Monday, October 5, 2009

Aristotle's View of Induction: A Summary

[On Induction]: “The soul is so constituted to be capable of this process.” [Aristotle, Posterior Analytics 2.19, 100a14]
In the history of induction, Aristotle features prominently as the first person to explain what it was. While Socrates practiced induction and sought universal definitions, Aristotle was the first to discuss the process of inductive thinking itself. And even though Aristotle thought that “[what] sort of thing induction is, is obvious,” he nevertheless took some effort in explaining its origin, its logical process, and the benefits that could be gained from using it (Topics 8.1, 157a8).

Now that I've spent a few months studying him and other inductive thinkers, I'd like to present a summary on his view of induction. In this summary, I'd like to cover four things, specifically: (1) Aristotle's mention of Socrates as the originator of induction, (2) his overall portrait of the process of induction given in Posterior Analytics 2.19, (3) the more specific elements of induction which he adopts, and (4) what induction essentially is, as opposed to what it is not.

Induction: with a Tip of the Hat to Socrates

Aristotle credits Socrates with the invention of induction:
Socrates was occupying himself with the excellences of character, and in connection with them became the first to raise the problem of universal definition. . . . It was with good reason that he should be seeking the essence, for he was seeking to argue deductively and the beginning of deductive arguments is the essence. . . . For two things may be fairly ascribed to Socrates—inductive reasoning and universal definition, both of which are concerned with the starting point of science. (Metaphysics 13.4, 1078b24-30)
Socrates was seeking deductive conclusions, such as whether virtue could or could not be taught, and in order to argue his point, he needed to know what the term “virtue” meant, its definition (in the Meno, 71a-b, d). He realized that deduction would be useless for discovering this, since deduction relies upon pre-existing knowledge, and he had no knowledge of what “virtue” even was as yet, only tentative guesses. (For instance, he reasoned that one of virtue's properties was that it could be granted to men by the gods. But this was only tentative knowledge; to be certain of this, he had to know what “virtue” is (Meno, 100b).)

In order to reach the essence of “virtue” and similar moral topics (e.g. courage, friends), to define it, he set out on inductive quests, questioning others about what particulars hold in common, which would allow him to discover this identical attribute, or essence. Aristotle agreed with and adopted Socrates's inductive method, and proceeded to explain the role it plays in our lives, in passages spread out across his works.

Posterior Analytics 2.19: From Perception to Memory to Experience to the Universal

One of the most important explanations of what induction is comes from Aristotle's Posterior Analytics. The work follows the Prior Analytics, which is fundamentally about deduction, specifically the elements of the syllogism such as “premise” and “term,” the syllogistic figures (moods), and how we can gain knowledge through syllogistic/deductive reasoning, something which Aristotle calls “demonstration.” The Posterior Analytics is fundamentally about the starting points of knowledge, the primary and universal principles, and whether or not a process exists by which we can reach such principles.

Book 1 of the Posterior Analytics starts with the claim that all learning and teaching by means of argument proceed from pre-existent knowledge, and that all subjects that can be taught or learned follow this principle. Even the syllogistic and inductive forms of reasoning follow this, he adds; deduction assumes the audience already knows and accepts its premises, and induction assumes the particular from which an implicit universal is exhibited (Posterior Analytics 1.1). While deductions give us justified conviction when properly carried out, they all rest on primary premises, and exactly how we gain these is an open issue. In the third chapter, Aristotle rejects two theories, (1) that all knowledge is false because of an infinite regress, and (2) that all knowledge is true because we can use circular demonstration to prove anything. He notes that not all knowledge is demonstrative (produced by deductive thinking), and that there is a process or “originative source” from which we gain definitions (chapter 3) and primary premises or principles. In chapters 4 through 12, he describes this process: by some means, we form universals (which serve as the “middle term” and constituent terms of premises and of syllogisms) and come to know primary and universal principles, which are true by the essential nature of the subject matter. In turn, these primary principles can become the premises of deductions (though not always).

Book 2 is an extended treatment of issues that were brought up in Book 1, on the relations between causes, definitions, essential natures, and demonstrative reasoning. In chapter 7, Aristotle denies that the discovery of essential natures can be carried out by definition or by demonstration, and in chapter eight he states that to know the essential nature of something is to know the cause of the thing's existence. Chapters 11 through 18 discuss the relations between causes, effects, forming universals, and definitions. The final chapter, 19, brings us back to issues which confronted us at the beginning of Book 1, concerning the starting points of knowledge, and how we come to know primary premises. He concludes that these premises cannot be innate in us (from birth) or developed from higher kinds of knowledge (such as from demonstrative knowledge, which he denied earlier), but instead is developed from sense-perception.
Thus from perception there comes memory . . . and from memory (when it occurs often in connection with the same thing) experience; for memories which are many in number form a single experience. And from experience, or from all the universal which has come to rest in the soul . . . there comes a principle of skill or of understanding. (Posterior Analytics, 2.19, 100a3-9, trans. Jonathan Barnes. Quoted in McCaskey, Regula Socratis: The Rediscovery of Ancient Induction in Early Modern England, 44)
Almost immediately after, he restates this process, but this time drops his earlier mention of memories and experiences, and focuses instead on the progression from particulars to universals:
When one of a number of logically indiscriminable particulars has made a stand [been perceived], the earliest universal is present in the soul: for though the act of sense-perception is of the particular, its content is universal-is man, for example, not the man Callias. A fresh stand is made among these rudimentary universals, and the process does not cease until the indivisible concepts, the true universals, are established: e.g. such and such a species of animal is a step towards the genus animal, which by the same process is a step towards a further generalization. (Posterior Analytics, 2.19, 100a12-100b1, trans. G.R.G. Mure. Brackets mine.)
It is in connection to this progression from particulars to universals that Aristotle mentions “induction,” as if the whole of the Posterior Analytics has been a build-up to this statement: “Thus it is plain that we must get to know the primitives [premises] by induction; for this is the way in which perception instils universals” (Posterior Analytics, 100b2-3, trans. Barnes).

This connection between induction and the primary premises was suggested earlier, in Posterior Analytics 1.18, in which Aristotle describes a hierarchy regarding universals, perception, particulars, demonstrative reasoning, and induction. In this hierarchy, Aristotle claims that:
(1)Knowledge of particulars depends on sense-perception.
(2)Induction proceeds from particulars, and thus induction is impossible without sense-perception.
(3)Universals, which are predicated of particulars, cannot be grasped except through induction.
(4)Demonstration (the deductive form of argument and knowledge) is developed from universals.
Precisely like Francis Bacon, Aristotle holds that induction is the basis for our concepts, which in turn are the basis for our propositions, premises, and deductions. (I'm referring to Bacon's famous statement that “a syllogism consists of propositions, and propositions consist of words, and words are the tokens and signs of notions [ideas],” New Instrument, 1.14.) More importantly, book 2 chapter 19 explains that induction is our ability to reason from perceptions to conceptual generalizations, and is the process by which we gain our most basic conceptual knowledge, and form more complex conceptual products. It solves Aristotle's initial riddle as to what process, if any, is responsible for the starting points of knowledge.

“This is Clear from Induction”

So now that we know how induction comes to exist, what are the other features of induction, and guidelines for making them? What is induction really about, according to Aristotle?

Induction and Deduction
Induction is one of two ways to reason, persuade, learn, teach, come to have beliefs, and obtain premises, and the other way is syllogistic thinking/demonstrative reasoning (deduction) (e.g. see Posterior Analytics 1.1, 71a6 for his comment on induction and reasoning in general). And as we learned from Posterior Analytics 2.19, induction is the fundamental kind of reasoning when compared to deduction (syllogistic reasoning), as it provides the premises required by deductive thinking. (Part 3 of my series “Aristotle's 'Two' Views of Induction: McCaskey's Resolution” elaborates on how induction provides the premises for deductions, for those interested.)

More specifically, induction is a reasoning process of moving from particulars to universals, as Aristotle explained in Posterior Analytics 2.19. And as he implies in the earlier quote, the “particulars” are not simply the objects of sense-perception that induction starts with, but also less abstract universals (“man”) when considered in a progression to a more abstract universal (“animal”). Induction is thus a method of achieving higher and higher levels of abstraction and generalization.

Aristotle also notes that induction is easier to understand than deduction (Topics 1.12 105a15-19). Indeed, induction is more useful for persuading or convincing people who either haven't been exposed to the sort of issue you're presenting an argument for, or are unconvinced of a certain point in your argument. He makes this kind of point by suggesting that when arguing with others, induction should be used for addressing a common crowd, whereas deduction should be used against skilled debaters; induction with a youth, deduction for the more experienced, mature thinker; induction to add support to a point (Topics 8.2, 157a19-20; 8.14 164a13; 8.1 157a6).

Induction as Limitless
Another characteristic of induction is that it's an open-ended process: the application of an induction extends beyond the particulars that were originally used to form it. An example of induction Aristotle gives is that of what makes someone the “best”: "...Induction, however, is a proceeding from particulars to a universal. For instance, if the pilot who has knowledge is the best pilot, and so with a charioteer, then generally the person who has knowledge about anything is the best" (Topics 1.12, 105a10-19). Here Aristotle is illustrating how one would go about generalizing from particular instances of someone being “the best” in some field, such as in piloting ships or being a charioteer, and suggests that it is possessing knowledge which is what makes someone the “best” in a given field. He makes this suggestion by generalizing “being the best” to all fields or professions, beyond those of piloting ships or of being a charioteer, to any profession and any person who has knowledge in his profession. He is able to do this because induction leads to universals, and universals are the sorts of things that can be applied to countless particulars.

As Dr. Greg Salmieri explains in his essay on Aristotle's account of universality,
Universality [...] is a characteristic of our thinking and, in some sense at least, of what our thinking is about. A universal is whatever holds of some multiplicity of things as a whole—it is something that 'by its nature is predicated of many things ([On Interpretation] 17a39-b2, cf. Metaphysics Z.13 1038b11)...' [Salmieri, Aristotle's Conception of Universality, p. 7]
Similarity and Induction
Induction is a progression to universals, but it isn't simply on the basis of the number of particulars that we actually think inductively, but their similarity. As Aristotle states, “[the] study of what is similar is useful for inductive reasoning . . .because it is by induction of particulars on the basis of similars that we claim to bring in the universal” (Topics 1.18, 108b7-12). Things are similar when any attribute that a group of things possess is the same (Topics 1.17, 108a18). The skilled inductive reasoner is one who is trained in drawing out parallel cases, of making comparisons and discerning what is similar (Topics 8.14, 164a16).

One example of this is Aristotle's discussion of goodness in the Eudemian Ethics, that goodness is the best disposition or faculty or state of something that has some functional use or work, for he says afterward:
This is clear from induction, for we posit this in all cases: for instance, there is a goodness that belongs to a coat, for a coat has a particular function and use, and the best state of a coat is its goodness; and similarly with a ship and a house and the rest. So that the same is true also of the spirit, for it has a work of its own. [1219a]
Here, Aristotle brings up a variety of objects, points out something similar about all of them—that they have some particular use or work—and reasons that their “goodness” is the best state of each object, as this allows the object to best perform its particular function. A good house is a house that is in the kind of condition that allows it to perform its function as a place of shelter, so it has features like a roof and walls with a strong integrity, a good foundation, and made of materials which allow it to withstand typical natural events like gusts of wind and rainwater. (Oddly enough, the nursery tale of the “Three Little Pigs” and the big, bad wolf, is very illustrative of my point.)

It is on the basis of the similarity of particulars--what characteristic they have in common--that we attempt to form a new universal, goodness for instance, and discover one of the senses in which anything at all can be “good.” And this kind of reasoning occurs for other universals in Aristotle's works, such as for “triangle,” “contrariety,” and “longevity” (found in the Posterior Analytics 1.5, Metaphysics 10.3 and 10.4, and Prior Analytics 2.23, respectively).

Discovering what is similar about particulars is also how we come to understand what universals--our very concepts and propositions--are about, and indeed what induction is even for.

The Essence of Induction, and What it is Not

As Aristotle said, Socrates was concerned with the essence, with finding what a group of things held in common, so that he could define a concept he had in mind and use it as a term in a deduction. Although he himself never said this explicitly, Socrates was seeking “inductive reasoning and universal definition”; it was Aristotle who would later point this out, and adopt this peculiar method.

Unfortunately, Aristotle doesn't focus on induction as nearly as much as other topics, such as the soul in general (On the Soul), on “being” as such (Metaphysics), and even induction's counterpart, deduction (Prior Analytics). Fortunately, what Aristotle does say about it (and what we've managed to recover of Aristotle's works) is enough to understand what Aristotle truly meant in using the term, what its “essence” is.

In my last few posts on Aristotle and induction, I've stressed (agreeing with Dr. John McCaskey) that we have to stop relying on Aristotle's discussion of it in Prior Analytics 2.23 as the passage on Aristotelian induction. No progress in understanding Aristotle's views on induction, and on coming to gain knowledge, can be achieved without understanding that passage in light of the Topics, Rhetoric, and Posterior Analytics 2.19.

To accept Prior Analytics 2.23 as the best source on induction for Aristotle, and thereby interpret him as advocating enumerative induction, is to ignore his comments from Posterior Analytics 1.5 and 2.7. In 1.5, he states (as I discussed previously) that knowing something to be true of all triangles individually is not the same as knowing something to be true of triangles essentially or truly universally, but rather is to know it in a sophistic manner; and in 2.7, he states that we can't prove an attribute to be essential to some kind/group by bringing in all instances of that group and finding the attribute to belong to each, as this only shows that the attribute is held in common, not that it is essential. (I really have to thank Dr. McCaskey for drawing my attention to this on page 46 of his dissertation.)

If read carefully, Prior Analytics 2.23 merely distinguishes between two different kinds of deductions, not of a “deduction” on the one hand, and an “induction” on the other. The chapter itself gives us a few indications of how this is so. For starters, the supposed “definition” of induction given in chapter 23 states that it's about a deduction: “Induction, then--that is, a deduction from induction--is deducing one extreme to belong to the middle through the other extreme” (68b15-16; my emphasis) While Aristotle repeatably states that induction is a progression from particulars to universals, his discussions of induction outside of chapter 23 never state that it's about deducing anything, or that an induction can be demonstrated through one of the syllogistic figures, as he states here of the “induction” in question.

Perhaps most importantly, those who view Aristotelian induction as an inference ignore the fact that Aristotle's examples of induction weren't inferences at all. His examples of induction discussed what is similar about the objects being discussed in regard to a universal, what property made them of a genus or kind, such as people being the “best” in their professions similarly having the most knowledge of their respective professions. Furthermore, the examples of induction suggested a definition of the universal/term being considered or at least proposed some feature that was unique to the particulars being considered; in other words, his examples of induction focused on clarifying what a given universal means, whether by suggesting an actual definition or at least discussing some distinguishing (though not definitive) characteristic of the relevant particulars. The examples were about what it means (in some sense) to be a “triangle” or a “contrary” to something else, or to be “long-lived.” In his accounts of induction, Aristotle consistently discussed or exhibited some general feature of the particulars subsumed under a universal in light of the examples given (the particulars he would discuss), but never argued that the inductive conclusion could be deduced or inferred by studying the particulars.

In an enumerative induction, the enumerated cases serve as premises, which, if true, allow an inductive conclusion to follow or be inferred which would be true in virtue of the true premises. But such an induction cannot belong to Aristotle's account, because if “inference is a kind of reasoning by which, if the premises are true, something else follows from them specifically because they are true, not only is this not Aristotle's view of induction, it is his very definition of induction's opposite, i.e., of deduction” (McCaskey, Freeing Aristotelian Epagôgê from Prior Analytics 2.23, pp. 365-366).

As opposed to coming to a definite inference, Aristotelian induction was essentially no different than Socratic induction. Socrates, we must remember, wanted to deduce certain things from his terms, like “virtue,” or “friend,” and before he could do that, he had to identify the essence of those universals, what made them the kind of things they were: in this way, he would have definite knowledge of “virtue” or “friend” and would be in the position to state other things about such terms. Like Socrates, Aristotle's practice of induction was an exercise in clarifying or exhibiting the meaning of a universal in light of analyzing particulars. The “essence” of induction is that it is an instrument of our reason, one which allows us to form clear/well understood conceptual generalizations (whether concepts or propositions) by identifying the essential nature of the things being conceptualized.


  1. are you still working on this blog, particularly the philosophical basis of induction? I am writing a dissertation on this subject; you have some good ideas and clear presentations here, and I could use some conversation partners.

    1. Yes, I am. Thanks for asking. It's been slow-going this past year, but I am reading the next philosopher of induction after John Herschel: William Whewell, the philosopher-scientist who coined the term "scientist." He wrote a 3-volume "History of the Inductive Sciences," and then worked out a theory of induction that expands on the theory of Francis Bacon in his work, "The Philosophy of the Inductive Sciences, Founded Upon their History," in 2 volumes.

      Email me at:

      I'd love to discuss induction with you for your dissertation.

  2. Thank you very much for this post!

  3. terrific post. I needed to say something about Aristotle's theory of induction for a philosophy of science class I am teaching. you gave me all the best sources to read, and some excellent commentary of your own. Thanks so much