Forum on Conceptual Structure

ABSTRACTION/GENERALITY/INCLUSIVITY
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From: Bruce Schuman
Date: Tuesday, March 4, 2008, 4:14 PM
Subject: Abstraction/generality/inclusivity
Reply to: 262484
ID: 259953


Patrick, I thought I would go through the details of your message, and address a few of the questions you raise.

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Patrick: Ausubel postulated that cognitive structure was organized hierarchically (subsumption theory). Novaks research was driven by this theory and eventuated in instruction that took the form of hierarchically organised knowledge. As knowledge was being expertly mapped superordinate concepts would come first and act as advance organisers for future subordinate concepts. The superordinate concept would be progressively differentiated and related concepts would be integrative reconciled (feels more like a network structure).

Bruce: I looked up Ausubel, and it seems he is a contemporary psychologist. I was not familiar with him, or with Novak. But let's see if I can make sense of this.

Here's a link to his work -- I will check this out in more detail: http://tip.psychology.org/ausubel.html

I, too, would argue that "cognitive structure is organized hierarchically" -- or, to put this more accurately -- "cognitive structure can be organized hierarchically -- or maybe better yet, "cognitive structure can be interpreted as a hierarchy, without loss of data".

I think it might be a mistake to argue that all cognitive structure is organized in this way -- because people vary widely -- and suggesting that, for some people, their cognition is "organized" at all might be a stretch...

So, I have always tended to a view -- a kind of methodological posture -- that suggests that we should really see this kind of hierarchical parsing as a heuristic -- a practical method -- rather than an attempt to describe the actual structure of cognition taken from an empirical sample. We might say something like -- it is always possible to organize whatever is happening in somebody's mind (perhaps with the caveat that it is rational) in hierarchical terms - regardless of whether they themselves see it this way or not.

In this sense, we are talking about the pure properties of categories, and suggesting that we can create a hierarchical model of their thinking. On the question of whether this is a "mere heuristic", or a general theoretical claim -- I usually want to suggest that calling it a heuristic avoids controversy, and is probably "better science" -- but that in the end, it just kind of turns out that "reality itself is hierarchical after all (and not just our models of it)" -- but let's not get hung up in that claim too quickly....

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So, you were saying that Novak built on Ausbel's idea. "Subsumption theory" would mean that broader and more inclusive categories and concepts include or "subsume" lesser and more specific categories. The category "animal" subsumes the category "cat".

Now -- you talk about Novak's ideas about knowledge.

Novaks research was driven by this theory and eventuated in instruction that took the form of hierarchically organised knowledge.

Hmm. "Instruction". So, if I understand this -- we might be saying that broader categories -- "subsuming categories" -- would in some sense be "instructing" lower level categories" -- perhaps as to their behaviour. In other words -- the "general instruction set" for "animals" would always be valid for "cats" -- though cats would have additional instructions that are not valid for all animals...

If we wanted to build a mechanical cat -- we would be looking for an instruction set....

As knowledge was being expertly mapped superordinate concepts would come first and act as advance organisers for future subordinate concepts.

The category "animals" would be prior to -- "in advance of" -- the category "cats". All categories subsumed under the category animals would behave according to the animal instruction set, at a minimum.

The superordinate concept would be progressively differentiated and related concepts would be integrative reconciled (feels more like a network structure).

Hmm. Do I understand you right...

It sounds like what you are saying -- is that the "instruction set for animals" might be "learning from" the instruction set for cats" -- ie, as it is "progressively differentiated".

. . . and related concepts would be integrative[ly?] reconciled (feels more like a network structure).

This sounds like a pattern of interdependent relationships where each point in the network grid is influencing every other point in the network grid. Two different kinds of cats, with slightly different behaviors, both influence the superordinate "animal" concept -- or maybe particular instances of cats influence the "cat" category (superordinate to particular instances). And maybe, if I get this -- there is some "up and down the hierarchy" influence going on -- a kind of learning process by all the points in the grid. All the categories, at all levels, are influencing one another -- maybe under the one caveat that some "cat"egories are more inclusive than others....

This hierarchy would be mapped in two dimensional space with the higher abstract ideas/concepts first followed by less general concepts (note the interchange of general and abstract) until at the bottom of the hierarchy would be concrete examples of the events/objects that the higher level constructs point to.

Right. Particular concrete instances (particular actual cats) appear at the bottom of the taxonomy.

Just to get this diagram into the discussion -- here is a drawing of this sort of hierarchy, taken from Hampden-Turner's Maps of the Mind, Map 47, on Arthur Koestler (who coined the word "holon").

So, are we we close on track here?

There's a lot that can be said about all of this, of course -- but maybe we are coming up with a framework that can take us into some higher levels of precision.

Patrick:

This immediately made me think about multiordinality. If the concept map was truly a map then every concept within this schematic could have a ranking/value in Cartesian space. The fixedness of this presented me with problems, namely contextual meaning. My thinking on concepts and meaning in brief conflicted with this dimensionality idea. As I understood it the configuration of concepts (conceptual structure) is reliant on the focus question being asked which allows me to visualise the schematic as being rubbery (like a rubber mat) whereby a concept further down the abstraction ladder can be pulled to a higher point depending on the focus/root concept.

Now -- I am not sure I fully understand exactly what you are saying -- but let me look at the particulars.

I DO feel that we should be to say that "every concept within this schematic could have a ranking/value in Cartesian space". In fact -- this is generally what is meant by the concept "level of abstraction" -- or, indeed, "The Bridge Across Consciousness".

"The Bridge" would be the prime dimension of this Cartesian space -- a simple linear measure along a directed vector or axis -- so that every point along the dimension would be "higher than" or "lower than" every other point (and some boundary value that we say "is the ranking of that category").

In other words, on the graphic hierarchy I posted above, there are the three value-levels "tissues, cells, organelles" (values D, E, and F along the vertical axis). I think we could safely say, with a few caveats, that this kind of description is useful in almost any sort of analysis, where wholes can be decomposed into parts.

Ok, that's my claim.

Now -- you raise a concern -- not really an "objection" -- just an issue to look at.

The fixedness of this presented me with problems, namely contextual meaning. My thinking on concepts and meaning in brief conflicted with this dimensionality idea.

This is a very valid concern -- a critical one. This is something we might need to talk about in more detail, because this is really an essential issue.

But very briefly -- let me quickly introduce an idea that I believe helps overcome this issue -- in a powerful and liberating way. We probably need some better examples to illustrate this -- but we can get into those in another exchange. Let me offer one methodological principle here, that I think opens this entire issue to the kind of strict linear analysis that a computer scientist would really hope to employ.

The idea is: these kinds of taxonomic structures are only valid in a general kind of way -- and are not exactly reliable in the specific instances of real-world usage.

I talk about this concern in Part 6 of my essay on Synthetic Dimensionality -- which is concerned with what I call "Ad Hoc Top-Down Decomposition".

http://originresearch.com/sd/sd2.cfm#part6

Years ago, I was auditing a graduate seminar, and the professor introduced the idea of "stipulative definition". This idea grew in my mind, to become a explosive postulate in my own understanding of cognition. The idea, put simply, is that when a person speaks, or "undertakes an act of verbal communication" -- the meaning of the words they use is "stipulated". That is to say -- that the actual meaning intended in any instance of language can be seen as intended and stipulated by the speaker.

In other words, to paraphrase Lewis Carroll from Alice in Wonderland -- "words mean what I want them to mean".

This is a powerful thought, and can (I suspect) vastly simplify the problems of analysis.

Now, of course, it is true that "word meaning out there in the world" is floating in a vast sea of social and historical interdependencies -- and there is no one single meaning for any word that is true in all specific instances and contexts -- and that attempting to impose such uni-meaning on the world would be horrific. It doesn't work.

But -- in a specific instance -- we can (I claim) develop a strict top-down hierarchical model of intended word meaning. Seeing an intended act of communication in these terms -- I am guessing -- can liberate our analysis from the huge confusion that results when we attempt to ground word meanings in social convention.

When I use the word "cat" in a particular instance -- I know what I mean/intend -- and am guessing that you probably know what I mean (based on my sensitivities to social convention). So -- based on my guess, I go ahead and use the word. But my act of communication is actually a kind of feedback-probe -- a test -- to figure out whether you really do know what I mean by "cat". So -- as we talk -- I am testing and probing -- looking for uncertainty in the definition and understanding. I would say that most conversations take this form -- people are testing and probing the underlying conventions of understanding, until they are pretty sure that "boundary values are within acceptable error tolerances".

In other words, to shift examples -- if I tell you that I am going to "wash the dishes" -- you probably know what I mean. But if I take on that task, and you feel that some dishes are still dirty when I say I am done -- you are going to wonder if we mean the same thing by this phrase. "You call THOSE washed dishes?? They don't meet the standards for my definition-set -- my "private dictionary" -- clean dishes gotta be cleaner than that..."

That's a stipulated boundary value and an "acceptable error tolerance". Those dishes don't have to be atomically sterile -- but that smear of egg-yolk has got to be washed off...

So -- this is a principle that I feel can liberate this study. "Stipulative definition understood as top-down ad hoc decomposition".

*****

Ok, that's enough for the moment. There are a couple more paragraphs in your comments -- and I do want to get into this issue of "ordinality" -- it's another very interesting subject -- but let's let this float for a bit....