Monday, September 23, 2013

An Observation on Deduction

Consider the following syllogism:
Major Premise: All elephants are grey.

Minor Premise: Nellie is an elephant.

Conclusion: Therefore Nellie is grey.
This is a formally valid syllogism, but it is unsound. The reason why it is unsound is that the major premise is false: while most elephants are grey, some albino elephants exist. If Nellie were a real life elephant that we have never seen before, there is the possibility that Nellie is an albino elephant, and not grey.

But how do we interpret the epistemological status of major premise?:
All elephants are grey.
If this is meant to assert information about the real world (that is, real world elephants), it must be synthetic a posteriori. We can establish its truth by experience, empirical evidence and inductive arguments.

In this case, as we saw, it is false, because albino elephants exist, and it is also logically possible, though improbable, that a genetic mutation might occur which makes an elephant some colour other than grey or white.

Nevertheless, one could also take “all elephants are grey” as an analytic a priori proposition. We can assert it as true, but only as an empty and hypothetical statement where elephants are arbitrarily defined as having the property “grey.” In this case, we do not care about real world elephants, because they are irrelevant to a purely tautologous proposition we have devised that asserts something merely as an imaginary definition, true by stipulation.

One could even claim that asserted of purely imaginary elephants that are grey by definition, even the conclusion is true, and the argument has necessary a priori truth in our imaginary world of purely grey elephants.

But, of course, what has happened is that we have rendered all the propositions and the whole argument vacuous, empty and tautologous, so that it says nothing necessary of the real world. The propositions and inference would be all true by arbitrary definition of terms, and necessary truth is a purely verbal construct.

And once applied to real world elephants, it all collapses and empirically we know the argument is unsound.

But we can even apply a similar type of analysis to a syllogism that is both valid and sound:
Major premise: All humans are mortal.

Minor premise: Socrates is a human.

Conclusion: Socrates is mortal.
Here both the major and minor premises are synthetic a posteriori and true in the sense that we can construct a set of inductive arguments, from empirical evidence, to the effect that it is extremely probable that all human beings are mortal, and it is extremely probable that the historical person we know as Socrates was human.

The conclusion is necessarily true, but only if the premises are true.

But, when the conclusion is applied to the historical person we know as Socrates as a synthetic a posteriori statement about him, the necessary, apodictic truth is not preserved. Why? The reason is that both the major and minor premises are synthetic a posteriori, and can only ever be highly probable but still fallible.

In order to question the truth of the premises, we have to think of some possibilities that are ridiculous or highly improbable, but nevertheless they are logically possible. Suppose it is possible for a genetic mutation to make a human being immortal in the sense of living without aging. Say Socrates was such a person. Say, his death was staged and he still lives to this day.

Suppose, as an even more outlandish idea, that Socrates was secretly visited by aliens or humans from the far future. Using science, they made him immortal and his death was only staged, so that he still lives.

Of course, these are all either outrageous or extremely unlikely possibilities, but the fact remains that synthetic a posteriori propositions can never be apodictically true: some doubt must remain.

When the syllogism above asserts that “Socrates is mortal” as its conclusion, one can speak of this truth as necessary, only if the premises are taken to be absolutely true.

But, just as in the first case above, we can see how this creates a necessary truth that is ultimately a logical construct (or de dicto necessity) because it banishes all doubt about the truth of the empirical premises and renders them analytic a priori.

Of course, these days, after the work of Putnam and Kripke, analytic philosophers are willing to recognise the existence of certain metaphysical (or de re) necessities, such as (1) identity statements involving proper names or definite descriptions and (2) scientific essences of certain natural kind phenomena, but I do not think this is inconsistent with my comments above on deduction.


  1. There are also statements that have a moral or normative weight. Laws, for example, are such statements and they form the basis for our society -- the primary law being, of course, the incest taboo.

    Understood correctly both neoclassical and Austrian economics fall into this category -- although both largely disavow this -- and so the deductions made need not be credible. The neoclassical/Austrian argument against albino elephants would, if you'll excuse the analogy, that they are an aberration as they fall outside the taxonomical norm and so need to be exterminated.

    What I'm saying, of course, draws on the work of Michel Foucault who is so well ridiculed as not being serious philosophy and being literature criticism by the Analytic philosophers whose, it should be obvious by now, has truly run out of steam. For an introduction to Foucault's work I recommend the following:

  2. Relevant quote:

    "[Foucault] develops a highly sophisticated analysis of the human sciences"dubious" sciences that never attain the level of Kuhnian normal science-and their political, social, and cultural functions. Foucault will argue that the fact that the human sciences (and those linked to psychiatry in particular) have contributed little objective knowledge about human beings and yet have attained such importance and power in our civilization is precisely what has to be focused and explained. Why and how this scientific shakiness becomes an essential component of modern power is an essential theme in Foucault's later works." (p10)

    1. "human sciences (and those linked to psychiatry in particular) have contributed little objective knowledge about human beings"

      Does "human sciences" mean "social sciences" here?

      Since I find it unlikely that Foucault was thinking of the natural sciences, presumably it was.

      If that is so, even this is a bit dubious to me.

      After all, anthropology, linguistics, archaeology, history, and psychology have made serious contributions to "objective knowledge".

    2. Yes, he means social sciences and a few disciplines masking as hard sciences -- like psychiatry.

      I agree with Foucault on this. These discourses don't add to our knowledge, they merely frame how we talk about Man.

    3. If I understand Pilkington correctly, he's saying that Mises and his followers are not trying to _describe_ or _explain_ "human action" and economic behvior....they're trying to _change_ it. By pretending to explain it.

    4. @Anonymous

      Yes, that is what I'm saying. But I'm also saying it for marginalist economics more generally. And perhaps for all social science, to a greater or lesser degree.

      I wrote about this here:

  3. Philosopher: "What color is the sky?" Student: "Blue." Philosopher: "Let us then proceed from the fact that the sky is blue to reason thusly...." If only the student would observe that the sky is not always blue: it can be gray on a cloudy day, it can be black at night, and sun, moon, stars, clouds, birds, etc. can all make it different than plain, solid blue. If we say the sky is blue, that is not a fact: it is a vague observation or generalization, ignoring the many exceptions, ignoring the scientific explanation of scattering of sunlight and privileging daytime over nighttime conditions. It is not a valid premise that philosophy can be built upon. Most philosophy actually starts with such invalid premises, and it is not too difficult to spot them.

  4. So in the end how does this apply to the action axiom? I've gotten the impression from yor recent posts on Mises and deduction that you are in complete disagreement with the approach. But I'm failing to see what a better approach is, and why.

    1. This post is not specifically directed at Mises's praxeology, though it is relevant to a critique of it.

      As for the action axiom, that is synthetic a posteriori. Mises cannot formally deduce all his theories from it, even with the other axioms, a he requires a vast amount of additional empirical evidence and theories.

      Just one example, Mises's case probability and class probability are not deducible from the action axiom: