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Topic: Visual Presentation of Real Number System
Replies: 61   Last Post: Dec 11, 2013 11:12 PM

 Messages: [ Previous | Next ]
 Robert Hansen Posts: 11,345 From: Florida Registered: 6/22/09
Re: Visual Presentation of Real Number System
Posted: Dec 11, 2013 5:19 PM

On Dec 11, 2013, at 3:06 PM, Joe Niederberger <niederberger@comcast.net> wrote:

> GS Chandy says:
>> Scientific American has recently re-published a pretty good article by Natalie Wolchover (from Quanta Magazine) under the title "Dispute over Infinity Divides Mathematicians" that looks at several of these issues - http://www.scientificamerican.com/article.cfm?id=infinity-logic-law&offset=2&posted=1#comments . The remarks from readers (both at SciAm and at Quanta Magazine) are worth some study).
>
> Of possible interest:
> http://www.personal.psu.edu/t20/papers/objectivity.pdf
>
> Cheers,
> Joe N
>

This caught my eye because he is crossing paths with my own studies in AI?

1. According to Objectivism, knowledge (i.e., human, conceptual knowl- edge) is ?grasp of an object by means of an active, reality-based process which is chosen by the subject.?
2. According to Objectivism, objectivity is a specific kind of relationship between reality (?out there?) and consciousness (?in here?).

I identify ?information? as everything outside our head and ?knowledge? as everything inside. Everything inside our head is contextual and either has a real basis (what he calls objectivism) or an imagined basis (what we generally call abstract). Note, imagining a real object, like a new car, is not what I mean by imagined basis. That has a real basis. Imagining something like a triangle has an imagined basis. A real basis involves the physical world. An imagined basis does not. Gravity has a real basis. Our mathematical model of it, does not. In fact, our mathematical model of anything does not.

3. All knowledge is contextual, i.e., it must be understood within a context. Moreover, the ultimate context is the totality of human knowledge. Therefore, all of human knowledge must be integrated into a coherent system. Compartmentalization is strongly discouraged (more about this later).

I also state that all knowledge, real or imagined, is contextual. I don?t subscribe to the notion of an ?ultimate context?, a schema of everything. I dropped that idea long ago, primarily because ?context? is what is inside our head (or an artificially conscious machine) and no such entity would or could have a context for everything (despite Kirby?s comments to me). Secondly, there is no need for these individual context spaces (in our heads) to be part of some ultimate context. We are able to transfer context between each other through language, specifically, natural language. In fact, that is the fundamental purpose of language, to transfer context.

4. In integrating human knowledge into a coherent whole, the method of integration is logic, defined as ?the art of non-contradictory identifica- tion.? Here ?identification? refers to the conceptual grasp of an object or entity in reality.

Context does not involve ?logic?. It is just the store for knowledge and knowledge is by itself, nether logical nor illogical. Logic requires conscious thought and thought is not knowledge, even though it involves knowledge and may produce new knowledge.

5. All knowledge is hierarchical. Concepts must be justified or validated by reference to earlier concepts, which are based on still earlier con- cepts, etc., all the way down to the perceptual roots. This validation process is called reduction.

I started with this belief 20 years ago (everyone does) but knowledge (the contextual itself) is not hierarchical. We often organize our thoughts this way, but the contextual elements are stored (for lack of a better word) in a way that preserves details and relation, not classification. Classification, taxonomy and hierarchy are elements of language. And this is one of the hardest things about trying to model knowledge and conscious thought. We are so used to organizing our thoughts using language that it obscures the actual underlying structure. We have to push ourselves hard to not think in language's terms.

Bob Hansen

Date Subject Author
11/21/13 Jerry P. Becker
11/21/13 Dave L. Renfro
11/21/13 Gary Tupper
11/25/13 Gary Tupper
11/25/13 Robert Hansen
11/25/13 Gary Tupper
11/25/13 Robert Hansen
11/25/13 Robert Hansen
11/25/13 Joe Niederberger
11/21/13 Robert Hansen
11/24/13 Joe Niederberger
11/25/13 Robert Hansen
11/25/13 Joe Niederberger
11/25/13 Joe Niederberger
11/25/13 Robert Hansen
11/25/13 Joe Niederberger
11/25/13 Robert Hansen
11/25/13 Robert Hansen
11/25/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Robert Hansen
11/26/13 Robert Hansen
11/26/13 Robert Hansen
11/26/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Louis Talman
11/26/13 Joe Niederberger
11/26/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Gary Tupper
11/26/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Joe Niederberger
11/26/13 Joe Niederberger
11/27/13 Joe Niederberger
11/27/13 Robert Hansen
11/27/13 Joe Niederberger
11/27/13 Robert Hansen
11/27/13 Joe Niederberger
11/27/13 Robert Hansen
11/27/13 Joe Niederberger
11/28/13 Robert Hansen
11/27/13 Joe Niederberger
11/28/13 Joe Niederberger
11/28/13 GS Chandy
11/28/13 Joe Niederberger
11/29/13 Robert Hansen
11/28/13 Joe Niederberger
11/29/13 GS Chandy
11/29/13 Joe Niederberger
11/29/13 Joe Niederberger
11/29/13 Robert Hansen
11/29/13 Joe Niederberger
12/4/13 GS Chandy
12/4/13 Joe Niederberger
12/11/13 Joe Niederberger
12/11/13 Robert Hansen
12/11/13 GS Chandy