Consider a square. Look at a side. Now look at the diagonal. The diagonal is clearly longer than the side.

What common unit is omitted in comparing the diagonal of a square to its side?

Answer: None. The diagonal and the side have no common unit of measure.

Ba'al Chatzaf

Bob,

Then how do you know one is longer?



(I don't even know why I bother. I'm done... )

Michael

From Euclid's axioms. One can prove that the longest side of a triangle lies opposite the largest angle of the triangle. In the case of the square you have a 45-45-90 degress right triangle and the diagonal is opposite the 90 degree angle (the corner angle). In general the way you prove line segment A is shorter than line segment B (whether or not they are co-measurable) is to construct a line segment A' lying entirely B where A' is derived from A by constructing equilateral triangles. I think that is Prop 3 in Book I. See Heath's translation of Euclid's Elements.

The existence of a common unit is not necessary (and in general, not possible) to compare lengths of line segments within Euclid's geometry.

If you are upset with the non co-measurement of the diagonal and the side of a square, think of how Pythagoras must have felt, when one of his students discovered this disconcerting fact. The story goes (I think it is just a story) that this student was murdered to keep news of his finding from being spread far and wide. The bottom line (sic!) is that ratios of integers (rational numbers) are not sufficient to deal with measurement. Which is why we have real numbers. And so it goes.

Ba'al Chatzaf

Bob,

You have a weird definition of unit of measure.

One line is bigger than the other. There are exactly two common units of measurement right there. Actually there are three if you want to use the stub left over.

How you quantify all this is another matter, but you can certainly measure both according to the same standard. If you can use it on both, it is common to both.

You can't say, there is no common unit of measurement because the comparison doesn't add up.

How I would prove one line is longer than another and in what quantity is take a string... then... er... "measure" one of the lines by making it the exact length (1 = 1) and then line that up with the other line. It will be less than that one or more. You have a fraction right there. This is really basic. Why try to talk your way around a basic with sophistication?

Are you bothered because the math of one standard does not work exactly the same as for the other and there is a piece left over?

(Why am I doing this? Apparently people are getting murdered over it... )

Michael

u is a unit of measure for a line segment x if and only if the length u divides the length x an integral number of times.

Take out a common ruler. Do you see all those intervals a 1/16 or 1/32 of an inch long? Sure you do. 1/16 of an inch is the unit of measure ment for that rules.

Now consider the diagonal of a square d and its side s. If there were a common unit u then u would go into d an integral number of times, say m. u would go into s an integral number of times, say n.

The ratio of the length of d to the length of s is m:n. But also notice d is the diagonal of the square (by hypothesis) so d^2 = s^2 + s^2 (Pythagoras theorem). So that d^2/s^2 = (m/n)^2, But d^2/s^2 = 2, hence (m/n)^2 = 2. We may assume without loss of generality that m and n have only 1 as a common divisor. Do a little algebra and get m^2 = 2*n^2. Since m^2 is even (a multple of 2) it follows that m is also even, hence m = 2^k for some integer k. Going back to the equation we get 4*k^2 = 2*n^2. Divide both sides by 2 and get 2^k^2 = n^2. But this implies that n is also even hence 2 divides both m and n. But we assumed that m and n have no other common divisor than 1. Contradiction. Therefore there exists no such integers m, n for which the presumed unit u divides d m times and s n times. Hence no common unit.

Q.E.D.

I can tell that you are upset. Think of how Pythagoras must have felt when he got this bad news. He believed all linear lengths were co-measurable. But he was wrong. Pythagoras believed in unit omission, but he was wrong.

Ba'al Chatzaf

Bob,

Really? I was right. That's a weird definition of unit of measurement.

The length used as a standard of measurement, whether the small one or large one, can and must be set by humans, not by an accident. You are leaving out the really fundamental part. "u" is a measurement of space in general, not just the line. Space is much bigger than your line and contains your line within it. There is no "u" measurement of a line that does not measure the rest of space.

But even on a metaphysical level, a violin string, for instance, will issue overtones according to nodes starting at exactly one half the length of the string (defined by the pressure points at each end).

So even if metaphysics boiled down to a line with a beginning, middle and end, I still don't see how I could agree with you. But space is not a line. It is infinite and eternal, at least from our human perspective.

That is, unless you do some tricks with math. But those who claim things like the beginning of the universe based on math projections are also quick to claim that math is not based on reality. I find that an odd form of reasoning.

No, I'm not upset, at least not with you. I'm exasperated at me for letting myself get into a discussion that promises to go nowhere. I am behind in my work.



Michael

I'm with you, Ba'al, not even all lengths are commensurable, as every high-school student knows (or should know.)

Universal commensurability is not possible. (That doesn't create a problem for Objectivist epistemology, though.) I'd go on, but this is science, etc., and going on is epistemology...

--Mindy

I disagree. The -fact- of non comeasurability of length blows the notion of measurement omission to smithereens. One will have to look elsewhere to find out how we conceptualize.

Ba'al Chatzaf

Just a question from a person who left high-school long ago.

Other than infinity, which lengths cannot be measured? I have always thought length was a standard of measurement. That's what any online dictionary will tell you.

To me, saying length cannot be measured is a stolen concept, since length is a form of measurement.

That fact kinda blows some affirmations to smithereens.



Michael

The normal measures; length, area, volume, hypervolume are measured by real numbers. However real numbers require a limiting process to define.

Start with the integers. Now consider ratios of integers, the so-called rational numbers. It turns out that lengths of Euclidean lines cannot be measured (in general) with rational numbers. So what is required? Infinite sequences of rational numbers which converge to a real (but non-rational) limit.

Length are are rational numbers or non-rational reals.

Measurement means (literally) to apply a unit length an integral and finite number of times to a given length. It has been known for over 2000 years that the there is no such unit length that will divide the side of a square and its diagonal an integeral number of times. The square root of two was the first number to be proved non-rational.

Measurable lengths are a proper subset of general lengths (those given by real numbers).

So I give you the side of a square and its diagonal and I ask you what is an omitted measurement applicable to both? Do you have an answer?

Ba'al Chatzaf

Bob,

You just made a salad of concepts. Do you understand what measurement omission means in concept formation? Your comments show clearly that you are talking about something else.

You certainly did not answer my doubt, which is how a standard of measure cannot be measured. You even called this a fact: "The -fact- of non comeasurability of length...".

How can red not be a color? How can a goose not be a bird?

How can length not be a measurement when it is defined as a type of measurement? You even stated: "The normal measures; length..."

I don't understand how A can be A and not A. I use a different standard of logic.

Michael

In general length requires an infinite process to define, to with the convergence of a sequence of rational numbers to an irrational and real limit. That is not what Rand hand in mind.

By the way, what you call word salad is mathematical precision. Apparently to you are complete stranger to mathematical precision otherwise you would not have confused it with a jumble of words. There is a realm of knowledge to which you are a stranger. Either ignore it or enter it with the work necessary to do so, but do not denigrate it.

I am tone deaf and musically illiterate and I cannot carry a tune in a bushel basket, but I do not mock or denigrate music.

Ba'al Chatzaf

It's a matter of "A and A'." From the Merriam-Webster Online Dictionary:

length - 1 a: the longer or longest dimension of an object, b: a measured distance or dimension

The first refers to an attribute of an object per se. The second refers to that attribute in relation to a measuring tool such as a ruler.

Bob,

I wasn't mocking or denigrating.

You simply talked about one thing and said it disproved something else entirely. Blew it to smithereens you said. Heh. That's quite a lot of bluster, so a minimum requirement to take that seriously is for you to be talking about what you are disproving. But you were not.

All this leads me to believe you do not understand what measurement omission means in Objectivist concept formation and are going on the term as you understand it outside of context.

All measurement omission means in Objectivist concept formation is that a measurement can exist in any quantity in the concept, but no quantity is specified. In other words, to establish a concept, a measurement standard is stipulated but not used. Stipulating the standard helps define the concept, not any specific use of the standard.

After the standard is stipulated, math can be applied but is not at that moment.

Many things are measured in a concept, including importance of a characteristic, and many different standards chosen. Measurements can be also be cardinal or ordinal. In this system, even things like love can be measured, as Rand stated explicitly in ITOE.

None of that is what you have been talking about or blowing to smithereens.

And you still not have explained how a standard of measurement cannot be measured, if you really believe that like you said.

I hold that consistency is important.

Michael

Merlin,

Of course I agree that a word can have more than one meaning, but they were talking specifically about measurement.

They were talking about length that cannot be measured. Something any high-school student should know.

At the best, this is an attribute for which a standard of measurement cannot be established.

I finished high-school, but I have no idea what that is.

Michael

Yes, I know your dispute is with Bob. I was again pointing out how Rand confounded the two meanings in ITOE and assumed knowing the first meaning implies knowing the second meaning.

Quite so. Ok, consider the straight line connecting the point (x0, y0) to (x1,y1). The length of that line is sqrt ((x1 -x0)^2 + (y1 -y0)^2), a number that is in general not rational and cannot be specified (in general) by a finite decimal representation of a number. Now I ask you again what measurement is omitted from the lengths (x1 - x0) and (y1 - y0). I keep asking, but you keep on not answering. If it turns out that (y1-y0)/(x1-x0) is the ratio of two integers m and n, the there exists a unit length that divides (y1-y0) m times and (x1-x0) n times. but if the quotient (y1-y0)/(x1-x0) is not such a ratio then what can we say?

It is unfortunate that Rand did not no much in the way of mathematics. If she had, she would not have come up with measurement omission.

Ba'al Chatzaf

The mathematical theory of numbers is very different from everyday intuitive understanding. The foundation of the real numbers is necessary for building integral and differential calculus and has very little to do with measuring the length of something. If you have a right triangle with sides=1 and you measure the diagonal with your ruler you will actually be estimating dimensions and you might say the diagonal is 1.414 in length, depending on what you read on your measuring device. Measuring physical objects is not the same as calculating theoretical dimensions in pure mathematics. Of course we know the real (mathematical) dimensions are 1,1, and sqrt(2) but the sqrt(2) actually represents an infinite process that we are free to terminate whenever we want to.

Aux Contraire. To define length precisely one needs integral calculus.

Ba'al Chatzaf

Many rational numbers cannot be specified by a finite decimal representation either. For example, 1/3 is 0.333333333....


If you gnu how to spell, I'd agree even more.

I don't follow, could you be more specific? Seems to me you only need a metric space to define length.

That works for straight line segments. To do the same for curves you need an integral. Pythagoras' theorem as at the base for both the length of straight line segment and length of curves.

See:

http://en.wikipedia.org/wiki/Curve_length

Ba'al Chatzaf

I agree that it "blows" measurement omission! I'm just saying we don't need "measurement omission" to "validate" concept-formation.
Mindy

Bob,

You keep on asking and challenging about what type of measurement, not that measurement does not exist. The type of measurement is not the issue if you want to blow Rand's process of measurement omission to smithereens. And so far you haven't come closer than an unfounded opinion.

Look at it this way (to oversimplify). The existence of measurement is a metaphysical issue. Using the different types of measurement is a scientific one. The standards of measurement (length, intensity, importance, etc.) pertain to both.

Just because one kind of measurement does not work, that does not mean another kind of measurement cannot work, i.e., that measurement per se does not exist. You can't measure a curve by a straight line? OK. Then measure it with curve units.

Note that for Rand to omit measurement, it had to exist in the first place.

Michael

What kind of measurements are omitted when we form conjunctions, or form concepts such as "justice"? What concepts are omitted when we learn how to ride a bike?

I'm not surprised that Objectivist discussions of this are generally limited to chairs and tables.

[EDIT: I haven't been following this thread, so I hope my post isn't off-topic.]

-NEIL

Mindy,

You have expressed this opinion twice, but I see the same error that Bob is making, i.e., saying one kind of measurement does not work for a specific case, and insinuating that this means no measurement at all is possible for that case. That is the only premise I see in your position so far in trying to prove that measurement omission is an invalid idea in concept formation and that premise is a false one.

Do you have another premise? I am curious.

Michael

Neil,

Oodles. Go the other way.

What standards of measurement do you think are present in the concept "justice"? Or do you think there are no standards that can serve as basis for comparison? That would make "justice" arbitrary, no? Ditto for riding bikes (which is not exactly concept formation), except you would fall all the time trying to be arbitrary on essential moves that were not gaged correctly.

Reality is not as forgiving as our speculations are.

Michael

Michael,

The theory of measurement omission says that all differences are measurements. I don't believe that that can be sustained. Qualia, qualities as experienced, cannot be reduced to quantities (measurements) of something else. This is, as you know, an involved issue. I have three theses to propose to deal with that; with the problem that Rand makes conceptual meaning both abstract and determinate; and with the problem that sentences that predicate an omitted measurement would fall through the cracks in terms of Rand/Peikoff's solution to the A/S dichotomy.
I'd like very much to present these ideas, but I think a blog might be more appropriate, because it can be dedicated to that subject...

I started to write such a blog, but I can't get access to the blog I set up--and haven't been able to get through to the right person to show me what I did wrong. BTW, your in-box is full, won't take any more PMs.

--Mindy

Mindy,

This is another related issue. I happen to agree with you on this point and this is one of the weaknesses of the measurement omission theory. It bears fleshing out.

For the record, I do not agree with many of the critics I have read of the measurement omission theory since I adhere in general terms to Rand's idea of comparison against a set standard being a form of measurement and this has been a point they disagree with when things get more complex. But I agree perfectly with this business of difference in kind (or qualia as it is experienced).

I still don't understand your earlier part about some kinds of length not being measurable.

As to the blog, I suggest you open a thread here on the forum with your theses (which I didn't quite understand from your description) and copy your work to your blog for easy reference. That way your ideas will get better traffic, but the important work will be easy to find if many discussions ensue.

Michael

The issue of qualia is solved by recognizing that what is omitted during abstraction doesn't have to be limited to measurements. The advantage of omitting nothing but measurements is that what is measured is not omitted. Thus, Rand says a pencil must have some length but may have any length (paraphrased.) That a pencil has a length is not omitted. Exactly what length a given pencil has is omitted.

I suppose it is common knowledge that the importance of saying that what is omitted in forming a concept is "just measurements" is that that makes all true statements "Analytic." And if all true statements are analytic, there is no analytic/synthetic dichotomy, so certainty isn't limited to trivial statements such as, "A bachelor is an unmarried man."

(I believe that solving this problem (A/S dichotomy) is the chief aim of Rand's theory of concept-formation and conceptual meaning.)

My solution: The relation between measurements and the differences they document has a broader categorization. In the pencil example, the measurements are variations on the variable, length. The different colors of flowers are variations on the variable, color. "Male" and "female" are variations on the variable, "sex." Logically, anything that can be described as measurements of a characteristic can also be described as variations on a variable. Notice that the structure remains the same--the differences can be omitted while the characteristic is retained: the variations are omitted while the variable is retained.

The advantage in using a broader terminology, of substituting "variable" for "standard of measurement" and "variations" for "measurements," is that there is no need to interpret qualities quantitatively, as measurements. Actual measurements are in fact variations on a variable, so there is nothing lost in using the broader terminology.

--Mindy

Mindy,

I like your idea of variable very much. It fills some large holes in the theory and includes measurement under it. Very, very good thinking.

In fact, I have been groping in this direction for some time now. If you look over my past discussions of measurements, it is clear (at least to me) that I am really targeting variables without realizing it.

I am seeing the possibility of developing an epistemological method that intimately links concept formation and logic as Rand wanted, induction and deduction, and, believe it or not, top-down and bottom-up thinking.

Imagine a theory of concepts that included the ideas of non-contradiction, variables, holons (or other terminology meaning the same thing), reductionism (for lack of a better term right now), mathematics, a consistent method of arriving at fundamental characteristics, some manner of making the genus more than just the semi-arbitrary designation it presently is, and developmental psychology (for validation and maybe explaining exceptions).

I might have left something out, but this is starting to look very, very good from my view. I think the seed of something important is being planted in this idea.

EDIT: I have another thought to add to this. I do not consider the human mind to be a freak of nature, so I believe it mentally organizes information about reality in the same manner as reality exists. This is a bit different than Rand's view. At the start of ITOE, she made it clear that forms or patterns did not exist in reality, but only in the mind processing reality. She used other words, in fact, she called them "abstractions existing in reality," said Aristotle was the unfortunate father of this notion, etc. That part has always confused me.

I don't recall her ever mentioning anything else about this other than insisting that all information comes from reality via the senses. Other than that, just off the top of my head, I only remember her making her standard stand-alone proclamations (usually in the form of "man needs..." or "the nature of the mind is to..." or something like that) to describe how the mind works in epistemological terms.

Michael

If length is not measureable it's not length. But you don't have to measure all of it. Hence, infinite length even if not an infinite line. Infinity is in our heads. So is measurement. (I admit to not really knowing what I am talking about.)

--Brant

Length is surely defined, but it requires ininitary operations, such as taking the limit of an infinite sequence. Rand rejected infinite operations. The only definition of length measure consistent with Rand's restrictions is the number of times a fiduciary unit has to be repeated to match the length of a given line segment. In the case of the diagonal of a square and its side there is no such fiduciary unit, so her definition of unit omision fails.

It turns out we do wave the concept of -long- by abstracting from instances of skinny extended things such as narrow sticks and stretched threads. To get to that concept we do not need units of length omitted or not. Pull a string taut and you have long and longer from which you arrive at length comparison without units. This string is longer than that string, etc.

There are many concepts which do require unit omission. For example the concept of a dog. This is a dog and that is a dog. There is no numerical measure of dogness to omit. Rand's unit omission notion is to narrow to capture the idea of a concept.

Ba'al Chatzaf

Bob,

Where?

Michael

Mindy,

I have another thought to throw into the heap.

Rand claimed that you cannot make a concept out of a single entity, thus, as an example, a proper name is not a concept. This always struck me as strange, sort of like saying you can only have 2 on up, but never 1.

I see nothing wrong with forming a concept, i.e., a mental abstraction, of a single existent. This is one point where I believe here idea of basing concept formation on algebra pushed the math idea too far (i.e., you can't have a math operation with just 1, then equating a concept with math operation).

Michael

Mindy,

You might be interested in my article "Omissions and Measurements" here. There is also a slightly different version in JARS 7.2.


Her claim was in relation to the "problem of universals", a universal being single term or idea with multiple referents. A concept with its wider meaning can be made from only one referent. Proper names and some other concepts, e.g. "the universe", fall in the latter category, but not the former.

Merlin,

Rand wrote (ITOE, p. 9):


I do not understand this to mean that a proper name is a concept. On the contrary. I am unaware of any place she mentioned concept "with its wider meaning."

The idea of universals as you stated sheds some light on it, but still, there exists something more than quantity for a universal truth to be true. Here is one:

Me.

My existence is a universal truth and it underlies that concept.

If quantity has to be a fundament, then for me to say "me," this has to include existence, i.e., "an unlimited number of concretes of a certain kind."

To deny that "me" is a concept is to make a variation of the stolen concept. Both the underlying concepts are ignored and the identity of the entity qua concept is denied.

I find the same objection to be true of universe, which cannot exist apart from its components.

Michael

I believe the problem with abstracting from a single instance is that there is nothing to guide the separation into what is omitted and what is retained. The commonalities among different individual things of the type is normally what sets that up.

It may be that "universe," though a singular instance, demonstrates abstraction that is "longitudinal" rather than "lattitudinal." I mean by that that the universe changes over time, in terms of what is in it, while remaining at all times what encompasses everything. The identities of particular things have this sort of abstraction. You are you whether you are sitting or standing, talking or silent, etc. Your identity is abstract, omitting all the sorts of changes a person can go through over time.

That is "longitudinal abstraction" while "lattitudinal abstraction" is the usual sort of side-by-side comparison of multiple, similar things in concept-formation.

--Mindy

Also, Merlin, that link didn't work.

--Mindy

She didn't say it the way I did. However, see ITOE, p. 1: "The issue of concepts (known as "the problem of universals") is philosophy's central issue."

So I believe it should be pretty much taken for granted that when she used "concept" in the rest of the book she meant "universal", unless specifically stated to the contrary. Apparently she declined to use "universal" in order to try to disassociate herself from its traditional, historical meanings.

Mindy,

I find there to be plenty. Even Rand stated that the act of identification was based on integration and differentiation (similarities and differences). Look at the rest of existence and see what is similar and what is different. You thus have a unit of one.

But setting aside the math, doesn't holon resolve this issue very nicely?

btw - You said "single instance" and this gives a connotation of time. "Single existent" would probably be more exact. Rand even talked about entity.

Michael

Merlin,

I agree that there is more than one meaning of the term concept and that Rand's meaning was as a universal.

I need to read up on classical universals before I can discuss this properly, but, from my present state of knowledge, I do see a problem with including quantity as a fundamental characteristic.

Michael

Did you mean "do not"?

In any case, the issue is whether or not all differences among the units included in a concept (universal) are measurements (or even quantities). Rand said they were, and I disagree.


Here she did not include quantifiers. She did not literally say that it is only measurements that are omitted. But if there were anything other than measurements omitted, it would have been simple enough to say so. Moreover, per the Appendix she said:

Merlin,

If I were trying to defend a pet theory or defend Rand at all costs, I would say "do not." Since my aim is to understand correctly and arrive at the truth, I say "do." It is far more important for me to use reality as my non-negotiable standard than to use Rand's works or some pet theory I have developed.

Where people get confused with me at times is that they get Rand's meaning wrong and I say, "Rand did not mean that at all." Just because I try to correct their misunderstanding, this does not mean that I agree with Rand 100% on that point. I might or I might not, depending on what the point is. But I strongly believe if someone is going to disagree with Rand, the least they could do is make sure that what they say she means corresponds to what her works actually convey.

A case in point is with the works of a harsh critic, Bob Wallace. He blasts Rand for scapegoating and I perceive this is one of her rhetorical methods, so I have to agree with that. But when he tries to develop his arguments, he turns into a fiction writer himself and attributes meanings to her that simply are not there. He gets really nasty and snarky, too. When I point out the errors, and, ironically his own scapegoating of her, some people interpret this to mean that I support her scapegoating or deny that it exists.

That is just an example, but the process is the same in areas that are not so blatant. For instance with epistemology.

Michael

Historically, LP used her theory of concepts in his essay arguing against the A/S dichotomy. Her ITOE articles were published in July '66 - February '67; LP's A/S piece was published in May - September '67.

In part II, he writes:



Hard to say what came first. Maybe it's a chicken-and-egg thing and both her views on concepts and on the A/S dichotomy developed together. As far back as 1960, at latest, during her conversations with Hospers, she lambasted the A/S dichotomy, and she had some glimmerings back then of her views on concepts.

The two -- the theory of concepts and the strictures against the A/S dichotomy -- are definitely entwined, but I doubt that she set out with anything so deliberate as the goal of developing the theory of concepts in order to solve the A/S dichotomy.

Ellen

___

"Instance" can mean time, but that's not its first meaning, and I didn't mean time, but you saw that.

You can't "integrate" over one instance or existent, nor can you differentiate a thing from itself... since it is a singular existent, it won't have a group of similar things to be compared to. That is for the case of conceptualizing unique things, such as "universe."

A name is meant to individuate things, the opposite of grouping things, as a concept does.

As I understand it, a "holon" pertains to living and social systems...I don't know how it is being used here.

--Mindy

Mindy,

A holon is a self-contained system comprised of self-contained systems. It is also part of a larger self-contained system, but I think this doesn't have to be a requirement for the idea I have in mind.

The universe is singular, and so is the human species. Would you deny that "human species" is a concept? I don't see how it can be denied without the theory of concepts becoming so esoteric as to be useless to all but a very few.

In terms of holons, even a singular me is made up of things like kidneys, which in this case can be transplanted to other human beings, although that is not a requirement of a holon. And I belong to both the human species and the universe.

Maybe there is only one me, but there are oodles of quantities in the stuff that makes me up and in the stuff I belong to. There is no way to divorce me from those.

Even so, I think the idea of quantity in concepts needs to be relegated to one type of concept, not the whole shebang as is done in ITOE.

I even have another pertinent idea I have been mulling over: a crossover point for human experience. A human being is a thing while the human species is not. Yet human species obeys the same holonic structure as its parts. Going the other way, A human cell is a self-contained whole, but it is so much a part of us that we do not call it a thing. (A germ might, though, if it could speak.)

In thinking downwards, I see that there is a range of sizes for things to be called things, after which they are called parts. There is a lot of leeway here because one part of a big thing (like a kidney) can be much larger than a small whole thing (like a bacteria). But on a scale from subatomic to the cosmos, this is a relatively small range. Going upward, there are systems that display organization but we would not call any one of them a thing. I mentioned species. Solar system and galaxy are others.

So I see a crossover point (or range) where things are things and this point (or range) is approximately human size perception. Something like microscopic to the size of a star. Outside of this zone, things are parts on one end and loose systems on the other. Here in the middle, there is some blurring, like I mentioned with size differences, but there are some really intriguing things to think about, also, like insect swarms.

I am thinking about how to include this idea of human perception range and the metaphysical differences I mentioned (part of thing, thing and group of things) in concept formation. After all, concepts are for human beings.

Michael

Micheal, the human species does nothing and obeys nothing.

--Brant

Brant,

The human species exists. Or is it an illusion? Or maybe all human being simply turn out similar and are able to reproduce only with each other because of a cosmic coincidence?

Michael

Michael,

I'm afraid I'm not following. But I may be able to clear up one thing: I was not taking the position that "universe" or other singular things cannot be conceptualized! My distinction between "lattitudinal abstraction" and "longitudinal abstraction" was to offer a way that such things can be conceptualized though they cannot be compared to other instances. That way is through longitudinal abstraction which basically pulls out the constant aspects of a thing and omits the varying aspects. No matter what exactly exists in it, the universe always encompasses all that exists. The invariance is its being all-encompassing, the variations are what exactly it contains as time goes by, things change, and objects are created or destroyed.

I still don't see what problem you are addressing with "holon." I guess I need to read about them. The size at which things are really things, or are recognized as such...I don't know what that's about.

--Mindy

Of course it exists. Does nothing.

--Brant