Sunday, September 13, 2009

Aristotle's "Two" Views on Induction: McCaskey's Resolution (Part 2)

In part 1, I explained that Aristotle is currently understood to have advocated two conflicting views on induction. I said that the interpretation of him adopting enumerative induction is the far more popular interpretation, despite the understandable confusion that results from anyone reading Prior Analytics 2.23 (PrA 2.23). I also said that John McCaskey has found an approach which does away with the popular “enumerative inductivist” interpretation. In addition, it gives even more support to the conclusion that Aristotle, when talking about induction, is almost always referring to the induction presented in his Topics and Posterior Analytics 2.19. Lastly, I said that this approach also presents to us how inductions become the general premises for deductions (syllogisms). Let us now turn to this approach.

Criticism of the Conventional Interpretation

Returning to something I said in part 1, the conventional interpretation of Aristotelian induction is that it is validated by complete enumeration of cases, that it is just a kind of deduction, and that its applicability doesn’t extend beyond the particulars which originally formed the induction. Are these claims really substantiated by all that Aristotle has to say on induction? McCaskey would say "no," and proceeds to show us why through the majority of his dissertation’s first chapter and in his essay "Freeing Aristotelian Epagōgē from Prior Analytics II 23."

In general, McCaskey proceeds through every use of the word “induction” (epagōgē) in the known Aristotelian works, beginning with passages whose overall meaning is clear, and proceeding to the more confusing ones; this method allows us to learn about the meaning of induction by understanding the passage. For instance, McCaskey begins his journey through the 96 uses of “induction” in the Topics, book 1, chapter 12, lines 105a10-19, in which four claims are clearly made about induction:
[Induction] (1) is different from and a counterpart to deduction, (2) is a proceeding from particulars to a universal, (3) results in a universal generalization that extends beyond the particulars that went into its formation, and (4) is generally easier for people to grasp than deduction. [McCaskey, “Regula Socratis,” page 23]
These four claims about induction are repeated multiple times throughout Aristotle’s works, and make it highly doubtful that he would suddenly adopt a view of induction that contradicts one or more of these claims, as would be the case if the conventional understanding of PrA 2.23 is correct. Indeed, McCaskey uses this survey of “induction” to not only elucidate the meaning of the concept “induction,” but also to point out how erroneous the conventional interpretation must be.

Two of his counter-arguments to the conventional view should suffice before I move on to his revisionary interpretation of PrA 2.23.

(1) McCaskey notes that in the vast majority of Aristotle’s inductive arguments, the particulars subsumed in the generalizations are countless and cannot be enumerated successfully before making the generalization, such as his argument that what makes someone the “best” in a profession is their knowledge (in the Topics) or his argument about the nature of goodness I mentioned in part 1. Aristotle never presents (and defends) a completely enumerated list of cases and forms an inductive generalization from them, nor states that an induction can only apply to the cases enumerated and not, for instance, presently unobserved cases.

(2) In Posterior Analytics 1.5, Aristotle gives possibly his only example of a complete enumeration. As McCaskey summarizes it:
He says that knowing something to be true of scalene, isosceles, and equilateral triangles is not sufficient for knowing it to be true of triangles qua triangles [as in their essential nature]. It may be known of each triangle taken singly, but not of triangles ‘primitively and universally,’ not ‘of triangles as [triangles].’” [McCaskey, page 46]
Here, there should have been a perfect case for a defense of enumerative induction, which Aristotle supposedly supports according to the conventional interpretation, and yet Aristotle flat out denies that something can truly be known about triangles by considering each individual triangle--the very method that an enumerative inductivist would be forced to use by his own doctrine. Here, he suggests that truly knowing something about triangles has something to do with identifying the essence of triangles, rather than completely enumerating cases. This gives support to the other interpretation of induction, because it is closely related to the inductive arguments in Aristotle’s Metaphysics, Physics, and Eudemian Ethics that strongly suggest that induction is a tool for identifying the essence or nature of something.

McCaskey has several more counter-arguments in his arsenal, but none more powerful than his reinterpretation of PrA 2.23, the key passage cited in support of the enumerative induction interpretation.

1 comment:

  1. Whenever someone brings up triangles, as is common to such discussions of epistemology, it needs to be mentioned that triangles are an invention of the mind. So it is as if someone is trying to argue from a mental invention to objective reality. Now THAT is not as terrible as it seems at first, in fact it most likely reflects the method by which we become acquainted wtih an objective reality in the first place - by inventing objectively definable "conditions" in the mind and then testing sensory reality against them to determine how well they fit together in the mind. So naturally we use the simple triangle example, in this case, as a kind of absolute measuring-stick, which was never induced to begin with, against which to "measure" other kinds of judgments.

    And yet McCaskey here takes a triangle (following Aristotle's lead) as some kind of naturally given entity from which we generalize to a definition and then, as in the case of swans, we can never know when we will encounter a black swan, that is, an exception to the definition. So it is not possible to know "triangle" universally (as the triangle qua triangle), according to McCaskey, only individually.

    Now obviously, triangles are not even LIKE swans. Triangles were not produced by nature, they were produced by the mind of man. Every triangle you will ever encounter was produced by the mind of man. Thus it is possible to universalize to a "triangle qua triangle" because it already exists in the mind. And it is, indeed, the very pattern by means of which we so readily recognize a given particular triangle. That pattern is no stated formula or definition, it is a simple, not inducted, intuitive fact, resting in the mental faculties, by means of which we recognize a triangle when we see one because it "fits" the known created pattern. It cannot be otherwise because we invented the pattern, and each individual mind, while it learns about triangles, simply reinvents the pattern (recognizable as the well-known "a-ha!" or light-bulb experience of the learning/discovery process when the cognitive dissonance is finally resolved at the end of the process).

    Swans are no mere invention, however, the intuitive pattern within which the particular swan "fits" is an invention, thus the reason why the triangle example is always mentioned in this context.