Mill’s Methods (toward insight)

John Stuart Mill is known for his creation of the ethical system of utilitarianism.  The basic idea of utilitarianism is that an action is good (it has utility) to the extent it makes people happy.  There follows a complicated bit of hand-waving whereby happiness is (conceptually) measured and actions are ranked by the predicted amount of happiness they will produce in sum across the population.

What J. S. Mill is not known as well for are his rules for inductive reasoning.  And that’s a shame, because induction is a remarkably important part of the reasoning process, and it’s usually not taught at all, or taught badly.

Deduction is reasoning from rules and facts:  given that Socrates is a man, and given that all men are mortal, it follows deductively that Socrates is mortal.  But in reality, where do we get our givens?

Well, we can say that we know Socrates is a man because he fulfills the definition we have of “man.”  But that just pushes off the problem; where did we get the definition?  And, how do we know that all men are mortal?

(Now here’s one for you:  All men are mortal; Diotema is not a man; therefore Diotema is not mortal.)

Where We Get Generalizations (usually)

Well, we get our definition of man by looking at all men and finding out what they all have in common, which things that are not men do not have.  And this is supposed to be helpful later on down the road, when we come across something that we don’t know whether it’s a man or not; because we can compare it to our definition, which is a shortcut for comparing it to all men we’ve examined before.

Similarly, all men we know of who have gotten old enough have died; we don’t have anyone hanging around who has lived radically longer than the normal life span — nobody 10 or 20 generations old — so it seems likely.

These are rules if they are always true; they are trends if they’re usually true.  Depending on how persnickety you want to be about your rules, you’ll allow more or fewer of them; but the important thing to keep in mind is that one exception breaks a rule.  The wrong thing to do in that case is to wave the exception aside; the right thing to do is to see what’s wrong with your rule.  (Probably, it’s too general.)

By the way, if you have problems with the phrase, “the exception that proves the rule,” you’re right; logically speaking, it’s an abomination.  Very irritating when others use it to weasle out of your vice-like logic; but very useful when you yourself have some weasling to do. 

It’s a bad translation of the phrase “the exception that tests the rule” (I want to say from French, but I can’t swear to that), and the idea was that you’d now have the exception and the rule duke it out and see who lived; in other words, that you’d investigate, and that the survival of the rule was on the line.  But English speakers didn’t take it that way, either because they couldn’t speak French or because they had a lot of weasling out of logical arguments to do.

Facts and Rules

Now, very often we want to get some rules out of a collection of facts.  Having a collection of facts is itself a neat trick, because a fact is a descriptive statement grounded in observation, and it’s always true.  Calling something a “fact” means nobody can argue with it — that is, people will argue with it, but you’re telling them they can’t.  The same goes for words like “observation,” or “truth.” 

If you don’t like someone else’s facts, the way you argue with them is to go and make your own observations and write them down — if you don’t write them down they don’t count.  Or if you’re feeling lazy you can look up someone else’s written-down observations in a reference, like Wikipedia.  Wikipedia is an especially convenient reference, because if you don’t find the fact you’re looking for, you can always put it in.

So you have a collection of facts, and you want to make rules about them.  We’re especially interested in finding out rules that are causally related, because sorting out what is making what happen gives us great understanding of our environment and power over it.

So, how do we go from a collection of facts to rules about them?  As humans, we’re pretty good at doing this; but it would help to have a set of methods explicitly laid out.  Just as having a definition of “man” helps you figure out who’s mortal, just as having a definition of “person” helps you figure out who you’re allowed to kill, and just as having a definition of “prisoner” helps you figure out who you can and can’t torture, more than our intuitions about who is and isn’t a person, prisoner, or man, so also having our rules for making rules explicitly laid out  can help us in complicated cases.

Mill’s methods of rational induction are:

#1 – Under different circumstances, when we have A, we have x; therefore, A is a cause of x.

Now, this is tricky, because it’s not always true.  There might be a lot of other things going on; maybe it’s coincidence that A and x are appearing together; maybe there’s something you can’t see that’s causing them both.  These methods do not produce certainties; they produce hypotheses which you then must test.  But, they’re very good at producing hypotheses.

This is called the Method of Agreement.  (The names aren’t very important.  Nobody will ever call on you to say by which of Mill’s methods you’ve formed your induction.  The idea is to internalize the thinking, to smarten up your intuitions.)  The basis of this method is to build up examples of the “different circumstances” under which we have A and x together.  The more examples we find, the stronger a case we make.

#2 – When we take away A, we lose x; therefore, A is a cause of x.

This is the opposite of #1.  Here, we have a before-and-after, ideally, of some case where we’ve taken away A, and x has vanished.  But we can also apply this with two cases that are otherwise very similar, with only A and x missing in one of them.  This is the Method of Difference.

#3 – Under different circumstances, A occurs with x; and, when we take away A, we lose x; therefore, A is a cause of x.

 This is simply the first and second methods combined, providing a stronger argument than either of them singlely.  This is called the Joint Method of Agreement and Difference.

#4 – A occurs with B, C, x, y, and z.  B is known to cause y.  C is known to cause z.  Therefore, A must be a cause of z.

This is pretty devious.  Basically, the idea here is that you factor out the stuff you know about, to get a case like #2, where A occurs with x, and implicitly, without A, x has not occurrd (which is part of knowing the relations between B and y, and C and z; neither x nor A has been a factor).  This is the Method of Residues.

#5 – When we have more A, we have more x; when we have less A, we have less x.  Therefore, A is a cause of x.

This one is very useful, because often we can’t remove A entirely.  But, if we can vary it a little, or look for different circumstances in which it varies, and see what varies along with it, we can find a causal relationship even so.

Keep in mind the inverse case, where more A reduces x, and less A amplifies x, which is logically the same thing, and indicates that A has a damping effect on x. 

This is the Method of Concomitant Variations.

There’s a prettily-done page on Mill’s methods on the Critical Thinking Web, with some simple examples about food poisoning.  Also you can look up the term (“Mill’s methods”) on the web or on Wikipedia.

Other Uses

Primarily, these are understood to apply to the sciences — chemistry, psychology; stuff like that.  But we can apply Mill’s methods anywhere we want to think clearly and rationally about cause and effect.  In other words, cultivating a scientific mindset is especially useful in non-scientific domains of inquiry.

An excellent example of applying Mill’s methods to history is Jared Diamond’s classic book, Guns, Germs and Steel.  He goes through the historical record pretty exhaustively, looking for the collapses of civilizations, and at the events that lead up to them.  His methods for unravelling cause and effect are basically Mill’s; he finds comparable cases with different results, and different cases with the same results, and compares calamitous collapses with gradual peterings-out.

These methods are also used by hypnotists to convey emotional arguments to the unconscious mind.  The unconscious doesn’t respond to rules or logic, but it understands metaphor and unravels cause and effect very intelligently.  (Sometimes too intelligently; very often, we do hypnosis to counter-act what is basically an over-generalized emotional rule.)

They’re also a good tool for interpreting symbolic information, like literature and dreams; in general, anything that has a rich set of invisible rules.  Once you understand how to categorize the phenomena, so that you can identify when the “same” kind of thing is going on, you can start applying Mill’s methods.

Published in: on July 9, 2009 at 11:31 am  Comments (3)  
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3 CommentsLeave a comment

  1. Hi Conrad,

    You did it again. At least one good guffaw and carrying your signature of light (or heavier) cynicism.

    Well done.

    On the other hand, sometimes it seems as if there is absolutely no ‘truth’ and no absolute truth and you certainly can’t believe anything you read in the papers.

    With respect always,


  2. I love your blog.. very nice colors & theme. Did you design this website
    yourself or did you hire someone to do it for you?
    Plz reply as I’m looking to create my own blog and would like to know where u got this from. appreciate it

  3. Thought it wondlu’t to give it a shot. I was right.

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