Deduction versus Induction

We cannot fully understand the nature or role of inductive syllogism in Aristotle without situating it with respect to ordinary, “deductive” syllogism.  

Aristotle’s distinction between deductive and inductive argument is not precisely equivalent to the modern distinction.  

Contemporary authors differentiate between deduction and induction in terms of validity.  (A small group of informal logicians called “Deductivists” dispute this account.)  

According to a well-worn formula, deductive arguments are valid; inductive arguments are invalid. 

The premises in a deductive argument guarantee the truth of the conclusion: if the premises are true, the conclusion must be true.  The premises in an inductive argument provide some degree of support for the conclusion, but it is possible to have true premises and a false conclusion.  

Although some commentators attribute such views to Aristotle, this distinction between strict logical necessity and merely probable or plausible reasoning more easily maps onto the distinction Aristotle makes between scientific and rhetorical reasoning (both of which we discuss below).  

Aristotle views inductive syllogism as scientific (as opposed to rhetorical) induction and therefore as a more rigorous form of inductive argument.

We can best understand what this amounts to by a careful comparison of a deductive and an inductive syllogism on the same topic.  

If we reconstruct, along Aristotelian lines, a deduction on the longevity of bileless animals, the argument would presumably run: All bileless animals are long-lived; all men, horses, mules, and so forth, are bileless animals; therefore, all men, horses, mules, and so forth, are long-lived.  

Defining the terms in this syllogism as: Subject Term, S=men, horses, mules, and so forth; Predicate Term, P=long-lived animals; Middle Term, M=bileless animals, we can represent this metaphysically correct inference as:  Major Premise: All M are P.  Minor Premise: All S are M.  Conclusion: Therefore all S are P.  (Barbara.)  

As we already have seen, the corresponding induction runs: All men, horses, mules, and so forth, are long-lived; all men, horses, mules, and so forth, are bileless animals; therefore, all bileless animals are long-lived.  Using the same definition of terms, we are left with:  Major Premise: All S are P.  Minor Premise: All S are M (convertible to All M are S).  Conclusion: Therefore, all M are P.  (Converted to Barbara.)  

The difference between these two inferences is the difference between deductive and inductive argument in Aristotle.

Clearly, Aristotelian and modern treatments of these issues diverge.  As we have already indicated, in the modern formalism, one automatically defines subject, predicate, and middle terms of a syllogism according to their placement in the argument.  

For Aristotle, the terms in a rigorous syllogism have a metaphysical significance as well.  In our correctly formulated deductive-inductive pair, S represents individual species and/or the individuals that make up those species (men, horses, mules, and so forth); M represents the deep nature of these things (bilelessness), and P represents the property that necessarily attaches to that nature (longevity).  Here then is the fundamental difference between Aristotelian deduction and induction in a nutshell.  

In deduction, we prove that a property (P) belongs to individual species (S) because it possesses a certain nature (M); in induction, we prove that a property (P) belongs to a nature (M) because it belongs to individual species (S).  Expressed formally, deduction proves that the subject term (S) is associated with a predicate term (P) by means of the middle term (M); induction proves that the middle term (M) is associated with the predicate term (P) by means of the subject term (S).  

Aristotle does not claim that inductive syllogism is invalid but that the terms in an induction have been rearranged.  In deduction, the middle term joins the two extremes (the subject and predicate terms); in induction, one extreme, the subject term, acts as the middle term, joining the true middle term with the other extreme.  This is what Aristotle means when he maintains that in induction one uses a subject term to argue to a middle term.  

Formally, with respect to the arrangement of terms, the subject term becomes the “middle term” in the argument.

Aristotle distinguishes then between induction and deduction in three different ways.  First, induction moves from particulars to a universal, whereas deduction moves from a universal to particulars.  The bileless induction moves from particular species to a universal nature; the bileless deduction moves from a universal nature to particular species.  Second, induction moves from observation to language (that is, from sense perception to propositions), whereas deduction moves from language to language (from propositions to a new proposition).  

The bileless induction is really a way of demonstrating how observations of bileless animals lead to (propositional) knowledge about longevity; the bileless deduction demonstrates how (propositional) knowledge of a universal nature leads (propositional) knowledge about particular species. 

Third, induction identifies or explains a nature, whereas deduction applies or demonstrates a nature.  The bileless induction provides an explanation of the nature of particular species: it is of the nature of bileless organisms to possess a long life.  The bileless deduction applies that finding to particular species; once we know that it is of the nature of bileless organisms to possess a long life, we can demonstrate or put on display the property of longevity as it pertains to particular species.

One final point needs clarification.  The logical form of the inductive syllogism, after the convertibility maneuver, is the same as the deductive syllogism.  In this sense, induction and deduction possess the same (final) logical form.  

But, of course, in order to successfully perform an induction, one has to know that convertibility is possible, and this requires an act of intelligence which is able to discern the metaphysical realities between things out in the world.  We discuss this issue under non-discursive reasoning below.