Thursday, November 24, 2016

Friedman as Logician (i)


"Few persons care to study logic, because everybody conceives himself to be proficient enough in the art of reasoning already. But I observe that this satisfaction is limited to one's own ratiocination, and does not extend to that of other men". Charles S. Peirce.
"You seem a little confused. You [sic] first statement ‘all dogs are mammals' is indeed circular". Phil Stein.

If the proposition "good reasoning is unimportant" were a human being, it would surely be an extremely unpopular and sad character: few would like to be seen in her company. In particular, economists and econo-aficionados of all stripes glory themselves in their assumed, but frequently unproven, logical thinking.

Milton Friedman is no exception to the rule. Indeed, in his "The Methodology of Positive Economics" he goes further. Formal logic, Friedman asserts, plays an important role in economic theory and, to avoid misunderstandings, he repeats that. Three times.

This is the first one:
"The canons of formal logic alone can show whether a particular language is complete and consistent, that is, whether propositions in the language are 'right' or 'wrong'."
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Before tackling Friedman's essay, it may be wise to do something he neglected doing: learning a few basic terms (it won't hurt a bit). Those more ambitious, however, are encouraged to try the Logic Café, possibly the bestest self-learning, free, intro course to logic ever.

This is a very simple argument:

(A) If you are a human, then you are mortal.
(B) As it turns out, you are a human.
(C) Therefore, you are mortal.


I imagine readers will have no difficulty with it. Roughly speaking, it makes good sense, it "clicks".

Arguments are collections of propositions (in red), "assembled" in a specific way, perhaps with some connectives (in blue). Some propositions, called premises (A and B), justify one's belief in another proposition: the conclusion (C).

Another example:

(A') If you are a green alien, then you are mortal.
(B') As it turns out, you are a green alien.
(C') Therefore, you are mortal.


Compare both arguments. Excepting "human" and "green alien", everything is the same, in spite of which, the second example seems less "waterproof" than the first. Why?

Let's proceed by steps. Both arguments are "assembled" similarly. They are said to have a common form (the "formal logic" Friedman mentioned refers to that), which allowed logicians to name, classify, and study them: this one is called modus ponendo ponens. There are other forms (disjunctive syllogism, modus tollendo tollens, etc). The point of studying forms is that deductive arguments based on them are demonstrably valid: if their premises are true its conclusion must be true, it cannot be false.

Following Friedman's example, let's insist on that, to avoid misunderstandings:
  1. Arguments based on the correct application of those forms can be proven valid. Their conclusions are logically necessary.
  2. It's impossible for a conclusion validly deduced from true premises to be false. In other words: if the premises are true and the argument is valid, then the conclusion obtained from them must be true.
  3. The truth or falsehood of the premises, however, is an empirical matter: if the premises aren't known to be true, there's nothing a priori one can say about the truth/falsehood of the conclusion.

Both arguments also share the same obviously true conclusion (C and C'): a prediction (namely, you will die -- sorry!).

Their premises, however, are different (compare A and A' and B and B'): the problem must be there. The first example is unassailable because (i) it's a valid argument (ii) based on true premises (logicians call arguments with those two properties sound), and (iii) its conclusion is true; the second is unsound: while it's still valid and its conclusion, too, is true, its premises aren't both true (B' is evidently false). That's why it doesn't "click".

Sound arguments yield only true conclusions (in blue):

Argument\Premises |      True       |     False
==================================================
Valid             | True conclusionConclusion?

--------------------------------------------------
Invalid           |  Conclusion?    |  Conclusion?
==================================================


Observe: with unsound arguments it's possible to validly deduce true conclusions from false premises (the second example). It's also possible to deduce false conclusions:

(A") If you are a human, then you are mortal.
(B") As it turns out, you are not mortal.
(C") Therefore, you are not human.[*]


Unsound arguments are the red cell, to the right of the blue "True conclusion" label: one needs additional information to ascertain their conclusions' truth or falsehood.

For that matter, exactly the same applies to invalid arguments (the other two red cells). It's irrelevant whether the premises are true or false, one can arbitrarily "deduce" true (or false) conclusions from them (try it, and if you can't, drop me a line for examples).


Sound arguments are useful because they provide true, but as yet unknown, conclusions. If one already knew the truth of the conclusion, there would be no need whatsoever to deduce it. Which raises the question: why bother building a valid argument, at all? We'll have more to say about it in a future post.

At any event, by now this should be evident: Friedman's methodology allows unsound arguments, like our second example. Among other things, so to speak, it allows Friedmanite economists to presume one is a green alien, in order to conclude one is mortal.

Fine. So what?

In the next post we'll see what.

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Those few key concepts (form/formal logic, proposition, premise, conclusion, true, false, valid/validity, sound/soundness) are important and we'll return to them later. It's not only Friedman's methodology, but his own logic, that needs revision.

Note:
[*] Note the connectives (in blue): that's an example of the modus tollendo tollens.

3 comments:

  1. i get the phil-stein joke. im not sure i get the quote, though.
    - the oo

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    Replies
    1. Hi, the oo,

      Simple. That passage illustrates Peirce's observation.

      There is nothing "circular" about "all dogs are mammals". There cannot be. Circularity is a property of arguments, not of "statements" (actually, propositions).

      Example: a circle is a geometrical object with diameter and circumference, it has an area. Those are properties of a circle.

      A point is another geometrical object, but it has no dimensions (this is one of its properties); area and circumference are not properties of a point.

      Circle is to "circular" argument as point is to "statement": an argument is said to be "circular" when it begins with a premise and ends with the same premise: the premise is the conclusion. The argument, figuratively, described a "circle".

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      And there's nothing wrong with "all dogs are mammals".

      It is an instance of a universal generalisation, known to philosophers and logicians at least since ancient Greece. This is a very well-known example:

      All men are mortal.
      Socrates is a man.
      Therefore, Socrates is mortal.

      That Phil Stein, who claims to be a philosopher and a logician extraordinaire, thinks it's some kind of fallacy is nothing short of scandalous.

      What Phil Stein says is similar to the patron who, returning the menu to the waiter, says: "I'd like my right triangle medium-rare, with a side of fries, thanks".

      It makes no sense; it does not compute.

      In his defense, I'll say that Phil Stein is merely parroting a similar load of crap Joan Robinson once made infamous. She, evidently, was successful.

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      UPDATED to correct a term misapplied.

      Delete
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