On need for mathematics of emotions

(from post to JCS-online @ 2010-11-27)

 

This is an outline of several things about science of mind/consciousness, which should be pointed out separately.

Structure of fundamental

The axiomatic system, in all sciences, is a system of object classes and relations, which can not be reduced to anything else in that axiomatic system. By proving that any one axiom could be built and proven by other axioms will take away it's axiomatic status.

The fact that an emotion, a qualia etc. can not be reduced to mathematical construct, has two main applications:

- Physical entities as pure mathematical constructs (structures of causalities) can not define the whole.

- Computer as purely mathematical computing device can not be programmed to have mind or feelings.

Thus, the mathematics itself must be evolved. We can not build a new physics without having new math. We can not reduce mathematical construct to a feeling - say, when we have some math formula like $a = integral of f(x)$ -, we can't prove, using formal mathematical rules, that there is some feeling or qualia.

I have already used that idea in some letters, but I try to reword it in this, more general context here.

Say that we have a feeling or mind state - say, "joy". Say that physical world _is_ physical information. We assume that this physical information can be represented as mathematical information (this is roughly what we mean by word "information"). Now, we must define "joy" to be proven to exist in some construct. As "joy" is not a neutral information, like $integral of f(x)$, we actually have no way to $define$ it, mathematically - any definition should give a complete picture of what we try to define. Whatever definition of "joy" - say, "x = 2y" or "x = y + z" if you know what I mean - must be actually pointing to "joy" in wholeness and completeness of this word. In case we have several different concepts, which are marked by this word, they all should have such definitions. Basically we should able to define "joy" in terms of set theory - as most of math is defined for now - in such way that it makes sense; in such way that pure, detached mathematical investigation would, knowing the actual meaning of "joy", show by formal mathematical reasoning that this definition includes any and all properties of pure joy. Those properties must include feelings of joy, thus they must include some feeling of it - and we can't, using math of today, formally prove any such property of an object described by mathematical formula - looking just the basic formal rules of mathematical reasoning, there is clearly no way to show that joy or some feeling must result from some mathematical construct. Thus, given that physics is based on mathematics, physics can not contain any of those feelings.

Now, as physics will not be physics anymore in case it would not be based on math and any modern theory of consciousness must have a physical explanation - but it can also develop physics to level, where such explanation is possible -, we need mathematics of mind to be built.

We need a theory, which is the following:

- It's neutral in sense that it does not directly say anything about physical world, the world outside our minds.

- It's a modelling language - it allows us to model different real, possible or coherent realities to test their reality by experiment.

- It's capable to capture essences of our minds sharply and completely.

Science of object or a path

Clearly, such mathematics needs a mind, which is capable to understand it with clear sharpness - as much as math needs mathematically sharp mind. We need minds, which allow to discriminate those feelings clearly and understand their fundamental compounds. Which can try to find more basic elements and show that some larger ones can be reduced to those - and this kind of reduction is not only reduction to smaller, it's also reduction to the whole in it's simplicity. Emotions are not necessarily composed of smaller parts, they might also be reflections of bigger wholes.

Here, the new math needs to be worked out - and only in terms of this new math can we work out the new physics. Many religious traditions, also discussed here in this list and journal are giving us different systems - but we need the new European tradition to be started, which would develop synchronously to what we can test in our current mind states; once again, we mostly need an idea of such science to be considered plausible and important in describing world as it is.