The Senses as Necessarily Valid

Epistemology is the branch of philosophy that studies the nature and means of human knowledge.  The field lays out the rules and principles to guide the formation of concepts, the construction of logic, and generally how to gain knowledge and show its validity.  Objectivism holds that metaphysics and epistemology combined are the theoretical base of any philosophy.[1]

There is a little more context needed than metaphysics to fully confront the issues in epistemology. We must first discuss 2 topics that make the field of epistemology possible: sense-perception and volition (free will).  I’ll also cover the axiomatic concept of “self” at the end of this series, as I think it’s a subject that needs to be discussed for a complete understanding of Objectivism.

Now we can begin with the role and validity of human sensory-perception.

Objections to the Axioms (Part 5)

Objection: The Axioms Equivocate on Their Content

This objection concerns exactly what it is that the axioms are explaining and implying.  It highlights a seeming equivocation:

[…]In the Logical Structure of Objectivism, David Kelley makes the following observation:

Notice that neither [the axiom of existence nor the axiom of identity make] any specific statement about the nature of what exists. For example, the axiom of existence does not assert the existence of a physical or material world as opposed to a mental one. The axiom of identity does not assert that all objects are composed of form and matter, as Aristotle said. These things may be true, but they are not axiomatic; the axioms assert the simple and inescapable fact that whatever there is, it is and it is something.

Very well. Now consider what Rand draws from these very same axioms:

To grasp the axiom that existence exists, means to grasp the fact that nature, i.e., the universe as a whole, cannot be created or annihilated, that it cannot come into or go out of existence. Whether its basic constituent elements are atoms, or subatomic particles, or some yet undiscovered forms of energy, it is not ruled by a consciousness or by will or by chance, but by the law of identity. All the countless forms, motions, combinations and dissolutions of elements within the universe—from a floating speck of dust to the formation of a galaxy to the emergence of life—are caused and determined by the identities of the elements involved. 

In other words, she draws from these axioms: (1) that the universe is permanent and can neither be destroyed nor created; (2) the universe is not ruled by will or chance, but by the ‘law of identity’; (3) everything that happens is caused by the ‘identities’ of the elements involved. She also implies that the basic constituents of the universe, whatever they may happen to be, are non-mental (i.e., atoms, particles, or forms of energy). How does Rand draw all these things from these axioms when, according to Kelley [quoted earlier in the blog post] (who, in this instance, is being entirely orthodox) these axioms only assert that ‘something’ distinguishable exists?[1]

I’ll sum up this objection as: “Objectivism equivocates between axioms not specifying content (e.g. specific identities, specific actions), and inferences about reality that supposedly follow from the axioms (e.g. the universe cannot be created or destroyed, reality isn’t ruled by chance).”

Objections to the Axioms (Part 4)

Objection: The Axioms are Circular

The axioms rest on the law of noncontradiction for their validity, but the law of noncontradiction itself rests upon the axioms.[1] 

The Validity of the Axioms

The (basic) axioms do not rely on each other for their validity. Direct experience or sense-perception is the means of validating the basic axioms.[2] Derivative axioms like "self" and "volition" rely on the fact of the basic axioms and direct experience for their validity, but not the basic axioms themselves. Further, the basic axioms being part of the validation of derivative axioms does not mean that the derivative axioms are deductions from the basic ones, or logical consequences. In Objectivism, the material required to form the basic axioms of existence, identity, and consciousness are discovered simultaneously. Peikoff mentions in a lecture course that: "'A is A' is independent of consciousness for its truth, but it’s not independent of the existence of consciousness to be grasped."[3]

Objections to the Axioms (Part 3)

Previous: Objections to the Axioms (Part 2)

Question: “Are Axioms Proven or Merely Assumptions?”

“Are first principles or the axioms of logic (such as identity, non-contradiction) provable? If not, then isn't just an intuitive assumption that they are true?[...]”[1]

The axioms are neither “proven” nor “assumed.” 

(In the Objectivist view of axiomatic corollaries, Aristotle’s “Laws of Thought” are corollaries of the Existence axiom.  And more specifically, the Law or Principle of Non-contradiction and the Law of the Excluded Middle are restatements/corollaries of the Law of Identity, which is a corollary of “existence exists.”[2] So I’ll consider this question as broad enough to encompass any first principle, including the Objectivist axioms.)

I’ll make several points about why this can’t be the case when speaking of actual axioms.

Objections to the Axioms (Part 2)

Previous: Objections to the Axioms (Part 1)

This next objection is about the utility of the axioms.  

Objection: “Axioms Must Have Deductive Implications”

[...]A first principle is only useful and workable if you can deduce the rest of the worldview from it. You can't deduce anything from 'whatever exists exists'. You can't deduce any kind of epistemology (ie, how we know that whatever exists exists, how we know that we know, etc); we can't deduce any kind of metaphysic (ie, what is the nature of existence, what is the ground of existence, etc); and we certainly can't deduce any ethical or anthropological propositions (ie, what is right and wrong, what is the nature of man, etc).[...][1]

Objections to the Axioms (Part 1)

Previous: The Order of the Objectivist Metaphysics

The axioms lay the proper foundation for a philosophy.  But for any statement or expression, there is almost always someone who disagrees.  Axioms are of no exception.  Of the people who are dismissive of Objectivism, I believe many are especially opposed to the Objectivist axioms.

Since I covered the metaphysical axioms of Objectivism in this series of posts, I’ll take the time to answer a series of actual objections to the axioms of the philosophy, and one objection to the idea of axioms as unprovable, originally answered by Aristotle.

The Order of the Objectivist Metaphysics

Previous: The Metaphysically Given as Absolute

With the final principle of the Objectivist metaphysics articulated, we can now see the structure of this branch of philosophy.

The Basic Axioms, and Their Corollaries

We begin with the metaphysical axiomatic concepts and axioms, which I’ve already discussed in my essay on the axioms (the others will be discussed in the following essays on sense-perception and free will):

The Primacy of Existence

Previous: The Law of Causality (Cause and Effect)

Objectivism is named for one of its key concepts that it emphasizes and upholds—the concept of “objectivity.”  Ayn Rand said this about objectivity in part: “It pertains to the relationship of consciousness to existence. Metaphysically [by the nature of reality—my comment], it is the recognition of the fact that reality exists independent of any perceiver’s consciousness.”[1] In general philosophy, this “recognition” is a position called “metaphysical objectivity”; in Objectivism, it is known as the “Primacy of Existence.” 

Like the law of causality, it is a law inherent in existence, and it describes the precise role of consciousness in relation to existence.  It is the most important principle in Metaphysics, and is a further corollary of the axioms and the law of causality.  I will describe how one could reach the primacy of existence from experience.  Then I will explain the opposition to this view, the primacy of consciousness.  Afterwards, I’ll explain a process for reaching generalized knowledge like the axioms without using strict induction, using the process of Aristotle’s that has been named “intuitive induction.”  Lastly, I’ll answer an objection about the mind’s control over the body in light of the primacy of existence.

The Law of Causality (Cause-and-Effect)

Previous: On Axiomatic Concepts and Axioms

Causality is something inherent in reality; it is an inescapable law of existence. In Objectivism, it is the first principle of Metaphysics after the identification of the basic axioms. I will give an inductive investigation of sorts into how this law can be formed. Afterwards, I will show why it can’t be an induction strictly speaking, and is rather a self-evident corollary of the Law of Identity.

Inducing Cause-and-Effect

Causality, or cause-and-effect, is the view that the world is lawful, orderly, or uniform in its operations. To understand what this means, we’ll have to revisit a number of concepts I discussed previously in my essay on axiomatic concepts and axioms.

On Axiomatic Concepts and Axioms

Reaching the Axioms

All topics and all fields of research have a beginning or starting point. Philosophy may be the most abstract field that we study, but it is no different. Whether they admit to them or deny them, all philosophies rest on a set of axioms, or starting points. Axioms are self-evident propositions that indicate the bases of all knowledge and are at the base of all statements and claims. Philosophical axioms must be accepted in order to make any statement or claim to knowledge of any subject, because philosophy is the backdrop for all other areas of study. Aristotle was perhaps the first individual to discuss the importance of axioms, and Objectivism is the most recent philosophy to emphasize their role in knowledge.

Induction of Aristotle’s Theory of Four Causes

The aim of this essay is to retrace the steps Aristotle had to reach in order to induce his revolutionary theory of causality, second only to his theory of logic in philosophical importance. In presenting these steps, we’ll also see several philosophical problems he solved in the process of reaching his theory of four causes.

Reduction of Aristotle's Theory of Four Causes

Let’s start with the definition of “causality”: “the principle that agents bring something about; a person or thing that gives rise to an action, phenomenon, or condition.”

In Aristotle’s mature view, there were four ways for something to be a cause, to be an explanation of a fact: the material, formal, efficient, and final. 

Induction of Objectivity (Ayn Rand)

[Previous post in the series: "Reduction of Objectivity (Ayn Rand)"]

The reduction of Rand’s idea of “objectivity” complete, we can now work through how she induced her redefinition of objectivity as involving both facts about the world and facts about human consciousness.

The induction will take two series of steps:

The first, basic series:

1. Assuming Aristotle’s knowledge, discover that knowledge has an order.
2. Discover that knowledge involves integration.
3. Find out that measurement is the essential means of moving beyond percepts.
4. Discover that consciousness has identity.

The second series:

1. From Aristotle’s discoveries and the above four, reach Ayn Rand’s theory of concept-formation.
2. Integrate her theory of concepts with Aristotle’s view of objectivity, and note the amendments that this involves, which include a reformulation of what it means to “follow logic,” and what it means to “be objective.” Two elements of knowledge that Aristotle only implicitly recognized, that knowledge is formed in a context and it exists in a hierarchy, will be explicitly included in logic, as it was in Rand’s view. This is the way that we’ll know how to adhere to reality by following a certain method, because we’ll be explicating that very method further than it was explained before by Aristotle.

Reduction of Objectivity (Ayn Rand)

[Previous post in the series: "Induction of Objectivity (Aristotle)"]

Now that we’ve reduced and induced Aristotle’s idea of “objectivity,” we can start the reduction of Rand’s concept of “objectivity,” which is an important advancement over his idea.

Let’s start with Ayn Rand’s definition, though presented in Leonard Peikoff’s words: “volitional adherence to reality by following certain rules of method, a method based on facts and appropriate to man’s form of cognition.”

The “rules of method” is Aristotelian logic, but there are important epistemological discoveries within Rand’s version of objectivity that we need to focus on. Aristotle wouldn’t have focused on man’s form of cognition as something worth analyzing in order to understand how we reach knowledge.

Whereas, for Ayn Rand, it wasn’t enough that our method is based on facts; our consciousness offers something in the acquisition of knowledge, concepts are partly human, and as a consequence, objectivity has to take this element into account. So, to reduce the idea of “a method based on facts and based on human consciousness,” we need to understand Rand’s theory of concept-formation, specifically why it is that concepts require both reality and human consciousness.

There’s some kind of element involved in forming concepts, and recognizing this element will allow us to learn something that is inherent in all concepts, to then form Rand’s theory of concept-formation, and after that we can amend Aristotle’s view of objectivity.

The next step down is: how did Rand reach her theory of concept-formation? What observations did she need to reach it?

There four elements of consciousness that we need to know before reaching her theory of concept-formation:

1. We need to know beforehand that consciousness has a specific identity, the principle that identity is the means to knowing reality, not the impediment.
2. The identity of concepts includes the fact that it does something with measurements, and this is the means by which concepts can surpass and rise above percepts.
3. An understanding of cognitive integration is necessary before we notice that aspect of the identity of concepts; we need some general awareness that integration plays a crucial role in gaining knowledge.
4. Of course, before we can put things into a sum, integrate them, we must be able to take things apart, go through a certain sequence, a series of steps. This leads to our earliest understanding that knowledge inherently has a certain kind of sequence—concept-formation involves a process of forming one concept, and then forming another based on the earlier one, etc. To understand integration, we need to reach the idea that there’s an order to knowledge.

And this is where we’ve reached the end of the reduction, since below “an order to knowledge” are specific items of knowledge that we later relate as being in a certain sequence or pattern, and these are available to introspection.

[Next post in the series: "Induction of Objectivity (Ayn Rand)"]

Induction of Objectivity (Aristotle)

[Previous post in the series: "Reduction of Objectivity (Aristotle)"]

Objectivity now being reduced, we can work through the steps Aristotle had to in order to induce his principle of objectivity. It’s essentially five steps:

1. Grasp the distinction of percepts and concepts.
2. Understand that concepts are capable of error, whereas percepts are not.
3. Learn that the functioning of concepts is under our control, whereas percepts are not.
4. Discover that we can somehow use percepts as a means to measure concepts.
5. We’ll then know that a method is necessary, and that it is possible because we know what it would consist of, by reducing the fallible part to the infallible part.

Reduction of Objectivity (Aristotle)

[Previous post in the series: "Induction of Justice"]

The aim of this essay is to reduce the idea of objectivity so that we can inductively reach Aristotle’s understanding of the concept. It’s important because we need his understanding of the concept to really understand Ayn Rand’s discoveries. After inducing this, we can induce the full, Objectivist understanding of objectivity from Aristotle’s development.

The definition of objectivity Aristotle would have given: “volitional adherence to reality by the method of logic.”

Dictionary definition: “Not affected by personal feelings; based on facts.” Based on facts, and not based on feelings—this is the main thing people understand about objectivity.

It isn’t enough to set aside your feelings in a cognitive context without some other means of understanding facts, and “based on facts” can’t simply be about percepts, because all conceptual knowledge would be barred from the approach of objectivity. So the dictionary definition informs us that we need a method or rules of thinking that ties thinking to facts, instead of feelings.

The first step down from this idea of objectivity is: “The method of adhering to reality to gain knowledge,” and we learn what the method is later. How would we grasp the idea that we even need a method?

It isn’t as simple as: from observation and induction we know that man is capable of error, he’s fallible; from this, we can deduce that you can’t be certain of your conclusions and that therefore, we can deduce that we need a method of gaining knowledge to guide us: this is a rationalistic argument.

It is necessary to grasp that we’re capable of error if we hope to even reach the concept of objectivity, but “objectivity” and “error” are vastly far apart from each other, cognitively speaking. The understanding of the fact of error came very easily, going way back into prehistory: people would bring home the wrong animal to eat, bring the wrong things needed to start a fire, etc. The striking fact, which the rationalist would overlook, is the idea that people are fallible didn’t suggest to anyone before the Greeks that we were in need of a method for checking our thinking and conclusions. In effect, the rationalist is taking as common sense what was actually a monumental discovery by the Greeks, by specifically Aristotle. The pre-Greeks had a means to deal with errors, but it wasn’t objectivity, but intrinscicism: authority, their faith in authority. The Pharaoh knows, or God knows, or whatever. It’s an invalid leap to go from “people are capable of error” to “we need a method of checking our thinking.”

So, to grasp why we would need a method at all, we need to know something about the mind, specifically what its operations are, what is possible of the mind, where it goes wrong, and how. If we don’t know how it goes wrong, or where, or what it could be doing that is different from what it’s doing, then we have no means to improve the mind. The first thing we need to know is that there are some areas or operations of the mind in which it is safe, or infallible. We have to know that first, before we can start looking for a method, as that knowledge gives us a clue as to what we can do when we’re using a fallible process.

Once we know that some part of our mind is error-free, we can figure out later that we can guide our minds reliably by using the safe data to check our fallible data, which is the essential process of objectivity. Later, we determine that the way to check this is to reduce all conceptual products to sensory observation. This idea of infallible data is important, because without it, we could never devise a method of guiding ourselves to the truth, and we could not count on it as underlying our conclusions, including our conclusion as to how we can improve our mental processes. There are then important distinctions which exist within our individual consciousness, which we have to discover before we could construct a method for correcting our errors, or even preventing them.

How could someone discover that there’s a process that can go wrong as opposed to a process that is safe?

Well, we know that we have free will, that we have control over something in our consciousness, because it would be impossible to wonder about how to guide our thinking, or find ways to improve our conclusions, if the whole operation of the mind is out of our control.

The idea we’re getting to is that Aristotle had to make a crucial discovery: there’s a part of the mind that can go wrong, and that’s the part that we’re in control of, where our free will reigns, and that there’s a part of the mind that is safe, where we don’t need control. As a result, we can decide to check the part that can go wrong using the other, error-free part. That’s what we have to know before we can search for a method of guiding our thinking.

What obvious major discovery about consciousness had to be made before we can determine that one part is fallible while one isn’t, and that one part is controlled by our mind, while the other is not. What’s the basic distinction of consciousness that had to be discovered before we could discover other distinctions and thus grasp the need of a method? The distinction between percepts and concepts. Not those exact words: for instance, Plato and Aristotle called the distinction “the realm of sense” and “the realm of ideas.” Ideas or Forms or Universals or Essences: how we word it is irrelevant. The point is that without this distinction, we would have no footing in prescribing guidance.

So, we couldn’t reach the method of logic until we knew that the method was necessary and possible, and to know these we would need to know three things:

1. We need to know what kinds of error are possible. That means that we would have to discover what kind of mental content is fallible vs. infallible. This is necessary, because it gives us a clue as to what we’re trying to correct (the fallible part), and that we’re trying to accomplish this by somehow measuring the fallible part against the infallible part.
2. We have control over the fallible part—free will reigns over the fallible area. There’s no point in prescribing a method if we have no control over the relevant part of the mind.
3. What is the relationship between these two areas? How could we relate, measure or reduce the fallible to the infallible?

Once we know those three, we’ll know that a method is both necessary and possible. The final issue, between percepts and concepts, is directly observable, one by extrospection, the other by introspection.

[Next post in the series: "Induction of Objectivity (Aristotle)"]

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).

Induction by Enumeration and Sophistry

A person who upholds “induction by enumeration” is one who believes that, by counting instances, limiting one's reasoning to some finite list of particulars, or in some way including all the particulars that one is reasoning about (such as saying “etc.”) he can reach an inductive conclusion that is true.

Aristotle's "Two" Views of Induction: McCaskey's Resolution (Part 3)

McCaskey’s Revision of Prior Analytics 2.23

Throughout this series, I’ve maintained that there are two conflicting interpretations of Aristotelian induction, and that Dr. John McCaskey has discovered a way to resolve the issue, to the detriment of one of those views. His resolution is essentially a revisionist interpretation of Aristotle’s Prior Analytics, book 2, chapter 23 (PrA 2.23); an interpretation that, if correct, will make the eight uses of the term “induction” (that is, those uses that originally posed the controversy) consistent with the other eighty-eight uses of the term that support McCaskey’s interpretation.

PrA 2.23 is composed of three paragraphs and is found near the end of the book, after Aristotle finishes a lengthy exposition on the syllogism and conversion of terms, and the chapter starts as he compares the role of conversion with types of argument such as “example” or “objections.”

The first paragraph says nothing that damages McCaskey’s interpretation of induction, and the last sentence of it is consistent with that interpretation: “[f]or we have conviction about anything either through deduction or from induction.” (PrA 68b13-14. Compare with Aristotle’s other claims that there are two ways of reasoning or arguing, one is induction and the other is deduction.)

It is the second paragraph that poses the difficulty. To understand the basis for the conventional interpretation, let’s follow McCaskey’s approach, and summarize how Aristotle is interpreted in light of this paragraph.

The second paragraph begins, “Induction, then--that is, a deduction from induction--is deducing one extreme to belong to the middle through the other extreme.” Afterwards, Aristotle gives this example (I‘m abbreviating Aristotle‘s argument for sake of length):

(1) Man, horse, and mule are long-lived.
(2) Man, horse, and mule are bileless.
By conversion of (2): (3) Bileless animals are man, horse, and mule.
By (1) and (3): (4) Bileless animals are long-lived.

Here, Aristotle is drawing a universal conclusion (“B is A”: bileless animals are long-lived) by deducing one extreme (“A”: long-lived) to belong to the middle (“B”: bileless) by means of the other extreme (“C”: particular types of animals, specifically man, horse, and mule). The deduction is valid if the conversion from (2) to (3) is valid (that is, if “man, horse, and mule are bileless,” can be restated validly as “bileless animals are man, horse, and mule.”); and the conversion is valid only if the only bileless animals in the world are men, horses, and mules. According to the conventional interpretation, Aristotle is asking us to presume that this is true for the sake of illustrating his point. The paragraphs ends with, “One must understand C as composed of every one of the particulars: for induction is through them all.”

Therefore, he is saying that the only valid induction is a complete enumeration (“for induction is through them all [the particulars]”); that induction is ultimately a kind of deduction (a “deduction from induction” that “[deduces] one extreme to belong to the middle through the other extreme”); and that induction is reducible to a deduction, since the “inductive” argument here is really a syllogistic argument that enumerates all the particulars. This is what the conventional interpretation concludes about Aristotle’s view of induction.

The “Deduction from Induction”

Now, how does McCaskey challenge this interpretation? Answer: by using the surrounding text to elucidate what Aristotle means by a “deduction from induction.” McCaskey says that an “alternative interpretation can be found by reading the chapter from the outside in rather than from the inside out.” [p. 50] I said earlier that PrA 2.23 consisted of three paragraphs; McCaskey is suggesting that we imagine that the second, substantive paragraph is missing and has to be reconstructed from the surrounding passages (the first and third paragraphs).

The first paragraph states that all knowledge becomes such through the syllogistic figures presented earlier (the chapters before 23), and ends with the statement that we have belief about anything through deduction or from induction. None of this suggests a new understanding of induction is to follow. Now we ignore the second paragraph, assuming it exists but pretending that its contents are unknown, and focus on the third paragraph. It begins “This is the sort of deduction that is possible of a primary and unmiddled premise,” which indicates that the second paragraph must have been about a “deduction of an unmiddled premise.” The next sentence plainly states that there are two kinds of deductions: (1) deductions of middled premises in which the premise is the conclusion of a syllogistic argument with a middle term, and (2) deductions of unmiddled premises, in which the role played by a middle term is carried out by an induction. McCaskey decides to call the first a “deduction-from-a-middle” and the second a “deduction-from-induction,” and notes that the second paragraph must have been an example of a “deduction-from-induction,” instead of the “deduction-from-a-middle,” which had been treated substantially in earlier chapters. McCaskey argues that paragraph three is consistently about the differences between the “deduction-from-a-middle,” and the “deduction-from-induction.” Afterward, he shifts our focus back to the second paragraph, taking what we’ve learned with us.

Based on the third paragraph, we expect to see an example of a “deduction-from-induction” in the second paragraph, and we are not disappointed. Again, the second paragraph begins “Induction, then--that is, a deduction from induction--is deducing one extreme to belong to the middle through the other extreme.” [My emphasis] The example given is the argument that all bileless animals are long-lived, which will be addressed in the next section.

Students and commentators have had difficulty with those first four words (“Induction, then--that is“), as the phrase seems to indicate that “induction” is really a shorthand for the more specific “deduction from induction,” which implies that our understanding of induction in his other works should be corrected by considering them as “deductions from induction.” McCaskey rejects this conclusion, and claims that the “induction” shorthand only applies to the few sentences that follow in the second and third paragraphs; this would mean that Aristotle is only using “induction” in those paragraphs as a lecturer’s shortening of the long-winded phrase “deduction from induction,” and therefore is not to be confused with the “induction" discussed in the Topics, for example. As McCaskey aptly states, either his own interpretation of “induction” here being a shorthand is correct, or we must accept the absurd conclusion that, “without warning, Aristotle has proposed a new understanding of induction, inconsistent with the rest of the corpus [that is, his other works] and inconsistent even with the immediately preceding sentence.” [p. 54]

Converting a Deduction from Induction

Even if the phrase “deduction from induction” doesn’t mean that induction is a form of deduction, doesn’t the example given justify the conventional interpretation, that induction is a complete enumeration that can be turned into a deduction? Here is where McCaskey suggests an alternative interpretation for PrA 2.23, specifically the second paragraph, one in which we learn how inductions become the premises for deductions.

He begins with a broad overview of what the first two paragraphs are about:

From the opening of the [second] paragraph and from what Aristotle said in the preceding, introductory paragraph we know he wants to exhibit how a deduction-from- induction ‘comes about through the figures previously mentioned,’ that is, through the syllogistic figures. His tool for doing so will be conversion, the subject of discussion in the preceding chapter and the subject Aristotle mentioned right at the beginning of this one. His subject for the chapter’s middle paragraph, then, is how conversion is used to effect a deduction-from-induction. Aristotle will first present the relevant syllogistic figure using a simple example, an example in which the conversion is justified by a method other than induction, in this case by surveying one or a few particulars or kinds of particulars. He will then expand the example by replacing a conversion justified by survey with a conversion justified by induction. He will spend the bulk of the paragraph setting up the simple example and discussing the role that conversion plays. He will execute the expansion in the paragraph’s final words.

He then notes that the example which follows is an application of a conversion rule Aristotle brought to our attention--and proved--in the preceding chapter, PrA 2.22. “When A and B belong to the whole of C and C converts with B, then it is necessary for A to belong to every B.” This is exactly what Aristotle is arguing to be the case with a deduction from induction--that it has this syllogistic figure:

(1) All C is A.
(2) All C is B.
By conversion of (2): (3) All B is C.
By (1) and (3): (4) All B is A.

Aristotle lets “A” stand for “long-lived,” “B” stand for “bileless,” and “C” stand for particular long-lived animals, such as a man, horse, or mule. We are left guessing if he means one particular man, horse, or mule, or several of them, or whether he means specific men, horses, or mules, or particular kinds of long-lived animals. But what we do know is that Aristotle is not saying that men, horses, and mules are the only long-lived animals in the world: he is only using those three animals as a surveyable and illustrative list of long-lived things--a “sample” of such things, as McCaskey puts it.

The argument then becomes:

(1) All particular things on the list are long-lived.
(2) All particular things on the list are bileless.
By conversion of (2): (3) All bileless things are particular things on the list.
By (1) and (3): (4) All bileless animals are long-lived.

Here, we have a deduction from a surveyable list: all of the samples of particular things Aristotle introduced are both bileless and long-lived, and the conclusion is that everything bileless is long-lived, since the conclusion only extends as far as the surveyable list. This is not yet a deduction-from-induction, but Aristotle sees no difficulty in expanding it to be so. To do so, he redefines C, “But one must understand C as composed of every one of the particulars: for [a deduction-from-]induction is through them all.” [page 58 of McCaskey’s PDF] Earlier, Aristotle defined C as particular long-lived things (with man, horse, and mule as examples), but now means C to be all particular long-lived things, because a deduction-from-induction is not a deduction from a surveyed list, but through all the particulars. With this, Aristotle proceeds to the next paragraph, and his expansion of C finishes his demonstration of how a deduction-from-induction is presented in a syllogistic figure and how it is properly converted.

Unfortunately, Aristotle doesn’t completely explain his line of reasoning: from the looks of it, those of us reading him have seemed to miss a step. With his redefinition, we now have:

(1) All particular long-lived things (men, horses, mules, and others) are long-lived.
(2) All particular long-lived things (men, horses, mules, and others) are bileless.
By conversion of (2): (3) All things bileless are particular long-lived things (men, horses, mules, and others).
By (1) and (3): (4) All things bileless are long-lived.

Aristotle justified the earlier conversion by surveying the particulars in his sample; he now justifies this expanded conversion by means of induction.

Ingeniously, McCaskey remarks that the justification lies somewhere else, outside of this paragraph; Aristotle isn’t saying that he’s justified in extending his argument to all particulars because of the list of long-lived things surveyed in the earlier argument. (Contrary to the conventional interpretation.) “He is saying that because of some induction performed elsewhere, he is justified in claiming that not only are all particular long-lived things bileless (2), but that every particular thing (or kind of thing) that is bileless is also long-lived (3).”

The question then is: what would justify premise 3? Premise 3 would be justified if Aristotle believed that lacking bile was the essential cause of longevity in all animals; if this were the case, then the conversion would be valid, and the universal statement (premise 4) would be true. This relates back to what Aristotle said about triangles, to the fact that knowing something to be true of all triangles does not make it valid to conclude that it applies to triangles as triangles: justifying the conclusion would require identifying the essential nature of the universal’s subject. And this, identifying the essential cause of something being the kind of thing it is, is what Aristotle believes induction is, as McCaskey’s survey of his works has persuasively argued. As McCaskey points out, “It was an ancient view that lack of bile was the essential cause of longevity in animals, and Aristotle agreed. That belief is the step that Aristotle presumed we knew, and that he presumed we knew was a discovery reached by induction.” [page 59-60]

(Aristotle affirms that lack of bile was the essential cause of longevity in animals in Parts of Animals, book 4, chapter 2, lines 677a30-35. He calls bile a “purifying excretion,” in one translation, suggesting that its leaving the body extended the health of animals.)

A “deduction from induction,” then, utilizes the same syllogistic figure and is validated by the same law of conversion as the earlier deduction from a surveyed list, but the justification for the conversion itself is understanding that the universal statement is valid for all the particulars due to their essential nature. What’s important to know here is that “(4) All things bileless are long-lived.” is not the inductive generalization, but rather is the deductive conclusion. “Induction operates in the premises, not in the conclusion,” as McCaskey aptly remarks.

Aristotle is not here arguing for an inductive generalization, but rather is demonstrating that once one knows the premises by induction, it is possible to then form a syllogism, a deduction from induction; the induction here does the work that a middle term does in a deduction-from-a-middle. The third paragraph said that the second was about a “deduction from induction,” in which a deductive conclusion results from an induction operating in the premises, and if read correctly (McCaskey’s interpretation), that is what the second paragraph is about.

If McCaskey’s revision is correct, then PrA 2.23 is not about an induction being proved by complete enumeration, or that an induction can be changed into a deduction by assuming that men, horses, and mules are the only bileless and long-lived animals that exist. It has nothing to do with coming to an inductive conclusion whatsoever.

As to what PrA 2.23 actually is about, I‘ll let McCaskey have the last words, as I don‘t think I can put the point any better myself:

[The passage in PrA 2.23] is about the reason and method by which inductive conclusions, once reached, can provide the premises for syllogisms. The reason they can be is that conclusions reached inductively are universal. They apply to all particulars of a kind, not just those surveyed in performing the induction. The method by which they can be is the swapping of subject and predicate by conversion.

Such conversion is the goal of identifying essence. If one can determine by Socratic induction that the essence of being the best is having the most knowledge, then one can convert ‘All men who are the best in a profession are the ones who have the most knowledge of that profession’ with ‘All men who have the most knowledge of that profession are the best in that profession.’ If, as in the Metaphysics, it can be claimed that contrariety is the maximum difference of two ends of a continuum, then ‘contrariety’ and ‘maximum difference of two ends of a continuum’ can be interchanged in a syllogistic premise. Induction, for Aristotle, is a process by which such equivalences can be reached, and thus premises for deductions generated. [p. 61]

Comments would be appreciated.

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.