Mill's Examples of False Analogy

It's interesting to look at Mill's examples of what counts as false analogy, as he considers them in Book V of A System of Logic.

(1) Paternal government and despotic government. Paternal government is good, so too will despotic government be good. This is a false analogy, says Mill, because it implies that despotic government shares with paternal government that feature which makes it good, namely, that there is a responsible authority (who cannot be the children in the familial case or the general populace in the case of the state); but, in fact, the goodness of paternal government is due to two features it does not share with despotic government, namely the superior experience of the parents and the affection of the parents toward their children.

(2) Individual stages of life and political stages of life. As human beings and animals go from youth to maturity to old age to death, so do nations. But in human beings and animals this progress is due to "the natural progress of those very changes of structure which, in their earlier stages, constitutes its growth to maturity" but political bodies die not because of the progress of their structures but because of the stagnation and regression of their structures.

(3) Immutability and unpunishability. An argument made by Hooker: As natural bodies require an unmovable mover in order to have motion, so political bodies require an unpunishable member in order to have punishment. Mill doesn't give a specific reason for the falseness of the analogy; he gets distracted by the fact that he also thinks its premise (about immovable movers) is false.

(4) Monetary utility and utility of resources. An example taken from Whately: “It would be admitted that a great and permanent diminution in the quantity of some useful commodity, such as corn, or coal, or iron, throughout the world, would be a serious and lasting loss; and again, that if the fields and coal-mines yielded regularly double quantities, with the same labor, we should be so much the richer; hence it might be inferred, that if the quantity of gold and silver in the world were diminished one-half, or were doubled, like results would follow; the utility of these metals, for the purposes of coin, being very great. Now there are many points of resemblance and many of difference, between the precious metals on the one hand, and corn, coal, etc., on the other; but the important circumstance to the supposed argument is, that the utility of gold and silver (as coin, which is far the chief) depends on their value, which is regulated by their scarcity; or rather, to speak strictly, by the difficulty of obtaining them; whereas, if corn and coal were ten times as abundant (i.e., more easily obtained), a bushel of either would still be as useful as now. But if it were twice as easy to procure gold as it is, a sovereign would be twice as large; if only half as easy, it would be of the size of a half-sovereign, and this (besides the trifling circumstance of the cheapness or dearness of gold ornaments) would be all the difference. The analogy, therefore, fails in the point essential to the argument.”

(5) Metropolis and heart. Also an example taken from Whately: As the metropolis is like a heart, and as significant increase of the heart is a disease, so too significant increase in the size of the metropolis is a disease of the political body.

(6) Pythagorean analogies. There are proportions in the monochord that give music; there are similar proportions in astronomy, and thus a music of the spheres, "as if the music of a harp had depended solely on the numerical proportions, and not on the material, nor even on the existence of any material, any strings at all." Likewise there are various numerological and cosmological speculations through history that later are held to be fanciful. These often identified real resemblances (proportions and the like) but drew the wrong conclusions from them.

(7) Technical defect and moral defect. From arguments of the Stoics, an example taken from Cicero. Suppose a number of lyres that are out of tune; we can say that they are equally out of tune; therefore all departures from the rule (of right living) are equally departures from it, and so all are equal. Likewise a navigator has equally failed at his task whether he loses a ship carrying straw or he loses a ship carrying gold; likewise, it doesn't matter whether a man beats his father or his slave if he does it without due cause.

Some of these are interesting; with regard to (7), for instance, Cicero himself identifies the problem as equivocation, which makes for dissimilar similars. Mill rejects the navigator/abuser analogy because he holds that a failure of skill and a moral failure differ precisely in that interest is irrelevant to the former but not the latter; Cicero rejects it because the actual cargo doesn't affect our assessment of skill but who gets beaten does affect our assessment of justice. (But Cicero also denies the premise of the comparison, saying that when we consider negligence, it does matter whether the cargo was straw or gold.) But what's notable is that every single one of the responses that clarifies why the analogy is false argues that it is a false analogy because the causes involved in each are not really and truly the same kinds of causes. As he explains:

In these and all other arguments drawn from remote analogies, and from metaphors, which are cases of analogy, it is apparent (especially when we consider the extreme facility of raising up contrary analogies and conflicting metaphors) that, so far from the metaphor or analogy proving any thing, the applicability of the metaphor is the very thing to be made out. It has to be shown that in the two cases asserted to be analogous, the same law is really operating; that between the known resemblance and the inferred one there is some connection by means of causation.

That is, each analysis purporting to show that the Fallacy of False Analogy has been committed is simply an argument that the similarities have been used improperly as a basis for generalization.

This Fallacy [of False Analogy] stands distinguished from those already treated of by the peculiarity that it does not even simulate a complete and conclusive induction, but consists in the misapplication of an argument which is at best only admissible as an inconclusive presumption, where real proof is unattainable.

It looks very much like analogical inferences are not allowed defeasibility on Mill's account; the very failure of the inference to get the right conclusion is itself sufficient evidence that it commits the Fallacy of False Analogy. This is an unusual use of the word 'fallacy'; fallacious reasoning isn't usually taken to be proven by the mere fact that you got a wrong answer. But this broad usage is not unique to Mill; Bentham regularly uses the word in something like this way, too. And it ties in with the fact that Mill thinks of 'fallacy' as naturally connected to evidence: a fallacy is a case where apparent evidence is not real evidence or apparently conclusive evidence is not actually conclusive, so that a false conclusion is drawn. Thus the very test of a fallacy in Mill's sense is that the evidence results in a false conclusion, or involves a false assumption. So, for instance, Mill says (3) is doubly fallacious: it involves false analogy and it inolves the scholastic error of thinking that motion requires an immutable mover. A great deal of philosophical content is being packed into this understanding of fallaciousness. When you take it in this sense, one sees that all the false analogies are analogical inferences that Mill thinks result in incorrect conclusions. This is all well and good for people who agree with Mill about (for instance) the nature of the body politic, but it means that Mill's conclusions about the Fallacy of False Analogy -- including the claim that there is such a fallacy -- are not necessarily consistent with non-Millian views.

False Analogy

I've occasionally sketched out some rough criticisms of Wikipedia's false analogy article. The current version is much better than the versions I've seen before. But it still seems to be struggling with finding any good examples. Here's the current example being used:

An example of a false analogy between energy and mass would be to assume that since E=mc2, then energy and mass must be identical. Energy and mass are not identical, energy can travel at the speed of light while mass cannot. Analogies should never be mistaken for establishing an equivalence. Not recognizing the misapplication of analogy can be as potentially disastrous as not recognizing a misapplication of logic.

It's certainly true that analogies should not be confused with equivalences or identities, but it's hard to see how such a confusion is supposed to be an example of a fallacy of false analogy, given that the whole problem is that the analogical character of the relation is not being recognized. It's also not obvious that the proper way to think of the equality in the E=mc2 example is as establishing an analogy rather than something else. It's possible, though, the idea is that E=mc2 establishes that measurements of energy and mass have a proportion or analogy to each other, and that the mistake is to think that this analogy implies or is identical to a different analogy, between energy and mass themselves. In any case, the way in which this is supposed to be an example of false analogy is obscure in both ways.

But, as I think I've suggested before, the problem here is not in Wikipedia or its editors but in the fact that standard accounts of false analogy are neither consistent nor well-motivated. Part of it is that standard accounts of almost all the fallacies are patchwork, crazy quilts sewn out of striking pieces of accounts that are not obviously consistent and sometimes are obviously not consistent, because the accounts are built up in the way any folklore is, however philosophical this form of folklore may be.

Part of the problem, however, is historical; we seem to owe our special confusion about false analogy to John Stuart Mill and his readers. Mill, in A System of Logic, doesn't seem to be the originator of the label, but his account of it was for a very long time the most widely read account. his account, however, has a number of idiosyncrasies. On Mill's view there is one legitimate form of analogical inference, which is basically nothing other than an inductive argument to raise the probability that this or that cause is operative in a certain kind of phenomena. In other words, since induction is primarily taken to be about causes, analogy is a form of causal generalization; false analogy is a form of bad causal generalization. We see the residue of this in the fact that a number of late nineteenth century authors treat false analogy as a lapse in causal reasoning, non tali causa pro tali causa. In order to be legitimate, the bare analogical inference is not enough; you need in addition a reason to think that it takes into account all the relevant causal conditions. It is because of this that his description of false analogy almost makes it sound like all analogy is out the window:

There is another, more properly deserving the name of fallacy, namely, when resemblance in one point is inferred from resemblance in another point, though there is not only no evidence to connect the two circumstances by way of causation, but the evidence tends positively to disconnect them. This is properly the Fallacy of False Analogies.

All analogical inference requires that there be "evidence to connect the two circumstances by way of causation." This is an extraordinarily strong condition on analogical arguments -- one can see the reasoning behind it, but very few people think that the field of legitimate analogical reasoning is this sharply restricted. For instance, many people think that there can be legitimate analogical inferences to the relevant causal conditions; these would all arguably be either illegitimate or circular on Mill's account. What seems to have happened, then, is that some of Mill's claims about false analogy continued to be accepted, but detached from Mill's unusual account of analogical legitimacy. The result is incoherence: on almost any newer account the line between legitimate analogy and false analogy is arbitrary because Millian claims about the fallacy are still fairly standard but are unsupported by any of the very distinctively Millian reasons why Mill originally made the claims.

In order to have a good account of false analogy, then, one needs a good account of analogy. And while some accounts are no doubt better than others, there is no general consensus as to the best account of analogy. I've already mentioned Mill's, in which there is one and only one class of analogies that are good. It's interesting to contrast it to another notable historical account of analogy, namely, Hume's. Hume doesn't talk about On Hume's account of analogy, analogical inferences can be stronger or weaker, but there is one and only one class of analogies that could be taken to be candidates for false analogy: those that essentially posit a similarity between existence and nonexistence. In other words, on Hume's account as long as there is any real (i.e., not purely verbal) similarity an analogy has force. (This is actually somewhat important for understanding Hume and his project, but getting into this would be too long a digression here.) I would suspect that most people have a view of legitimate analogical inference that lies somewhere between Mill's minimalism and Hume's maximalism. (Hume has always seemed to me to be obviously right on this point, but I have found that many people do not agree.) The problem with regard to false analogy should be clear enough: even assuming that there is some coherent fallacy here, the slate of possible candidates for examples of such a fallacy varies wildly depending on what, exactly, your view of analogical inference is. Finding even a reasonably uncontroversial example of false analogy will be fairly difficult, given that people don't even agree as to what makes an analogy bad in any sense.

UPDATE: Reworked some of the statements for greater accuracy. Also, it should be pointed out that, despite the label 'minimalism' used here, Mill actually allows quite a bit of room for analogical inference -- what makes him a 'minimalist' is not that he thinks there is very little value to analogical inferences or that they should be used minimally but that on his account all analogical inferences have to meet fairly restrictive conditions to be of significance.

In Memoriam

Two recent deaths in philosophical circles:

David Hull died Wednesday; he was well-known for his work in philosophy of science. John Wilkins has some discussion and a bibliography.

Mary Anne Warren died Monday. She was a well-known feminist philosopher.

Arguing by Cudgel

Argumentum ad baculum is a form of argument in which the middle term is taken from the topic of punishment or torture; hence the name, which means 'appeal to the stick or cudgel'. Three legitimate uses of ad baculum:

Brian Magee on free will (Confessions of a Philosopher, Random House [1990] p. 152):

I am entirely confident that if you subjected any determinist who is not a psychopath, however amoral his life, to outrageous and cruel ill-treatment, he would become indignant with you and protest that you ought not to treat him in that way. Ought and ought not would spring to life for him then, and he would insist on attributing to you the ability to behave otherwise.

Scotus on contingency (Reportatio IA prol. q. iii art. i; in Philosophical Writings, Wolter, tr., Hackett [1993] p. 9):

And so too, those who deny that some being is contingent should be exposed to torments until they concede that it is possible for them not to be tormented.

And, of course Scotus is adapting Avicenna on noncontradiction (ibid., with a minor change):

Those who deny a first principle should be beaten or exposed to fire until they concede that to burn and not to burn, or to be beaten and not to be beaten, are not [the same].

What makes these legitimate arguments is that in each case the punitive middle term is doing real argumentative work: it is relevant to the subject at hand, and it does link to the conclusion by giving a reason to think that the person holding a position (that there is no free will, that nothing is contingent, or that to be and not to be can be the same) is claiming something they would not consistently be able to uphold, and, perhaps, accept only verbally. Any experience, in principle, would do; the reason for going to the stick is that it's an extreme case, where it's difficult to deny that you'd accept the principle (without sounding implausible). In none of these cases is it demonstrative; on its own it just shows the difficulty of consistently holding some claims, nothing more.

Have you come across any other instances of argumentum ad baculum that are legitimate, i.e., that appeal to what one would be able to hold under torture or beating, that do so in a way that is actually relevant, and that aren't merely threats, but arguments that a position cannot be held consistently through the full range of human experience?

Ba-Umf

Karawane
by Hugo Ball
14th july 1916

jolifanto bambla ô falli bambla
grossiga m'pfa habla horem
égiga goramen
higo bloiko russula huju
hollaka hollala
anlogo bung
blago bung
blago bung
bosso fataka
ü üü ü
schampa wulla wussa ólobo
hej tatta gôrem
eschige zunbada
wulubu ssubudu uluw ssubudu
tumba ba-umf
kusagauma
ba-umf

To appreciate it, you really have to hear it; and nobody has ever done it better than Marie Osmond. The poem, of course, is all nonsense; Hugo Ball was one of the better Dadaist poets, although, over all, his wife, Emmy Hennings, was probably superior.

Notes and Links

* I am something of a complete idiot; until Tom's recent post on De Morgan's spicular notation, I had never noticed the connection between the spicular notation and Euler diagrams. That makes so much sense, and I don't see how I could have missed it; and given that one can use different conventions in drawing Euler diagrams, it shows that spicular notations actually form a family, rather than a single arbitrary notation, of which De Morgan's version is only one. This opens up the possibility that there may be possible spicular notations that are better than De Morgan's. And as Tom notes in another post, recognizing the link between spicular notation and Euler diagrams makes clear the value of the former as a quasi-diagrammatic notation.

* Enbrethiliel has a post that, in its general points, pretty much sums up my view of the recent furor over Anne Rice's conversion to noninstitutional Christianity.

* Kim Sterelny on apprenticeship as a learning model for cultural learning. (ht)

* Steve Matheson on randomness in embryo growth, i.e., organized processes involving stochastic processes as subprocesses.

* Stanley Fish argues that plagiarism is not a big moral deal. I think he's right; the analogy between stealing and plagiarism has never actually been very strong. But it still can get you an F in my class. Plagiarism is a problem not because it is immoral in general but because it obscures evaluation on the actual merits of one's work in fields where reputation or money are important. And he's right about something more important, namely, that we should stop pretending the rules governing plagiarism are easy and obvious: students do not usually find them so. They have difficulty seeing the proper line between common knowledge and what must be cited; they have difficulty seeing the relevance of particular methods of citation; they don't have a clear conception for how paraphrase fits into the scheme of things; and so forth. Moreover, the conventions governing plagiarism are not uniform across all fields. If you want to be a lawyer dealing with contracts, for instance, you will succeed best if you have a large file of very different kinds of prior contracts that you can simply copy and adapt and mix-and-match whenever new occasions arise, rather than absurdly trying to start from scratch each time. Nobody will ever get bothered by the fact that the contract language is exactly the same as some other contract; reputation and money for lawyers simply doesn't depend on how much work they themselves put into the particular contract language used. And while that's an extreme case, there are lots of fields where common practices would count as plagiarism if they were done in some other field.

That said, Fish is simply wrong that if plagiarism is an artificial and conventional concept rather than a fundamental moral one that there is no point in looking at its philosophical underpinnings; philosophers have been looking at the philosophical underpinnings of purely conventional practices since Socrates. And, in fact, it's those philosophical underpinnings that show that, contrary to common belief, originality or literary property has nothing to do with it; plagiarism conventions exist not to protect originality or literary property but to limit rewards to people who actually and consistently do the work, to prevent people who let others do the work from being rewarded as if they had done it. This is why plagiarism conventions have to vary somewhat across fields -- what counts as 'the work' is itself something that varies across fields.

* For the first time in a long time it looks like there's a promising answer to the question of whether P is equal to NP. It's something of an esoteric question, but like many esoteric questions in mathematics, it has practical implications: if P is equal to NP, many codes and computer security systems are breakable that would be relatively unbreakable if P is not equal to NP. (If I haven't garbled that too badly; it's well outside my field.)

ADDED LATER: John Perry clarifies in the comments: "If P = NP, it's not quite true that many codes would become unbreakable: they would, rather, be unbreakable in a number of operations that is deterministically polynomial in the worst case. However, that worst case could have a quite high and impractical exponent, and could occur frequently enough in practice to render the method useless in many cases."

* The physics of the Beacon of Gondor. As some of the commenters notes, the system is based on the Malverns. A beacon of fires similarly conveys word back to Argos that Troy has fallen in Aeschylus's Agamemnon, but there are notorious problems with both time and geographical location in Aeschylus's description of it. Aeschylus is probably trying to give a plausible system for the Greeks that would do for them (i.e., give advanced notice) what the Persian rider-system (one of the things the Greeks admired about the Persian empire) did for the Persians. Tolkien is very clear, I think, that the beacon-system is actually combined with a rider-system, which would be the most reasonable way to do it: the beacon would provide an alert, details to follow by fast horse. So all the beacon ultimately has to do is outrun the horses, warning each station in advance to start getting riders ready because an emergency message is coming. This would massively cut down on wasted time, the biggest problem with a rider-system; and it would prevent the beacon-system from breaking down (even if station B doesn't pick up station A's signal, this will be fixed when the riders from A reach B and the beacon begins again). There still would be room for the system to break down, but the chances are that everyone would at least know that something was up. You want a fast alert system, but fast alert systems don't usually carry a lot of information (when the Horn of Buckland blows you know there's a big problem somewhere, but you don't know if it's bandits or floods or fires); and you want an adequate message system, but adequate message systems usually have a lot of inefficiencies. It makes sense to combine the two.

* The Library of Historical Apologetics (ht)

* Last week my sister took me to see Inception at the Alamo Draft House (for my birthday this past weekend); very good. One of the reasons it is good is that it is about the only movie that captures dreaming properly: conveying not only its surreal association but also the fact that these associations flesh out very logical correspondences and implications. If you see any big Hollywood movie this year, this is it. It's basically a caper movie, but I was impressed as to how well the characterization was done, given that by it's nature it's not a character-driven story but a plot-driven one.

Non-Become and Imperishable

The entire world of becoming is permeated by that order which permits every created being (ens) to strive for its own perfection and to aid other created beings on their way to perfection. This order itself, however, is not subject to becoming and passing away, but is non-become and imperishable. And just as that which is signified by the term "human being" [Mensch] is neither born nor passes away, so als o that which is signified by "holiness" (denoting the perfection of a person and, in a derivative sense, that which ministers to the perfection of a person or bears the stamp of a person) is not subject to any becoming, notwithstanding the fact that holiness may become actual and may therefore become the goal of striving.

Edith Stein, Finite and Eternal Being, p. 316. Today, of course, is the feastday of Edith Stein, also known as St. Teresia Benedicta of the Cross, who died on this day in 1942 in the concentration camp at Auschwitz, along with her sister Rosa.

Hansai

I have been accused of being “high-minded.” I must be saying “You may not do evil that good may come,” which is a disagreeably high-minded doctrine. The action was necessary, or at any rate it was thought by competent, expert military opinion to be necessary; it probably saved more lives than it sacrificed; it had a good result, it ended the war. Come now: if you had to choose between boiling one baby and letting some frightful disaster befall a thousand people—or a million people, if a thousand is not enough—what would you do? Are you going to strike an attitude and say “You may not do evil that good may come”? (People who never hear such arguments will hardly believe they take place, and will pass this rapidly by.)

[G. E. M. Anscombe, "Mr. Truman's Degree".]

On this day in 1945, American forces dropped the plutonium-based "Fat Man" bomb over the Catholic district in Nagasaki. The bomb exploded within 500 meters of the Urakami Cathedral. At least 40000 people, and perhaps as many as 70000, died within one minute of the bombing. There's a famous book by Takashi Nagai, called The Bells of Nagasaki, which describes the event and its aftermath. Nagai was himself a survivor of it, and was asked later that year to deliver the Funeral Address at the Requiem Mass for the dead; in it he referred to the Catholics who had died as a hansai, which is the word used in Japanese for a whole burnt offering -- a holocaust.

Wagering on Seeking

According to the doctrine of chance, you ought to put yourself to the trouble of searching for the truth; for if you die without worshipping the True Cause, you are lost. "But," say you, "if He had wished me to worship Him, He would have left me signs of His will." He has done so; but you neglect them. Seek them, therefore; it is well worth it.

Pascal, Pensées 236. Note that the argument here is that we should inquire; this is a theme that comes up a number of times in Wager passages. It also shows indirectly why the too-common practice of focusing on 233 (the larger Wager fragment) is problematic, since there are other fragments that put the Wager in perspective. It's a flaw in Hajek's otherwise interesting SEP article, for instance. But a certain amount of leeway can be allowed, given that we face with Pascal's Wager a problem we don't usually face: the Pensées are posthumously published fragments. Pascal was building up a Wager argument but we don't have it. What we do have are a bunch of draft fragments. I think we have enough to piece together quite a bit and determine approximately what Pascal would have ended up with, but it takes work; so it's not surprising that people just focus on the largest Wager fragment as if it were 'the' Wager argument, rather than (what it certainly must be, given other fragments) merely a sketch of part of it. But the result is that people lose sight of just how much of Pascal's argument, if completed according to the notes we have, would have had to do not with belief but with inquiry. (Another result is that people lose sight of the fact that most of the Wager-relevant fragments show clearly that Pascal is arguing against a particular group of people who are arguing that Christians are irrational not to suspend judgment, and it is this he is attacking, not atheism.)