An Introduction to Objectivist Epistemo;ogy -- Discussion and Study Thread
Text is: Introduction to Objectivist Epistemology, Expanded 2nd edition (Kindle)
Discussion Starts with Chap 1: Cognition and Measurement
Discussion Starts with Chap 1: Cognition and Measurement
I’ve been trying to follow your arguments, and they are not working for me. I’m sorry to say that it is actually kind of frustrating. I will give you two examples:
First, when you say
- “A ‘unit’ is not a thing; it is not an attribute of a thing; and it is not an action performed by a thing”
Yet here it seems like you are ignoring Rand’s statement:
- “The concept of “unit” involves an act of consciousness (a selective focus, a certain way of regarding things), but that it is not an arbitrary creation of consciousness: it is a method of identification or classification according to the attributes which a consciousness observes in reality.
Then, you go ahead and say in the example of the lead ball:
- "Mass" is certainly one of its attributes [of a lead ball]. But the unit "1 kilogram" as a way of measuring its mass exists in consciousness, not in the lead ball: without consciousness there might, indeed, be lead balls, but there are no "units."
But there would definitely be mass. You seem to be claiming that the unit “1 kilogram” (and by extension the idea of units in general) is an arbitrary act of consciousness. But they are not arbitrary – they are based on observations of the nature of the entity.
Suppose someone uses a big slingshot to shoot a lead ball at you. If you see it flying at you, you will move out of the way. Why? Because you are conscious of the nature of objects flying at you. A squirrel would react the same way for the same reason. Neither one of you needs to know the quantity of kilograms to know it is dangerous.
The difference between you and the squirrel is you can analyze what happened after the fact.
You can compare the projectile to other projectiles, for example.
You can identify similarities and differences among to other projectiles (a class). You can learn the object is made of lead and in the shape of a ball. Depending on your purpose, you can analyze, theorize, and experiment to the point where you discover the ball has 1kg of mass. That's how Galileo and Newton identified the concept of mass in the first place. If it didn’t exist in reality, you would not be able to identify – to become conscious of – any of these things ...
Whatever thinking method you used seems to have made you claim Rand was saying the opposite of what she said. Here is another example:
- A "unit" is always a unit OF SOMETHING.
- So if two stones are two units, what are they units OF?
- Blank out.
This is not a blank out at all. She is saying two stones are units of the class of items called stones. She is assuming you share enough experience with other humans to be able to consider a group of similar of objects as a class or group, commonly referred to as stones.
We have not gotten to Chapter 2 of the book which gets in to the exact mechanism by which this happens.
I’m having a hard time with is seeing why this is mysterious or difficult for you.
You seem to have a lot of knowledge about philosophy. Your illustration about “unit” in Aristotle was interesting. Constructive, even. Rand’s whole thesis is that our senses and our brains function in a specific manner, and that this can be understood. You demonstrated a lot of insight to the complexity of light perception. But the fact remains that the result of all that complexity is that we do perceive color. So it is confusing to me that while you are explaining all these detailed things about that point, at the same time you are trying to undercut the point.
From, the exposure I had to the kind of philosophy they teach in the universities I can understand why Rand’s view and their view is difficult to reconcile. My experience was bad – the philosophy classes they made me take were a joke. For example, the professor for my class in Logic refused to define the term “logic,” and spent the entire semester comparing “particulars” the snowflakes coming at you in a snow storm. This was before I ever read anything by Ayn Rand. The university experience was mentally crippling.
But for purposes of this discussion group, which I was delighted to discover, presumably we believe Rand made a unique contribution to how man’s conceptual faculty works. Perhaps we can agree on two things:
- To the extent that her theory enlightens the world, it has something to do with our ability to distinguish similarities and differences among entities and to classify these as members – units – of a group. Stop trying to undercut this.
- Her achievements require going back to first principles; they correct horrible errors made by earlier philosophers. Lets try to understand it.
Perhaps instead of trying to prove Rand wrong you could take the role of contrasting her view to that of traditional philosophers instead of undercutting it.
I for one want to understand more about what she said. Please stop trying to destroy what she said without offering anything constructive in its place.
EF does not believe in an objective reality. He is not honest enough to state that. He either is a Platonist or he believes his emotions create reality. He writes long winded diatribes that use the language Objectivism but not the philosophy of Objectivism. His point is to prove that God exists or is necessary.
I appreciate the reductionist tendencies of "philosophers" but at some point, the law of diminishing returns kicks in and it becomes a process without a worthwhile product.
If you recall from The Fountainhead, Ellsworth Toey was a man of Ideas and he brought down athe Daily Banner.
Glad of your response. I was a little worried that the sense of humor had dried up in these precincts. Glad to be proven wrong.
cognition can be split into 1) conceptual and 2) mathematical (math being the science of measurement).
she states the purpose of measurement is to expand the range of man's knowledge beyond the perceptual level. we make the universe knowable by bringing it within the range of man's consciousness. by establishing its relationship to man, it serves to expand the conceptual level of his consciousness.therefore, if the goal is to gain knowledge, we must use methods in compliance with objective rules (like math provides) and facts.
is this a proper understanding? i had never thought of math in that way, although it seems obvious now. anyway, this bit helped me understand why and how rand may have started objectivism.
my question is this (assuming my understanding of math and it's purpose is correct in the first place): is this saying that all knowledge must be measured? and if something can't be measured--is it not knowledge? what happens to that unmeasurable idea (or emotion) in that case?
I think Rand's statement about math is overly narrow. She is only concerned with measurement. This field of science is call Metrology http://en.wikipedia.org/wiki/Metrology.
Mathematics is about building pure logical systems. For instance, Euclidean geometry is about the logical system built on the idea that two parallel lines go on forever and do not intersect (actually there are 3 assumptions). Algebra is based on the assumption that A=A among others http://library.thinkquest.org/2647/algeb...
Science to me is a method of identifying object attributes and the methods between related objects - related meaning that one object may exercise a method to affect another object. Mathematics is the study of methods - how much force must be applied to move an object, quantifying the effects of gravity based on the masses of two objects, the relationships of the sides and angles of a triangle, etc. Mathematics attempts to define the inputs and outputs of a given interaction (thus the equals sign).
In theory, even emotions could be quantized into mathematical relationships. The challenge is the sheer number of variables involved, the rapidity of change of the variables' values, and the range of behaviors that can be elicited as a result. The complexity involved in deriving such a model exceeds even climate change and turbulence studies in its computing requirements.
1 - awareness of objects, which is the concept of entity
2 - awareness of things we can distinguish from other things on a perceptual field, which becomes identity (e.g. distinguishing a chair from a table)
3 - grasping relationships among entities by their similarities or differences. these entities then become units once they're grouped.
the ability to regard entities as units is man's distinctive method of cognition.
okay--i think i understand all that. but my confusion struck when the text said: the criterion of classification is not invented, it is perceived in reality.
what does that mean? my understanding was that the most we can do is just see the differences between two things--that we cannot create the differences between two things. is that correct? if so, what's a real world example of this?
"Since it [i.e., 'existent'] is a concept, man cannot grasp it explicitly until he has reached the conceptual stage. But it is implicit in every percept (to perceive a thing is to perceive that it exists) . . ."
A human consciousness doesn't grasp the idea of "implicitness" until, again, it has reached the conceptual stage. So her suggestion that a concept is "implicit" in a percept *even before* one has reached the conceptual stage, is (among other things) concept-stealing: a human consciousness at the conceptual stage can grasp the notion of "implicitness" and claim that, upon perceiving something, the concept "existent" or "it exists" is implicit in its perception of it; one cannot, however, take one's existing consciousness — including ideas about "implicitness" — and turn back the clock to infancy, a time when one did not have a conceptual consciousness — and still claim that any idea or concept is "implicit" in a mere percept.
"Percept" and "implicit concept" are mutually exclusive. nothing is "implicit" in a percept qua percept. A percept merely *is*.
When you look through a camera at an object — a tree, for example — and carefully focus and adjust your exposure, you — the adult photographer with the conceptual consciousness — might implicitly realize that to see the tree is to also admit that "it exists"; but the camera itself — as an analogy to a human infant who, presumably, only perceives — has nothing to do with "implicitness." Whether the lens of a camera, or the lens of a human eye, "perceiving", per se, is all about the explicitly given of the perception; there's nothing implicit about the percept, per se.
If, as Miss Rand asserts, the concept "existent" is implicit in the simple perception of a tree, qua percept, then it must also be so for a non-conceptual consciousness, like a squirrel's. A squirrel perceives the tree, just as the child perceives the tree (how the image of the tree appears in a squirrel's mind is, of course, an unknown, but it most certainly perceives the tree on which it climbs up and down). Would Miss Rand claim that the concept "existent" is implicit in the percept of the tree in a squirrel's mind?
If she is indeed claiming that an "implicit concept" is carried along with a percept, but only in a human pre-conceptual mind, such as the mind of an infant, it must be because the child is *potentially* capable of grasping concepts at a certain point in its growth. So, is Miss Rand saying, therefore, that to a potentially conceptual consciousness (such as an infant's) concepts as such are implicit in percepts as such? If so, is this true for all of its percepts, or only some of them? If true for only some of them, why? If Rand is going to assert that the concept "existent" is implicit in every percept of a not-yet-conceptual human consciousness, then why not other concepts as well? Why not the concept, "generates a gravitational field"? That's a sophisticated higher-order concept — the idea that all masses have the attribute of gravitational attraction — and, of course, we wouldn't expect any consciousness to grasp that concept until it was both conceptual and had received a good deal of training in physics and mathematics. But since it is true, is it not also true that it is implicit in the infant's perception of a tree?
I can't tell if this is what Miss Rand is really claiming. If so, then it's a kind of inverted Platonism: instead of his doctrine of "innate ideas," in which actual knowledge already pre-exists inside one's mind at the moment of birth, and the act of bringing that knowledge to full conceptual consciousness he likens to an act of remembering, Rand seems to claim that conceptual knowledge automatically resides "implicitly" inside percepts, and since the source of percepts is some physical stimulus starting outside one's body and mind, it seems that the act of bringing implicit knowledge to full conceptual consciousness she likens to mere perception.
This may or may not be what she's aiming at. In any case, at worst it is just plain incorrect; at best, it is confused and badly expressed.
Consciousness, as a state of awareness, is not a passive state, but an active process that consists of two essentials: differentiation and integration.
Rand, Ayn (1990-04-26). Introduction to Objectivist Epistemology: Expanded Second Edition (p. 5). Penguin Group US. Kindle Edition.
(to perceive a thing is to perceive that it exists)
Rand, Ayn (1990-04-26). Introduction to Objectivist Epistemology: Expanded Second Edition (pp. 5-6). Penguin Group US. Kindle Edition.
The ability to regard entities as units is man’s distinctive method of cognition, which other living species are unable to follow.
Rand, Ayn (1990-04-26). Introduction to Objectivist Epistemology: Expanded Second Edition (p. 6). Penguin Group US. Kindle Edition.
Thus the concept “unit” is a bridge between metaphysics and epistemology: units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships.
Rand, Ayn (1990-04-26). Introduction to Objectivist Epistemology: Expanded Second Edition (p. 7). Penguin Group US. Kindle Edition.
Measurement is the identification of a relationship— a quantitative relationship established by means of a standard that serves as a unit. Entities (and their actions) are measured by their attributes (length, weight, velocity, etc.) and the standard of measurement is a concretely specified unit representing the appropriate attribute.
Rand, Ayn (1990-04-26). Introduction to Objectivist Epistemology: Expanded Second Edition (p. 7). Penguin Group US. Kindle Edition.
this is what i wrote down on my notes:
existence is a concept that man cannot grasp *explicitly* until he's reached the *conceptual stage*. he understands it *implicitly* on the *perceptual* level. it's the implicit knowledge that allows his consciousness to develop.
explicit - very clear, without a doubt
implicit - without qualification
conceptual - based on mental concepts
perceptual - based on senses
just my take on it...feel free to correct me or tell me that i didn't understand your question in the first place.
"This series of articles is presented “by popular demand.” We have had so many requests for information on Objectivist epistemology that I decided to put on record a summary of one of its cardinal elements— the Objectivist theory of concepts. These articles may be regarded as a preview of my future book on Objectivism, and are offered here for the guidance of philosophy students."
Rand, Ayn (1990-04-26). Introduction to Objectivist Epistemology: Expanded Second Edition (p. 1). Penguin Group US. Kindle Edition.
I take from this that this is not the clear and final statement of her philosophy. It is designed to be a guide for the student philosopher to learn the basics and be ready for the study of the final philosophical statement of Objectivism.
Those of us in this discussion thread should view the material in that manner.
She didn't say that existence is implicit in perception; she said that the notion, the idea, the concept, of *existent* (not *existence*) was implicit in a percept.
I claimed that was, at best, a kind of inverted Platonism. Concepts are not implicit in percepts. Nothing is implicit in a percept. A percept is an irreducible datum of the senses (it can, of course, be broken down into sensations — nerve impulses, etc. — but we don't experience something called a "nerve impulse", which is discovered inferentially; the name of the primary datum we experience is called a "percept").
And a percept simply *is*. Nothing is implicit "inside" of it; no notions, ideas, or concepts, are carried along with it.
If, as Miss Rand claims, the concept "It is an existent" is implicit in the perception of a big rock, then why shouldn't other concepts be implicit in that percept, too; e.g., "It exerts a weak gravitational pull on other masses" or "It's composed of granite" ("to perceive a big rock is implicitly to grasp that it is composed of granite"), etc.
It's an odd view of knowledge as somehow being wrapped up, whole and complete, inside — "implicit in" —a percept.
The upshot of her position is that it leads not just to an Objectivist Theory of Knowledge, but also to an Objectivist Theory of [other people's] Ignorance. If Joe Objectivist perceives an entity, asserting all kinds of things about it which he claims are implicit in his perception; and if Mary Christian perceives the same object and claims otherwise, Joe Objectivist will respond in one of two ways: "You're not perceiving correctly" (which would include not using reason correctly, since reason and perception are tightly linked in Objectivism); or, "You're perceiving what I'm perceiving, and you jolly well grasp all those implicit truths that I grasp, but you are claiming otherwise in order to promote some other agenda. Since you are attempting to alter or deny reality, you are guilty of a moral transgression."
I'd say those two responses sum up most of the discussions many people have — or try to have — with Objectivists.
Now, "to perceive a big rock is implicitly to grasp that it is composed of granite," is to be guilty of an unwarranted assumption; namely, the "big rock" in question could just as easily be a large nugget of gold, be composed of quartz or iron, or any number of other elements or compounds.
Regarding Joe and Mary, it isn't "[y]ou're not perceiving correctly", it is "you are not correctly evaluating that which you perceive." So there is a third alternative response which has been excluded.
Even the squirrel can GRASP that the tree exists.
>In that respect, perceiving something is, implicitly, to perceive that it exists.
I prefer this:
"A percept is a percept."
"To perceive something is to perceive something."
Period. Nothing is implicit in the percept. Not knowledge, not concepts, not additional assertions. Nada.
Furthermore,
"A is A"
Period. Nothing is implicit in that statement. Not, "Well, if A is A, then it necessarily follows that to grasp 'A' is to grasp that 'B' must be the next letter."
No it doesn't. If you *later* discover that "B" follows "A", hey, that's great. The only proviso is that the statement "B follows A" NOT CONTRADICT the original assertion that "A is A." And, of course, there is no contradiction involved here. But that "B follows A" is consistent with "A is A" does NOT mean that it is "implicit" in that original tautology.
Same with perception.
To perceive something is to perceive something.
To perceive something that exists is to perceive something that exists.
If *later*, upon adult philosophical reflection one concludes that one ONLY perceives that which exists, it doesn't mean that the statement "one only perceives that which exists" is implicit in a percept, and certainly not in a pre-conceptual consciousness (such as a human infant's), and most definitely not in a non-conceptual consciousness (such as a squirrel's).
>One cannot have a perception of the non-existent
By your logic, that last statement — "one cannot have a perception of the non-existent" — must itself be implicit in a percept, along with all other knowledge that only later becomes known; e.g., "to perceive something is implicitly to acknowledge and grasp that it is composed of matter and energy", and "to perceive something is implicitly to acknowledge and grasp that it is composed of atoms", etc. According to Miss Rand, then, all knowledge — e.g., all of quantum physics and quantum chemistry — is implicit in merely perceiving something.
As I posted earlier, that's an inverted Platonism. Instead of knowledge being innate and accessed through a mental act similar to remembering something, knowledge for Rand is exterior to man, carried along in the exterior stimuli itself, and accessed (i.e., converted from "implicit" knowledge to "explicit" fully-conscious knowledge) by means of logic.
It's an odd view of knowledge.
>man grasps it implicitly on the perceptual level---i.e., he grasps the constituents of the concept 'existent' . . . "
Gibberish. There is nothing to "grasp" in a percept except the percept. A percept is pure explicitness. That's why you *perceive* it. "To grasp" something is an act of *intellect*, not perception.
The confusion in ITOE is part of the price Rand paid for paying lip-service to Aristotle and St. Thomas but not really studying them deeply. The dichotomy between "perceiving a thing" (using one's senses) and "grasping a TRUTH ABOUT a thing" (using one's intellect) was fundamental to their system. Rand asserts that merely to perceive something is ALSO to grasp a truth about it, an absurdity she tries to soften by claiming that the truth is grasped only "implicitly", which then (I suppose) is acknowledged "explicitly" when one reaches a conceptual level of consciousness and decides to introspect.
"Metaphysical truth is perceptually grasped, even without a conceptual level of consciousness, because metaphysical knowledge is buried inside percepts!"
It's weird, but that's what it amounts to. More than weird, it's actually a species of mysticism.
>Now, "to perceive a big rock is implicitly to grasp that it is composed of granite," is to be guilty of an unwarranted assumption; namely, the "big rock" in question could just as easily be a large nugget of gold, be composed of quartz or iron, or any number of other elements or compounds.
Now you're claiming that conditional statements linked disjunctively — i.e., "The big rock could be gold; or the big rock could be quartz; or the big rock could be iron; or the big rock could be some other element" — are ALL implicit in a 1-month-old human infant's perception of a big rock, when it has no knowledge of rocks, gold, quartz, iron, or elements. I'm not even confident that it has any knowledge of what "big" means.
I'll sum it up for you:
Miss Rand's idea of "implicit knowledge" — as she is using it — is pure stolen concept. Rand is guilty of the same transgression in logic that she has so often (and so justifiably) accused others of committing. The concept of "implicit" only makes sense in reference to the "explicit." First comes explicitness, then comes implicitness. It is only after one reaches the conceptual stage of consciousness where knowledge is held in explicit form that one can ferret out things one hadn't noticed before and claim, "Aha! These little truths were implicit in something else I already knew explicitly!" Nothing wrong with that. But that sort of statement doesn't suggest that the implicit truths were "tucked away, inside" a mere perception.
>Regarding Joe and Mary, it isn't "[y]ou're not perceiving correctly", it is "you are not correctly evaluating that which you perceive."
"Evaluate"? I don't understand what it means to "evaluate" a perception. To "evaluate" means to form an idea of the amount, number, or value of some bit of knowledge. Perceptions aren't knowledge. Perceptions are subjective experiences of an individual consciousness. You don't evaluate them. You experience them.
No, if Miss Rand is really asserting that there's a certain species of conceptual knowledge that lies dormant, implicit, within simple percepts, then the upshot would have to lead to disputes over whose perceptions are "normal" (i.e., those claiming that the implicit knowledge they have uncovered and made explicit is true) vs. whose perceptions are accused of being distorted in some way.
>Even the squirrel can GRASP that the tree exists.
Except that squirrels (as far as we can tell) lack the faculty of *intellect* and can therefore grasp nothing ("grasping" is an act of the intellect, not the senses). It was just a bit anthropomorphic of you to assert that. Next thing you know, you'll be claiming that squirrels potentially have a benevolent sense of life and are potential Objectivists.
I *get* it. I really do.
But (to repeat) to grasp a tree with claws is not the same thing as grasping a truth about the tree with intellect.
How We Know presents an integrated set of answers to these and related questions, based on Ayn Rand's Objectivist philosophy, including her unique theory of concepts.
How We Know explains how following methods of cognition based on the facts of reality and on the nature of our cognitive equipment makes it possible to achieve rational certainty, no matter how abstract the issue.
More here:
http://www.how-we-know.com/Excerpts-list...
I have long thought that the epistemology is the weakest part of Objectivism, and the weakest part of that weakest part is the notion of "unit," which is the heart of Rand's theory of concepts. If her ideas on "unit" fall, so does her theory of concepts.
Rand defines "unit" as follows:
(1) "A unit is an existent regarded as a separate member of a group of two or more similar members. (Two stones are two units; so are two square feet of ground, if regarded as distinct parts of a continuous stretch of ground.)"
As I'll show in finer detail below, there is already a problem with this definition and with the two examples she gives, i.e., two stones and two square feet of ground, each one, in her view, being "two units of something."
Continuing:
Rand asserts that a "unit" is an existent — an existent regarded as a separate member of a group of two or more similar members, but an existent nevertheless. So let us look at how she defines existent:
(2) "The building-block of man's knowledge is the concept of an 'existent', of something that exists, be it a thing, an attribute or an action."
Putting definitions (1) and (2) together, we have:
A "unit" is a thing, an attribute of a thing, or an action performed by a thing.
Before proceeding, I'd like to point out that this is already mistaken.
A "unit" is not a thing; it is not an attribute of a thing; and it is not an action performed by a thing.
Take, for example, a lead ball. "Mass" is certainly one of its attributes. But the unit "1 kilogram" as a way of measuring its mass exists in consciousness, not in the lead ball: without consciousness there might, indeed, be lead balls, but there are no "units". Without consciousness, "lead" exists, but "gram" does not. Without consciousness, "lead" exists, but the unit number — "1" — does not.
Using Aristotle's "Categoriae" as a reference, we can say that a "unit" is not a thing — not a "substance", as Aristotle would have understood that term — but rather, it falls under the category of "relation", and a relation among three things: the "whole" attribute of an entity (i.e., the entity's whole mass, the entity's whole weight, the entity's whole length, etc.); a "part" of that attribute (some division of mass, weight, length, etc.); and the mental act of comparing that PART to the WHOLE by naming the part "1".
So we need three things for a "unit": The whole of some attribute; a part of that attribute; the mental act of mathematically comparing the part to the whole by calling the part "1" plus a name: thus, we have the whole of mass of some entity; we arbitrarily take a part of that whole and call it "1" + the name "gram". We can now use that part to compare to other entities with the same attribute of mass. We have the whole length of something; we arbitrarily take a part of that whole and call it "1" plus the name "inch", and we can use that part for comparison against any other entity that has the whole attribute of length.
The "part-of-the-whole" relation (known in logic as the "partitive relation") is obviously essential to the idea of "unit." All units are, by definition, 1 part of the whole attribute being measured. There's a simple grammatical substitution test one can do to test if something is really a unit: just put it into a partitive phrase with "of" as the preposition linking the antecedent idea (the part) to the consequent idea (the whole). For example
"a gram of mass." (a "gram" is one unit of a whole attribute called "mass")
"a meter of length." (a "meter" is one unit of a whole attribute called "length")
"a gallon of volume." (a "gallon" is one unit of a whole attribute called "volume")
etc.
Of course, we are usually accustomed to substituting the right side of that partitive phrase with the name of the actual substance we are measuring, e.g.,
"a gram of lead"
"a meter of rope"
"a gallon of water"
etc.
But notice, it's not really "lead", per se, that we are comparing to the gram, but rather one of lead's attributes, i.e., mass. So to be a real stickler for precision both grammatical and logical, we ought to say, "a gram of mass of lead," and "a meter of length of rope", and "a gallon of volume of water".
It is, perhaps, all right that we not say this, but we should *think* it, and *mean* it, when we employ the more common constructions of "a gram of lead", etc.
pages 5-6:
"[An] 'existent' [is] something that exists, be it a thing, an attribute or an action."
pages 6-7:
"A unit is an existent"
MAJOR PREMISE:
An existent is something that exists, be it a thing, an attribute, or an action."
MINOR PREMISE:
A unit is an existent.
CONCLUSION:
Therefore, a unit is something that exists, be it a thing, an attribute, or an action.
In other words, a unit is either a thing, or it's an attribute of a thing, or it's an action of a thing.
This is what I posted earlier, and what I looked at critically.
>Objectivism is good
I said nothing about "good" or "bad." I said the epistemology was the weakest part of Objectivism.
If these two were not stated as axioms, you would have to show both to be true, a formidable task.
Thanks!
>The real question is are the major and minor premises true.
I agree that's a *different* question, but not necessarily the *real* question. A syllogism establishes the validity of an argument, not its truth. "Truth" is correspondence to reality; "validity" is internal coherence.
>The minor premise is also an axion .
Miss Rand merely provided a definition of "unit" (an incorrect one, in my view). I don't see where she ever claimed that her notion of "unit" was an axiom.
>If these two were not stated as axioms, you would have to show both to be true,
I disagree, and I think that misapprehends the purpose of deductive logic. Aristotelian logic — sometimes called "predicative logic" and sometimes called "minor logic" — is strictly concerned with correct form, not substance. As long as the form of an argument can be compressed into a syllogism such as,
Every Y is X;
(A) is Y;
Ergo, (A) is X,
then it doesn't matter what you substitute for the variables Y, X, or (A).
Conversely, you could have a syllogism in which every proposition is true, but which is nevertheless invalid as an argument because the conclusion cannot validly be inferred from the premises. For example,
MAJOR: Every deeply profound subject is often difficult to master;
MINOR: Advanced differential and integral calculus is often difficult to master;
CONCLUSION: Therefore, advanced difference and integral calculus is a deeply profound subject.
I suppose there might be some differences of opinion regarding the truth of those statements, but most educated people who have studied mathematics and intellectual history would agree that the calculus is, indeed, a profound subject, full of original insights into the nature of motion and change.
Yet, in the above syllogism, the conclusion cannot be validly drawn from the premises; so even though we might agree that the premises and the conclusions are true — i.e., they correspond to reality — the reasoning by which we drew the conclusion is faulty, and the argument, as such, as invalid.
(It's an example of a formal fallacy called "The undistributed middle term", e.g., "Every (A) is X; Y is X; ergo, Y is (A)." Or, "Every man is mortal; Lassie is mortal; ergo, Lassie is a man.")
.
Now, if you understand that a unit is always some part of a greater whole attribute that we wish to measure, then it behooves us to ask what, precisely, is the meaning of Miss Rand's assertion that "two stones are two units."
It makes no sense.
"Two grams (of mass) of lead" makes sense, because of the parenthetical "of mass" phrase, which tells us that "gram" is itself a little bit of mass given the label of "1". Remember that the test of "unit-ness" is that partitive phrase — the "of ____". If that phrase cannot be completed intelligibly in a sentence, then the meaning of that sentence has nothing to do with "units". We could even put that sentence into the following form for the sake of consistency with Miss Rand's sentence:
(3) "Two grams (are two units of mass) of lead"
Returning to Miss Rand's assertion, let's see if we can apply the partitive test by putting it into the same form as (3):
(4) "Two stones (of ______) are two units (OF WHAT????)"
A "unit" is always a unit OF SOMETHING.
So if two stones are two units, what are they units OF?
Blank out.
Miss Rand confuses the issue for herself as much as for her readers when she immediately continues that assertion with the following:
"so are two square feet of ground, if regarded as distinct parts of a continuous stretch of ground."
Notice, please, that Miss Rand inadvertently makes use of that partitive construction we saw as necessary to all units: "so are two square feet OF ground." The precise construction, of course, should be, "so are two square feet (OF area) of ground."
Yes, two square feet of area truly are two units of area of ground — and they need not be continuous, by the way: if one square foot is in New York and another square foot is in Beijing, adding the two together still give "two square feet of area".
But "two stones" are not two units OF anything — they're simply "two stones." They would only be two units OF something of there were a unit called "the stone" by which we measure some other entity that had the attribute of "stone."
But "stone" is not an attribute of some other entity; a "stone" — as used by Miss Rand in her assertion — is itself an entity.
There are a number of other problems with Objectivist epistemology, at least as it is expounded in ITOE. I'll mention one more:
A unit OF something (notice again, please, that all-important partitive construction with "of", showing the part-to-whole relation on which the idea of unit logically rests) must comprise the same attribute as the "whole" one is measuring. In other words, a unit of length must itself be a little bit of length; a unit of mass must itself be a little bit of mass; etc.
In ITOE, Miss Rand asserts that the unit of color is the wavelength of light (e.g., the angstrom, which is 1/10^10 meter). Putting aside quantum quibbles regarding whether or not light is a wave, it's obvious that wavelength, or the angstrom, is a unit of LENGTH, not of COLOR. To be a true unit of color, the unit itself must have the attribute of "color", just as a unit of mass (e.g., the kilogram) itself has the attribute of mass. "Length" is not the same attribute as "color" and cannot be used as a unit thereof. The most we can say is that length — specifically, wavelength — seems to CORRELATE with the subjective experience we call color, through a complicated process of perception, physiological processing, and cognitive computation; thus a wavelength of X "correlates" with the subjective experience of a color we recognize as "blue." But the "wavelength" and the "blue" are two completely different things, and the former is not a unit of the latter.
The wavelength of the photons which we call blue cluster around 475 nanometers (nm). If I take a picture of a blue object, are you asserting that the object has no color until it is observed? Is my camera subjective? Or is it the case that 475 nm and blue are merely two different expressions of the same objective unit?
As to whether characteristics are inherent or perceived, if the purpose of a characteristic is to differentiate one instance of an object from another, are we not really arguing the need for identification in the first place? If there is only one object of a particular type, the primary purpose in describing it as blue to would be to help another individual identify and characterize the instance of that object with which he/she is not familiar or to standardize a frame of reference, would it not?
To me, blue is not a unit - blue is an attribute. One can not have two units of "blue".
The main point was that an attribute of an object should not be treated as an object, and attributes can not be added together. It is incorrect to say two blues, two reds, etc. One must say two red birds, two blue cars, etc. and the purpose is to differentiate and identify the specific object (or group of objects) in question.
Only sometimes. Not necessarily.
>If I take a picture of a blue object, are you asserting that the object has no color until it is observed?
No. I'm saying it isn't "blue" until it is experienced by an eye-brain-mind system as being "blue." The wavelength of 475 nm is an objective component of light that *correlates* — in some contexts but not all — with the perception and conscious experience of something called "blue."
Wavelength and color CORRELATE, but they are not the same thing.
>Or is it the case that 475 nm and blue are merely two different expressions of the same objective unit?
Color has no objective unit since it's a subjective experience. Color qua color exists in consciousness.
Some "ad hoc" units of color have been created for various practical purposes, but one adopts them in ad hoc fashion, i.e., for immediate practical purposes. I'm thinking of the various color-swatch systems such as the Munsell system and the Pantone color matching system.
Inventor and physicist Edwin Land proved not only that color perception is much more complicated than originally assumed, but — more startlingly — that color is not so much "perceived", but literally *computed* by the retina/cortex system, which he dubbed the "Retinex" theory of color computation.
It appears that there is no *necessary* connection between a wavelength of, e.g., 475 nm and the perception of the color "blue."
And in a famous experiment (which was first published in 1958 in the Proceedings of the National Academy of Sciences, and later published as a more popular summary in a 1958 edition of Scientific American) Land proved that it was possible to photograph a full-color scene (red tomatoes on a green vine, for example) USING BLACK & WHITE FILM for creating slides, and using either white light or monochromatic light diverted from a prism, to pass the white light or the monochromatic light through the black & white slide transparencies, and project the original, full-color image on a screen.
It wasn't an illusion; it wasn't some retinal "after-immage"; it was real color projected on the screen from white light passing through black & white slide transparencies.
In fact, the cover of that 1958 edition of Sci. Am. was a photograph of the image Land projected onto a blank screen to an amazed audience.
I bring all this up to support the point I made earlier: the objective phenomenon called wavelength and the experience in consciousness we call color are *correlates*; the former is not in any way a unit of the latter.
Again: a "unit" OF something must itself partake of the attribute one wants to measure. A gram is itself a mass (which is why we can choose to call it "1" and use it to compare to other masses). A wavelength, however, is a unit of length and is not itself a bit of color, so it cannot be a unit of color.
Think of it this way:
Joe is a summer associate at a law firm. His office has 48 square feet of floor space. His salary is 48K (4K/month). Mary is a long-time senior partner in the same law firm. Her corner office has 150 square feet of floor space. Her salary is 840K (70K/month).
Is there some sort of "correlation" between the amount of floor-space each has, measured in units of "the square foot", and each one's salary? Yes. Square-footage at this firm certainly correlates with income. Could we therefore say that the "square foot" is a unit of wealth, or a unit of salary? No.
The relation between square-feet and salary is one of correlation, similar to the relation between wavelength and color perception.
"No. I'm saying it isn't "blue" until it is experienced by an eye-brain-mind system as being "blue.""
This is a difficult concept for me to grasp EF. It sounds similar to the Copenhagen interpretation of QED. As an Objectivist, I believe that when I hold a prism up to the sunlight the resultant color spectrum exists even if no "eye-brain-mind-system" exists to experience the colors. Do you believe that the wavelengths of the photons exist?
Sure. But wavelength measures the *length* of something, not the color of something. Only through lots of processing (first by the retina, then by the optic nerve, then by the visual cortex) is a quantity of length subjectively experienced by an individual consciousness as a quality called "blue."
The relation between the input quantity of length and the output quality of subjective experience is called *correlation*, and not "unit measurement."
Two more points:
1) As mentioned earlier, there is no necessary connection between a wavelength of 475 nm and the visual experience of the color blue. Edwin Land (inventor of the Polaroid camera, among other things) proved experimentally — and explained theoretically — that using only blue light diverted from a prism and black-and-white slide film, he could project a full-color image on a screen, complete with reds, oranges, yellows, greens, etc.
2) Even if we accept that a length of 475 nm is one unit of blue (for the sake of argument), it would have to follow that to get two units of blue we would multiply by two, i.e., 475 nm x 2 = 950 nm. Under the usual conditions, a length of 950 nm is in infrared territory. So your logic of using wavelength as a unit of color leads to the conclusion that 1 unit of blue = blue, but 2 units of blue = infrared (instead of simply "more" blue).
A corollary to this would can be found in the works of CS Lewis when he talks about the English language and how many people confuse the "being" verbs to indicate action rather than a state. It's been a while since I read it, but I believe that "The Problem of Pain" is the one I am after. The example he gives is in using statements such as "I am hungry" or "I am cold" when in fact you are neither. You are in reality affected by the cold or affected by hunger, but neither of these effects has changed your core being. They are semantics of language, but important semantics. We are not equivalent to our feelings nor are we a sum of them. We exist independent of our feelings, but we may allow our feelings to drive decisions.