IGS Discussion Forums: Learning GS Topics: General Semantics and Equality
Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, May 29, 2007 - 07:54 am Link to this messageView profile or send e-mail

Both "the President is an idiot" and "I feel convinced ... errors in judgement" are abstract judgements that cannot be indepenedently verified by "an innocent observer". "It is recorded that George Bush vetoed such and such bill.", however, is a verifiable observation statement because, with the appropriate factual information, where its recorded, the identification of the bill, how to perform such a check, etc., an "innocent" observer can perform the check and discover that such a record (still) exists.

Such an "observation statement record" is about the only type of extensional statement of the type that "we CAN say ... FOR SURE".

Even our memories of what we said or saw in the past, however are not so reliable. Much research on eye-witness testamony has shown that it simply is not reliable. When asked "What color was the getaway car?" many witneses will not only provide a color, but give additional details about "the car", and swear that they saw it, even when there was no car involved.

Personal abstraction statements indexed by time and other qualifiers can feel like they are absolutely true, but research has shown them to be unreliable. "I am remembering seeing X, and I feel absolutely confident about it, but I also have experience that shows my memory can be in error - even when I feel certain about it." seems to be the uncertainty that we must live with.

Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, May 29, 2007 - 09:06 am Link to this messageView profile or send e-mail

Even what we feel, at the moment, with "absolute conviction", has been shown not to reliably correspond with what other observers can report. This should tell us something about our sense of being absolutely convinced".

As I noted elsewhere, "I perceive that what I perceive may not be."

Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, May 29, 2007 - 12:08 pm Link to this messageView profile or send e-mail

I vividly recall an incident in my own life back in 1973 or 1974. I was on my way to a contractor site in the Bronx, and I got caught by a red light. I was in a hurry, and I wanted to move. I can recall watching the light for signs of change, and I saw it cycle through a change of permission. I vividly remember seeing the light for me turn green. I started to move, but the other cars on the sides just kept coming. I looked back and forth a couple of time, "cursing" the cars, saying, "I've got the light.", continuing to see the "green light" and blowing my horn, but the cars kept coming from the side street. Finally I settled back, resigned to wait, at which time I saw that the light was red. I had "seen" a "green light" with "absolute conviction" at a very objective level. I saw what I "wanted" to see; not what was there, and I saw it with such vivid conviction that I "knew" that it had changed to green. The car in the lane right next to me never moved, and I vaguely remember thinking why aren't you going too? The point is that I'm vividly aware that what I perceive may not "be", and this incident remains in my consciousness of abstracting. "Identification" was ocurring at some level below consciousness in my nervous system, "identification" that "equated" "'green' (expectation)" with "green (perception)" at a pre-verbal level. Obviously, in today's retrospective view from the perspective of neural nets, the expectation network over-balanced and biased the perception network to activate the "seeing green" network instead of the "seeing red" network.

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, June 1, 2007 - 09:39 am Link to this messageView profile or send e-mail

Nora wrote: We have the ability to say "a is b" even though the two things themselves "are not" identical; [I'm just using this as a jumping off point.]

This presumes that we are speaking from the semantic perspective on the use of language, where the symbols 'a' and 'b' are taken as used to refer to "things" in what is going on (WIGO). If we want to look at this from the general semantic perspective, then we would presume that the symbols 'a' and 'b' are to be taken as referring to "objects" in our respective individual nervous systems. In that case, we have made two separate abstractions that arrive at one and the same higher level semantic reaction or response. Our (individual) neurological categorization subnet, which we might call Cleveln+1, is activated by Aleveln and it is also activated by Bleveln. The activation of "C" is the neurological equivalent of thinking of the category that A and B are seen as members of related to "sameness".

When we take, however, the logic perspective, the symbols 'a' and 'b' are not taken as referring to anything in particular, and the 'is' in the sentence is not taken even as "identity". The logic level formalization of "a is be" is a conditional of the form "IF x r a THEN x r b" where 'r' stands for an arbitrary relation. It is also usually presumed to be quantified by "for all" or "for every" which can be written (x). In the logic perspective, "a is b" could be written in formal symbols as (x)[x r a implies x r b].

At logic levels "is" generally means "is a" where the subject is an element and the predicate is a set, category, class, etc, capable of having multiple members.
"Identity" at logic levels is expressed by the phrase "if and only if", not by "is" or "is a", and the subject and predicate are taken as not having any referents. We would say "a is b and b is a" or better yet, "all a are b and all b are a". Remember that 'a' and 'b' do not refer to anything at logic levels.

Our (current) model of WIGO holds that continuous change is going on and that identical conditions never occur, so we presume "a is b" is always false (assuming the universe of discourse is about WIGO). General semanticists may treat a heard utterance "a is be" as indicating a semantic reaction of the speaker disclosing his or her categorization strategy, provided they have projected consciousness of abstraction (awareness of their own as well as attributing awareness to the speaker). In my experience, it seems that "novice" initiates of general semantics, particularly those with little or no experience with logic or higher mathematics are inclined to think only in terms of the semantic perspective, and rail against any use of the word "is".

For me, it is always necesssary to infer the intended perspective among these four levels whenever 'is' is used, and respond to the context accordingly, as well as to make allowances for those who appear to lack the experience with all four perspectives.

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, June 2, 2007 - 12:47 pm Link to this messageView profile or send e-mail

Hey Milton!

If general semantics was formulated as an extensional discipline, does that mean we should always be looking for an extensional referent for any languaging we are doing?

Can we be said to be using general semantics if we are to talk about "stuff" where no extensional referent can be observed? Or, possibly, would being fully extensional mean we should not be talking about such "stuff" "at all"?

In other words, does non-identity preclude any notion of "equality" while remaining engaged in "extensional discipline"?

Author: Ralph E. Kenyon, Jr. (diogenes) Sunday, June 3, 2007 - 11:01 am Link to this messageView profile or send e-mail

David, Google produces 42,100 hits for "functional orientation" and 616 for "functional orientation is".

When you say "functional" do you mean something like functionalism? Or this? One of these?

I understand mathematical functions. A mathematical function is a relation that, given a unique set of inputs, produces a unique output. But in the domain of a mathematical function multiple different inputs can produce the same output. The simplest example is the constant function, for example f(x)=1. The more complex f(x)=x2 producess the same output for x=1 and x=-1, namely, 1. Under this rubric, the expression "4" and the expression "2+2" both evaluate to the same numerical value - in other words f(4)=f(2+2) [only when "f" means the numerical result], but the grammar, the sense, and the formulation all differ. When I'm teaching algebra, "4" and "2+2" are not functionaly equivalent, because one illustrates a number or a term whereas the other illustrates a compound expression involving an operation that must be learned. "Function" then depends upon the context and the purposes of the speaker, and that is an individual abstraction. We cannot speak of "functional orientation" assuming it unambiguously means only one thing.

Author: Ralph E. Kenyon, Jr. (diogenes) Monday, June 4, 2007 - 08:41 am Link to this messageView profile or send e-mail

I wrote: "Function" then depends upon the context and the purposes of the speaker, and that is an individual abstraction.

David replied:
If you substitute the word "Meaning" for "Function", I can agree with that proposition; otherwise, I would not agree.

The substitution does not work to convey my intent.

You seem to be treating the word 'function' as having a univocal meaning. It does not; see define:function.

My "function" as an algebra teacher is to facilitate my students learning the language, operations, procedures, etc., and that involves looking at language expressions, seeing the parts, and being able to perform the operations.

As Tom Lehrer sang in his song New Math, after an error in addition, "well, the important thing is not to get the right answer, but to understand what you are doing."

The expressions you cite all "function" in the context of learning mathematics to drill the student in learning addition (except the last one), and they are not "functionally equivalent" in this regard, because the student is learning a different element in the sum table. When it comes to appying the word 'function' outside of mathematics, the variability is much greater. I repeat my claim. The meaning of the word 'function' and the phrase functionally equivalent depend on the context and especially on the purposes of the speaker.

Every element in the sum table must be learned if the student is not to "count on their fingers", and each expression functions to train a different neural net. "2+3" is not even "functionally equivilent" to "3+2" in this regard because the sequence is different. If your "function" is only to compute the sum, then the result is the same, but if your "function" is to teach and drill in memorizing sums, the expressions are not "functionally equivalent".

A flash card with "2+3" is not functionally equivalent to a flash card with "4" on it.
The flash card with "2+3" asks the student to perform the operation and add 3 to 2. But a flash card with "4" on it does not function in the same way; it would get a "Huh?" from the sudents in the context of arithmetic drill.

"Equality" in general, relates to classifications, and "numerical value" is only one such category.

Author: Ralph E. Kenyon, Jr. (diogenes) Monday, June 4, 2007 - 01:19 pm Link to this messageView profile or send e-mail

David wrote: - A flash card with "2+2" IS functionally equivalent to a flash card with "4" on it.

These do not serve the function of teaching, so they are NOT functionally equivalent.
Your example suggests that you view "functionally equivalent" UNIVOCALLY to mean "evaluate" to the same numerical value.

FunctionDavid=sum. Functional equivalenceDavid = evauates numerically to the same thing.
FunctionRalph=teach. Functional equivalenceRalph = drills the student in the addition of the same two numbers in the same order.

Two flash cards for drilling in addition would be functionally equivalent if they have the same numbers in the same order, but the cards could be different sizes, different colors, shaped differently, etc, that is to say structurally different, but with the same symbols on them.

My point is that the "function" is determined by the purpose of the speaker, and so is "functional equivalence".

Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, June 5, 2007 - 10:27 am Link to this messageView profile or send e-mail


You first wrote, When considering this proposition from a functional perspective, it seems correct to say that 2 plus 2 *is* the functional equivalent of 4

Does adopting a functional orientation change how we view this topic?"

You emphasized the word 'is' with asterisks.

I replied by pointing out that "function" depends on the purpose of the speaker, and gave an extensional example that "2 + 2" is not functionally equivalent to "4" (written on flash cards) when it comes to drilling students in addition.

You responded with - A flash card with "2+2" IS functionally equivalent to a flash card with "4" on it.

Since you simply repeated your previous claim, you did not address my alternative view, that functionality is dependent upon the speaker's purposes.

You simply emphasized the word "is" by capitalizing it.

Moreover, you included the gratuitous Six of one, half dozen of another. Ralph.

You also said Ralph, in an effort to show how two things of different structure may also be equal, I stated this:
> it seems correct to say that 2 plus 2 *is* the functional equivalent of 4

That is my proposition.

Can you show me an example where the expression "2 plus 2", or the expression "4" evaluate to a number other than 4?

Note that you said 2 plus 2 *is* the functional equivalent of 4 and the expression "2 plus 2", or the expression "4" evaluate to a number other than 4?. These do not express the same notion, because "functional equivalent" is very different from "evauate to a number".

I have no problem with "2 plus 2" evaluates to 4. But I do have a problem with saying that that "2+2" is "functionally equivalent to "4", I see "functional equivalence" as very different from "evaluates to".

You appear to have missed, ignored, misevaluated, or otherwise not understood, etc., both my extensional example as well as my explanation in earlier posts in this thread.

Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, June 5, 2007 - 02:34 pm Link to this messageView profile or send e-mail

In mathematical terms I would call such a statement "degenerative" or "trivial", because there is nothing to "evaluate". I would not use such a statement because "evaluate" presumes a function or operation which requires some processing from one level of abstraction to the next. In the context of "quotation", however, evaluating the (trivial) expression "4" produces the number 4. Evaluating the (non-trivial) expression "2 plus 2" also produces the number 4. This action involves a semantic mapping from an expression to a numerical value - a map between a noun or a phrase and a possible referent.

From a semantic perspective "4" is a simple name symbol for the number 4, and "2 + 2" is a complex expression which picks out the same extension as the simple name symbol "4".

This does not deal at all with my point that "function" does not automatically and always mean "evaluate". "Function" can be thought of as a second order logic variable, itself having many possible interpretations.

The intension of these expressions ("2 plus 2" and "4"), however, is different. Only one of many possible "functional orientations" picks out the extension.

I did ask you what you meant by "function" and "functional orientation" in this post.

Your answer in this post suggested an idea fixe that "functional equivalence", by your five examples, was univocally numerical evaluation. Compare that with this.

So, the simple answer would be, "It depends.", or, with an intended pun, it's a function of the context and the purposes of the speaker.

Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, June 5, 2007 - 10:39 pm Link to this messageView profile or send e-mail

As a stand-alone formulation it's extremely abstract and open to a great variety of interpretation and varied application, because neither "structural" nor "functional" are well defined, not to mention the fact that "equal" is especially controvertial in general semantics circles.

My perspective when contrasting things is that it depends on the level of abstraction chosen by the observer. Any two subjects may be "viewed" at sufficiently high a level of abstraction as to ignore any differences or at a sufficiently low level of abstraction as to emphasize differences.

Author: Ralph E. Kenyon, Jr. (diogenes) Wednesday, June 6, 2007 - 10:19 am Link to this messageView profile or send e-mail

In response to David's earlier post...
Well clearly the word "sufficient" depends also on the observer and the context, and of course it's "binary" distinction pair, "insufficient" as well. I'm inclined to think that these get "defined" neurologically by our underlying neural nets and the way neurons fire and rest, a more or less binary distinction.

I do not think of "function" and "structure" as having any such binary relation (as comparable at multiple levels or not). In object oriented programming an "object" acts as both a structure and a function - a "structure" because it can be a parameter in a function, and as a function because it can take parameters and produces a result.

I also do not think of "function" as singular. Any structure can have many functions, depending on the use to which a person or other entity wants to put it. If I don't have an elastic band, a string might "function" to hold a bag closed (different structures, same function), and a string might function to hang a bag from a hook or to pull a sponge through a pipe (same structure different functions).
So I conceive of the general relation between "function" and "structure" as many-to-many, even after allowing for multiple dictionary definitions.

Organic, natural, communication, it seems to me, is an area where "function" can be complex enough to be comparable at different levels of abstraction.

For example, when the boss says to the employee arriving late, "Do you know what time it is?", one level of abstraction is the literal question, and that function is to get information. Another level of abstraction is to give information - namely "I'm the boss, and I know you are late, so you better have a good explanation.". The inflection might be enough for some to figure out if one is meant over the other, but perhaps not to all, so the level of abstraction of the observe might produce, same as "He's just asking if you know what time it is" (high simple level just noticing the words) or "He wants you to know he knows you are late." (lower level noticing inflection and the words).

So, I think both can be compared from the perspective of different levels of abstraction.

Author: Ralph E. Kenyon, Jr. (diogenes) Wednesday, June 6, 2007 - 02:46 pm Link to this messageView profile or send e-mail

A is "functionally equivalent" to B <--> f(A)=f(B).
How about B is "functionally equivalent" to A versus A is "functionally equivalent" to B?

Is "functional equivalence" always communitive?

Author: Ralph E. Kenyon, Jr. (diogenes) Wednesday, June 6, 2007 - 05:30 pm Link to this messageView profile or send e-mail

In mathematics an "equivalence" relation is always communitive. It's the way we use English where the question would apply, particularly with respect to what we mean by "is". When I thought about English usage, it seemed open to question. I'm happy with "not always", but I'm having trouble finding an example where A is functionally equivalent to B, but B is not functionally equivalent to A. Anyone have examples - ones that do not equivocate on the meaning of the word 'function'?

Author: Ralph E. Kenyon, Jr. (diogenes) Wednesday, June 6, 2007 - 08:16 pm Link to this messageView profile or send e-mail

Commutative it is. Spelling checker doesn't work on this system.

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, June 8, 2007 - 12:46 pm Link to this messageView profile or send e-mail

I disagree with the translation. The "function" is not "meeting"; meeting is an object that fuction takes, so you can't simply identify the two words.


This yields y=f(x,w,z), and that would be the "correct" formal logic translation.

An Elglish sentence that could be translated to your example would be: "Luck is meeting preparation opportunity."

Better, however, is the notion "Luck is preparation for meeting opportunity".

Luck =fpreparation(meeting,opportunity).
Luck =fpreparation(gmeeting(opportunity)),

depending on whether "meeting" is a noun or a verb.

The later example is a compound function, a function of a fuction, of opportunity.
We meet opportunity provides the first functional possibility. This is "functional" because we can take actions to increase our opportunities through increasing the opportunities for meeting chances.
(Example: The bachelor who goes out increases his potential opportunites to meet someone over the bachelor who sits at home.)
Being prepared to take advantage of opportunities would also functionally enhance our "luck", (although some would say it is not "luck" in this case).

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, June 8, 2007 - 04:32 pm Link to this messageView profile or send e-mail

My prevous post gave examples of treating meet or meeting as both a noun (independent variable) or as a verb ("operator" or secondary function named "g").

What do you think about "translating" natural language into formal symbolic notation?

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, June 9, 2007 - 12:45 am Link to this messageView profile or send e-mail

David wrote I was wondering if the math concept referred to as "operator" mapped the natural language concept referred to as "verb". Based on your reply, it sounds like you would agree with that mapping. Is that the case?

I, and, in my experience, others would translate an english verb, especially one that takes an object, as a fuction. "Operator" can be synonymous with "fuction".

Here are some examples.

We call "+" the sum or addition operator.

+(a,b) prefix notation.
(a+b) infix notation.
(a,b)+ Posfix or Reverse Polish Notation.

f(a,b) = a+b

The primary difference between whether or not we think of these as a function or an operator depends upon if we are looking at a computational procedure (operator) or the set of points in the product space.

For example z=x+y can be represented as a triple of the form (x,y,x+y) and it is a subset of all possible triples (x,y,z). (1,1,2) is in the set, but (1,1,1) is not. We call it a function if it is the whole set of triples; we call it an operator if we pick out the triples one at a time.

The "operator" picks out the values as we need them, but the function is all the values.

If I say "Jack drove home", I could represent this as home=drove(jack) where "drove" is the function, persons names are the domain, and destinations are the range, so the verb drove becomes the function or operator which maps persons to destinations.

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, June 9, 2007 - 01:36 am Link to this messageView profile or send e-mail

The thread topic is general semantics and equality. It was brought forth from a prior topic by quoting my statement.

The highest level abstraction of the notion of "equal" is the mathematical and logical definition independent of all contexts, although it requires a context to provide an extensional example. As general semantics is an extensional discipline, it seems to require getting down to examples, but at that level we cannot find "equality", because we have non-identity not only of "entities" but through time for any particular entity.

In mathematics an equivalence relation is one that satisfies the following three properties.
Reflexivity: a ~ a
Symmetry: if a ~ b then b ~ a
Transitivity: if a ~ b and b ~ c then a ~ c.

General semantics is fond of saying a is not a, and that denies the reflexivity relation for any extensional examples. It is also fond of saying that for all a and be no a is b, so that denies the hypothesis of both the symetric and transitive properties. But students of logic know that a material implication with a false hypothes has an overall value of true.

Once, however, we abstract from extensional examples into "categories", then we can use membership in the category to define an equivalence relation. All members of the category, that is, all members that are abstracted by the abstractor into one categories are equivalent. Denial of this is failure to perform the "same" abstraction.

"Equality" exists, then, only as abstractions, and abstractions require formulators. Consequently, two subjects are "equivalent" relative to an abstractor's formulation.

General semantics, it seems to me, denies any instances of extensional "equality", but, it would seem, allows abstract "equality", but that always boils down to someone performing the abstraction. So the interpretation of any formulation, including the Declaration of Independence, depends on who is abstracting what meaning from the words in the formulation.

If we say that all "men" (human beings) were "created", then we can say they were "equivalent" in that they are all in the category of "created" - a trivial pun in which "created equal" becomes a redundancy in terms. Since the declaration makes no attempt to define equality, it's an abstraction to be interpreted by the reader, and as history has shown, by the legislature and the courts - which are consensus formulations representing negotiated agreements among individual "men".

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, June 9, 2007 - 10:24 am Link to this messageView profile or send e-mail

To summarize...

I quote the phraseology of a number of contemporay general semanticists without quotation marks or attributions others than personifying general semantics. These quotes include "extensional discipline", "A is not A", "no two things are ever identical, equal, etc.", "nothing remains the same", "non-Aristotelian", and a number of others.

I personally think many of these abstract formulations illustrate a failure to deeply understand science, mathematics, logic, philosophy, and how Korzybski put these together.

General semantics has many facets, and I would describe them in a top-down manner.

The structural differential is an extremely abstract model that can be abstracted from two sources - the process of individual humans acquiring understanding or "knowledge" and the process by which scientific knowledge is accumulated. Both process involve building abstract models and projecting those models onto what is going on - one nerologically and one formulationally. The background in which this is happening is the social cooperation inherent in using symbolic communication - time-binding.

People are time-binders who cooperate in order to communicate and build shared abstract models of what is going on using logic and mathematics and empirical testing of the models so produced.

We have learned about the failure of models, so we hold the models conditional upon continual validation. In two specific areas we have physics and its major paradigm shift from the Newtonian model to relativity and quantum mechanics as well as mathematics and its discover in geometry that the Euclidean fifth postulate was independent - leading to the discovery and creation of non-Euclidean geometries. Geometry has been used as a primary source metaphor for applying the "non-" prefix for generating the term "non-Newtonian" (physics).

Korzybski used the term "non-Aristotelian" in this metaphorical sense to "inform" his insights; reasoning with the analogy "non-Aristotelian" relates to Aristotelian as non-Newtonian relates to Newtonian and non-Euclidean relates to Euclidean.

This metaphorical mapping only works part way; it fails at more details levels of abstraction.

Some of the people who avow general semantics treat the "non-" as "anti" or as a direct opposite, and appoint themselves as guardians of "non-Aristotelian" purity by accusing individuals of exhibiting a "two-valued orientation".

Korzybski noted that people use fallacious reasing (non-logical methods) and he lamented the fact by compaining that even scientists fail to rigorously apply scientific methods of the laboratory in daily lives. He called this use of non-consistent logic and non-scientific approach, which includes jumping to conclusions and failing to check them out, among others, "un-sane" behavior thus creating a "middle ground" between "insane" and "sane".

In his magnum opus, he associated using the methods of science, valid logic, and mathematical methods with his newly defined "sane" in the title "Science and Sanity", and he used the metaphor based on "non-" in the sub-title "an introduction to non-Aristotelian systems".

Note that non-Euclidean geometries represent equally consistent and valid branches that differ from Euclidean geometry. All are equally consistent; they are just incompatible models.

Note that so-called non-Newtonian physics includes general relativity, which shows Newtonian physicis to funcion as a very good first approximation that works well at small velocities, medium or human scale distances, and medium sized or human scale durations. Theoretical physics, in the form of quantum mechanics, has produced abstract models using advanced mathematics that defy our ability to produce a human-scale, human-experience based metaphor to allow picturing the theory without understanding the mathematics involved, for example the wave-particle duality. Like non-euclidean geometries, both the wave and the particle views are each independently consistent, though incompatible in the sense that they cannot be simultaniously applied to the same phenomenon, although de Broglie gives the mathematics relating one to the other.

Note that adwanced mathematics and logic are extensions of basic math and logic; they do not invalidate the basic logic relations. In that regard "non-Aristotelian" reasoning is an extension of basic logic (parochially called "Aristotelian" in general semantics circles). Tarski's "model theory", probability theory, and multi-valued logics are all extensions; they neither replace nor invalidate basic logic. The difficulty is more with which to apply when.

Considerable human miscommunication can be traced to the use of invalid reasoning methods. Considerable human misery can be attributed to un-tested assumptions about others motives and meanings. Considerable human misery can be attibuted to holding and acting on un-tested and untestable beliefs about people, our environments, what is going on, etc.

In a nutshell, Korzybski said the equivalent of we can improve things considerably if people would just consistently use mathematics, valid logic, and and empirical testing in our daily lives. A good percentage of the rest of Science and Sanity includes an exposition of the then current science and philosophy of science as it had evolved up to that point in time, as well as the rudimentary understanding of cell biology (surmised at the time to be collodial behavior). It also includes the "extensional devices" designed to assist the lay persons as well as the scientists when outside their laboratories.

I believe it is only the mathematically naive who would insist that general semantics actually denies any form of "equality" based on an overemphasis on the extensional. Its throwing out the baby with the bath water. Mathematics and valid logic, and here's the rub, "correctly applied" allows us to test the consistency of our models.

Taking the words of the Declaration of Independence out of its social context and out of the interconnected network of "meaning" relations among the words we use, as well as out of the context of the prevailing social culture, including the untestable belief systems in that culture, it seems to me, is the mistake of rigidly misapplying abstractions out of context.

"All men are created equal." The belief system of creation by an omnipotent entity (untestable) stands behind the word "created". Other documents point to a system of ethics as to how people desire other people to behave towards each other, and the word "equal" goes back to this abstract categorization structure.

Misapplying "equal" to mean physically identical in all respects seems to be one of the things that many so-called general semanticist do. Confusing the individual physical beings (extension) with an abstract category (intension) is an example of what general semantics applies the term "identification" to.

To say that "general semantics denies equality in the name of non-identity" is just a summary statement of these misapplications. The "personification" in this case represents a generalization from many examples of the statements of quite a few people in general semantics circles. I shan't name names. It's not actually my view.

This thread has shown a variety of perspectives on various aspects of applying or misapplying "identity", "equality", "extensional", as well as problems in translation among languages in general and mathematics in particular, and differenences in individual abstractions vis-a-vis the technical terms and application of them, not to mention common abstract English words, "function" in particular.

Thank you all for your participation.

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, June 9, 2007 - 04:16 pm Link to this messageView profile or send e-mail

Nope. I never did hold that view myself, but I have been known to "bait" general semanticists.

My exact words were In my case, general semantics denies "equality" in the name of non-identity. I however, hold to the notion of equal rights in our society, but I recognize that it is intensional and contrary to general semantics notion that we should always differentiate, so as not to "identify".

The first sentence is somewhat "tongue in cheek" as it represents my view of the "prevailing winds" of many current practitioners. It is not, and never has been, my "actual" belief, because, in part, I too have mathematics degrees in both pure and applied mathematics, and my philosophy specializes in epistemology, metaphysics (the philosophical kind), and the philosophy of science.

The last clause also reflects my perception of the "prevailing winds"; but it sharpens the "hook".

Values are applied intensionally. If used well, they direct actions contingent upon abstractions from the extensional. Korzybski erred, I think, in thinking and advocating that values and ethics can be abstracted through the application of the scientific method. We can infer values from observations, but I believe it takes more than abstraction to create values, especially values to live by in a social context.

Equal rights, it seems to me, is such a value that, applied intensionally, informs our decisions in the case-by-case ever-changing experiences we abstract from. Where do we get such values? I think not from our consideration of abstracting; I think from time-binding, particularly at our mother's knee, but occasionally altered by life experiences.

Author: Ralph E. Kenyon, Jr. (diogenes) Sunday, June 10, 2007 - 12:00 pm Link to this messageView profile or send e-mail

My generalized perception is still that many general semantics have railed at any form or use of "equal", "same", etc., in the name of non-identity, so my perception "In my case, general semantics (a personification) denies ..." still represents an abstraction from my perceptions. Equally valid is my perception that many general semanticists continue to emphasize differentiating so as not to "identify".

Intentionally "misinform" and "mislead"? No such nefarious motives are involved at all. Is your question indicative of such a judgement on your part?

I also think that these behaviors and the inferred orientation is an overly simplified assimilation of general semantics, so stimulating discussion of this very issue just might bring some additional light to the issue.

Do you prefer the Socratic method?

Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, June 12, 2007 - 12:41 am Link to this messageView profile or send e-mail

Have you used "baiting" in the way you described? Much?

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, July 14, 2007 - 11:46 am Link to this messageView profile or send e-mail

From my perspective the notion of "equal rights" is essentially a prescription for behaving that is largely instantiated in our legal system - itself an extremely high level of abstraction based on many different aspects of our symbolic environment including a number of "concepts by intuition". "Created equal" in the given context invokes this prescription. I think the notions of "functional equivalence" and "structural equivalence" are too ill-defined in our culture to serve as a principled distinction without a correspondingly large supporting set of "concepts by intuition" and relations.

Darren makes reference to a number of such concepts by intution.

Consider 'it' in the following:

A Caucus-Race and a Long Tale

They were indeed a queer-looking party that assembled on the bank--the birds with draggled feathers, the animals with their fur clinging close to them, and all dripping wet, cross, and uncomfortable.

The first question of course was, how to get dry again: they had a consultation about this, and after a few minutes it seemed quite natural to Alice to find herself talking familiarly with them, as if she had known them all her life. Indeed, she had quite a long argument with the Lory, who at last turned sulky, and would only say, `I am older than you, and must know better'; and this Alice would not allow without knowing how old it was, and, as the Lory positively refused to tell its age, there was no more to be said.

At last the Mouse, who seemed to be a person of authority among them, called out, `Sit down, all of you, and listen to me! I'LL soon make you dry enough!' They all sat down at once, in a large ring, with the Mouse in the middle. Alice kept her eyes anxiously fixed on it, for she felt sure she would catch a bad cold if she did not get dry very soon.

`Ahem!' said the Mouse with an important air, `are you all ready? This is the driest thing I know. Silence all round, if you please! "William the Conqueror, whose cause was favoured by the pope, was soon submitted to by the English, who wanted leaders, and had been of late much accustomed to usurpation and conquest. Edwin and Morcar, the earls of Mercia and Northumbria- -"'

`Ugh!' said the Lory, with a shiver.

`I beg your pardon!' said the Mouse, frowning, but very politely: `Did you speak?'

`Not I!' said the Lory hastily.

`I thought you did,' said the Mouse. `--I proceed. "Edwin and Morcar, the earls of Mercia and Northumbria, declared for him: and even Stigand, the patriotic archbishop of Canterbury, found it advisable--"'

`Found WHAT?' said the Duck.

`Found IT,' the Mouse replied rather crossly: `of course you know what "it" means.'

`I know what "it" means well enough, when I find a thing,' said the Duck: `it's generally a frog or a worm. The question is, what did the archbishop find?'

The Mouse did not notice this question, but hurriedly went on, `"--found it advisable to go with Edgar Atheling to meet William and offer him the crown. William's conduct at first was moderate. But the insolence of his Normans--" How are you getting on now, my dear?' it continued, turning to Alice as it spoke.

`As wet as ever,' said Alice in a melancholy tone: `it doesn't seem to dry me at all.'

`In that case,' said the Dodo solemnly, rising to its feet, `I move that the meeting adjourn, for the immediate adoption of more energetic remedies--'

`Speak English!' said the Eaglet. `I don't know the meaning of half those long words, and, what's more, I don't believe you do either!' And the Eaglet bent down its head to hide a smile: some of the other birds tittered audibly.

`What I was going to say,' said the Dodo in an offended tone, `was, that the best thing to get us dry would be a Caucus-race.'

Source: Alice's Adventures in Wonderland

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, July 14, 2007 - 06:58 pm Link to this messageView profile or send e-mail

I did not say that I was baiting general semanticists with that particular remark; I said that it represented my general impression that some (more than a few?) general semanticists in my experience seem to hold that view. I characterized it as somewhat "tongue in cheek" in that the "for me" did not mean what I believed, but what I surmized about others. I let that impression ride, and having done so, that could be construed as having allowed the appearance of "baiting". My conscious "baiting" is usually accompanied by a smiley.

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, July 14, 2007 - 09:23 pm Link to this messageView profile or send e-mail

You stated so right in your opening post.

I wonder how many of my parenthetical inserts also go apparently unnoticed or ignored.

She said "Nobody on this forum but you ...", and that sounds like the kind of allness claim that can be checked. A search revealed several instances in two topics.

How to spend less time ...
Ignore them?

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, August 18, 2007 - 11:29 pm Link to this messageView profile or send e-mail

Vilmart wrote 1. E-Prime implies the identification "Word = thing"


Author: Ralph E. Kenyon, Jr. (diogenes) Sunday, August 19, 2007 - 01:44 pm Link to this messageView profile or send e-mail

Vilmart "stipulated"

1. E-Prime implies the identification "Word = thing".
2. E-Prime forbids equality.

I think this stipulation needs cleaning up. Formulating using the mathematical notation symbol '=', which we understand to mean that the subject and predicate nominative refer to items placed in or evaluated to one (the same of many) equivalence class, in other words, not "identical" but "equal". Consequenly labeling a statement of "equality" as an "identification" fails to apply either term in the customary manner or in the general semantics idiolect.

Second, E-prime does not forbid equality, it forbids using the "is" of identity (and the is of predication). We cannot say in E-prime that "A and B are equal", but we can say in E-prime, "We evaluate A as equal to B.", "We classify A and B as equal", or even "We classify A as equal to B".
We can also say, "Let A equal B.", and we can use the mathematical symbol for equality as in "A=B"; none of these formulations violate E-prime. Moreover, "A is equal to B" "is" an example of the "is of predication", because "equal to B" describes a property of A.

A revised formulation of your stipulation:

1. E-Prime implies the identification "the Word is the thing".
2. E-Prime forbids identity.

Because general semantics (personified) denies 1, you will have a hard time getting general semanticsts to even entertain such a stipulation. Ostensibly E-prime prevents such identification as you stipulate it entails.

If we apply the notions of concepts by postulaton and concepts by intuation, then the former admits of identification and uses valid logic rules of inference to insure consistency, while the later does not admit of identification and uses empiricism to eliminate non-corroborated models. Moreover, the former remains as a syntactic level process/structure while the later attains a semantic level process/structure.

We evaluate the consistency of scientific models through mathematics and logic, rigidly applying proof techniques and valid rules of inference to insure that only predictions consistent with the stipulated postulates result. (It would not due to use a rule of inference that would predict something not consistent with the starting assumptions.) Applying the models, however, moves from a single level of structure - syntactic (relations between words or symbols) - to a dual level of structure - semantic (relations between symbols and referenents) - where we know not the "actual" relations among putative "things" supposedly represented by the tokens in the language. In this case we must use empirical techniques to either disprove the model or get test results that "corroborate" (not confirm) the theory by validating tested predictions.

Author: Ralph E. Kenyon, Jr. (diogenes) Sunday, August 19, 2007 - 02:42 pm Link to this messageView profile or send e-mail

Physics "names" a science.

Author: Ralph E. Kenyon, Jr. (diogenes) Monday, August 20, 2007 - 01:07 pm Link to this messageView profile or send e-mail
Author: Ralph E. Kenyon, Jr. (diogenes) Monday, August 20, 2007 - 02:43 pm Link to this messageView profile or send e-mail

"I think not.", said Descartes, and promptly disappeared.

Taking a limit to get a value at an undefined discontinuity does not give the function a value at the point of discontinuity. It maps the original function to a new function with a change in definition at the points of discontinuity.

I purposly used "belongs to" to get away from strict set theory connotation. I intended it as more general than just the set theory context.

Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, August 21, 2007 - 01:51 am Link to this messageView profile or send e-mail

A is B expands to (x){IF x is A THEN x is B}

Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, August 21, 2007 - 10:59 am Link to this messageView profile or send e-mail

Vilmart, you are specifying a more limited context in which you are sticking with set theory.
My discussion is more general than that.

The symbol you refer to, shaped like a "U" lying on its side, has contextually different meanings. If open on the right it means "is a subset of".
If open on the left it is a variation on the material conditional. The first is set theory, the second is propositional logic. There may be different contextually defined uses, as I don't presume to be familiar with "all" the branches of math and logic, in spite of it having been my speciality.

One cannot replace the word 'is' on one side without replacing it on the left also, unless you are specifying a definition by postulate for the word 'is'.

A is B expands to (x){IF x is A THEN x is B}
A -> B expands to (x){IF x -> A THEN x -> B}
A (is a subset of) B expands to (x){IF x "is in" A THEN x "is in" B}

Author: Ralph E. Kenyon, Jr. (diogenes) Wednesday, August 22, 2007 - 07:20 am Link to this messageView profile or send e-mail

Mathematics is the domain of the intensional.
We define concepts by postulation.
We use valid rules of inference to prove or disprove propositions consistent or not consistent with other propositions.
Even in model theory the "objects" are completely specified, although often implicitly.

"Reality" is "corroborated" by empirical testing, and that involves the extensional.
Mathematics is confirmed by logical testing, and that involves the intensional.

We build theories with the intensional structures of logic and mathematics to insure they are consistent.

If, and only if, we intend to use a theory as a model of "reality", then we must deal with the modeling relationship, and that can only be done using trial and error empirical testing.

Consciousness of abstracting, however, is part of the meta-language in which we talk about mathematics and process of proving theorems.

Consciousness of abstracting could be the label to use when we are teaching about valid versus invalid rules of inference in the teaching process of how to learn and use mathematics and logic.

Consciousness of abstracting applies in the process of using any model or theory as a map of any territory.

I'm currently developing a paper on the relationship between intensional and extensional. When ready for comment I'll post a link.