A, B, C, D – a fallacy

I don’t know whether this fallacy has a name of its own – I’m sure that Mike LaBossiere can tell us if it does – but how often have you seen somebody argue along the following lines?

P1. X believes A, B, and C.
P2. Y and Z (and others) believe A, B, C, and D.
C. (Therefore) X believes D.

What then happens is that X is criticised for believing D, even though D may be a proposition that X has never argued for, expressly relied upon, or even affirmed. In some cases, D may be some horrible proposition that would suggest X is of bad character if X actually believes it. In other cases, it may merely be something absurd, clearly false, or highly controversial.

As it stands, the argument that X believes D is straightforwardly invalid. It is no more valid if it takes the following variant form:

P1. X believes A, B, and C.
P2. Y and Z (and others) believe A, B, and C because they believe D.
C1. (Therefore) X believes A, B, and C because X believes D.
C. (Therefore) X believes D

Reversing the two premises, arguments like this are similar to the classic (and straightforwardly fallacious):

P1. Some Xs are A’s.
P2. X-1 is an X.
C. X-1 is an A.

Perhaps, however, there is something more going on in the minds of people who use arguments such as I’ve identified.

Perhaps, on a particular occasion, they think that A,B,C without D is somehow an incoherent package of beliefs, and so they attribute to X what they see as the more coherent A,B,C,D.

Or perhaps they are reasoning inductively from a sociological observation that most people who believe A,B,C also believe D, so X probably believes D. Or maybe, related to the previous paragraph, they think that you could only, rationally, come to believe A,B,C on the basis of first believing D. Or the idea might be that believing D, which is widespread, causes a widespread bias in favour of people believing A,B,C (though D is highly controversial, or clearly false, or some such thing, once it’s explicitly identified).

Although it’s always open to someone to put these sorts of arguments, they are obviously going to be tricky in any particular case. Reasons have to be given as to why D produces a bias, why D might be widely (perhaps subconsciously?) believed even though it is clearly false, or absurd, or whatever, once identified; why the position A,B,C, without D, is incoherent; why there is no other basis for thinking A,B,C; and/or whatever else might be required to make out the particular argument. You need to be careful before you move too quickly to saddle somebody with the absurd or clearly false or highly controversial or just plain horrible proposition D.

That said, the temptation to move quickly and incautiously down this path seems to be a strong one. Often we have enough background beliefs of our own (“Surely no one could possibly believe A,B,C unless they first believe D!”) that we find it very natural to draw the final inference intuitively and almost unconsciously. I know that I sometimes feel this temptation, and I’m sure I’ve often succumbed to it. I don’t think there’s a lot of point in castigating people for it, or even in apologising when caught doing it.

Hasty reasoning of this kind, leaving out steps, and failing to recognise just how difficult and inconclusive such arguments tend to be, is all too tempting. It’s lazy. It cuts corners. It can lead to you paying insufficient attention to what an opponent is really saying. In the extreme, it might encourage you to demonise an opponent (X surely “must” believe the horrible proposition D!) without a good basis. But it is not the sort of thing done only by irrational or ill-willed people.

My proposal is not so much that we go around castigating this way of thinking, which is almost ubiquitous. I don’t want to give real examples of it (and I could, as mentioned above, almost certainly find cases where I’ve done it, too). However, it’s something that we might be more aware of and careful about, given all that I’ve said, and especially as it provides a route to misunderstanding and even demonising opponents. And in some cases, our opponents are right there, taking part in discussion with us, so we can simply ask them: “Are you relying on proposition D?”

All in all, attributing beliefs to opponents needs to be done with great care if they have not expressly relied on or otherwise asserted those particular beliefs. Speculating about what your opponents really think (but are not saying) may not be the worst of intellectual crimes, and it may be very tempting. Sometimes these speculations might even be relevant and useful (say your opponent claims to be relying on “nice”, attractive, good-for-their-public-image premises E and F, but you have independent reason to think they are really reasoning from discredited proposition D).

As always nuance is important, but if we want to be fair, make progress, and avoid flame wars, let’s at least be careful about the kinds of reasoning I’ve discussed. At their worst, they are obviously fallacious. Even at their best, they are highly uncertain and need a lot of work before they can be employed cogently.

Leave a comment ?


  1. Couldn’t quite follow your first example. You say you ‘could’ find examples. Have you? Or is this a hypothetical fallacy?

    Your example is not a fallacy, particularly – it is not an argument. Because it is not really about the implications of the propositions A, B, C, D, but about the beliefs of the subjects X, Y, Z and others.

    P1 is a simple premise that X believes something.
    P2 is a simple premise that Y, Z (and others) believe something else.

    These are two independent statements about belief from which neither C1 or C can be drawn.

    Is it a fallacy to argue that there is an argument when there isn’t one? Or simply wrong. I suppose it depends on the argument that there is an argument is itself an argument, and that it is an invalid one?

    This seems more realistic:

    Y, Z (and others) make this argument:
    P1. X believes A, B, and C.
    P2. Belief in A, B, C is implied by belief in D
    C. Therefore X believes D

    This is a straight forward fallacy affirming the consequent buried in details about beliefs. As you pointed out in your second example, but in the form of this fallacy, and burying the belief elements in the labels:

    If D then A, B, C
    A, B, C
    Therfore D

    I see this far more often:

    Y, Z (and others) make this argument:
    P1. X believes A, B, and C.
    P2. Belief in A, B, C implies belief in D
    C. Therefore X believes D

    The argument of Y, Z (and others) is valid. If we take P1 to be true, as stated by X so it’s reasonable for Y, Z (and others) to use it, then that leaves P2 as suspect.

    Having said all that there are real examples where arguments are based on *the belief* that some proposition is true implies it is true. They can generally be narrowed down to this:

    I believe there must be a God.
    Therefore there must be a God.

    But they are often buried in many levels of theistic ‘reasoning’. Even this is a simplistic version of their reasoning:

    I (some believer) make the argument:

    P1: Presupposition of God.

    This is not noticed to be a presupposition, or is taken as an obvious premise not in need of verification. It is rarely stated explicitly up from. Arguments usually start from something like P2, where P1 is clearly buried.

    P2: I believe the Bible was written by people inspired by God and witnesses to real events and so must be true.
    P3: I believe the Bible tells us about Jesus Christ.
    P4: I believe the God of the Bible would not lie to us about his existence.
    C1: Therefore there must be a truthful God.
    C2: Therefore P1 – P4 must be true.

    And, cherry on the top:
    P5: You cannot prove me wrong.
    C3: Therefore I am right.

  2. I’m a bit confused by all this, Ron. Perhaps I need to read it more closely, but you threw me at the start. How is it not an argument?

    It is an argument to the conclusion: “X believes D”. It’s not a valid argument to that conclusion, but I don’t know why you say it’s not an argument. People draw conclusions, and make accusations, about each other’s beliefs, motives, etc., all the time, and that’s what the post is about.

    And no, it’s not meant to be a hypothetical example. I see this sort of thing every day – people drawing conclusions about each other’s beliefs, etc., (apparently) based on this sort of reasoning. I go so far in the post as to say that it’s ubiquitous in real-world discussions – people quickly reaching a point of accusing each other of believing things that they actually may not believe, apparently based on this kind of reasoning. If you find that implausible, just watch out for it over the next few weeks if you’re reading any debate going on on the internet.

    If you don’t want to say it’s fallacious, I’m also a bit puzzled. If this style of argument is not valid (or cogent in some other way they falls short of deductive validity), why not say it’s fallacious? Do you have some more specialised meaning of the word “fallacious” in mind? Would you be satisfied with some other expression such as “not cogent”? But “fallacious” seems to me a better word to convey the point in ordinary English.

  3. But in the wild, isn’t it often in this form?

    P1. X believes A, B, and C.
    P2. Y and Z (and others) believe A, B, C, and D.
    P3. D is bad.
    P4. I want X to shut up.
    C. (Therefore) I will shame X by saying that X believes D.

  4. Patrick – yes, I do think it often takes that form. However, I don’t think we can assume that it’s always (and I know you only said “often”) in such bad faith. I think that just as often what is going on is that the person is intuitively reaching the conclusion that X believes D. They may be wrong, and perhaps they should be more careful, but they may still be sincere.

    I suppose this might be placed under pressure if there are reasons around, or if they come up, to suggest that X does not actually believe D. Persistence in believing that X believes D, in the face of contrary evidence, might itself be evidence of bad faith or bias or something of the sort.

  5. I’ve been a bit worried that my very abstract and formal presentation of some of this in the original post may be off-putting, and it may even distort some of what I was really getting at. I kept it at that level to try to avoid getting tangled in, or derailed into, the merits of any actual debates that are currently going on Out There.

    But here is a real-life example, to try to make it more concrete.

    I am often accused of being a political libertarian. This is usually because I take very liberal positions on such things as freedom of speech, sexual conduct, and certain biomedical issues (such as the rights and wrongs of human cloning). Political libertarians tend to take similar positions on these matters.

    However, political libertarians also hold to certain positions that I do not hold to. E.g. they believe that there is something highly problematic about taxes (perhaps even that taxation is theft), that the welfare state should be dismantled, that the proper roles of government are very limited, etc. I’ll call these distinctively libertarian positions.

    So the inference is drawn that because I take the same (or similar) highly liberal views on certain issues, and that lots of other people take these positions, while also taking the distinctively libertarian positions on the other issues, that I, too, must take the distinctively libertarian positions on those other issues.

    And this can be used, at least rhetorically, to debunk me in the eyes of many people.

    As it happens, however, I don’t hold to the distinctively libertarian positions. Nor do I justify my highly liberal views on the first group of issues with any distinctively libertarian arguments that should logically commit me to the distinctively libertarian positions.

    What I’m suggesting in the original post is that this kind of thing is pretty much ubiquitous, and we ought to be careful about it if we want to make intellectual progress, understand our opponents, be open to seeing strengths in opponents’ positions and to modifying our own, etc.

    Again, I don’t think that all such arguments are fallacious. E.g. what if one of my positions actually were, “Taxation is theft”? That’s a position that really would be difficult to support except with libertarian arguments. If someone put that particular position, it would be a fairly safe bet that they were a political libertarian.

    The trick is to be careful and discerning (as well as arguing in good faith).

  6. Great post, I see this problem happening ALL the time.

    I think you have already brought this up in the comments, but I think what is really going on is something like “based on their stated beliefs, P1 and P2 are both members of Group G, and Group G has so-and-so as a standard belief; so P1 and P2 both must believe everything that group G does.”

    Of course you have to wonder if P1 really is part of G and even more importantly is it true that all members of G really subscribe to the belief in question!

  7. That kind of reasoning is basically a heuristic tool. I don’t think human communication would really be possible without it. If I were to say something like “freedom of speech is a good thing”, it wouldn’t be unreasonable to assume that I think that because I appreciate the tradition of western political thought from Socrates to Mill rather than because Cthulhu told me so in a dream. But of course, reasoning like that can go wrong as well. Writers who hold positions that are oftentimes held for different reasons than their own just have to explain their position in more detail. If there is an easier solution, I don’t see it.

  8. Actually, Russell, your first argument is excellent. The line of reasoning, to the extent there is reasoning involved in examples of this in the wild, is sound.

    Patrick’s response recognizes the way the fallacy is used in support of social constructs- prejudices designed to control people by separating them from groups that might present challenges to a powerful social order.

  9. Russell, the most libertarian (i.e. classically liberal) position would be that which permits you to make your own value judgements without adherence to a particular social norm. In other words, your belief in A, B, and C does not constrain you to belief in D just because the larger population may take D to be a position held by most libertarians.

    The libertarian ideal assumes that natural alliances will develop around issues of particular importance, much as multi-cellular organisms have developed, starting with the dual-organism alliance of lichens. It is possible, therefore, for a libertarian to agree with a modern liberal on many issues and for another libertarian to agree with a conservative on many issues simply by virtue of the importance they give to certain ideas.

  10. I have recently taken to using the term “property rights libertarian” for those who believe that taxation is theft or some variation of that idea. (At least in the US, that belief is considerably more common than identification with libertarianism as a political movement.) That term provides an easily understandable contrast to social libertarians, who would be defined pretty much the way you characterize your libertarian-like positions. (I consider myself a social libertarian, but am fundamentally opposed to property rights libertarianism.) Also, in the US, political libertarianism is usually understood to include a position that individuals have a fundamental right to possess and carry firearms, which I don’t see as necessarily associated with either social or property-rights libertarianism.

  11. An Ardent Skeptic

    I enjoyed this post about the very easy trap we fall into about making bad assumptions about all the beliefs others hold based on limited information about some beliefs they hold.

    There is one statement for which I do take exception, however.
    It’s the following:

    “or even in apologising when caught doing it”

    If we wish to promote civil discourse, which requires a charitable attitude towards others, we should be very willing and quick to apologize when we have made bad assumptions about the beliefs of others.

    Saying “I’m sorry” is not a crime. Sincere apologies are given by those with great strength of character and should not be perceived as weakness.

  12. So, Gnash, shall we take your comments to mean you disagree with Russell’s original point? A, B, and C DO entangle one with D?

  13. Lee: Absolutely not. What in my comment gave you that idea?

  14. I always thought this was a form of the straw man fallacy.

  15. Russell,

    I could have been clearer, so I’ll try again.

    The first part of my comment is really asking when a list of statements actually becomes an argument. Simply prefixing one of them with ‘therefore’? And in brackets, as if the ‘therefore’ is implied?

    But the second part was for me more significant. The premises you gave, P1, P2, were simply stating that something was believed. It is that X, Y, Z (and others) believed something that is being claimed to be true by asserting each premise. What they are claiming to believe may well be A, B, C or D, and may or may not be true, but the actual truth of these is not specifically asserted in the premises you give, only that X, Y, Z (and others) believe them.

    So that’s why I went on to point out that this is an example I see often, that people form arguments around beliefs, and then further on assume they have proved that the content of the beliefs are true, rather than the mere believing of them. It’s something theists do often.

  16. Gnash, my question arose from your use of “brand” identification for various kinds of libertarianism. The assumption appears to be that if someone can pin a certain brand of the beast on someone else he has them all figured out. The difficulty of things like this can be illustrated with church affiliation. I’m a United Methodist. Someone with a little knowledge of recent politics might assume from that that I would be in broad agreement with another member of the United Methodist Church, like Hillary Rodham Clinton. This would present a quandary to another member of the denomination named George W. Bush.

Leave a Comment

NOTE - You can use these HTML tags and attributes:
<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>