Wednesday, September 23, 2009

Fun with fallacies: Poisoning the well

An unfortunate byproduct of philosophical training, other than the obvious of annoying everyone at the dinner table, is that I cry inwardly every time I see terms such as “fallacy” or “invalid” misused. On the theory that I shouldn’t complain about it if I’m not doing something about it, I figured I’d start an irregular series on critical thinking and logical fallacies. So, welcome to the inaugural edition of Fun with Fallacies…

First, some background. There are two different dimensions along which to evaluate arguments: one, the truth of premises and, two, the validity of argument structure. Premises (the content of arguments – e.g. “Scotland is in the Northern Hemisphere”, “All monkeys are purple”) are either true or false. Arguments (the logical structure linking premises – e.g. “If A then B, A therefore B”, “A and B, therefore C”) are either valid or invalid. And these two dimensions, importantly, are separate. In logic, saying a premise is invalid makes no sense: it is much like saying someone has scored a touchdown in soccer. Similarly, arguments cannot be true or false; they are only ever valid or invalid. As the perceptive reader no doubt noticed, my first example of a premise was true and the second was false and my first example of an argument was valid (if you like your Latin, this particular structure is known as modes ponens) and the second was invalid. Note that you can have an invalid argument with true premises and a true conclusion (“Elephants are mammals, Elvis Presley is dead, therefore homeopathy is bollocks”), that you can have a valid argument with false premises and a false conclusion (“All women are pregnant, Angela is a woman, therefore Angela is pregnant” "All women are pregnant, Michael is a woman, therefore Michael is pregnant") and so on. These dimensions are entirely independent of each other. When an argument is (1) valid AND (2) has all true premises, we say it is sound (and therefore one you should accept); otherwise, it is unsound.

But what exactly is validity? It’s quite simple really. A valid argument is one where the truth of the premises guarantees the truth of the conclusion. In other words, if the premises are true, it follows, by the laws of logic, that the conclusion must be true. (But not vice versa). If this is the case, we say the conclusion ‘follows’ from the premises or that the truth of the premises 'transmits' truth to the conclusion. So if “A” and “if A then B” are both true, then you are forced to conclude that “B” is true (this is modes ponens again). Or, in words, if Paris is the capitol of France (“A”), and Paris being the capitol of France entails that the French seat of government is in Paris (“if A then B”), then it follows that the French seat of government is in Paris (“B”).

Okay, so what’s a fallacy? It’s just an argument that is not valid – that is, it’s an argument where the conclusion does not follow from the premises. Notice, however, that the fact that some argument is a fallacy does not mean the premises are false, nor does it mean the conclusion is false. Indeed, saying an argument is fallacious (i.e. invalid) entails nothing whatsoever about the truth of the premises or the conclusion. (You can, after all, defend a true conclusion with an invalid argument). Conversely, just because an argument is valid does not mean the conclusion is true, nor does it mean the premises are true: it’s just that if the premises were true you would have to accept the conclusion. (So if it really were the case that all monkeys are purple and that I am a monkey, I would be forced to accept that I’m purple). The upshot is that a concern with validity and detecting fallacies is only one aspect of evaluating positions but, of course, it’s an important part.

That’s about enough background, I think, so on the our first actual example… Regular readers will recall that I recently took on a local (i.e. South African) homeopath, one Johan Prinsloo. In a section of his website that he’s now edited but which is still available on Google Cache as I first saw it, Prinsloo made the following argument (emphasis in original):
The one thing that always catches my attention is the fact that generally the skeptics of Homeopathy also tend to be anti-religion or at least skeptical of religion.
What’s going on here? Well, it’s a beautiful example of poisoning the well, which is a sub-type of the ad hominem fallacy (‘arguing to the man’). Ad hominem is pretty widely misunderstood; some people seem to think that any insult or negative assertion about an opponent makes an argument fallacious. This is not correct. In fact, ad hominem has the form: “Sarah believes that P, Sarah has negative quality X, therefore P is false”. Clearly, this argument is invalid: there is no premise linking having negative quality X and the truth or falsity of P. The important bit, though, is that a conclusion is being drawn about a claim from the purported negative quality, if this is not done no fallacy is being committed. I might say, for example, that: “Homeopathy is bollocks”, “homeopaths tend to be dumb”, “the law of infinitesimals is false” and so on. As long as I’m not drawing an inference from “homeopaths tend to be dumb”, all I’ve done is thrown around an insult (which may or may not be true), I have not committed a fallacy. (Remember, truth and falsity is independent of validity and invalidity!). It’s possible, in fact, to make the argument about Sarah valid (so it’s no longer a fallacy), despite the fact that it’s still about a negative quality. All I have to do is insert the missing premise: “Sarah believes that P, Sarah has negative quality X, everything people with negative quality X believe is false, therefore P is false”. Note that the conclusion now does follow from the premises and it’s thus no longer a fallacy, but at the cost of making the ridiculous missing (or ‘suppressed’) premise explicit.

In Prinsloo’s case it’s clear that he’s attempting to preempt criticism of homeopathy by (in his mind) tarnishing the reputation of the skeptics: he is, in other words, poisoning the well. He is implying that critics of homeopathy have a negative quality (being religious skeptics), and therefore their views on homeopathy can be dismissed. This argument is obviously fallacious as it stands: there is no premise linking being a religious skeptic to having false beliefs about homeopathy, and thus the conclusion does not follow from the stated premises. To make the argument valid, Prinsloo would have to say something like "everything a religious skeptic believes is false" or "everything religious skeptics say about homeopath is false" and once you see that, it becomes obvious why the premise was kept implicit: it's ridiculous on the face of it. As far as I am aware, there is not even correlational evidence between religious skepticism and having false beliefs (indeed the opposite might be true), let alone evidence that religious skeptics are invariably wrong.


  1. As someone who also "cr[ies] inwardly every time I see terms such as “fallacy” or “invalid” misused", I feel compelled to point out that many good/sound/cogent arguments are not valid - simply because they are not deductive arguments, and therefore can never aspire to be valid in the first instance.

    This post focuses exlusively on the deductive form, without ever mentioning that, so a logicoramus may leave with a false impression.

  2. This is a bit off topic but I couldn't help but laugh at this :

    "Tony Blair's sister in law, Lyndsey Booth, changed careers from being a lawyer to being a qualified homeopath"

    To almost any British person this would be a surefire argument against homeopathy, Tony Blair is really not very popular any more! It's so quaint...

  3. Jacques -- my position on the deductive / inductive / abductive / whatever-ductive debate is a bit odd and I intend to post about it at some point, but I figure I'd test drive it here. Please do let me know what you think.

    Basically, I think all we really need is deductive arguments. All invalid arguments (except self-contradictory ones) can be made valid by the addition of suitable premises. The inductive form (which is of course invalid by definition) can be turned into a deductive argument, which, as it were, transfers the uncertainty from the logical form to the truth of the added premise.

    An example. "I've seen only black crows, therefore all crows are black" is an inductive type. It seems to me to be extremely hard to evaluate as-is. Much better is to make it deductively valid by inserting "Seeing N crows is sufficient to draw conclusions about all crows, I've seen at least N crows, all the crows I've seen are black, therefore all crows are black". Now I can evaluate the added premises with the tools of science, and it makes explicit what kind of evidence I have to look for.

    There's no need for the inductive / abductive form: you can transfer all the uncertainty to premises, and then the premises can be evaluated, without the uncertainties attending evaluating non-valid logical arguments.

    What do you think?

  4. You're getting away with only needing deductive arguments by redefining what "deductive" means, so your suggestion strikes me as probably circular. To use your example, "Seeing N crows is sufficient to draw conclusions about all crows":

    "Sufficient" here probably means something like a low enough margin of error at a decent confidence level, etc. So you're importing a tool from the I-S model into something you are calling "deductive", where to me it simply looks like a normal I-S argument, except that you've left out the "probably" in your conclusion. I don't see your warrant for doing so, in that we can't have consensus (except in a strict deductive model) about how large the N should be (where the N would be 100% of crows for deductive validity).

    In short, it looks like a con to me. I'd be more inclined to try to eliminate deductive arguments from our arsenal, in that they are rather limited in application and present people with a overly demanding ambition, where they should most likely rather learn how to properly reason about probabilities (ie. the inductive model).