Less [adjective] than Zeus

Proving Too Much

The fallacy of Proving Too Much is when you challenge an argument because, in addition to proving its intended conclusion, it also proves obviously false conclusions. For example, if someone says “You can’t be an atheist, because it’s impossible to disprove the existence of God”, you can answer “That argument proves too much. If we accept it, we must also accept that you can’t disbelieve in Bigfoot, since it’s impossible to disprove his existence as well.”

I love this tactic so much. I only learned it had a name quite recently, but it’s been my default style of argument for years. It neatly cuts through complicated issues that might otherwise be totally irresolvable.

Because here is a fundamental principle of the Dark Arts – you don’t need an argument that can’t be disproven, only an argument that can’t be disproven in the amount of time your opponent has available.

In a presidential debate, where your opponent has three minutes, that means all you need to do is come up with an argument whose disproof is inferentially distant enough from your audience that it will take your opponent more than three minutes to explain it, or your audience more than three minutes’ worth of mental effort to understand the explanation.

The noncentral fallacy is the easiest way to do this. “Martin Luther King was a criminal!” “Although what you say is technically correct, categories don’t work in the way your statement is impl – ” “Oh, sorry, time’s up.”

But pretty much anything that assumes a classical Aristotelian view of concepts/objects is gold here. The same is true of any deontological rules your audience might be attached to.

I tend to get stuck in the position of having argue against those Dark Artsy tactics pretty often. And the great thing about Proving Too Much is that it can demolish an entire complicated argument based on all sorts of hard-to-tease-apart axioms in a split second. For example, After Virtue gave (though it does not endorse) this example of deontological reasoning:

I cannot will that my mother should have had an abortion when she was pregnant with me, except perhaps if it had been certain that the embryo was dead or gravely damaged. But if I cannot will this in my own case, how can I consistently deny to others the right to life that I claim for myself? I would break the so-called Golden Rule unless I denied that a mother in general has a right to an abortion.

It seemed unfair for me to move on in the book without at least checking whether this argument was correct and I should re-evaluate my pro-choice position. But that would require sorting through all the weird baggage here, like what it means to will something, and whether your obligations to potential people are the same as your obligations to real people, and how to apply the Golden Rule across different levels of potentiality.

Instead I just thought to myself: “Imagine my mother had raped my father, leading to my conception. I cannot will that a policeman had prevented this rape, but I also do not want to enshrine the general principle that policemen in general have no right to prevent rape. Therefore, this argument proves too much.” It took all of five seconds.

Sometimes a quick Proving Too Much can tear apart extremely subtle philosophical arguments that have been debated for centuries. For example, Pascal’s Wager also proves Pascal’s Mugging (they may both be correct, but bringing the Mugging in at least proves ignoring their correctness to be a reasonable and impossible-to-critique life choice). And Anselm’s Ontological Argument seems much less foreboding when you realize it can double as a method for creating jelly donuts on demand.

Interestingly, I think that one of the examples of proving too much on Wikipedia can itself be demolished by a proving too much argument, but I’m not going to say which one it is because I want to see if other people independently come to the same conclusion.

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50 Responses to Proving Too Much

  1. Hand of Lixue says:

    That nicely sums up my issue with Pascal’s Mugging, actually: Given that one is required to accept a proposition with epsilon probability as a prerequisite, you’d also be required to equally accept all OTHER propositions with the same (epsilon) probability, and that would include the converse outcome that giving them 5 dollars will lead to them torturing 3^^^^3 people.

    Gosh, it’s nice to finally find a succinct way to express that :)

    (P.S., why are there two “Leave a reply” boxes, one beneath the other? o.o)

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  2. Doug S. says:

    Because here is a fundamental principle of the Dark Arts – you don’t need an argument that can’t be disproven, only an argument that can’t be disproven in the amount of time your opponent has available.

    In other words, a One Way Hash Argument.

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  3. cool rich guy says:

    How is that a fallacy and not a valid logical technique? You seem to think it’s a valid logical technique too.

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    • Sean Walker says:

      It’s valid because the proofs are about showing A => B, where B is the desired fact. You need to actually have A for it to work, so the “Proving too much” technique shows that A => C, and that C is false, so then A must be false, defeating the argument for B.

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    • Scott Alexander says:

      Yeah, it’s very confusingly named. The fallacy is (having an argument that proves too much), the logical technique is (pointing out that the argument proves too much). I did a poor job distinguishing between those two concepts.

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      • The problem is in your opening sentence: “The fallacy of Proving Too Much is when you challenge an argument because …”. You could clear the confusion up by changing that to “The fallacy of Proving Too Much is when an argument …”.

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  4. Vanzetti says:

    >>>I cannot will that my mother should have had an abortion when she was pregnant with me

    This is sooo much bullshit. You can will anything about the past, the past is unchangeable. You are already a person, an aborted embryo is not and will never be.

    Why is deontological reasoning seems to involve imaginary time travel?

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  5. Alex says:

    I too like using this tactic but it seems very different for people to grasp. Take for instance the following scenario:
    Person A: “Slavery is wrong because some slave masters beat their slaves”
    Person B: “This proves too much – this would suggest that marriage is also wrong because domestic violence exists”
    Person A: “How dare you compare slavery to marriage! There are all sorts of difference between slavery and marriage like …”

    Of the more convincing reply that A could have given is:
    Person A: “Actually that proves too much, you’re argument would suggest that violence is an invalid criteria for judging institutions.”

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    • Faul Sname says:

      Person B actually is right. Slavery isn’t wrong because some masters beat their slaves. It’s wrong because slaves were trapped in an environment in which they might be beaten without the ability to get out of that environment. With marraige, one can leave an abusive partner, so marraige does not share the characteristic that makes slavery bad. And that’s probably where the argument would have gone from there, possibly with person A accusing person B of being pedantic.

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    • Deiseach says:

      Explain this more to me, because it would seem to me in the first example that Scott gives, that there is a difference between the claims made for Bigfoot and the claims made for God, and that there is a way we can argue that disproves Bigfoot that would not work for God.

      Using “Your argument proves too much” as a blunt instrument akin to the Courtier’s Reply seems to me to undercut all kinds of areas where distinctions need to be made.

      After all, we could use the “Your argument proves too much” rejoinder to say that SETI is worthless, or that transhumanism is a fairytale that will never come true, or about a lot of matters that are not amenable to the “cut a slice off it and show it to me right now” type of reasoning.

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      • g says:

        If it’s true that one can disprove the existence of Bigfoot, then indeed the proves-too-much argument fails.

        It seems to me that some theists claim one can’t prove the nonexistence of God on grounds that would also apply to Bigfoot. I’m not sure whether, or how often, those same people also say that this is enough to mean one shouldn’t be an atheist.

        How do you use the proves-too-much principle to show that SETI is worthless? Is the idea that it’s too much like Pascal’s wager?

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        • Deiseach says:

          Shamelessly lifting Scott’s argument:
          Person A says “You can’t be an atheist, because it’s impossible to disprove the existence of God”.

          Person B says “That argument proves too much. If we accept it, we must also accept that you can’t disbelieve in the abduction by UFO testimony of so-called survivors, since it’s impossible to disprove the existence of life on other planets as well.”

          “However,” Person B goes on to add, “since neither you nor I believe that Billy-Bob Lee and Cletus Jones were abducted by grey aliens in a flying saucer that landed in the Ozarks in 1954, why should we pay good money to keep something like SETI going? There’s as much chance we will contact a genuine alien civilisation as, well, flying saucers landing in the Ozarks”.

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        • Deiseach says:

          That’s why I was suggesting it is possible to apply tests to winnow out the validity of accounts of encounters with Bigfoot or alleged hair samples, footprints and so on while still believing (or disbelieving) in a deity, just as one might believe that SETI was a worthwhile project while not believing that gray aliens in flying saucers are mutilating cattle in Arizona right now.

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        • g says:

          (I’m replying to Deiseach’s comment that begins “Shamelessly”.)

          I’m confused. What does the bit of that that’s arguing against SETI have to do with the proving-too-much argument, other than that you wrote them down next to one another?

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  6. suntzuanime says:

    This seems like it would be vulnerable to the reverse non-central fallacy. “Your boyfriend is a bad influence on you because he’s a criminal” “That proves too much, dad! Martin Luther King was a criminal and he wouldn’t have been a bad influence!”

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    • Anonymous says:

      The reply is valid. The father’s accusation is too general, and he should’ve instead specified what negative attributes or qualities this boyfriend had.

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      • Eric Rall says:

        One counter-reply would be a Baysian statistical discrimination argument: presumably, the proportion of criminals who are bad influences is much higher than the proportion of members of the general population who are bad influences, so knowing that someone is a criminal provides a fair amount of evidence suggesting that they are a bad influence even though that evidence is not absolutely conclusive.

        Alternately, he could refine his argument by specifying the crimes the boyfriend commits and why: MLK’s criminality is generally excused because he was violating unjust laws in order to protest their injustice, which doesn’t have the same sting to it as knocking over liquor stores for personal material gain.

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      • Carinthium says:

        Martin Luther King would in some ways have been a bad influence. He was a clergyman, overestimated what non-violence could do(it works in countries such as Britain or America, but would never have worked in Nazi Germany or Stalinist Russia), and made mistakes on many small things (Tolstoy, for example, and his moral character).

        If I had a daughter who knew Martin Luther King, I would let her (assuming she wanted to be more, not less selfless, otherwise it’s tricky), but warn that his moral authority does not mean he isn’t mistaken on a lot.

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  7. Walter Block’s claim that “‘markets w/ imperfect competition should be regulated to bring them closer to that ideal’ proves too much because if you want to do that, then you should want government regulation toward *any* arbitrarily property of any object”, if Wikians haven’t just paraphrased him poorly by “Substitute for perfect competition objects moving faster than the speed of light, or people having more than two arms and further government intervention can easily be justified”, is a lame attempt. It’s hardly universally agreed that we should have very little government regulation.

    He’s leaving out the part where there are arguments that intense competition is good for society, arguments which are usually part of the anti-central-planning pro-capitalist case. The template for a “proving too much” attack should be something like “the intended purpose of this arrangement A of society is P, which is supposed to happen by means of processes Q consequent A. but we see less Q than we hoped for, and regulation R can give us more Q and thus more P, and we think it’s worth the cost C”. If you disagree with an instance of this template, then you can probably object to some part of it.

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  8. komponisto says:

    I don’t like this tactic very much. Not that I’m unwilling to use it at times; but it often gives a feeling of not trying to understand the opposing argument and simply trying to embarrass the opponent for not having formulated their argument in an “airtight” fashion. In other words, it conflicts with the Principle of Charity and feels like a debating tactic.

    Indeed, often the response to a “proving too much” accusation is to point out a subtle, inferentially-distant distinction between cases or concepts, which will sort of automatically look to the audience like an exercise in motivated cognition. So making such an accusation itself feels somewhat Dark-Artsy.

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  9. Oscar_Cunningham says:

    Nice post! One thing to note is that showing that an argument proves too much doesn’t tell you where the flaw in the argument is. It only tells you that there is a flaw somewhere. This is one of my favourite quotes from Good and Real

    There are two ways to rebut an argument. We might call them countering and invalidating.

    +To counter an argument is to provide another argument that establishes the opposite conclusion.

    +To invalidate an argument, we show that there is some step in that argument that simply does not follow from what precedes it (or we show that the argument’s premises—the initial steps—are themselves false).

    If an argument starts with true premises, and if every step in the argument does follow, then the argument’s conclusion must be true. However, invalidating an argument—identifying an incorrect step somewhere—does not show that the argument’s conclusion must be false. Rather, the invalidation merely removes that argument itself as a reason to think the conclusion true; the conclusion might still be true for other reasons. Therefore, to firmly rebut an argument whose conclusion is false, we must both invalidate the argument and also present a counterargument for the opposite conclusion.

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    • Sniffnoy says:

      Yes — proving too much isn’t a fallacy in the proper sense; rather, it’s an indicator that there’s a fallacy somewhere. Which is *why* it has the properties Scott likes; using it to show an argument is wrong is a lot easier than finding the actual fallacy. (Which, ideally, should still be done, but you don’t necessarily have time for.)

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  10. Gilbert says:

    Saying that something proves too much always relies on an analogy. If that analogy is wrong one can construct a similarly wrong analogy to go meta and show that the proving too much argument itself proves too much. Since the analogicity of analogies is almost always tricky, most proving too much arguments are arguably vulnerable to that kind of metaness.

    Applying it to the three examples on that Wikipedia article:

    The proving too much argument on slavery assumes that slave-beating relates to slavery in the same way wife-beating relates to marriage. That is wrong, because treating persons like objects is the point of slavery and an abuse in marriage. Analogy with the same error: Droit du seigneur and property rights. So the argument itself proves too much: By that logic someone using the droit du seigneur for sexual coercion wouldn’t be an argument against it, because otherwise the possibility of a very rich guy leaving a destitute woman with only the fake choice of prostitution and death would also be an argument against personal property.

    The government intervention example assumes that perfect competition and faster-than-light travel are both terminal goals. That is wrong, because a lack of perfect competition is already a counter-argument to the argument that government should keep out of economics because perfectly competitive markets would regulate themselves, so we are interested in impossible faster-than-light travel itself but in perfect competition only instrumentally. Analogy with the same error: A perfect immune system is impossible so we vaccinate and faster-than-light travel again. So the argument itself proves too much: By that logic immune systems not being perfect would not be an argument against anti-vax quacks because doctors don’t give us faster-than-light travel either.

    The Prop. 8 recusal example assumes that the interest of gay people in gay marriage is only about as motivating as the interest of straight people in its absence. That is false, because the question clearly affects gay people much more directly and they therefore care much more strongly about it. Analogy with the same mistake: A shareholder being interested in how much tax a company pays and a citizen being interested in how much tax that company pays. So the argument itself proves too much: By that logic a judges holding shares of a company suing about its taxes shouldn’t recuse themselves, because then non-shareholders interested in extracting maximum revenue would have to recuse themselves too, thus eliminating virtually the entire judiciary.

    Of course most interesting arguments are equivalent to arguments about analogies, so appeals to proving-too-much are very often just a disguised way of begging the question.

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    • Multiheaded says:

      By that logic someone using the droit du seigneur for sexual coercion wouldn’t be an argument against it, because otherwise the possibility of a very rich guy leaving a destitute woman with only the fake choice of prostitution and death would also be an argument against personal property.

      “Would be?” It’s been a talking point for us commies for a couple centuries at least; one doesn’t even have to be a Marxist to see how women’s lack of economic bargaining power leads to systemic sexual coercion. In tribal societies without private property, men don’t wield this kind of power over women despite their distinct and separate gender roles.
      This is what mainstream feminists generally don’t seem to recognize; that “patriarchy” is a socioeconomic pattern first, and that its cultural manifestations which they try to stamp out – like “objectification” – are the effect and not the cause of women’s inequality. Marxists do often say that liberal movements shrink from questioning the self-perpetuating systems that underlie various inequities and abuses of power – such as the reign of “private property”.

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      • Joe says:

        Aren’t women in communist China forced to have abortions and to be sterilized? Doesn’t communism have a long history of oppressing everyone not just women?

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        • Zaxser says:

          I’m not certain that’s true. That’s just rumors right now, as far as I know.That and I’m sure you know enough to separate communism in theory from communism in practice. (Marx, as far as I know, never mentioned a perpetual police state.)

          Still. even given that, certain things really did improve under communism and women’s rights really is one of them. Foot binding was one of the first things to go.

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        • Joe says:

          Zaxser

          I think that the problem with most ideologies like communism and totally free market capitalism they seem great on paper but almost always neglect to account for humanities fallen nature. With out a rational moral culture. No matter what economic system you have will fail and up oppressive in some way. Communism happens to be an atheist ideology so might makes right not reason.
          Further more what is going on in China is no rummor
          http://www.npr.org/2012/07/05/156211106/after-a-forced-abortion-a-roaring-debate-in-china

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        • Joe says:

          Sorry about goofy sentence structure on my phone.

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      • Gilbert says:

        Yeah, but for argumentative effectiveness the “too much” part must be something the person making the original argument would disagree with. So this doesn’t prove too much for a Marxist, but most people arguing for slavery – at least under that name – aren’t exactly Marxists. No universally convincing arguments and all that.

        Personally I think poverty-induced prostitution is a fairly good argument against totally unlimited capitalism but not so much against property per se, which also can exist in a welfare state. But that’s an entirely different question.

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        • Multiheaded says:

          Personally I think poverty-induced prostitution is a fairly good argument against totally unlimited capitalism but not so much against property per se, which also can exist in a welfare state. But that’s an entirely different question.

          Oh, sure, sure. It’s just that “our” definitions of “private property” are more specific and involved than the colloquial understanding of “things you own” – Marxists, as usual, focusing on the system-wide effects of the institution which underlie the interactions of individuals.
          Who gets what particular share of resources is just a transient state of the system, ripples on the surface, not meta enough to fret about. What are the patterns behind this? What are the meta-patterns? How are the patterns themselves selected?
          (Which, at least in form, resembles the approach of the more intelligent arguments for “traditional marriage”, yeah.)
          http://en.wikipedia.org/wiki/Private_property#Socialist_perspectives

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        • Gilbert says:

          OK, study offer:
          I’ll have to admit I don’t know much about modern versions of Marxism though more about the original article.
          Here’s all Marxist theory I have absorbed: I did read all three volumes of Das Kapital and was underwhelmed. Basically the guy lived right before the marginal revolution and we now know he was empirically wrong on all his core assumptions. I also read about half of Die Deutsche Ideologie and some minor writings in the same volume of Marx-Engels-Werke before I decided it was more about Marx’s narcissism than any theory. I also read one Trotzkist book because it promised to analyze bureaucracy but it turned out to mean something very different than the everyday meaning of that term. I am semi-familar with the Cambridge Capital Controversy, the Calculation Problem, and some proposed solutions to the latter. And once I listened to a lecture by a Frankfurt school guy who not only seemed to think Marx was right on everything but so was Freud which seemed twice stupid. I haven’t read more than the usual Internet quotes on post-modernism, but I share the usual Internet prejudices about it.

          Based on that I decided I didn’t need to study more of what my prejudices classify as epicycles on a clearly failed theory. I realize this may be unfair like the standard atheist who reads the Bible, decides talking snakes are stupid, and then calls courtier’s reply on every explanation. On the other hand not-a-Marxist is less central to my identity than atheism to that of the stereotypical Internet atheist, I already absorbed way more than most people, and I don’t have time for everything. I haven’t read that Wikipedia article on Analytical Marxism yet, but I will do so tomorrow.

          So, based on that background, can you recommend me ONE more book, no more than 500 pages or 50€, that will make me think modern Marxism is worth thinking about? If so I will read it, but flip-side, if it isn’t positively brilliant it will probably reinforce me in my reactionary ways. So is there a Marxist Feser or something like that?

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    • Scott Alexander says:

      The stockholder/citizen analogy on the last issue was exactly the one I was thinking of in the last sentence of the post.

      I don’t agree with your example on slavery – beating a slave to death is not the “point” of slavery at all, and “treating people like objects” is a fuzzy category that wasn’t contained in the original argument and seems to be investigating a totally different line of inquiry. As far as I’m concerned, the original argument – that this practice occasionally in pathological cases leads to people being beaten to death, therefore it should be stopped – is indeed false.

      I think you, Block, and the original interventionist are all right on different levels about the free market example. The original interventionist correctly rebutted a libertarian argument that we don’t need intervention because markets are perfect, but failed to make a positive argument in favor of intervention. Block pointed that out. You pointed out that all Block did was point that out without himself positively establishing that intervention is not necessary.

      As for analogies, I agree that in the strongest sense it’s always possible to critique the analogy. But in many cases the appropriateness of the analogy will be much clearer than the point you were arguing originally – for example, in the Bigfoot example above I’ve kept the entire argument except substituting one word, which seems a lot clearer than arguing on what belief vs. proof is or trying to convince someone that all belief is probabilistic. Certainly the opponent could then switch to something like presuppositionalism, but that’s several levels more sophisticated than the original argument and less immediately plausible to a neutral audience.

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  11. Patrick (orthonormal) says:

    This could make a very good LessWrong post, by the way.

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  12. David Schaengold says:

    As you note, MacIntyre wasn’t offering the particular argument about abortion himself, and in the end it’s probably not decisive, but nonetheless it’s stronger than you’re making it out to be. Willing that you had been aborted is to will your own destruction as such, whereas the circumstances of your conception are only contingently related to your subsequent non-existence. For a deontologist, the essential character of the act is what matters, and an abortion is essentially a killing. Of course, for a consequentialist this distinction is meaningless, but if you just assume that a core deontological belief is meaningless then it’s easy to make deontologists look silly.

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    • Patrick says:

      This is not an answer.

      You’ve misinterpreted an attack made from separate grounds with a reinforcement of the original attack.

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      • David Schaengold says:

        I agree it’s not an answer to the post’s main point. Proving too much is indeed a telling feature of bad theories. I just wanted to point out that this particular argument, though hastily sketched by MacIntyre, has more going for it than it first seems.

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        • Patrick says:

          No, it doesn’t. You’re not reinforcing MacIntyre’s point. You’re offering a new point aimed towards a similar conclusion. What you haven’t answered isn’t the whole OP, it’s the critique of MacIntyre.

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    • Fnord says:

      If that’s true, then the argument is simply begging the question by making the fetus “you” in a morally significant sense, and hence human in a morally significant sense, and the substance of the argument is superfluous.

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  13. Paul Torek says:

    On the wiki (rot13)
    Vs n whqtr unf n ynetr fgbpx ubyqvat va KLM pbec., fur fubhyq erphfr urefrys sebz n pnfr jurer gur tbig vf fhvat KLM. Ohg vs fur’f abg n fgbpxubyqre, fur’f fgvyy n gnkcnlre. Pbyyrpgviryl, gnkcnlref jvyy jva nyy gur zbarl gung KLM ybfrf, vs gur tbig fhvg vf fhpprffshy. Fb fur fubhyq erphfr urefrys rvgure jnl! Orvat n gnkcnlre va guvf fpranevb zncf gb orvat fgenvtug-zneevrq va gur guveq jvxv rknzcyr. Abg rknpgyl, orpnhfr gur KLM pnfr vf n mreb fhz tnzr, ohg pybfr rabhtu.

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  14. Ronak M Soni says:

    “Interestingly, I think that one of the examples of proving too much on Wikipedia can itself be demolished by a proving too much argument, but I’m not going to say which one it is because I want to see if other people independently come to the same conclusion.”
    The government one, obviously. But, since there are only two arguments there, you’ve got way too high a probability of random agreement (if there were nuances to both the arguments etc.) (though I guess that being the case will have definite markers). I’m no longer sure if I made a point worth making, so slightly sorry about that.

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  15. For future convenience, here is a link to Wikipedia’s “Proving too much” article as it was when this post was written, in case someone eventually fixes the problem you see within the examples.

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  16. Pingback: Schrodinger’s Rapist Proves Too Much | Slate Star Codex

  17. Pingback: Intelligent design, creationism, and fundamentalism: a reply to Randal Rauser

  18. Carinthium says:

    In philosophy and sometimes in life, I’d criticise this argument because one can “bite the bullet” and challenge the claim said to be obviously false. Anselm comes into self-contradictions pretty quickly, but Pascal’s Mugging doesn’t.

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  19. Steve says:

    Hilariously proving too much, with a side of mind-killer: https://twitter.com/dcuthbert/status/375707158639566848

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