About Rationally Speaking

Rationally Speaking is a blog maintained by Prof. Massimo Pigliucci, a philosopher at the City University of New York. The blog reflects the Enlightenment figure Marquis de Condorcet's idea of what a public intellectual (yes, we know, that's such a bad word) ought to be: someone who devotes himself to "the tracking down of prejudices in the hiding places where priests, the schools, the government, and all long-established institutions had gathered and protected them." You're welcome. Please notice that the contents of this blog can be reprinted under the standard Creative Commons license.

Saturday, December 25, 2010

Michael’s Picks

By Michael De Dora
* WikiLeaks leader Julian Assange defends himself in The Australian by arguing that we shouldn’t shoot the messenger (him) but the message (the corrupt governments), while British journalist Johann Hari posits Assange has made us all safer.
* Meanwhile, the soldier accused of leaking those WikiLeaks documents is enduring some rough jail treatment, as detailed by Glenn Greenwald.
* One very interesting bit of information from those leaked cables: shows like Desperate Housewives and the Late Show with David Letterman are apparently “doing more to persuade Saudi youth to reject violent jihad than hundreds of millions of dollars of US government propaganda.”
* Philosopher Ned Block pens a critical review of neuroscientist Antonio Damasio’s new book on consciousness.
* A new study from the surgeon general further informs us about the harms of tobacco — even a single puff can have a negative impact.
* This story discusses a growing approach of abortion foes, already successful in Nebraska, to pass laws on the idea that fetuses can feel pain at 20 weeks.
* Logician Graham Priest writes about paradoxical truths on the New York Times philosophy blog. Tough subject for the general public, but he does a good job.

* And here's your Christmas special: a look at the religious beliefs of Abraham Lincoln, and a nation grappling with secession, during the Christmas of 1860.


  1. Tell me, Michael, what about Priest's dialetheism interests you? Do you suspect there is something correct about dialetheism or do you think it merely an interesting intellectual exercise?

  2. For a different take on dissecting or dissolving the classic liar's paradox, check something I wrote several years ago (which I've since revised but not necessarily for the better):

  3. @A,

    I do suspect there is something correct about dialetheism, though I should say that logic is very, very far from my area of expertise.

    As for your question, "or do you think it merely an interesting exercise?" I actually don't find the discussion entirely interesting, nor do I see much real-world appeal. I was more posting it for others who might feel differently.

  4. In Dr. Priest's article, where he says "A common suggestion of what it is for B to follow logically from A is that you can’t have A without having B. Given the principle of noncontradiction, if A is a contradiction, you can’t have it. And if you can’t have A, you certainly can’t have A and B. That is, everything follows from a contradiction.", I think he meant "...certainly can't have A and not B". Having A and while not having B is what one would need for it not to be the case that B follows logically from A.

  5. What I learned in my logic class was that the way to resolve the strengthened liar's paradox was to assign the proposition no truth value, and then no contradiction would arise since a contradiction is a claim that a proposition is both true and false.

    So, "This proposition has no truth value" has no truth value just axiomatically, so it's not true (despite appearances) nor false. (Note the difference from his example of "meaningless.")

    Not entirely satisfactory, but no contradictions arose that way. I would imagine it would impose some problems for a theory of truth, though. Dialetheism might be a bit less challenging.

  6. Timothy,

    Rejecting bivalence and positing a third truth value (“neither true nor false”) is a commonly employed solution to liars (Bas van Fraassen and Saul Kripke, e.g., elect for this solution). Unfortunately, however, to many such a solution is no solution at all.

    First, rejecting bivalence is not an available option for one who wishes to maintain classical logic, and, antinomies such as the liar's paradox aside, there remain good reasons to maintain classical logic. Of course, you may respond that one need only reject bivalence in this case (and perhaps very few others), hence leaving bivalence intact otherwise. However, this response borders on the ad hoc and seems largely unnecessary. For instance, we could adopt a less than elegant solution which saves bivalence and allows us to avoid the ad hoc reply (see, for instance, A.N. Prior's solution to the liar). In nuce, truth value gap remedies to liars seem as unsavory as the liars themselves, and one may want to avoid them entirely.

    Second, it is not at all clear that a truth value gap solution works. Consider the statement (1) 'This sentence is not true'. If (1) is true, then (1) is not true, in which (1) is either false or neither true nor false. However, if (1) is either false or neither true nor false then it is not the case that (1) is true. If it is not the case that (1) is true, then (1) is not true, in which case we have a contradiction, which, of course, truth value gap remedies sought to avoid in the first place.


    Your inexperience in logic aside, what do (you think) you find correct about dialetheism?

  7. It would seem that some of you have never heard of the law of the inevitable exception.

  8. I'm gathering from the commentary here that the unstated premise of the paradox of consistency is that things are either true or false. Which would seem, by that same classical logic, to be a premise that is neither true nor false.
    Just sayin'.

  9. Baron P,

    The assumption that every well-formed proposition / sentence, whatever, is either true or false- never neither, never both- has hardly gone unstated: note above the mention of 'bivalence' and 'truth value gaps'. Having said that, I must say I do not see how the rejection of bivalence may lead to a resolution of liars and other consistency paradoxes. In fact, extended liar paradoxes infect a three-valued glutty logic such as LP and a four-valued logic such as First Degree Entailment (which has truth values: true, false, neither tru nor false, and both true and false).

  10. A,
    Try true, false, or maybe. But seriously, the problem lies with our necessity for drawing inferences, no matter what the logical methodology employed. Our inferential mechanisms hold all such up to suspicion.

  11. A, thanks for the A.N. Prior reference. I agree the truth-value-gap solution, as you term it, is ad hoc, but your proposed counterexample to its efficacy doesn't seem to work, in my view, since the negation of truth is falsity, so "This sentence is not-true" is simply to say "This sentence is false."

    If you constructed an operator % to return the other two possible assignments (e.g., %A, where A is true, means A is either false or has no truth value) just brings us back to the strengthened paradox in the article: "This sentence is %-true" i.e. "This sentence is either false or lacks truth value" yields no contradiction by lacking truth value.

    It is ad hoc to say so, just as you point out, since it is an axiomatic departure from the general rule of assigning truth values, but from what I can see there's no instance of saying a proposition is true and false.

    Also, I learned this was not a departure from bivalence since when a sentence lacks truth value it is not a proposition. The way you combine the concepts - "proposition/sentence" - is a bit off, in my view, since there are many well-formed, grammatical sentences that are not propositions, even under the most conservative logic. The paradoxical self-referential sentences are simply a class of declarative sentences that are not propositions.

  12. Timothy,

    I believe there was some miscommunication on my part. Initially, I understood you as advocating a 3-value logic with the following truth-values as a resolution to the liar's paradox: true, false, and neither true nor false.

    Given the truth values, then, to assert 'P is not-true' is to assert either 'P is false' or 'P is neither true nor false.' Similarly, to say 'P is not-false' is to say either 'P is true' or 'P is neither true nor false'.

    However, per your most recent comment, you seem to have not advocated a 3-valued logic as a resolution, but rather that the liar's sentence is without a truth-value entirely; in short, it is meaningless because it is not a truth functional proposition. Is this correct?

    If not, please clarify. However, assuming this is correct, your proposal does not work. Why should one not consider the liar's sentence a truth functional proposition? Simply because it is a self-referential sentence? If so, many other self-referential sentences seem perfectly truth functional, e.g., 'This sentence has twelves letters' seems truth functional (viz., it's false) yet it is self-referential. Merely declaring liar's meaningless because they appear to be contradictory seems ad hoc and worse, question begging? (This is commonly Priest's answer to similar proposals as your own.)

    I combine propositions / sentences because there are some (e.g. myself, Hartry Field, and many others) who reject the existence of propositions as unnecessarily metaphysical. However, any distinction which could be made between propositions / sentences, whatever, should not matter for the present purposes: whether one views sentences, propositions, statements, whatever, as truth functional, liar sentences infect them equally.

  13. As I made an inadequate attempt earlier to infer, the liar's paradox was fashioned to essentially trick our assessment apparatus into a "feeling" that the assertions of both sentences, by any logical assessments of their intended meanings, were either false or lies. Truth was not left as a viable option.
    And by that reckoning, they are untrue, untrue, or without discernible value.

  14. A: "Merely declaring liar's meaningless because they appear to be contradictory seems ad hoc and worse, question begging? (This is commonly Priest's answer to similar proposals as your own.)"

    This reason is basically the right one of the ones you listed (although I have my hesitation in saying it's then meaningless, since truth-bearing is not the only source of meaning, but perhaps I'm wrong in this instance).

    It is ad hoc, but I fail to see how that makes it "not work" or "question begging." It does work, in the sense it allows classical logic to retain all its properties and avoid any contradictions. Labeling it "ad hoc" is true in a sense (but only in a sense - it's the only way I've seen that gets classical logic to cope with the strengthened paradox, altho I haven't looked up the Prior reference besides a skim of the apparently off-point Stanford entry), which is why I said it's not entirely satisfactory to me. But that's not enough to say it doesn't work, especially since we're dealing with axiomatic systems and any axiom set has a certain vulnerability to that accusation. What specifically doesn't work about it?

    Incidentally, your confusion shows why I wish logicians would stop labeling the truth-values of their many-valued logics the way they do. It just seems to add confusion to say the third truth value is "neither true nor false" and the 4th is "both true and false." Just say truth-value-3 and TV-4 and leave it at that - imo, anyway. Obviously none of them agree with me.

    A: "However, any distinction which could be made between propositions / sentences, whatever, should not matter for the present purposes: whether one views sentences, propositions, statements, whatever, as truth functional, liar sentences infect them equally."

    To me, this assertion seems question-begging. In deciding whether strengthened liar paradoxes are a problem for classical logic, you just decided at the outset the only solution I've ever seen "should" be off-limits. Why "should" it be?

  15. Haven't you boys ever heard of the conundrum of the missing purpose?

  16. Hint: What is the difference in the truth value of an intentionally false statement and an unintentionally false one?

  17. Come on, there is no difference. Unless of course it's true that I am lying.

  18. Well, it seems I have no takers to the baited questions left above, so I'll attempt my own answers and let this thread fade into the blogosphere.

    I'd argue that our less than conscious inferential processes assign a purpose value to behaviors, including communicative acts, that adds more levels of complexity to its assessments of "truth value" than we tend to give it credit for.

    First it has to be accepted that we expect/anticipate that all speakers/communicators intend to convey what's most believable, and truth/honesty is presumably the best policy.
    On that basis, the intentionally false statement is probably less false than the unintentional/mistakenly false. Yes, I rashly said less false. The unintentionally false will most often represent the opposite of an accepted (assumed probable) truth. The intentionally false is intended as the antithesis to what the liar believes to be true, but will likely be mitigated by his own conceptual inaccuracies, and in any event may simply be whatever mixture of the factual and the inventive will suit his purposes.
    Any questions? I thought not.


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