that you might nevertheless be able to reject Premise 5 — they noted that Premise 5 makes a statement about the truth of all the premises in the argument. But one of the premises it makes the claim about is Premise 5 itself. And perhaps that allows you to cut the knot:

Premise 5 is, at least, unsupportable. In order for all the premises to be true, premise 5 must also be true. The only way to justify premise 5 is by circular reasoning. Given that, maybe it’s not so surprising that you can support any conclusion X with the argument, since circular reasoning can establish any proposition as true.

–Lexi, comment (23 December 2015)

They’re certainly right to observe since premise 5 itself is among the statements premise 5 is quantifying over, its truth conditions would have to be something like:

(T5) Premise 5 is true ≡ Premise 1 is true & Premise 2 is true & Premise 3 is true & Premise 4 is true & Premise 5 is true

That might seem curious, and it involves a certain sort of circularity, but I can’t say I see how it makes the premise insupportable, if that is supposed to mean that you couldn’t give non-circular reasons to believe that Premise 5 is true.

After all, statements like this really are a part of ordinary language in non-philosophical cases. For example, Marco Polo begins his Description of the World by making the following statement in the Prologue:

. . . We will set down things seen as seen, things heard as heard, so that our book may be an accurate record, free from any sort of fabrication. And all who read this book or hear it may do so with full confidence, because it contains nothing but the truth.

This is a pretty common conceit in traveler’s tales: the author frequently assures the reader that everything they say — incredible as it might seem — is true.

But that statement is among the statements in Polo’s book; if he asserts that it contains nothing but the truth, then that sentence, inter alia, asserts that it is itself true:

(M) Marco Polo and his brothers traveled the Silk Road to China, and there he befriended the Emperor Kublai Khan, and along the way they observed the decadent customs of Lesser Armenia, and along the way they traveled among the Turkomans, and . . ., and (M) is true.

Which makes its truth-conditions something like:

(TM) (M) is true ≡ Marco Polo and his brothers did travel the Silk Road to China, and there he did befriend the Emperor Kublai Khan, and along the way they did observe the decadent customs of Lesser Armenia, and along the way they did travel among the Turkomans, and . . ., and (M) is true.

But here’s the thing. It doesn’t seem to me like (M) is insupportable or viciously circular. In ordinary cases, wouldn’t we determine whether it’s true or not by going through the book and checking out the other statements? I.e., some people reading the book might take everything else Marco Polo says there as true; and if so, then they’d take (M) as true as well. Call someone with this attitude towards (M) and its truth-conditions the True Believer. On the other hand, some people doubt parts of his tale — some people for example doubt that he even went to China at all. If so, they typically think not only that the first conjunct is false, but also the last one — if one of his statements is an assurance that all the statements are true, and any of the other statements are false, then that makes at least two falsehoods in total. Call someone with this attitude towards (M) and its truth-conditions the Normal Skeptic.

But now imagine a reader who insisted that they were a skeptic about Polo’s claims — but then, when asked one-by-one, signed off on every one of his other statements, except that they denied the statement that the book contains nothing but the truth. Call someone who takes this attitude towards (M) and its truth-conditions the Degenerate-Case Skeptic. Would Degenerate-Case Skepticism even make sense, as a position you might take with respect to the truth value of the claims in the book? Would it be a supportable claim? If so, how? If anything, it seems like the fault of circular here is mots easily attributed to someone who denies (M), or who mutatis mutandis denies Premise (5), based solely on Degenerate-Case skepticism. If (M) or (5) is false for no other reason that you even in principle could give other than its sui generis falsity, then that seems like a particularly radical form of question-begging.

Of course, you might say that it is insupportable, but so is the alternative, the True Believer’s claim that all the statements are true. So there’s no non-question-begging reason you could give to say that (M) or (5) is true, and there’s no non-question-begging reason you could give to say that (M) or (5) is false. Since the function of an argument is to give reasons to believe that its conclusion is true, if one of the premises cannot have any non-question-begging reason given either for its truth or falsity, then it seems like the argument can’t provide reasons for any conclusions that depend logically on that premise. (As the conclusion of any Self-Confidence Argument does; the MP in the conclusion cites Premise 5.) So you could say that. But now the question is, why say that? Isn’t it normally possible to give reasons for being a True Believer, and reasons for being a Normal Skeptic, even if there are no reasons you can give for being a Degenerate-Case skeptic? Is this kind of claim of radical insupportability the way we normally read texts that make assurances about themselves, like Marco Polo? Should it be?

If it’s not, and it shouldn’t, then should it be the way that we read Premise 5 here, even though it’s not the way we read Marco Polo? If there’s some difference between the two, that suggests reading Marco Polo in this way but not reading Premise 5 in this way, then what if any reason (preferably a principled reason that’s not question begging, and not simply ad hoc) could we give for the difference in semantic treatment?[1]

  1. [1]Or is it a difference in their semantics? Or a difference in something else, e.g. the pragmatics of their use?

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2 replies to The Self-Confidence Argument for Anarchism Re-visited: Premise 5 and Marco Polo Use a feed to Follow replies to this article · TrackBack URI

  1. Nathan Byrd

    I think the problem has to be with #2, though I’m not sure that I could articulate the best reasons for thinking that. The problem seems to be that it’s doing work that it would otherwise never be doing, which seems very suspicious.

    For example, if I made the following argument:

    1) All humans have two legs. (premise) 2) Socrates is a human. (premise) 3) Socrates has two legs (conclusion)

    It doesn’t seem that my argument is better by making it:

    1) All humans have two legs. (premise) 2) Socrates is a human. (premise) 3) If this argument is a valid deductive argument and all of its premises are true, then its conclusion is true. (premise) 4) Socrates has two legs. (conclusion) 5) (4) is true. (conclusion)

    It seems entirely superfluous in ordinary arguments. But in the Self-Confidence Argument, it’s a vital premise. So, something must be going on that is different. It seems that it must be self-referential (or self-supporting, if that’s significantly different) in some unique way here. (Either that, or it’s inherently suspicious or invalid in all other cases but doesn’t seem to have any effect, so we let it go.)

    • Rad Geek

      hmm, well, but it seems like we can have arguments where a premise like #2 does essential work for the validity of the argument, and where it doesn’t cause any logical problems. For example, this summer I had to lead some students through the classical Pythagorean proof that √2 is irrational. Suppose that I opened up a copy of the book, with the proof laid out in deductive form, and started pointing at the proof, and I said:

      “So you see, this argument (the one here in the book) is a valid deductive argument, right?”

      “And all of its premises are true? If there’s one that isn’t true, can you show me which one is false?”

      “Now if it’s a valid deductive argument and all of its premises are true, it’s conclusion must be true, right?”

      “And here’s it’s conclusion, right? It says, ‘√2 is not rational.'”

      “So then it must be that √2 is not rational, right?”

      And we could gloss this dialogue with the following argument:

      Commentary on Pythagoras

      1. This argument, here, is a valid deductive argument.
      2. If this argument is a valid deductive argument and all of its premises are true, then its conclusion is true.
      3. Its conclusion is “√2 is not rational.”
      4. If “√2 is not rational is true,” then √2 is not rational.
      5. All of this argument’s premises are true.

      And that would get us our conclusion:

      C. √2 is not rational

      by the same reasoning. Maybe I’m wrong, but it seems to me that the Commentary on Pythagoras is unproblematically a valid (and in fact a sound) argument, provided that I am in fact pointing to a correct rendition of the classic Pythagorean proof (that proof is a valid argument, and all of its premises are true, its conclusion really is that √2 is not rational, etc.).

      Is there any problem with the argument then, provided that, in context, this argument refers to the argument I’m pointing at in the book, rather than the self-same argument we’re laying out? Does the problem only arise in the Self-Confidence Argument case, where this argument refers to the Self-Confidence Argument itself rather than some other argument I’m pointing to? If it only arises in the Self-Confidence Argument case, then it seems like the problem, whatever it may be, can’t narrowly be attributed to the work that Premise # 2 is doing, because there’s no problem when it does that same work in the Commentary on Pythagoras case. So it seems like the problem must lie elsewhere.

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