Friday, August 28, 2009

Concepts from an Objectivist Perspective, Part 3

Part 1

Part 2

Unit-Economy, Words, and Definitions

In part 1, I said that concepts are typically represented or symbolized by words in a language. In addition, we typically have definitions for the words we use, or seek definitions when we don’t understand or need clarity on some idea or word.

But why is this? Do words and definitions serve some important purpose in our quest for knowledge? Or could we do without them? To answer these questions, we must understand an important fact about concepts, and about the human mind.

Tuesday, August 25, 2009

Concepts from an Objectivist Perspective, Part 2

Part 1

Differences, Similarities, and the Unit-perspective

As far as we know, other animals lack concepts, and even the ability to form them. While they have their own ways to perceive the world (some snakes see through processing infrared light, for instance), as we do, they cannot do anything more with their perceptions than act on them. Using sight and hearing, a lion can hunt and kill its prey, but cannot do something that we do all the time: in general, other animals cannot organize their perceptual field, the objects they deal with every day.

Animals notice that things around them exist and act in certain ways, but they cannot reach the next step: the recognition of similarities and differences among the identities of things. We’re able to notice that some things are completely different from each other. Birds have the characteristic of flight, but trees do not; we see objects in colors and shapes, but our thinking about our own thoughts lack such features; some things in the universe are life-forms, but other things possess no life processes. In observing the world, we can’t help but notice the plethora of features and characteristics that objects have (or don’t have).

However, we’re not restricted to only noting differences amongst things. We can also notice the ways in which things are similar, or are less different, in comparison with other things. In realizing that some things are alive and some things aren’t, we can then relate these living things as having a certain attribute in common, namely “life.” Some animals have legs and can run, making them similar in comparison to, say, snakes or snails that cannot run.

These two facts, our noticing of differences and similarities, points to another significant fact about the human mind: we’re able to group or classify things according to shared characteristics (flying, color, weight, speed, etc.), considering them as units or members of a group of similars. This is the “unit-perspective,” which Rand insists is the key or beginning of the conceptual level of consciousness.

A unit is an “existent regarded as a separate member of a group of two or more similar members.” [ItOE, p. 6] While perception allows us to become aware of certain characteristics of objects around us, such as appearing or feeling like they possess a certain length or a rough surface, the unit-perspective allows us to be aware of things as existing in certain relationships with other things due to their characteristics, whether the things being compared are different from or similar to each other. (I’ll note that the concept unit doesn’t apply only to perceptual objects, such as balls and dogs. Political systems and scientific theories can be units too, in relation to the concept theory for instance, but it’s important to realize here that our first units are of perceptual objects.)

As I said in part 1, concepts are things that relate certain knowledge as applying to a plethora of things that we’ve grouped together. Such a phenomena as a concept would be impossible if we didn’t group things together in the first place, if we didn’t regard things as units. Of special significance is the fact that, without a unit-perspective, we would not be to “count, measure, identify quantitative relationships [such as some object weighing 10 pounds]; [we] could not enter the field of mathematics.” [OPAR, p. 76]

This seeming coincidence is, as Rand argues, actually the means by which we can understand the connection between concept-formation and mathematics, and thus understand the nature of concepts themselves. “The process of concept-formation is, in large part, a mathematical process.” [Introduction to Objectivist Epistemology, p. 7]

The point of the next section is to see why that is.

Measurement, and Measurement-omission

To truly understand concepts, we need to understand the mathematical idea of measurement, both what it is and the reason why we measure things.

In Rand‘s definition, measurement, “is the identification of a relationship--a quantitative relationship established by means of a standard that serves as a unit.” [Ayn Rand Lexicon entry: Measurement] Typically, measurement involves two things--the thing being measured, and the other thing which acts as the standard of measurement. By taking a foot as a standard of “length,” for instance, we can compare/measure other objects with it and determine if they are longer or shorter. A foot is itself a unit of length, so it can be used to measure other units of length and give us knowledge about certain attributes, specifically information about the magnitudes of various objects, whether of large or small magnitude. A similar process occurs when measuring weight, density, volume, time, and other units of measurements.

What’s important here is that the real purpose of measurement isn’t to simply relate objects that we deal with in everyday experience, but to expand the range of what we can consider and learn about beyond the perceptual level, beyond individual feet, or seconds which we can count. We can observe something that weighs one gram, for instance, but we can’t comprehend the weight of the Earth by merely looking at it; instead, we need to compare it to other objects that we can weigh and form new standards of measurement, such as a kilogram, which we can relate to a perceptual unit (the gram). Our perceptual field is the foundation and standard, and we relate our more sophisticated and abstract measurements to units that we can perceive with only our senses.

A similar thing happens when dealing with objects classed under a concept; the objects have the same characteristic (as we realize from observation), but differ in the exact quantities of these characteristics. Two birds may have the same characteristic “flight,” but may differ in certain quantities relating to flight, such as how high they can fly, how swift, how fast they can take off from the ground, and so on (for a striking comparison, look at eagles versus flamingos). Correspondingly, this will lead to differences in our measurements of these quantities. The world, we realize, is filled with objects which have the same characteristics, but differ in various ways in regard to the particular quantities of such characteristics or features, and our measurements will differ when relating these objects to our units of measurement.

To form concepts, we retain the characteristic, but omit our measurements of the various quantities of things’ characteristics. To form the concept flight, we specify the relevant characteristics (a self-propulsion through a certain medium, pushing against the force of gravity, etc.), but omit/not specify the particular measurements of these characteristics (for instance, the kind of atmosphere, the speed of propulsion, the instruments being used to fly, the amount of gravity being counter-acted). We must be careful to recognize that in “omitting” measurements, we’re not pretending that they don’t exist: without measurements, there is no one relating the quantities of things, and thus no comparisons which would lay the groundwork for forming a given concept. Instead, the “principle is: the relevant measurements must exist in some quantity, but may exist in any quantity.” [Ayn Rand Lexicon entry: Concept-Formation]

This “some-but-any” principle, known formally in Objectivism as “measurement-omission,” is the process of abstraction. Omitting the particular measurements from our consideration of a given characteristic is the same process as abstracting a feature from the particular circumstances we observed it in (or originally thought about it being in). In omitting measurements, we’re able to determine the characteristics that a group of things have in common (or do not), and thus apply knowledge gained about this characteristic to all the instances or particulars included in the (future) concept, regardless of any irrelevant circumstances or measurements carried out.

Thus, we come to Rand’s definition of the concept concept, and simultaneously a single-sentence summary of her theory of concepts. A concept, in her definition, is “a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.” [Ayn Rand Lexicon entry: Concepts]

Now that we’ve discussed the nature of abstraction, we can learn about how concepts are completed, which is the purpose of the third (and final) part of this series.

Part 3

Monday, August 24, 2009

Concepts from an Objectivist Perspective, Part 1

As I said in my first post, I’m an Objectivist interested in understanding induction, and in sharing what I find out with others. I’m aware that there’s a connection between induction and concepts, as I discussed in my post The Importance of Concepts for Bacon. So I’d like to briefly discuss concepts as they are presented in my philosophy, Objectivism. In doing so, I hope to show that it is a persuasive account that others should adopt (if they haven’t already), and that it has important implications for the subject of induction. (Implications that may have to wait for another time, unfortunately.)

Monday, August 10, 2009

The Importance of Concepts for Bacon

Though Bacon adopted the term notion, he took discussion of it in a new direction. [McCaskey, “Regula Socratis,” 239]
Since about April of this year, if someone had asked what was Francis Bacon’s most important concept in his philosophy, I would’ve replied “‘induction’ , of course.” It wasn’t until reading Dr. John McCaskey’s Regula Socratis that I decided to change my mind. I’ve decided that the word “notion” is the most important for Bacon. The following is my summary of Bacon’s approach to knowledge in light of reading McCaskey’s dissertation.

Monday, August 3, 2009

Aristotle's "Two" Views of Induction: McCaskey's Resolution (Part 1)

In my studies of Objectivism and Aristotle, I’ve always thought that I understood what I was reading about and contemplating afterward. One of the exceptions to that understanding was my extended reading of Aristotle’s concept of “induction.”

My earlier note, “Aristotle on Induction,” was really one interpretation of his position, supported by the vast majority of Aristotle’s use of the term “induction” (epagōgē) in his known works. What I didn’t include in that note was the alternative view, the contemporary and dominant view, defended chiefly by citing Prior Analytics, book 2, chapter 23 (PrA 2.23); an account which seemingly presents an entirely different, even contradictory, view of induction than what is presented in Aristotle’s other works (and even the understanding of induction presented within the first paragraph of that 23rd chapter ). Upon reading this chapter, I wrote in my MS Word document for Aristotle notes: “I have problems with the view that Aristotle thought induction required ‘complete enumeration of instances’; it only definitely shows up twice, and isn’t consistent with his other statements on induction.” I simply could not connect this position on induction with, for instance, the views of induction presented in his Topics or Rhetoric.

Philosopher John McCaskey, in the first chapter of his unpublished dissertation “Regula Socratis: The Rediscovery of Ancient Induction in Early Modern England,” attempts to reconcile these two conflicting views by arguing that one position is actually Aristotle‘s position, and that the other position is simply a misunderstanding and misreading of Aristotle.

Before discussing the resolution, let’s review the details of these differing views on induction.

The Two Interpretations

McCaskey notes that the term “epagōgē” (induction) appears 96 times in Aristotle’s known works. The first interpretation, the one McCaskey accepts (along with a very few others in the history of philosophy, including myself), can be understood by reading the majority of those 96 uses of “induction.” It is primarily presented in the Topics, Rhetoric, and Posterior Analytics 2.19. This interpretation is summarized as follows:

Induction is a form of reasoning that moves from particular instances and rises to general and universal knowledge. It is founded on sense-perception and memory: from our senses and memories we gain experience, and from these experiences we gain universal knowledge via induction. The application of an induction extends beyond the particulars that were used in its formation, meaning that induction is an open-ended process, rather than limited to the two or three particulars that were used to form the inductive generalization. It is different from deduction, and a counterpart to that other form of reasoning. More precisely, induction is the fundamental method of reasoning in comparison to deduction, because it supplies the premises for deductions. Induction gets its force or legitimacy from the similarity of particulars, not their number. Lastly, induction is a tool for making conceptual generalizations by identifying the essential nature of things (this last from McCaskey, page 35 of the PDF).

A great example in support of this interpretation of induction is Aristotle’s comment on goodness (aretē), in the Eudemian Ethics. There, he states that it is “the best disposition or state or faculty of each class of things that have some use or work.” He then gives us reason to believe that he has identified the nature of goodness by using the example of a coat’s goodness, which belongs to a coat in virtue of it carrying out its particular function or use. The inductive generalization about goodness states the essence of the subject: what makes “goodness” the kind of thing it is; is open-ended in that it extends to all kinds of particulars that have uses (not simply the one coat or house that could be used to form this induction); points out the element of similarity which justifies the induction (things having particular functions or uses); and is related to sensory data and memories about things having various functions.

The second interpretation on Aristotelian induction has been supported by the majority of philosophers who have commented on Aristotle, including contemporaries such as philosopher of science John D. Norton. (Norton has originated a “material theory of induction,” and thinks that Aristotle supports the enumerative induction viewpoint (page 3 of the PDF).) It is supported by eight of the 12 uses of the term “induction” in the two-book Prior Analytics, specifically (PrA 2.23).

In this interpretation, induction is a kind of deduction that is validated by complete enumeration of cases. It cannot extend beyond the particulars used in forming the generalization, and if it does not include all of them then it is invalid. It is primarily a matter of deducing a property (major extreme) or feature to belong to all the particulars of a class (middle term) by arguing that the same property belongs to one or some of the class’s particulars (the minor extreme). This is then perfected by adding “etc.” or “and these are all the particulars.”

PrA 2.23 has baffled students of Aristotle and commentators alike, while at the same time it has been regarded as the chief chapter on Aristotelian induction. In the first paragraph, Aristotle states his often-repeated claim that there are two kinds of ways of having convictions: induction and deduction. In the very next sentence, the start of the second paragraph, he seems to contradict this by claiming that induction really is just a type of deduction.

McCaskey’s resolution of this dilemma not only clears Aristotle’s name from the list of enumerative inductivists, but also teaches us the process by which induction supplies the premises for deductions.

I’ll cover the approach of McCaskey’s resolution in Part 2.