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Abelard: "If I am not mistaken, then the Democrats will compromise."
Eloise: "I agree: if you are not mistaken then the Democrats will compromise."
Abelard: "You agree: what I said was correct?"
Eloise: "Yes."
Abelard: "Then I am not mistaken."
Eloise: "True."
Abelard: "If I am not mistaken, then the Democrats will compromise. I am not mistaken. Therefore, the Democrats will compromise."

Source (sort of): http://en.wikipedia.org/wiki/Curry's_paradox

Originally posted to gong on Tue Apr 26, 2005 at 01:38 PM PDT.

Poll

So which is it?

11%3 votes
15%4 votes
38%10 votes
26%7 votes
0%0 votes
7%2 votes

| 26 votes | Vote | Results

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Comment Preferences

  •  With apologies... (4.00)
    ...to Haskell Curry.
  •  I get the feeling (4.00)
    from Reid's most recent comments that they will.

    It may be better off overall to NOT shut down the Senate and so forth, and the offer does make Reid and Democrats look more reasonable,

    but even if they ultimately do I wish they'd hold off on offering the olive branch and let the theocratic wingnuttery absorb into the public's mind a little more.  

    Let it become a bigger issue.  Then Americans will remember...for two weeks.  Which I suppose is better than two days.

    Visit www.theseguys.com - a blended double-tequila margarita of pop culture & LA nightlife.

    by KB on Tue Apr 26, 2005 at 01:44:04 PM PDT

    •  i like your thinking (none)
      he is setting himself up as the reasonable one.if the other side goes all buster on the gov. they will look like out of control mafioso.closing down the gov. in a war of choice
    •  Shut down the Senate -- (4.00)
      everything they are doing is bad for America.  The GOP may have had a short-term loss when Newt shut down the government, but look at where they are now.  Plus, shutting down the Senate does not equal shutting down the government.

      Of course, if they were to shut down the Senate then they would have to demonstrate party discipline and get out there and effectively communicate to the country why this was the only option.  Not sure those mealy mouthed DEM Senators could do that.

      What FDR giveth; GWB taketh away

      by Marie on Tue Apr 26, 2005 at 01:58:43 PM PDT

      [ Parent ]

      •  I don't necessarily disagree (4.00)
        I'm not sure whether they should compromise or not...I'm open to arguments either way.  

        I read the Reid cSpan thread, though, and it sounds like they will if they can.  Unless Reid is SO sure Frist and Co. won't take him up on it that he's milking the situation for good Dem PR for all it's worth.

        That's the spin Kos tried to give it on the front page.  Brilliant work on Reid's part if true, but if Frist gives in (thinking that 4 or 5 wingnut judges are better than none) then, fuck, Frist called his bluff and we have 4 or 5 wingnut judges.

        I think it would be WAY bad strategy to offer to compromise in this situation if you didn't intend to follow through if they accept.

        Visit www.theseguys.com - a blended double-tequila margarita of pop culture & LA nightlife.

        by KB on Tue Apr 26, 2005 at 02:07:07 PM PDT

        [ Parent ]

      •  reid (4.00)
        could do it i think....no buster ..no functioning 2 party gov....gov. shutdown..no functioning2 party gov .saveing gov. from radical theocrates.no choice.
  •  Well I voted for gin... (none)
    ...of course.

    Someone voted "all of the above." Hmmm. Is someone using my joke against me?

  •  Armando (4.00)
    Said he was done with the democrats if they compromise.

    Then he had a conference call with Reid and asked us all to play along when it was done.

    Are our front pagers being compromised by access?

    I think you either like a course of action and say why or you don't and say why.

    To say you think the Dems need to stand tuff because of a, b, and c you shouldn't come back and say....after talking to the leadership you should trust me when I say trust them.

  •  Maybe I should say something serious (4.00)
    Of course I am too stupid and uninformed to have an opinion about what Reid and all should do. In fact I am too stupid and uninformed to have an opinion about most things political.

    What I am pretty sure about is that there are some views that ought to be in the public arena, and ought to be defended as well as people are able, and ought to be taken seriously. And one of these views is that an opposition party's job is to oppose, not to make deals. I'm not saying I'm sure it's right (I am too stupid and uninformed to have opinions about strategy), just that I'm sure it ought to be defended and ought to be taken seriously.

    An analogy (or anyway another case): I have no idea if socialism is correct. But I'm all but certain that a political discourse is impoverished if there's no one arguing against private property.

    On the other hand, the view that people on the vaguely-left should promote anti-choice pols but get all fundamentalist about blogs... really I'm not sure why that should be taken seriously.

    That said, I voted for gin.  ;)

  •  a weak paradox, imho (4.00)
    it's quite different from the liar paradox, because Curry's paradox pretends that Abelard and Heloise don't realize that when Abelard says "Then I am not mistaken", he was speaking about a different topic than the topic that Eloise agreed he was correct about.

    So any real-life conversation would go more like this:

    Abelard: "If I am not mistaken, then the Democrats will compromise."
    Eloise: "I agree: if you are not mistaken then the Democrats will compromise."
    Abelard: "You agree: what I said was correct?"
    Eloise: "Yes.
    Abelard: "Then I am not mistaken."
    Eloise: "We haven't discussed the question of whether you are mistaken about the underlying topic yet.  All we've agreed on is that if you are not mistaken, the Democrats will compromise"

    •  Curry's paradox (4.00)
      I disagree. The underlying paradox can be brought out more precisely, but it's a real paradox (and to me it's even more troubling than the liar).

      Sentence 1: If sentence 1 is true, then the Dems will fold.

      Suppose (a hypothesis) that sentence 1 is true.
      Then it is true what sentence 1 says: if sentence 1 is true, then the Dems will fold.
      It follows that the Dems will fold.
      So on the basis of the assumption that sentence 1 is true, we've proven that the Dems will fold.
      Therefore, if sentence 1 is true, then the Dems will fold.
      But that's exactly what sentence 1 says.
      So sentence 1 is true.
      So we've proven that sentence 1 is true, and we've proven that if sentence 1 is true, then the Dems will fold.
      It follows that the Dems will fold.

      (I can do it in symbols if you want. The wikipedia article I linked gives a set-theoretic version. But if you know any set theory, you've probably been trained how to avoid those paradoxes. It's harder with truth, because truth seems somehow familiar, and trustworthy.)

      •  No (none)
        Sentence 1: If sentence 1 is true, then the Dems will fold.

        NO.  Sentence one is: Abelard: "If I am not mistaken, then the Democrats will compromise."

        If Abelard IS mistaken, then the Democrats will not fold, and the sentence is still true.

        •  Er... (none)
          Ignore the version with Abelard and Eloise. Reread the precise version. Sentence 1 is "If sentence 1 is true, then the Dems will fold." Go from there.
          •  no (none)
            no, if you want to reword the paradox, you'll have to reword the whole thing.  If you do so, I'll be willing to analyze your re-worded paradox.
            •  Sorry... (none)
              ...from your tone I assumed you knew Curry's paradox, that you weren't just reacting to the informal version of it that I (mostly) lifted from wikipedia. My first reply to you includes the whole thing, reworded. If that doesn't satisfy, I really can do it semi-formally for you.
              •  I'm not a trained logician (none)
                the only logics class I took was a half-semester over twenty years ago; I'm sorry if my 'tone' misled you.

                Since beginning this discussion today, however, I have read up on the Curry paradox, and the crux of my objection, is that for it to be paradoxical, it requires a supposition.  Perhaps I am misunderstanding it.  But you don't seem to have addressed the specific point I made (when Abelard says "Then I am not mistaken", he was speaking about a different topic than the topic that Eloise agreed he was correct about) .  Given you newfound understanding that I am not a logician, could you please specifically address this point for my edification?

                •  Let me know... (none)
                  ...if my reply below doesn't answer your question. (I admit that it's a subtle point. I just wrongly assumed you already knew it.)
                  •  well (none)

                    I feel like I understand what you are saying perfectly, which is why I find it frustrating that  you are unwilling to specifically address the point I raised in comments 9 and 18.  Could you please try to do so?    Thanks.

                    •  Comment numbers (none)
                      I don't see comment numbers. But I assume that your worry is with the rule of inference "conditional proof."

                      Suppose that I assume that P (where P can be any proposition). And on the basis of that assumption, I can prove that Q. The rule "conditional proof" allows me to infer from this that if P then Q; and this conclusion does not presuppose that the original assumption (that P) was true.

                      Here's an example. For any proposition P, the proposition that if P then P is a tautology (a logical truth). You can prove this using conditional proof. Assume that P is true. On the basis of that assumption, of course you can prove that P. Then you infer that if P then P. And that conclusion does not presuppose that the original assumption (that P) was true.

                      You get a similar pattern with reductio ad absurdum arguments. In those arguments, you assume that P (where P is any proposition). And then, on the basis of P, you prove some contradiction. And then you conclude that P was false; and this conclusion does not depend on the assumption that P was true.

                      Suppose you know that if P then not-P. From this it follows by reductio ad absurdum that not-P. Here's how. Assume that P. From this and the premise (that if P then not-P) you can prove that not-P. But that contradicts your assumption, So the assumption must be false. So not-P. And this conclusion obviously does not presuppose that your original assumption (that P) was true.

                      I'm not sure I'm making sense; in my time zone dawn has just arrived, and when dawn has arrived and gin is involved, I am no longer responsible for making sense. But I hope that the explanation helps.

                      •  I asked twice, now I'll ask a third time. (none)
                        If you are unwilling to address it this time, I'll just assume you are actually yanking my chain rather than trying to have a discussion and I'll drop it.

                        THIS IS THE POINT I'M ASKING YOU TO ADDRESS>>>

                        when Abelard says "Then I am not mistaken", he was speaking about a different topic than the topic that Eloise agreed he was correct about)

                        please, if you can, address this specific point

                          Again, I feel that I understand what you are saying - I just don't see how it addresses my specific comment.

                         (ps, you can see the numbers of comments by hold your cursor over the comment's link)

                        •  Abelard (none)
                          Sorry, but in my very first reply to you I gave a version of the paradox that made no mention of Abelard. I am totally confused at the fact that you keep mentioning Abelard. That was an informal version of the paradox that I abandoned the instant anyone (I mean you) wanted to get at the real paradox.

                          If the question is: how would a real conversation go that started like the one in the informal version? Then I agree with you. Everyone would assume that "I am not mistaken" was short for "I am not mistaken that the Dems will fold"; whereas Abelard's subsequent argument takes it to mean "I am not mistaken that this very sentence is true." You're RIGHT about that. That's why the instant you raised the issue I abandoned that version of the paradox.

                          •  In that case I stand by my original comment (none)
                            in my oh so humble opinion, this is not a paradox, it's simply an example of circular reasoning:  If you accept the opening premise that the conclusion is correct, then it does indeed logically follow that the conclusion is correct.

                            From the few hours study I've put into it today, I recognize that what I characterize as a humble opinion is at odds with accepted thinking on the topic, but, gee, it still looks like a circular argument to me - but I guess I've already made the disclaimer that I'm not a logician, so what do I know?

            •  Clarification (none)
              I didn't know what you meant when you said 'reread the precise version'.  Now I realize you meant what you wrote in comment 12.  But I don't really think that is a very good statement of Curry's paradox.

              Right at the beginning you say: Suppose (a hypothesis) that sentence 1 is true.

              and I say suppose it's not.  

              Really what this comes down to someone asserting "If I'm right, then I'm right"   -- and sure if we take as a premise that their statement is true, than they are indeed right.  I just don't find it that paradoxical.

              •  Suppose (a hypothesis) (none)
                That's conditional proof (or if-introduction). The idea is that you assume a hypothesis, P. And then on the basis of that hypothesis, you prove that Q. Then the conclude that if P then Q; and this conclusion does not presuppose that the hypothesis is true.

                Let DEM abbreviate "the Dems will fold"
                Let Curry be the sentence "If Curry is true, then DEM."

                Then we have:

                1. Curry = "If Curry is true, then DEM" (stipulation)
                2.     Curry is true (hypothesis)
                3.     "If Curry is true, then DEM" is true (substitution of identicals)
                4.     If Curry is true, then DEM (from 3)
                5.     DEM (from 2 and 4, modus ponens)
                6. If Curry is true, then DEM (2-5, conditional proof)
                7. "If Curry is true, then DEM" is true (from 6)
                8. Curry is true. (7, substitution of identicals)
                9. DEM (6, 8, modus ponens)

                Note that from step 6 on, the argument does not presuppose that the hypothesis in step 2 is true.

                I do know what I'm talking about.

                •  Sorry (none)
                  The last line was uncalled for.

                  But then I did admit I've been voting for gin, right? ;)

                  •  Have you tried Grey Goose? (none)
                    Since I am a failed gin-aholic (never made there tho I am in a city of genteel gin drunks... ;) I thought I'd ask you...

                    ;)

                    •  Oh no (none)
                      I am very simple-minded when it comes to vodka (same as politics really; I don't know what vodka is best, but there are vodkas that I think people should be drinking ;) ).

                      The first time I ever had vodka must have been when I was about ten (twelve? maybe twelve). Somehow I convinced my parents that I should be allowed a martini during the Superbowl halftime. (In their defense, a TINY martini.)

                      It's possible that the first time I ever had vodka as an adult (well, sort of) was when someone in my residence in China poured out some room-temperature Finlandia. Ouch! (And this wasn't south-of-France-wine-cellar room temperature, this was middle-of-the-summer-Fujian room temperature. Even the beer bottles said: must be stored in the shade, must be kept below 35oC. Ouch again!)

  •  Logical sleight of hand (none)
    Abelard: "If I am not mistaken, then the Democrats will compromise."

    In this statement, Abelard sets up a conditional statement -- that if he is not mistaken (presumably based on some set of facts that are not listed), then folding will happen.

    Eloise: "I agree: if you are not mistaken then the Democrats will compromise."

    Eloise agrees with Abelard's conditional statement. However, whether the conditional is true or false remains to be seen.

    Abelard: "You agree: what I said was correct?"
    Eloise: "Yes."
    Abelard: "Then I am not mistaken."
    Eloise: "True."

    And here is where the three of clubs goes on the bottom of the deck. Abelard takes Eloise's agreement with Abelard's construction of the conditional statement for Eloise's opinion on the evaluation of the conditional.

    Abelard: "If I am not mistaken, then the Democrats will compromise. I am not mistaken. Therefore, the Democrats will compromise."

    Non sequitur fallacy, as the very first conditional statement -- whether or not the conditional is true -- has never been evaluated.

    To rephrase:

    Abelard proposes C: If A, then B.
    Eloise agrees with C.
    Abelard states that since Eloise agrees with C, therefore A is true, and therefore B.
    However, nothing has been said about whether or not A is true. Eloise merely agreed that C is correct.

    Its not a fallacy, it's just bad logic.

    •  Bilge (none)
      Feanor had (I think) the same worry about the argument. The point is (using your symbols) that A says that C is true, so if C is true, then A is true. The logic is perfectly fine.
      •  Using symbols (none)
        bilge:
        Abelard proposes C: If A, then B.
        Eloise agrees with C.
        Abelard states that since Eloise agrees with C, therefore A is true, and therefore B.
        However, nothing has been said about whether or not A is true. Eloise merely agreed that C is correct.

        gong:

        The point is (using your symbols) that A says that C is true, so if C is true, then A is true.

        No, those weren't the symbols that bilge used.  

        A says that C is true

        Nope.

         

        •  Umm (none)
          Bilge used the symbols A, B, and C.

          And my comment used the symbols A and C.

          So those were symbols that Bilge used. Right?

          Are you just pretending not to understand? Because your obtuseness is getting pretty irritating.

          •  Now that you've called me obtuse and irritating (none)
            I must admit, that any possible respect you might have been earning in my eyes has been lost.

            I happen to think you are obtuse and irritating and purposely pretending to not understand, but I refrained from making those comments out of a desire for civility and to treat you with respect -- but I no longer think you deserve respect.

            A says that C is true

            I just refuse to believe that you don't understand what bilge and I are saying:  That having as  a premise that your conclusion is true is not really a paradox, but simply poor reasoning.  Hey - maybe we are wrong - but simply pretending to not understand our point is lame, I would have been willing to accept the gin as an excuse, but I've come to the conclusion that my earlier suspicion is correct, you are just trying to yank our chains.

            •  The thing is... (none)
              ...you keep saying that the reasoning in question assumes that some premise is true, but that is just wrong.

              Assume as a hypothesis that all dogs are yummy.
              Suppose that it follows from this that all poodles are yummy.
              Then it follows that if all dogs are yummy, then all poodles are yummy -- right?
              And that conclusion does not presuppose that it is true that all dogs are yummy -- right?

              For part of your proof, you assume that a sentence S is true. And on that basis you prove that T must also be true. So you infer (correctly) that if S then T. And you're not assuming that S is true.

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