A Handle on Mind Space .Wading in the Ocean of Ignorance One way to get a handle on a slippery object is to ask an impertinent question of it: If ideas are like mathematical objects then what is the difference between a circle and the idea of a circle? The answer is none at all. The problem arises in contrasting a particular with the universal. If I am seeing or visually imagining a circle, how does that particular circle differ from the universal Circle? The difference is much less than you might think. For an immaterialist there is little distinction between seeing and thinking. To think about something is to attend to it in some context. You can think of me as a Platonist without the cave. The cave is just in our imagination.
There are circles, ellipses, loops and hoops. Which is the real Circle? They all are to a degree. A circle contains the idea of a loop and vice versa. Every idea contains every other, to a degree. This is simply the doctrine of internal relations. I do not have a mathematical model for internal relations at the moment.
How would a hula-hoop in my basement relate to the Circle? Well, it partakes of circularity, of inertia and of location. The latter two attributes are distinguishing, but they need be no less ideal. What holds these attribute together and in place if there is not a material substance? Surely there is a distinction between a substance and its idea. If there were it would be very hard to discover. Every idea has some sort of substantiality and locatability. Are there more hula-hoops than there are Circles? Every idea partakes of numericity, it depends on the context.
The relation between hula-hoop and Circle is not unlike the relation between person and God. Each contains the other. Which one seems more real can depend on the circumstance and perspective.
The external projection of ‘physical’ space and time will be central to our understanding of mind space. We should not doubt that there are many ways to skin this particular cat. With mathematics there usually is an embarrassment of riches. There are also extremals. There is incarnation and Incarnation. We are only wading in the ocean of ignorance. There will be opportunity for swimming.
(10-9-98)
--------------------Let’s do a retake on the circle problem. On the one hand there is an experience, and on the other hand there is a possible mathematical description of the mental dynamics of that experience. One would suppose that I could experience the description without having the experience, although it is possible that I could not correctly understand a purely mathematical description without a partial recall of the actual experience. In other words it could be that I would look at a novel mathematical object and then recognize the experience to which it corresponded. It might also be that there is a unique correspondence between every mathematical object and every experience. With this new understanding would come a decisive shift in consciousness.
It is even conceivable that every integer could function in this manner, to the extent that, as we seem to be finding in number theory, every integer can be associated with a unique, non-arbitrary mathematical structure. Questions concerning the countability of significant structures would have to be addressed.
Elsewhere I have stated that all mentation is based upon feeling. If that were the case then there would also have to be an intimate relation between math and feeling.
Normally one makes a distinction between form and substance or between structure and content. But if there were going to be an ontic and epistemic unity then one would have to posit that it is structures all the way down. This is possible.
Allegedly mathematics is reducible to pure logic. By the above arguments it ought also to be reducible to feeling. How these two reductions can both be carried out is beyond my present understanding, but it need not be a contradiction. Perhaps it is the case of transduction versus reduction.
It should be noted that, ironically perhaps, the challenge facing the monistic idealist is not entirely unlike that facing the materialist or now the functionalist. At least we can sympathize.
Later I hope to take up the role that quantum computing might play in shedding light on these difficult issues.
(10-15-98)
------------------P.P.S. If a color-blind mathematician were to examine the mathematical structure of color experience, would that person have a color experience? Perhaps this question is undecidable. Can color-blind people imagine colors they can’t see? Can the rest of us? Perhaps there will be cognitive restrictions that correspond to the sensory restrictions. One would have to consider the typology of the restriction.
One might say that in the more intuitive mathematics of the future, the mathematical structures would necessarily be more self-referential. The Godelian arithmetic would have to be greatly ramified.
Obviously there are some semiotic issues here that will need elucidation.
(10-17-98)
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rev. 10/17/98