In ITOE Ayn Rand mentioned the “lineage”, if you will, of concepts; how each concept is built from smaller concepts and smaller concepts in one massive hierarchy, all the way down to direct sensory-experience and axioms.
This has raised. . . So very many questions. But they all sum up to: how does one go about identifying this hierarchy?
How can you tell which ideas any idea is based on? I’ve been able to figure this out a few times with a sort of improvised guess and check policy but I really couldn’t explain how.
How can you tell which concepts are axiomatic? How many axioms are there (is it really only the three)?
I know an axiom is the very bottom of the hierarchy and, thusly, can’t be refuted with anything but stolen concepts (because any refutation is based on it). So is it simply a matter of thinking up all of the possible arguments against an axiom and checking if any of them aren’t based on it?
At the beginning of the chapter entitled “Abstraction from Abstractions” she writes:
“Starting from the base of conceptual development—from the concepts that identify perceptual concretes—the process of cognition moves in two interacting directions: toward more extensive and more intensive knowledge, toward wider integrations and more precise differentiations. Following the process and in accordance with cognitive evidence, earlier-formed concepts are integrated into wider ones or subdivided into narrower ones.”
An axiomatic concept is the widest integration possible, or the most extensive knowledge available. On page 59 of ITOE2 she elaborates:
“Since axiomatic concepts refer to facts of reality and are not a matter of “faith” or of man’s arbitrary choice, there is a way to ascertain whether a given concept is axiomatic or not: one ascertains it by observing the fact that an axiomatic concept cannot be escaped, that it is implicit in all knowledge, that it has to be accepted and used even in the process of any attempt to deny it.”
Chapter 4 of OPAR covers reduction of concepts. More is available in the lecture series “The Art of Thinking” by Leonard Peikoff, particularly lecture 2. There is a link to my notes on that lecture series in my signature.
So I’ve now read OPAR, and I still don’t have a very good handle on it (although I have identified a lot of my worst habits as stemming from context-dropping).
Per his example, the concept “friend” is a specific form of human relationship, as opposed to enemy or stranger. These relationships are all forms of reciprocal evaluation, as opposed to solitary valuation [unrequited love, etc].
Mutual valuation and solitary valuation are both expressions of value and consequently (deviating slightly from Peikoff’s example; I think I found a shortcut) I can trace “friend” back down to “value” by systematically comparing something with its opposite, eliminating the particulars and tracing it backwards one step.
But the opposite of “value” would be “nonvalue” and no matter how many examples I can think of to attempt to integrate, the only recurring commonality is “as understood by a conscious mind.”
So. . . Is the next step consciousness, the axiom? Or am I going about it wrong?
I’m trying to figure out a formal method of reducing concepts back to percepts, consistently; something sort of universal.
It occurs to me that if conceptual reduction were given the rigor and the structure of formal logic then, if anyone who disagreed with anyone else were to have their argument out thusly (with reduction and deduction, combined), the only way they could possibly fail to understand each other would be through evasion.
There would simply be no remaining obscurity to get lost in.
So that’s my goal; I’m working with the provisional “For X, identify -X and integrate” and I’m currently stuck at “value.”
The meaning of a concept is what it refers to, not its definition. One can witness the referents of the concept value by observing all kinds of living things in action. You don’t really need to go any further, except to ‘horizontally integrate’ value to life itself, and life is another first level concept.
There does appear to be a small step missing your proposed reduction, as value primarily refers to action but you want seem to want ‘friend’ to be merely a mental state (or 2 mental states to be exact).
One can witness the referents of the concept value by observing all kinds of living things in action. You don’t really need to go any further, except to ‘horizontally integrate’ value to life itself, and life is another first level concept.
Thank you!
So:
Friend (-Enemy)= Mutual valuation (-Solitary valuation)= Value (-Nonvalue)= Conditional existence of life!
And yeah; I treated it as a static relationship between entities because, while in reality it isn’t, I thought that might simplify things a lot.
Like the concept of ‘running’. The act of running involves a mind-boggling number of discrete movements, adjustments and readjustments; to specify each and every action which is part of ‘running’ would strain the limits of even the best attention-spans. . . Or you could simply visualize ‘running’ as if it were a constant and perpetual repetition.
At least that’s my reasoning behind it. Am I correct?
Because the concept life can be defined ostensively, wordlessly, by pointing out its referents. The meaning of a concept is its referents, not its definition. Of course we still need the word “life” to have a concept at all but a wordy definition can be dispensed with.
I know you use Dr. Peikoffs usage of “first-level” as deviated from Ms Rands two part criteria, but even given that departure, I dont see life as something you can point at, only living entities. I could never get across the difference between a rock and a rabbit to someone in this sense by pointing.
“the term “first-level concept” has sometimes been reserved for first-level concepts of entities, which are the only concepts which in no way presuppose prior concepts. I used the term this way occasianally in Salmieri 2006. I follow Peikoff 2005 and Harriman 2010 in adopting the wider usage here.”
From Concepts And Their Role In Knowledge, pgs 58-49 footnote 23
I could never get across the difference between a rock and a rabbit to someone in this sense by pointing.
That was my problem in further reducing “value”; you can’t point at the difference between desirable and undesirable, as such. Because it’s introspective.
But you could point at a rabbit and a dead rabbit, I suppose.
Using Harrison’s final point regarding life question it as a first level concept:
Pointing at a live rabbit and a dead rabbit suggests that some thing can be alive or dead. Life is abstracted from living entities as an aspect they have in common contrasted with entities which are not alive.. Could it be that “life” is an axiomatic rather than a first level concept?
Travis Norsen as well as myself have poinedt out that the “ostensive definition” confusion is related to equivocating axioms and conceptualized sensations with first -level concepts.
Actually, there are a great deal of perceptual characteristics of “life” just as much as “rolling ball”. Children are able to figure out what is alive or not at a very young age, and this can be done by just looking at limbs or movement. Basically anything alive moves, while non-living things do not move. So, yes, you can point at rabbits and rocks to get it across! No complex abstraction is necessary to develop the concept “life”, and it can even be defined ostensively. Like any concept though, you could specify better over time what is alive or not, but the referent isn’t changing or abstract in this case.
“a very important test of whether a concept is first-level would
be whether, within the context of his own knowledge, he
would be able to hold or explain or communicate a
certain concept without referring to preceding concepts.”
ITOE
Edit:
“certain concepts, s uch as concepts of function or action,even though perceptually observable,cannot be conceptualized without a prior conceptualization of the acting or functioning entities. So, if you are asking, “Can concepts of function be formed ahead of the necessary antecedent concepts?” I would say “no.” In that sense I agree with you. When you say there is something extra that is required—the something extra is the conceptualization of the entities involved, which is required before you can take the next step of conceptualizing the functions.
But we are referring here to the order of concept-formation. The fact that functions can be observed perceptually is not the essential issue here. A child can see a moving object directly, but he cannot form the concept “motion” until he has formed the concept “object.” Therefore, it is the order of possible conceptualization that is different here. This is what makes concept-formation hierarchical. This is what <ioe2_211> forms the dependence of certain concepts on certain others in human conceptual development. But as to which part of this conceptual hierarchy involves direct, perceptual observation and which is purely conceptual—that is a somewhat different question. On the lower levels of conceptualization—lower in the sense of first to be conceptualized—all that first material is available to direct perception but cannot be conceptualized indiscriminately, although certain optional elements exist on the lower level.”
The meaning of a concept is its referents, not its definition. Of course we still need the word “life” to have a concept at all but a wordy definition can be dispensed with.
I agree with him and I am not quarreling with that particular formulation.
If you mean me, I don’t know what I’m missing. Giving me quotes isn’t helping, because I’ve read all that before and thought about it. I didn’t say that life is even an action, I’m just pointing out that there are perceptual ways to think of life, even if later you incorporate concepts like “goal” and other essentials by inductive means. But you can at least create the concept. Looking at limbs, for instance, can be just as reasonable as looking at the legs of a chair. To be clear, I’m not talking about the process and function of life, I’m talking about things that are alive. To know that a dog is alive, you don’t even have to know that that it is goal-oriented. You can argue that “life” requires forming the concept dog, cat, and other animals first. On the other hand, I can argue that forming the concept of dog requires the concept of life. There are options available to the order, so we could make a fine-grained hierarchy, but I don’t think that’s important.
I’ll put it another way: in a conceptual skyscraper (how Peikoff describes conceptual hierarchy), life and dog are on the same floor, but life and dog are on different shelves on that first floor. You can start with either one, but they’re still first-level because they are perceptual and ostensively defined when starting out.
“You can start with either one, but they’re still first-level because they are perceptual and ostensively defined when starting out.”
The fact is you repeatedly ignore direct quotes contradicting explictly many of your positions.
Rand: "The fact that functions can be observed perceptually is not the essential issue here. "
Louie: “they’re still first-level because they are perceptual and ostensively defined when starting out.”
Rand: “Can concepts of function be formed ahead of the necessary antecedent concepts?” I would say “no.” In that sense I agree with you. When you say there is something extra that is required—the something extra is the conceptualization of the entities involved, which is required before you can take the next step of conceptualizing the functions."
Louie: " I can argue that forming the concept of dog requires the concept of life."
None of the “options” available to one regarding what a first-level concept includes involve contradicting what a first-level concept IS.