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Is there a name for the fallacy that refuting an argument refutes the proposition?

e.g. there is a belief in X..

somebody provides an argument for X.. or even a bunch of arguments for X.

Somebody refutes these arguments.

But they commit the fallacy, of thinking that since they have refuted these arguments for the conclusion X, they have thus refuted the proposition and shown ¬X. When really they've only refuted the arguments given for it.

Is there a name for that fallacy?

[an earlier edit had something added but that thing should be made into a separate question so i'll keep this question to what it is and maybe post a separate different question another time]

barlop
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    Inferring that since an argument is fallacious its conclusion must be false is called argument from fallacy, and sometimes the fallacy fallacy (sic!). – Conifold Apr 17 '17 at 19:10
  • re what I added, I think if it's the case that everything has a reason for its existence, and it were the case that all the arguments that have been refuted, are also all the reasons.. (Arguments are based on known evidence.. but all reasons would include undiscovered evidence), If all those reasons were refuted, then it'd disprove the conclusion. But that's never really the case. So the conclusion wouldn't be disproved. – barlop Apr 17 '17 at 19:21
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    Sorry, I do not follow the added part. All I can say is that reasons have little to do with causes (there are no causal relations between mathematical objects, but plenty of logical connections), many things have no "reason" for their existence (reasons are just our way of structuring information), and "all the arguments" may not be a meaningful concept, like the set of all sets. – Conifold Apr 17 '17 at 19:34
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    now you're asking 2 different questions, one about logical fallacies and one about the relation between logic and causality. plus i think you're confusing argument, premise, conclusion, and inference. in P->Q, there are no arguments or conclusions, and no sense in which P causes Q. It's just a proposition. if you say "P->Q, but P, therefore Q", then P->Q and P are premises, Q is a conclusion, and the licence to go from the former to the latter is the rule of modus ponens. –  Apr 17 '17 at 19:41
  • you have the right intuitions, you just need to master the technical vocab. –  Apr 17 '17 at 19:43
  • @mobileink You wrote ". in P->Q, there are no arguments or conclusions, and no sense in which P causes Q. " <-- But How can P->Q have nothing to do with causality / how can it in no sense mean that P causes Q? P->Q means that When P happens Q happens. So wouldn't that be saying that P is a cause of Q? (I know the modus ponens rule, though it's not relevant to the question i'm asking in this comment 'cos regardless of whether P is happening or not, so regardless of whether Q is true. P->Q means that when P happens Q happens, so surely, that P causes Q). – barlop Apr 17 '17 at 20:03
  • P->Q in (classical) logic is just a proposition. it means exactly that "P true and Q false" cannot be the case; or, "not(P and not(Q))". no causality. –  Apr 17 '17 at 20:13
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    ps. nothing "happens" in logic. propositions are true or false, inferences are valid or invalid, end of story. –  Apr 17 '17 at 20:15
  • just consider: (2 < 3) -> Paris is the Capitol of France. Perfectly in order logically. –  Apr 17 '17 at 20:23
  • @mobileink well, that wouldn't disprove the "happens" interpretation.. e.g. When (2<3) happens, (which is all the time), then paris is the capital of france. (though granted I see it's not saying A causes B), but still seems like the interpretation of when A happens, B happens, seems to hold. – barlop Apr 17 '17 at 20:36
  • Examples: if smoke then fire (smoke does not cause fire, it's the other way), if lightning then thunder (neither causes the other, common cause), if a triangle has equal sides then it has equal angles (no causal relation whatsoever). Implication really can have nothing to do with causality. – Conifold Apr 17 '17 at 20:57
  • if it's any consolation, i think you're butting into a problem that every budding logician confronts at some point: the "logic" of ordinary language is not logic. Logic is in fact very counter-intuitive in some ways. simple example: every true proposition follows logically from any false proposition ("principle of explosion" or "ex falso quodlibet") is wildly counter-intuitive. yet "(3<2) -> Paris is the Capitol of France" is logically a true statement. obviously there is no relation of causality. fwiw it took me a while to grok this sort of thing. logic is very subtle. –  Apr 17 '17 at 21:30
  • @Conifold Well, the statement When there is smoke, there is fire, is false. Because you can have smoke without fire. But let's pretend that whenever there is smoke, there is also a fire. I agree it's not a cause. The comment I wrote before this agrees with that - I concede that.. But in all these examples of A->B, they all still seem to match the When A happens B happens.. – barlop Apr 17 '17 at 21:40
  • @barlop I'd suggest removing the "added" part and submitting it as a separate question. You can of course reference them to each other with the "share" links, but I think the added part merits its own question and answer. – MmmHmm Apr 17 '17 at 22:53
  • I guess you could say that, but the "pattern" is vacuous, "if P happens then Q happens" just rephrases "if P then Q". And if "happens" has the literal meaning triangles do not match even that, they do not "happen", they exist eternally (on the usual view). The suggestion in the last sentence of the "added" part is certainly wrong, and I am not sure what the remaining claim and/or question there is. So I agree that you should delete it and ask a separate new question. But please explain more clearly what the question is. – Conifold Apr 17 '17 at 23:16
  • Lincoln was assassinated -> Julius Caesar was assassinated. Surely you do not think John Wilkes Booth caused the assassination of Julius Caesar. –  Apr 18 '17 at 19:47

9 Answers9

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One term is "argument from fallacy" - the argument concluding X is fallacious, therefore X is false. see https://en.m.wikipedia.org/wiki/Argument_from_fallacy

P.S. Note that this is not the same as denying the antecedent.

When you deny the antecedent, you show that a premise is false; you can form a fallacious argument from true premises (by using an invalid inference).

The fallacy fallacy instead is based on showing that the reasoning is unsound, as opposed to showing a premise is false. In other words, unsound reasoning is a broader concept that includes both reasoning from false premises and badly reasoning from true premises, or both.

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X is the conclusion you want to you prove here, suppose Y is the arguments given to support X. here, their logic is : Y, therefore X / Y=>X

You are saying bunch of people trying to refute by saying they refuted the arguments, or refuted the Y that is -Y=>-X

this is logic I believe is called Inversion

Ying Xiong
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  • you're onto something . It seems, To suggest that p->q implies the inverse, the inverse being ~p->~q is a fallacy, and the name of the fallacy, is https://en.wikipedia.org/wiki/Denying_the_antecedent .. however, i'll make an edit into my question.. 'cos what about the idea that if you refute all arguments. – barlop Apr 17 '17 at 17:41
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This is a weird form of "Argument from Authority". The overall argument of the "refuter" is that the "proponent" is an expert on arguments for the proposition.

The "refuter" assumes that if an irrefutable argument in favor of the proposition were available to the proponent, the proponent would have presented it. Since the proponent did not present such an argument, the refuter concludes that there is no such argument.

This is correct as far as it goes: It is reasonable to conclude that no such argument was available to the proponent for use in the debate.

There are two flaws:

  • The proponent/authority might not have enough expertise. Conceivably, there might be a valid argument that the proponent is unaware of.
  • The proponent might be concealing a valid argument. For example, intelligence agencies might prefer to lose a specific argument, rather than present evidence that betrays a source.
Jasper
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  • Those aren't really flaws. Is accepting that there's a cat under my table because I see it and hear it purring flawed because I could be hallucinating? They make one's conclusions uncertain, but certainty does not seem to be possible to humans anyway. (Perhaps we can be certain that we exist, but that seems to be about it.) It is, of course, a fallacy in formal logic. But normal reasoning and proof is not that much like formal logic. – David Schwartz Apr 18 '17 at 10:24
  • @DavidSchwartz I don't think that formal logic and normal reasoning contradict one another. Good rational human reasoning can perhaps be modelled with probability, and thre is fuzzy logic which I understand uses probability.. and fuzzy logic is apparently/i've heard,, a form of formal logic. But yeah that non-probability based style of logic seems to expect irrefutable arguments. But still, even if it were probability arguments, I think the fallacies this answer identifies, stand, if one changes irrefutation to eg 95%+. – barlop Apr 18 '17 at 10:31
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    You're talking about all different forms of formal logic. I agree, this is a fallacy in formal logic. But it's not a fallacy in normal reasoning. They don't exactly contradict each other, but they are very different. And it really has nothing to do with probability either. You don't have to show that gravity is 98% likely to always be a 1/r^2 force to accept that it's demonstrated to be a 1/r^2 force. Normal reasoning is about sufficient evidence and justification, where "sufficient" is very squishy. We can, for example, reject something we think arbitrary if the arguments for it are nonsense. – David Schwartz Apr 18 '17 at 10:51
  • @DavidSchwartz Aside from probability, I don't think there is a difference in normal reasoning and formal logic, on this.. When it comes to "rejecting something we think arbitrary if the arguments for it are nonsense".. We look at arguments, plausibility.. information we have.. And if we are are 50/50 we can say statement "A" we don't believe it's true and we don't believe it's false. If we see the thing is very implausible, then we can say statement "B". that it's very likely false or we believe it's false. – barlop Apr 18 '17 at 17:17
  • @DavidSchwartz I think what you say "rejecting something",is a bit evasive, because if somebody believes ¬X because something is very implausible, then you could call that rejecting. And if somebody is 50/50 doesn't believe one way or the other, then you could call that "rejecting". So I don't think the term rejecting is a good description of a position. Better to specify whether you mean not believing one way or the other,(which also means rejecting the idea that it's false). And that's s not clear if you just say rejecting the proposition. – barlop Apr 18 '17 at 17:19
  • @barlop Except that ordinary reasoning really isn't about probabilities at all. For example, if my wife tells me she had a bad day at work and I believe her, I will say I know she had a bad day at work and I will believe she had a bad day at work. But if you asked my what I thought the probability was that she actually had a bad day at work, I think I'd look at you like you were from outer space. And when we find someone guilty beyond a reasonable doubt, we don't have some probability in mind. Evidentiary justification is not about establishing a specific probability. – David Schwartz Apr 18 '17 at 17:50
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    @barlop fwiw formal and informal reasoning are very different, even incompatible, depending on your perspective. nobody i know without training would accept the idea that a false proposition proves any true proposition, but that's elementary in formal logic. –  Apr 18 '17 at 19:11
  • @mobileink They wouldn't in rational informal reasoning either. I don't really see the incompatibility – barlop Apr 18 '17 at 21:28
  • @DavidSchwartz One also wouldn't generally put much thought into one's level of confidence in their wife's claim that she has a bad day at work. But if a belief does concern/interest me for example, I am walking up a street and I can't remember where I parked my car, and I see a car in the distance that looks a bit like mine, then I do think to myself e.g. 80% chance it's mine, then as I get nearer I see more of the number plate, and when I see it all and my car in full, and it matches, it gets to 99.99+% chance it's mine / as good as one can know almost anything. – barlop Apr 18 '17 at 21:38
  • @DavidSchwartz But even if one didn't explicitly think in terms of probability and probability ranges, I think one can engage in rational thinking, and rational thinking can be modelled with probability. We have intuitive thoughts as to the confidence we have in this/that belief, and that maps well to probability or probability ranges. If we are more sure of A than B, A gets a higher probability, like rating films. – barlop Apr 18 '17 at 21:40
  • Maybe you. For most people, if they see a car and think it might be theirs and you ask them "what is the probability that it's your car", they'd look at you like you're from outer space and probably say they never even considered the question. And it makes concrete differences too. No matter how statistically likely I think it is that I won't flip ten coins and get heads on all of them, I never believe that I won't get all heads. However, I do in fact believe that my wife had a bad day at work, even though the probability she's lying might be higher (I don't even bother figuring it out.) – David Schwartz Apr 18 '17 at 21:41
  • Sure, you can model rational thinking with probability just as you can model rational thinking with formal logic. But they are very different. There are definitely similarities between believing something to be true and assessing it to have high probability. But there are core differences too. No matter how likely it is that flipping ten coins will produce at least one tails, I don't believe it will happen. Yet there are things that I believe are true that I would assign much lower probabilities to if asked to work them out. – David Schwartz Apr 18 '17 at 21:44
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From my Uni studies many years ago, I would refer to that as the "unicorn fallacy", though I don't think this is an officially defined term. It think it could also be described as a multiple-option false dilemma.

The fallacy is that given P1 --> C and P2 --> C and P3 --> C, disproving P1 and P2 and P3 disproves C.

It does not. You also have to prove that there exist no other Pn such that Pn --> C.

"Unicorns don't exist"

..... "How do you know."

"Because I looked in North America and South America and Europe and Africa and Asia and didn't see any. There's nowhere they can be, therefore they don't exist."

..... "But they could have moved around when you were looking. They could also be in Australia, where you never looked."

Greenstone Walker
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  • "But they could have moved around when you were looking. They could also be in Australia, where you never looked." If you accept that argument as valid, then nobody can ever know or prove anything. For anything you claim you know or to be able to demonstrate, I can come up with some possibility by which you would think it's true even though it's not that you cannot refute. Can I know that I'm posting on philopsophy.stackexchange.com? I can't prove that superintelligent aliens didn't delude me into thinking that's the name though it's not. (It's a fallacy in formal logic, of course.) – David Schwartz Apr 18 '17 at 10:22
  • @DavidSchwartz Maybe it's wrong to even use A->B to represent reasoning and conclusion, since if somebody says A=cats are animals B=the sun exists A->B is true but it doesn't really work as reasoning leading to a conclusion. – barlop Apr 18 '17 at 17:23
  • That's another difference between reasoning and logic. No only doesn't formal logic require any causal link or connection whatsoever between A and B for A->B to be true, but it doesn't really even try to represent such links. – David Schwartz Apr 18 '17 at 17:54
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Here is what I can offer.

Assume the proposition is: If and only if P, then Q. Then the refutation of P is also the refutation of Q, and vice versa.

Assume the proposition is simply: If P, then Q. The statement not-P is only the denial of the antecedent, and nothing follows; the denial of P allows other reasons for Q to occur. However, the contrapositive is: If not-Q, then not-P. Here, the denial of Q is also the denial of P.

18 April 17 edit. Barlop, given your description of the question, you might get closer to an answer by reviewing Bayes' Theorem and the recent work on that theorem by Colin Howson.

Mark Andrews
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  • yes I agree.. And I wonder whether if a person says, they've heard all the arguments for Q, or all the best arguments for Q, then would that to any extent, prove or make the case for not Q? – barlop Apr 18 '17 at 09:59
  • @barlop Not alone. You would need something else. For example, Q could be incompatible with something you knew. Or you could have reason to suspect that Q was arbitrary. Or Q would have to be implausible. For example, if Q was "two mice are having sex now on the dark side of the moon", that would suffice. But if Q were plausible, consistent with what you knew, and potentially had explanatory power, then just refuting every argument for it is not sufficient to accept that it's not true. – David Schwartz Apr 18 '17 at 12:00
  • @DavidSchwartz but is its plausibility an argument for it? – barlop Apr 18 '17 at 15:15
  • @barlop It depends on context. It's trivial to construct a plausible falsehood. But in contexts where intentional construction is not likely, then plausibility is an argument for something. For example, suppose I have something that is from 1800 and purports to be a report of a trip to Australia. Plausibility of the parts of the account that I can verify would bolster the parts I can't verify, assuming there's no way the author could have known what I could and couldn't verify. – David Schwartz Apr 18 '17 at 17:53
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I've heard this is called the 'fallacy fallacy'. Arguing that because one person used a fallacy when arguing for something automatically proves that their claim must be false.

An example would be someone denying that Neptune exists (some flat earthers deny the existence of planets outside of Earth). Someone counter-argues that scientists have discovered it and thus the claim can be trusted. The denialist then points out that this arguments constitutes an 'argument from authority', and this means that Neptune does not exist. I chose Neptune btw because its impossible to see with the naked eye, and in fact was only discovered by its gravitational influences on Uranus.

user8600
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Demonstrating that a proof for a fact is faulty doesn’t demonstrate that a fact isn’t true. In mathematics there are statements that are very strongly believed to be true, and believed to be so hard to prove that people trying to prove them are usually crackpots, and their “proofs” are usually not just faulty, but ridiculously faulty. And that doesn’t make the fact itself any less likely to be true.

But there are many things that might be reasonably believed to be provably true or provably false. If there are many reasonable but faulty attempts at proofs that may be sn indication.

gnasher729
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If I may venture something hopefully helpful:

The fallacy of "asserting the consequent": is the following inference: {P-->Q, Q} |- P. This is not what you are concerned with, but it is equivalent to it, by contraposition. The contrapositive of P-->Q is ~Q-->~P. The author claims to have refuted the argument,that is established ~P, which entails the belief, Q, and on that basis claims to have proven that ~Q. This is asserting the consequent on the contrapositive.

In your notation the belief is Q and the argument,X, is P.

лаетековский чайник
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  • You wrote "~Q-->~P. The author claims to have refuted the argument,that is established ~P, which entails the belief, Q," <--- Don't you mean "entails the belief ~Q" Also, that wouldn't be a fallacy. – barlop Apr 17 '17 at 21:55
  • however, I think if it were P<--Q i.e. When P is true Q is true and only when P is true, Q is true, then ~P->~Q – barlop Apr 17 '17 at 21:56
  • Sorry, perhaps I was confusing. The equivalent contrapositive statement to the one considered is ~Q-->~P. The belief is Q, and the argument is P. The argument P is claimed to entail the belief Q. This is agreed to be true. (Maybe that's a bad reading of the posters' question). It is established that ~P. It is then inferred from this that ~Q. This is the fallacy of asserting the consequent on the contrapositive. I'm not sure what is not a fallacy - asserting the consequent certainly is (just use a truth table or trust wiki: https://en.wikipedia.org/wiki/Affirming_the_consequent). – лаетековский чайник Apr 17 '17 at 22:30
  • Yeah ok, the argument is P, and P entails Q. The refutation of the argument is ~P. That wasn't quite clear in what you wrote in your answer, but is clearer in your comment. – barlop Apr 18 '17 at 10:26
  • And yeah I see they're taking the contrapositive and then doing the fallacy of affirming the consequent. – barlop Apr 18 '17 at 10:26
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A kind of cum hoc ergo propter hoc logical fallacy of "with this, therefore because of this" such that if the argument is false, then the premises are also false.

What you describe is simple fallacy tho as it does not follow that use of premise in a false or true argument has any bearing upon the premise's truth value.

MmmHmm
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