Understanding Objectivism Vs. Being an Objectivist

[thomtg]

Is it possible to understand Objectivism and not be an Objectivist? I think not.

The key word in understanding my above claim is in understanding what "understanding" is. "Understanding" is a comprehensive grasp of an aspect of reality by means of a concept. In this case, the "aspect of reality" is a particular philosophy, i.e., a body of thought pertaining to existence and man's relationship to it, i.e., an integrated conglomeration of mental identifications of external contents.

This "grasping" is analogous to the holding of a book. But unlike holding a book, say, a book on Objectivism, which you can release your hold and put it down; the grasping is a permanent grab. The grasping produces products in the mind: concepts.

In holding a book, there is a direct correspondence between the action and the object acted on, i.e., between the holding itself and the book held. But there isn't a "correspondence" in understanding something. Of course, you need something to grasp, some aspect of reality in order to understand; but once you have grasped it, what you understood becomes part of your permanent possession; you can't "put it down"; you go to sleep, wake up, think about it, and there it is again as an awareness, an understanding of that aspect of reality, even if you are presently not in any sensory contact with that aspect of reality.

Having permanent possession of a concept is a huge undertaking, especially if it is "Objectivism," which comprises hundreds if not thousands of analyzable concepts, which require tracing and reducing to handfuls of unanalyzable axiomatic concepts in one direction, interrelating all into one single integration in the other direction, and doing so without errors: innocent mistakes, evasive gaps, missing links, extraneous contents. It is easy to imagine people giving up the effort to acquire this level of understanding. It is easy also to imagine them failing to sustain the effort toward the purpose of understanding.

One may now ask, but is it necessary that understanding Objectivism makes one an Objectivist? Doesn't it require an act of free will? Yes, it does. It does require an assent that Objectivism is true. And if it is true, i.e., of recognizing it as facts of reality, then there can be no gap between grasping it as true and being an Objectivist. Let me explain.

There are two processes going on here. The first one is the process of forming a belief, and the second process is that of verifying it. For volitionally rational beings, we need to discover and use logical methods of inquiry for the former and logical methods of verification for the latter. (See DK "Religion and Objectivism.")

If I see this dog here sitting on a mat, and then I make the perceptual judgment, "The dog is on the mat"; I have assented to a fact of concrete reality. The act of seeing verifies the belief. The belief is assented as a self-evident truth, i.e., its truth is evident by my seeing, a truth whose evidence is given by the mere perception of it. There can be no question then that the seeing and judging altogether makes me a believer. It would be oxymoronic to question me on a witness stand whether I saw the dog and whether it was on the mat, and then--having both questions answered affirmatively by me--to wonder independently whether I believe the dog was on the mat.

At the perceptual level, perceptual judgments can be verified perceptually immediately. Above this level, however, the more abstract judgments may not have this immediate linkage of verification. The belief, as a product of the judgment, may langish, may be tossed around in the mind, may be entertained, all without ever being assented as true or false. Or it could be assented, but assented as imaginary not as a fact of reality.

Just read any fiction, a book of fantasy or of science fiction, for example. And let us suppose that it is written in English. When you read a sentence in that book, you convert what some author had judged in her mind into a belief in your mind. You don't assent that it is true of reality. For the sake of continuing in the reading, you assent instead to grant it as virtually true in your imagination. With each new sentence you read, you integrate a new belief as best as you can (without errors, etc.) If the story is a good one, your integrations stay together coherently. If it is a poorly crafted story, if the premises are implausible, even when you grant them every poetic, scientific license; then your integration doesn't hold together. In either case, because you know the story is fictional, you don't bother to evoke your logical methods of verification with respect to reality.

By contrast, in the case of Objectivism, the nonfiction books, beginning with For the New Intellectual, purport to be about reality, i.e., to be true with respect to reality by its author. So, every sentence if it is to be understood and integrated by the rational reader, requires on his part proper belief-formation and proper verification. And, assuming that someone has grasped Objectivism correctly, there can be no gap between understanding it and being its believer.

I can see two objections against the above paragraph. Objectivism may not be true. The integrator may suspend judgment for lack of evidence.

The first objection is that perhaps Objectivism at its roots and trunk is false. But so what? Anything can be said to be false. Where is the evidence or proof? If something is false, say, "2 + 2 = 5"; its falsity can be detected during verification and integration with the rest of one's knowledge. One's responsibility remains the same: form the belief correctly, and verify the belief correctly. And if anything is found false, it is not believed.

Alternatively, the objection may amount to a demand or an assurance ahead of time that something must be known true prior to actually knowing it. This is a demand for transhuman knowledge, for the answers from the back of the textbook, before attempting to find some. The reality is such that there can be no such back-of-the-book assurance.

And even if one gets the assurance without the doing, what one gets is not knowledge. If someone gives you an answer to a test question, and if you plug that answer in the test, you may get a good grade from it, but you still don't know it. What you have is right opinion, i.e., someone else's opinion that happens to be true. Knowledge is always a first-hand personal achievement.

Now let's examine the second objection. Suppose someone who studies Objectivism encounters, say, the sentence "Axiomatic concepts are the constants of man's consciousness, the cognitive integrators that identify and thus protect its continuity." (ITOE 56) If he does not understand the sentence, if the words in the sentence don't integrate into a single thought, then the integration of the sentence into the body of thought that is being formed about Objectivism stops. Any subsequent sentence that depends on this sentence cannot be properly processed. The integration of the entire section or chapter dependent on this sentence stops. It's like a big "game pause" for this branch of Objectivism. There may be many branches of Objectivism being paused this way.

But this is as it should be. This is the proper way of understanding Objectivism or anything abstract. The improper way is to skip the sentence, to continue reading without understanding, without grasping the relevant fact, and then to make the misintegration, to incorporate errors into the body of thought. So the issue of lacking evidence for integration of a piece of Objectivism is not an insuperable impediment. One keeps at it. Once the evidence for understanding some piece is found, the overall integration resumes.

Thus, if Objectivism is true, which I think it is, and if anyone understands it, ergo he is an Objectivist.

There may be a separate objection to this claim. Mustn't an Objectivist be someone who not only understands Objectivism but also acts on that understanding? This is akin to the point that you can't eulogize a man now dead as a brave man if while alive he knew of bravery but never had the opportunity to go to battle to exhibit it?

I agree with this, but only partly due to the context. Objectivism as a systematic philosophy is an intellectual good, not a moral good. To achieve this good, one has to do intellectual work, and this is sufficient. The work to be done is in the mental grasping, which requires persistence, courage, and many other virtues. That Objectivism is a philosophy for living on earth is an element in the philosophy. But applying the philosophy to one's own life is a separate issue from understanding it.

A person's life, if he values it, is his moral good. When a person applies a philosophy to live, he can be judged morally. Ayn Rand was an Objectivist, and she applied and practiced the philosophy in her life with integrity. Alan Greenspan is an Objectivist, but he sold out his Objectivist principles. So, being intellectually an Objectivist is one thing, and having moral integrity or hypocrisy regarding it is another.

Therefore, it is impossible to be in a state of understanding Objectivism while not being an Objectivist. I do think however that the converse is possible; it is plainly evident that there are people who claim themselves to be Objectivists but who, upon speaking their thoughts, do not understand Objectivism.

[Chris Grieb]

Thom; I completely agree with your last sentence.

[BaalChatzaf]

Is it possible to understand Objectivism and not be an Objectivist? I think not.

Wrong. I understand Objectivism quite well and there are parts of it I disagree with. For example the Official Objectivist Definition of logic. Also, Objectivism applied consistently leads to the conclusion that quantum physical theories are correctly predictive purely by coincidence. Objectivism has lead Dr. Lewis Little to propose his absurd and incorrect Theory of Elementary Waves and that the Big Bang hypothesis is not only wrong (which is possible) but absurd (which it is not). That is what happens when philosophy gets in front of physics and mathematics. Shi'ite Objectivism (the kind that Rand and Peikoff expostulate) also claims mathematics is the science of quantity, which at best is only a half truth.

I go along with Objectivism to the extent that it militates against over-large government and government fiddling with the economy. I agree most passionately that self sacrifice and self-immolation is insane. My "religion" is rational self interest. Past that point, my agreement with Objectivism dwindles. I get very antsy when Shi'ite Objectivists tell me that Beethoven's Music is Evil. I also part company with Objectivists who assert that there are Moral or Ethical Facts. Morality and Ethics is a kind of convention and has, at most, a loose connection to biological and physical laws which is why there are so many working ethical systems (not just one). I also resent it when Shi'ite Objectivists damn, curse and excoriate libertarian thinking to Hell and Back. Also the Shi'ite Objectivist treatment of David Kelley (the philosopher and logician) is a disgrace.

May I offer a piece of unsolicited advice? Do not assume that disagreement with X implies not understanding X. There is not a single philosophical system in existence (so far) which is both complete and error free. Systems that have no obvious logical errors and factual errors miss stuff. Systems that claim complete validity in all modes (metaphysical, epistemological, ethical and aesthetic) are somewhere erroneous or miss out on stuff. If I were smart enough (alas, I am not) I could prove something akin to the Goedel Incompleteness Theorem for "universal" philosophical systems. I believe that any system that says too much is wrong somewhere or has missed something. But that is a belief (based on some experience) and not a fact.

Ba'al Chatzaf

[Michael Stuart Kelly]

Shi'ite Objectivism (the kind that Rand and Peikoff expostulate) also claims mathematics is the science of quantity, which at best is only a half truth.

Bob,

Science of measurement, not science of quantity.

From ITOE, "Cognition and Measurement," p. 7.

Mathematics is the science of measurement.

All quantities can be measurements if used as a standard for such. Not all measurements are quantities, especially ordinal measurements, which can exist in any quantity. Math reflects this perfectly.

Actually it is imprecise to say that about quantity if quantitative relationships are considered, i.e., "bigger than," "smaller than," etc. The above statement is more precise as "Not all measurements are [fixed] quantities..."

In the "bigger than," "smaller than" sense, math does deal with quantities, since some quantity must be present to be compared to another.

English is a poor language for these things at times since the same word can mean so many different things.

Michael

[BaalChatzaf]

Shi'ite Objectivism (the kind that Rand and Peikoff expostulate) also claims mathematics is the science of quantity, which at best is only a half truth.

Bob,

Science of measurement, not science of quantity.

Still incorrect. There are branches of mathematics in which measurement (explicit or omitted) does not enter. For example category theory. Another example is abstract set theory. No measurements, no quantities.

The minimal requirement for a system of measurement is the existence of a partial ordering on the elements of the system, a kind of comparison. In the theory of groups there are groups which are not partially ordered.

Rand's error is understandable. Historically mathematics originated with counting separate objects and measuring length, area and volume. That is the -historical- origin of mathematics but not its essence.

The most general description of mathematics is the science/art/discipline of abstract structures.

Ba'al Chatzaf

Edited May 2, 2009 by BaalChatzaf

[Michael Stuart Kelly]

Bob,

Do you have any idea what Rand means by "measurement"?

You didn't about math until just now when I corrected you...

But the one absolute you hold is that Rand is wrong, as you often preach. That comes before any fact, irrespective of what that fact is. Your last mistake is a good example. You left no doubt that you believe Rand was wrong, yet you were incorrect in stating her idea (as if fact were a trifling matter in face of the overwhelmingly obvious truth of Rand's wrongness).

I wonder how someone can be so sure something is wrong when they don't even know what it s.

That's not a good standard.

Facts are facts and will not change with opinions. Knowing them correctly should come before any value judgments. That's my standard.

I'm just sayin'...

Michael

(Edit: Our posts crossed. You are close about measurement, but obviously not from reading Rand. Your comments on measurement appear as coming from your own figuring out what to say.)

[BaalChatzaf]

Bob,

Do you have any idea what Rand means by "measurement"?

Measurement is associating quantities with objects, for the purpose of comparison and ordering them. What do you think measurement is?

The basic quantity is cardinality, the next is rank, as in a well ordered set.

Rand's comments on mathematics are bounded by her knowledge of same. I read somewhere that she got as far as algebra.

Ba'al Chatzaf

[Michael Stuart Kelly]

Bob,

Here, let me do some more homework for you. ITOE, "Cognition and Measurement," p. 7:

Measurement is the identification of a relationship—a quantitative relationship established by means of a standard that serves as a unit.

In this sense, you need the following minimum requirements:

1. Two things (physical or abstract).

2. One common aspect of those two things (which you have to isolate by abstraction, i.e., imagining what it would be like as a thing in itself, but observing that both original things have it).

3. A delimiting of that aspect into a standard that can be abstractly expanded or diminished (i.e., imagined).

4. The abstract establishment of that standard as a unit as if the unit were a thing in itself.

5. Comparison of the two original things according to this new abstract thing (the unit-standard).

That's the absolute minimum and this never changes no matter how complex a measurement gets.

According to Rand, measurement is comparative relationship according to an abstracted standard just as math is an abstract method of organizing such relationships.

Michael

[tjohnson]

I think defining mathematics as the science of measurement is not a very good definition. I would describe it as the language of exact relations. It is not a science in any event - there is no experimenting done in mathematics. Surveying is a science of measurement, for example.

[Michael Stuart Kelly]

GS,

To my knowledge, Rand never defined what she meant by science. So you have to glean her meaning from her usage. I do know it is one of those words Rand sometimes used with different meanings and did not tell you when. So you have to get it from context.

I don't recall her ever restricting the concept of science to a specific method like experimentation, although "method" is a fundamental part of all her uses of the term science.

Here are two meanings of science Rand used drawn from her own words:

1. In a general sense, she used science to mean any hierarchical system of specialized knowledge developed by a specific method. She considered science to be what she called a "concept of method."

ITOE, "Concepts of Consciousness," p. 36

Concepts of method represent a large part of man's conceptual equipment. Epistemology is a science devoted to the discovery of the proper methods of acquiring and validating knowledge. Ethics is a science devoted to the discovery of the proper methods of living one's life. Medicine is a science devoted to the discovery of the proper methods of curing disease. All the applied sciences (i.e., technology) are sciences devoted to the discovery of methods.

Even grammar becomes a science in that meaning.

ITOE, "Concepts of Consciousness," p. 37

Grammar is a science dealing with the formulation of the proper methods of verbal expression and communication, i.e., the methods of organizing words (concepts) into sentences. Grammar pertains to the actions of consciousness, and involves a number of special concepts—such as conjunctions, which are concepts denoting relationships among thoughts ("and," "but," "or," etc.). These concepts are formed by retaining the distinguishing characteristics of the relationship and omitting the particular thoughts involved.

At other times, she distinguished science from philosophy. Here is her conceptual daisy-chain:

ITOE, "The Cognitive Role of Concepts," P. 74

Philosophy is the foundation of science; epistemology is the foundation of philosophy. It is with a new approach to epistemology that the rebirth of philosophy has to begin.

In all of Rand's writing, epistemology plays a much more fundamental role in philosophy than metaphysics. She essentially leaves learning about metaphysics to science, which needs to use cognitive methods based on epistemology to be valid.

The good part about science is that it uses the law of identity to validate the scientific method, whether the scientists own up to this or not. Even Popper's falsification principle is based on the law of identity (which is the grounds for non-contradiction when applied to logic in Objectivism—noting that the "system of logic" itself is an existent with a specific identity that cannot be contradicted on the very basic level). The law of identity is powerful stuff when applied to knowledge, scientific experiments and hi-tech production. So despite Rand's dire warnings about the collapse of science, instead we have the Information Revolution in full swing and all of the wondrous devices, drugs, food, etc. of modern living. (There is also crap, but the crap doesn't negate the existence of the wonderful stuff that did not exist in times past.)

Here is an interesting passage from her ITOE workshops.

ITOE, pp. 292-293

You cannot say philosophically what conditions you will ascribe to that which is not known. We cannot know by what means we will grasp something not known today. A hundred years ago you couldn't have conceived of the cloud chamber, the first instrument by which scientists could observe atoms simply by observing their effects on something. You couldn't have made the rule that unless you can touch, see, smell, and measure a given entity with a ruler, it cannot exist. That would have been crude materialism of some kind. You couldn't, a hundred years ago, have prescribed the means by which you would discover twentieth-century knowledge. And yet in making any kind of conclusions about the ultimate stuff of the universe, you are necessarily committing that error. You are prescribing conditions of what something not known to you now has to be.

The important thing here is this. You cannot say that you would define an atom by means of its charge, or that you would look further, or what you would do, because you have no way of knowing in what form you will become aware of that primary stuff. It might be through ten different instruments, and the interaction of one upon another, which would only tell you how you became aware of it. You wouldn't yet have defined it, metaphysically. All you could say is, "It is a something, which I discovered by the following method."

The only thing that concerns philosophy is that we can say: whatever it is, it will have to be what it is, and no contradictions claimed about it will be valid—as for instance, the current theories about a particle that goes from one place to another without crossing the places in between. Now you see that is metaphysically impossible, and you don't have to be a scientist to know that. A philosopher can tell you without ever entering a laboratory that that is not possible. But for a philosopher to attempt to define what kind of particle it has to be, or how we will determine its properties, that is unwarranted and Rationalistic. That is the province of science, not philosophy.

You see it isn't the job of philosophy to tell us what exists, it's only to tell us what has to be true of everything that exists [identity] and what are the rules by which you can claim knowledge. And in regard to the constituent elements of the universe, all we can say is that they would have to have identity. That we can prove. Any other conclusions we cannot draw philosophically.

Notice that she stated, "You wouldn't yet have defined it, metaphysically." She is talking about science doing the metaphysical defining, not philosophy.

Also notice that she talks about philosophy proving identity. This is done by direct experience, abstracting the fundamental axioms, and noticing that we need to use the fundamental axioms in order to negate them (i.e., imagine some other kind of direct experience).

Going back to the first meaning of science, she talks many times about the "science of epistemology."

This makes her writing very challenging to understand at times.

Michael

[Brant Gaede]

Understanding Objectivism requires studying it, of course, plus a logical, rational conceptual consciousness--courage, honesty and integrity. But it's not a package deal. The premise that Objectivism is complete and non-controversial and not tentative in all respects amongst those who have studied and properly understand it, and as such is a fully integrated ready to go philosophy, is self-contradictory.

Absolutism as an implicit if not explicit tenant of Objectivism through and through, is congruent with Objectivism, the philosophy of Ayn Rand, but not Objectivism properly understood. The first idea is incompatible with science, which is the essence of the problem. In the axiomatic premises is where you properly find the absolutism of Objectivism, less so elsewhere. This is also where you find the basic absolutism of science.

OPAR essentially represents dogmatism. One could give Ayn Rand something of a pass on this as she created the philosophy and had to defend her views against a hostile culture, not Leonard Peikoff and his ilk. OPAR should have been titled OPLP.

--Brant

Edited May 2, 2009 by Brant Gaede

[Rich Engle]

So, what the initial post implies is Objectivism is the only, most perfect-est way?

Mmmm...not so much.

What if you don't sign up? Sounds like you're pretty much screwed.

And, you will have trouble playing nicely with others in the pool.

[Selene]

Fuck em....

I'll swim in the ocean, lake, river, or stream of my choice and consciousness.

Damn now that sounds soooo objectivist, libertarian rushing to anarcho-capitalism [utopia].

Ah well.

Onward marching objectivists! To the barricades! "Aim small, miss small."

Adam

Edited May 3, 2009 by Selene

[BaalChatzaf]

Bob,

Here, let me do some more homework for you. ITOE, "Cognition and Measurement," p. 7:

Measurement is the identification of a relationship—a quantitative relationship established by means of a standard that serves as a unit.

In this sense, you need the following minimum requirements:

And there are branches of mathematics in which there are no quantitative relationships. For example, category theory. Rand missed on mathematics. That is because she barely knew any mathematics.

Mathematics is primarily about abstract forms and structures and not about quantity. There are same parts of mathematics that deal with quantity and there are parts of mathematics which do not. So there is nothing inherently quantitative about mathematics, qua mathematics.

Ba'al Chatzaf

[Alfonso Jones]

Bob,

Here, let me do some more homework for you. ITOE, "Cognition and Measurement," p. 7:

Measurement is the identification of a relationship—a quantitative relationship established by means of a standard that serves as a unit.

In this sense, you need the following minimum requirements:

And there are branches of mathematics in which there are no quantitative relationships. For example, category theory. Rand missed on mathematics. That is because she barely knew any mathematics.

Mathematics is primarily about abstract forms and structures and not about quantity. There are same parts of mathematics that deal with quantity and there are parts of mathematics which do not. So there is nothing inherently quantitative about mathematics, qua mathematics.

Ba'al Chatzaf

My caution: Watch out when an Objectivist starts speaking authoritatively about Physics or Mathematics. Most of the time they turn out to have extremely limited mathematics education - - - no graduate degrees in Math, Physics or fields of philosophy with stress on mathematical logic (I turned down an option of a scholarship I had been offered to do graduate studies at UCLA, with aim at studying under Alonzo Church).

Bill P

[Michael Stuart Kelly]

And there are branches of mathematics in which there are no quantitative relationships. For example, category theory.

Bob,

You keep harping on this, so I looked it up. To be honest, to fully wrap my mind around groupoids, functors, morphisms, topology, and so forth, I need to to apply more focused study than my time permits right now. But some things did stand out to me:

Whenever you have a category, you have a quantitative relationship: more than one according to a standard.

Whenever you have a set, you have a quantitative relationship: more than one according to a standard.

Whenever you have mapping, you have physical quantitative relationships, even if they are morphisms compared to a standard.

Whenever you have anything fundamental, you have a quantitative relationship: an ordinal "this is more important than that according to X standard," and that means at least 2 being compared and a division to set the standard.

I looked up "function" in Wikipedia. Here is how the article starts:

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced.

Two quantities? Dependence Heh. Sounds like a relationship to me.

Here is the start of the article on morphism:

In mathematics, a morphism is an abstraction derived from structure-preserving mappings between two mathematical structures.

I see the number two there. That is a quantity and an abstraction is a relationship.

Here is category theory:

In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects linked in diagrams by morphisms or arrows.

Abstracts from sets and functions? You mean abstracts from quantities? As in "establishes a relationship"? I won't even go into the quantitative relationships involved in mathematical structures that I looked up because this Master of the Obvious stuff is wearisome.

Everywhere I read on category theory, I saw quantitative relationships. Your opinion that category theory does not involve quantitative relationships did not convince me. I admit that because of my lack of training in this, the quantities I saw were on a primary level, usually "more than one" and things like that. But I don't need to see more to know that I saw quantities and relationships between them being formally structured.

It would be easier if you just said you think Rand was a dummy regardless of any facts. You are entitled to your opinion. There is no need to try to force facts that don't fit to fit your opinion.

Michael

[Alfonso Jones]

And there are branches of mathematics in which there are no quantitative relationships. For example, category theory.

Bob,

You keep harping on this, so I looked it up. To be honest, to fully wrap my mind around groupoids, functors, morphisms, topology, and so forth, I need to to apply more focused study than my time permits right now. But some things did stand out to me:

(snip)

Everywhere I read on category theory, I saw quantitative relationships. Your opinion that category theory does not involve quantitative relationships did not convince me. I admit that because of my lack of training in this, the quantities I saw were on a primary level, usually "more than one" and things like that. But I don't need to see more to know that I saw quantities and relationships between them being formally structured.

It would be easier if you just said you think Rand was a dummy regardless of any facts. You are entitled to your opinion. There is no need to try to force facts that don't fit to fit your opinion.

Michael

Some simple facts:

1) Rand didn't do substantial study in mathematics. I know she took some classes. But there is no evidence to suggest it was anything advanced.

2) She was not a dummy. The facts in evidence do not support that contention, if someone is making it. If she had maintained that she had a profound understanding of the "state of the art" in some field of advanced (meaning, research level!) mathematics as of, say, 1980, then we would have to seriously question whether she knew what that state was. But as far as I know she never made any such a claim. Has someone produced such a claim by Rand?

Now, I know that some idealize Rand to such a degree that they assume that if she "took classes" in mathematics, then she must have been the most brilliant one to ever to do so, and must have immediately leapfrogged to the state of the art in mathematical research in each and every field of mathematics. I have no reason to believe you are such a person, Michael - and much reason to believe that you are not. I am not. My profound respect and admiration for Rand's intellect and what she accomplished is not somehow lessened by me acknowledging that she was not the most knowledgeable person in every single field. At the school where I teach we have about 60 faculty. I don't know a one of them whose knowledge encompasses that of all the others - - - and am confident there is not a single person in the world who would so qualify. So what?

Some want to take the fact that Rand was not all-knowing and somehow twist that into some damning thing about her. Others feel (and I do mean FEEL!) that they are not being loyal to her if they do not maintain that she was the most brilliant human to ever live in every single field. Both are twistings of the observable facts, in attempted service of a predetermined evaluation of Rand.

I don't think you are guilty of this, Michael, not at all. I think some of Rand's critics posting on this board verge on the viewpoint of the first group.

Time to read Eric Hoffer's "The True Believer" again...

Bill P

[BaalChatzaf]

Everywhere I read on category theory, I saw quantitative relationships. Your opinion that category theory does not involve quantitative relationships did not convince me. I admit that because of my lack of training in this, the quantities I saw were on a primary level, usually "more than one" and things like that. But I don't need to see more to know that I saw quantities and relationships between them being formally structured.

It would be easier if you just said you think Rand was a dummy regardless of any facts. You are entitled to your opinion. There is no need to try to force facts that don't fit to fit your opinion.

Michael

It would be easier, but it would not be true. Rand was no dummy (i.e. stupid). She was ignorant of some fields, including mathematics and physics. We are all born ignorant.

Nowhere in the definition of a category do you see a quantity. There are only two kinds things in categories. Objects and morphs. Read any textbook on the subject. Categorical structures can be applied to number systems (certain types of groups, rings, fields) but need not be.

As to functions, a function is a relation between sets. Let A and B be sets. Then the relation R contained in AxB (the cartesian product of A and B, the set ordered pairs from A and B in that order) is a function from A into be if and only if R(x,y1) and R(x,y2) implies y1 = y2 and for x in A there exists y in B such that R(x,y). y1 = y2 is not numerical identity. It is just plain identity. It says y1 and y2 are the same element. The elements of the sets A and B need not be quantities. That is A and B need not be partially ordered, need not be linearly ordered (like the points on a line) nor dense in any ordering nor a compact linearly ordered topological space. In short -- NO QUANTITIES in the definition. Therefore no measurement. Mathematics is about abstract structures and relationships. Some of which may be numeric and quantitative, others not.

Yes indeed. Functions may map quantities to quantities. They also may map daffodils to daffodils too.

Michael. I recommend you stick to music.

Ba'al Chatzaf

Edited May 4, 2009 by BaalChatzaf

[tjohnson]

If you look closely I think you will find that mathematics grew out of counting and measurement, but now it is far more. I get the feeling that Rand maintained this view of mathematics which is an extremely common one even today. I think it is a conceptually difficult task to make the break from applied to pure mathematics - I know I didn't until my 3rd year studying mathematics at university. Just take group theory for example. it seems quite obvious that the idea of a commutative group came from arithmetic but it was generalized and formalized beyond that in group theory to the point where it no longer applies only to numbers.

[BaalChatzaf]

If you look closely I think you will find that mathematics grew out of counting and measurement, but now it is far more.

Correct.

Historically mathematics addressed the questions; how many and how much. Specifically it was used for counting distinct objects and measuring the size of other objects such as plots of land (areas and lengths) and capacities of jugs (volumes). Now-a-days mathematics addresses many more kinds of situations and asks many more different sorts of questions; such has how related, how true, how provable, how alike and of what kind. Mathematics also began cohabiting with logic in the works of Leibniz and were joined in matrimony by Boole and Frege.

To be sure, the parts of mathematics used in physics and engineering is still rooted in and based on quantities (hence measurements). Quantitative mathematics is indispensable for engineering and physics. Without high powered math physics would be stuck at the level of qualitative judgments about the world (bright, dull, hard, soft, hot, cold, dense, rare etc) which in the time of Aristotle were not quantified in any effective way. Humans have dealt with color since forever, but only understood color quantitatively since Maxwell identified color with wave frequency in the middle 19th century. Prior to Maxwell, colors were not measured (they were only compared). Since Maxwell number can be assigned to color.

Ba'al Chatzaf

Edited May 4, 2009 by BaalChatzaf

[Christopher]

Thom,

I'm having a bit of trouble thinking clearly today (headache), but looking over your post, here's what I'd have to ask:

1. Is being something a thought process or an action process? If being an Objectivist is an action process, then it doesn't matter what you think, it matters how you act. Both Rand and N.Branden were always action-centered when it came down to it.

2. If by understanding Objectivism you become an Objectivist, then doesn't that extrapolate to mean that understanding any other philosophical positions, you become a follower of those positions too? If I truly grasp a religion that is founded on principles of logic and epistemology, would I then become a religious follower by default? If not... does it mean I can never grasp anything without becoming identified to and defined by it?

Chris

[Michael Stuart Kelly]

Nowhere in the definition of a category do you see a quantity. There are only two kinds things in categories. Objects and morphs.

Bob,

Objects (plural) and morphs (plural)?

As in more than one?

Sorry, but more than one is a quantity. It is at least two.

Using a plural and eliminating the idea of "more than one" is a stolen concept. In other words, using plurals as conceptual foundations (objects and morphs) and saying there is no quantity is a stolen concept.

Even if there is only one existent, the moment you make it a category or set, you allow for the possibility that if another existent like that pops up somewhere, it will belong to that category or set. Then there will be two. In other words, you have an imagined quantity of more than one.

This cuts right to the core of how Rand applied algebra to concept formation.

I see what I see and just because you have studied math (and some other topics) in depth does not alter what I see. You can be the world's greatest genius on round, but if you tell me my round ball is actually square, I will not believe you. What's more, I will hold your opinions based on square roundness in discredit. I can respect your learning, but I respect facts more. There isn't even a contest. And that goes for everybody.

So you want me to stick to music? Heh.

As in: my mind is incapable of understanding math? Double heh.

That's a good sign, actually. It means my questioning is hitting the mark and causing discomfort.

It should, too. When pontificating instead of rational explanations are presented, like you are prone to do whenever you wish to say Rand was ignorant about this or that, it should be challenged. (btw - I agree Rand was not deeply studied in math. I do not agree that this automatically makes her thoughts on the subject invalid. Only facts contrary to her ideas can do that.)

I will not take you on faith and I think it is demeaning for you when you request and/or demand it (however indirectly). You can give me your opinion of you all day long and it will not make me think differently. But if you can explain to me why more than one is not a quantity, an unknown quantity but still a quantity—now that would cause me to take my hat off to you. Simply pontificating about this and that and how learned you are while ignoring the issue I raise will not.

I check all premises, especially when they run counter to common sense.

Michael

[DavidMcK]

It should be added too that Rand wasn't best at detailed comprehensive expositions of philosophical problems (a la Aristotle) but at essentialising the problem. She seemed to regard the more detailed and complete exposition to be grunt work, the hard part was getting at the essence of the problem. Notice that she would simply state that people made choices but it wasn't until Nathaniel Branden came along and offered his more detailed exposition of volitional consciousness that it was just an assertion. The true philosophers love fine distinctions, arguing over the best definition, subtle arguments and so on and sometimes never actually come to the bottom line. The bottom line was just about all that mattered with Rand, and what we need is someone who can do both.

[merjet]

Now-a-days mathematics addresses many more kinds of situations and asks many more different sorts of questions; such has how related, how true, how provable, how alike and of what kind.

Does your definition of mathematics amount to "whatever mathematicians do"? A mathematician could use Aristotle's syllogisms to deal with sets whose members could be numbers. Does that make Aristotle's term logic a part of mathematics?

Whenever you have a category, you have a quantitative relationship: more than one according to a standard.

Whenever you have a set, you have a quantitative relationship: more than one according to a standard.

Whenever you have mapping, you have physical quantitative relationships, even if they are morphisms compared to a standard.

Whenever you have anything fundamental, you have a quantitative relationship: an ordinal "this is more important than that according to X standard," and that means at least 2 being compared and a division to set the standard.

I'm glad to see "quantitative" here rather than "mathematical" or "measurable." The former does not imply the latter. That I may like one movie more than another, a kind of quantifying, does make my preference a part of mathematics. Sewing numbers on football jerseys is not mathematics, either. If a lion can see that one gnu is running slower than another, that does not mean the lion is doing math.

Sorry, but more than one is a quantity. It is at least two.

Using a plural and eliminating the idea of "more than one" is a stolen concept. In other words, using plurals as conceptual foundations (objects and morphs) and saying there is no quantity is a stolen concept.

Even if there is only one existent, the moment you make it a category or set, you allow for the possibility that if another existent like that pops up somewhere, it will belong to that category or set. Then there will be two. In other words, you have an imagined quantity of more than one.

Whoop-de-do. If a mother bear knows she has more than one cub, is she doing math?

[Selene]

Merlin:

These threads make my hair hurt.

No, but...

"...knows she..." the mother bear may "see" two cubs and her hard wiring will attempt to produce more for the two she sees and smells, but she does not "know" the difference and that there would be a 22nd if she could plan and produce twenty more.

Awareness of a flame and avoiding it because it hurts is different from image - ing a town with 50 places for that fire.

Adam