For the definitive discussion and resolutions of Zeno's paradoxes, and in particular "The Achilles", see this.

More. 10-1/2 years for the Philosophy degrees alone. The extrapolator notebook was started in the mid '70's, before there were even personal computers.

By the way, the time is now.

Language is NOT abstraction, and Abstraction is NOT language. Language is only one form of abstraction. There are many other abstraction processes that are not at the level of language. You cannot "equate the two". They are not at all synonoymous. Both are abstract notions which have no separate physical existence other than in the formulations that we write down.

I've never been able to find myself. Everything I look at is not me. ... when I find a thing,' said the Duck: `it's generally a frog or a worm.

I don't know for sure, as I have not yet died. I can project that I will know or I will not know, that's for sure.

Milton wrote "But these are words. let's get extensional. Try to come at "Structure is the only content of knowledge" by reviewing anything you claim to know. See where this does not involve structure, order and relations."

Descartes used the method of doubt, and he found that he could doubt everything he knew with one exception - that he existed in the process of doubting. "Cogito ergo sum." I think, therefore I am. Which is qualified as "[when I attempt to doubt my own existence, I see that, in the process of doubting, I exist as the doubter]." Every other "object" is doubtable.

Aside from that, everything we "know" is a map, and therefore it is not wholly "extensional"; it is "intensional". Getting "extensional" means getting to the object level direct experience, a process; whereas "knowing" is bringing forth one's map that tells one what to expect, and that is intensional. We experience processes more directly as we become more extensional; we abstract "knowedge" (build maps) as we become more intensional.

The effective time-binder uses intensional maps with an awareness of the process of using them as well as of his or her own process of abstracting, always prepared for the "knowledge" (map) to be in need of correction ("not ['similar' to] the territory").

To become completely and fully "extensional" is to become as reactive and uncontrolled as a leaf on the wind. Plans give way to the immediacy of the moment. He who grabs at every opportunity catches none. To be completely and fully "intensional" is to become completely unresponsive to opportunity. He who sticks to every plan, regardless of the circumstances, grasps no opportunity.

The effective time-binder balances the intensional with the extensional. It is theorized that with general semantics training the effective time-binder can be better at balancing plans with spontaneity - better than those without general semantics training.

How can we measure this claim so as to bring it into the scientific realm by formulating a falsifiable prediction. What will we choose (intensionally) as our measures to use for correlation testing?

Thomas Wrote, ""the carrying capacity of water varies with the cube of [its] velocity", as a hypothetical statement.

You'll need more than that, because, in English, the antecedent of the pronoun "it" is customarily the previously written noun, in this case the word 'water'. But "carrying capacity" implies that something else is being carried. Something is being carried by water? If it is being carried by water, then the relative velocity of it and the water is zero. Consequently the sentence is incoherent as written, because an object is "carried" by water without regard to velocity simply due to the objec having a lower density than the water.

How exactly is what to be "carried" by water?

Are you talking about a hydroplane?
A fountain lifting a weight in an upward jet of water? Something else?

It's clear that a more extensional description is needed - using much less abstract terms.

Ben, If you (or anybody else) says to me "I know what you mean.", I take that as communication without any substantive cognitive content. It can only express some self-evaluation of confidence by the speaker in his or her interpretation of what he or she experienced. We have different brains, and what you "know" (a response in your brain) is clearly not what I "mean" (a response in my brain). I never use such expressions because they can, in principle, convey nothing of cognitive substantive. They can, however generate a "feeling" of "empathy" and "emotional support", so they may be useful in a non-cognitive manner, but they are not capable of conveying "knowledge".

See this post. Note particularly "knowledge" and "structure"

Korzybski's general semantics uses the structural differential to illustrate the process of human "knowing". His answer to the question "how do we know what we know" is "with our senses and our nervous systems". By taking this approach in conjunction with the demand to be extensional and to corroborate our maps - that is, to be "scientific" - we have the process of creating a model inside our heads (both non-verbally and verbally) that we use to predict future experiences. Consequently, in the Korzybskian scheme of things "knowledge" is strongly corroborated models - whether they be non-verbal, such as being able to grab and use the car key without even thinking about it, or highly abstract verbalizations such as mathematical physics theories of relativity and quantum mechanics, as well as intermediate level corroborated models. Differentiate such "models" from "beliefs" - weakly corroborated or not at all corroborated models.

Now, let's look at the details of the structural differential.

The multi-ordinal term "characteristic" indicates a point or data element at each level. The term "abstraction" indicates a causal connection between two levels in which a characteristic at one level "causes", "is associated with", follows from, relates to, etc., a different characteristic at a second level. The characteristic at one level IS NOT the characteristic it was "caused" by from the previous level. Example: a putative "photon" "in" the event level is consumed in a photo-chemical reaction in a Rod cell initiating that cell to discharge. The change of state from not discharging to discharging may be described as a characteristic at the next level "of abstraction". Note that nothing selected in the event level is selected in the subsequent level - the photon is gone and a sensory cell discharges "as a result" of the causative interaction. We can subsequently trace a domino chain of reactions up nerve cells until we get to a point (not understood, but hypothesized) that involves "seeing a brief flash of light" and further abstracted to verbal levels described as 'seeing a brief flash of light'. At this experiential level we no longer speak of neurons discharging, so the selected "characteristic" at the brain processing level is NOT IN the selected characteristics ("seeing") at the "perception of the object level", and that non-verbal experience is NOT IN the verbal description, but all of these are causatively connected by the process which is label as "abstraction". We "know" the experience of seeing the flash, and we "know" the description "saw a flash of light ...". Now, suppose that this is in the smoke detector on the ceiling. Then, through our comprehensive model of experience, regulation, culture, and engineering, we "know" that the "smoke detector is still working". We have no evidence of a smoke detector that blinks periodically but cannot detect fire in smoke detectors that have been tested prior to installation. (Note this does not mean that something has not happend to render the theory inapplicable for this particular smoke detector. That is the general semantics rule that times 1,=2,=3,...,=n /-> =n+1 (the n+1st time may be different). BUT the model is strongly corroborated, therefore it is part of our "knowledge" of things in their contexts at their times.

If I say to you such and such a thing. And you paraphrase this thing such back to me, and I evaluate that my understanding of my memory of my original word and my understing of the words I heard from you agree to my satisfaction, then I can evaluate that I believe you undurstood me.

But If I say such and such to you, and you say "I understand". I have not such evaluative possibility. I only know from my understanding of the word "understand" that you believe you constructed a coherent - to you - model to account for my words that you heard.

In the former case you may or may not have a feeling that you "understood" what I said, but if I then say to you, "Yes, based on what I heard in your reply, I think you understand what I meant". In the later case, you may have the feeling, but All I can get from your communication is that you have such a feeling. I can not evauate your claim to have such a feeling.

A speaks
B paraphares
A evaluates the difference between speech and paraphrase and judges sufficiency.
A states "I belive you do understand".
B states "I understand".
A evaluates that B agrees with A's judgement because "I understand" is a direct paraphrase of "I believe you understand".

The order is one speaks, a second speaks, the first evaluates diferences and either ascents, dissents, or provides more clarification.

What is common to all knowledge? - mappings, corroboration - objects - formulations - imbedded in an ordered process that has no commonality among them. What's left is the structural differential an ordering of structures.

Individual knowledge has particular content, but "all" knowledge has no common content aside from the form of levels involving abstraction (a map from one set of objects to a different set of objects - with some causative connection).

So, if you want to look at the most abstract summation of knowledge, you move above any particular content to its overall structure.

Secondly, when you look at this structure you note that NOTHING from the source domain is in the destination domain (nothing from the event level travels unaltered into the high level abstraction domain). But we hypothesize, based on our experience with many different maps and especially the geographic maps we create as well as the abstract mathematical maps we create that both domains can be conceptualized as made up of parts (structures) that relate to each other in various ways and that many, many, humanly constructed maps preserve various ways of relating these parts in both the source and target domains.

Simple math example.

Let f(x) = 2x.
The f(a+b)= f(a)+f(b)
The relation is preserved under addition.

Counter example from math.

BUT f(ab) = 2ab is not equal to f(a)f(b) which would be 2a2b = 4ab.
The relation is NOT preserved under multiplication.


I have a road map of Williamstown. Most of the streets are there, but some are no longer useable - overgrown and not maintained, and some are not on the map (new developments). At one time the map had all the streets that were in use and none that were not. Changing times have left the map behind.

But of the streets that remain, including the overgrown ones, the physical relations betwen the streets is preserved in the map.

Now look at the relation between things and words. Only a few words, onomatopoeia, such as the names of a few sounds, "ping", "whee", etc., "sound like" the sound they represent. Here structural similarity is preserved to a degree. Not so with other words. At the level of words structural similarity ends. Verbal maps have no similarity of structure at the level of individual words. We can write a description using words whose meanings are taken for granted as assumed to "draw a verbal picture" of something. We can test the similarity of structure concept by giving the descriptions to third parties and asking them to reproduce the original from the description. Only in the case of such descriptions as produce a high degree of similarity in the resulting constructions can we say that the description entails any similarity of structure with the source. But if we try this trick with individuals not familiar with the language, the experiement fails, proving that the similarity of structure was not in the words, but in the cultural understanding by individuals of the words.

We get this ability through neurological mirror cells trained in the culture.

Any high level abstraction can be interpreted in many ways. "Structure is the only content of knowledge" is such a high level abstraction.

Above you have my take and my rationale.