# [time 274] Re: [time 273] Re: [time 269] Re: [Time 267] and [Time 83] and [Questionsabout Time and fuzzy hypersets]

Stephen P. King (stephenk1@home.com)
Mon, 03 May 1999 10:52:03 -0400

Dear Ben,

Ben Goertzel wrote:
>
> > How space and time are dynamical inverses is somewhat like a thought
> >that I have been mulling over for a long time! :) But I never thought of
> >it this way! ({X = ~X} -> (X = X}) <-> ({X = X} -> {X = ~X}) I think
> >that a infomorphism can be defined here! We just need to figure out the
> >classificatioons.
>
> I will work on formalizing this insight better

Excellent! :)

> > Could you explain your reasoning of why the Min() and Max() operators
> >of fuzzy logic are "not at all psychologically realistic"? This is
> >driving me nuts! ;)
>
> This is not a matter of reasoning, it is a matter of empirical science.
> There are numerous psychology papers on this.
>
> If a human assesses the degree to which a bird is big to be .1, and the
> degree to which a bird is hungry to be .9, then the human will NOT assess the degree to which
> the bird is "big or ugly" to be .1, nor will the human assess the degree to which the
> bird is "big and ugly" to be .9. Nowhere near!!!

I'll try to see if this can be fixed! ;) Is this a non-monotonicity
problem? ugly =/= hungry

> Now humans are not perfect reasoning systems, so you could argue that
> humans are just not doing things right.
>
> But in building an artificial reasoning system I have seen no reason to use
> Min and Max instead of probability theory. the use of Min and Max is based on the assumption
> that the distributive law must hold exactly for reasoning on properties of fuzzy degrees of
> certainty. I don't believe that the distributive law must hold. I believe in elementary probability
> which shows that in this case it does not hold.

Perhaps we can weaken the usual definition of Min and Max... ;) It is
just that the way that probabilities can be derived is too good to be
discounted. Also, Kosko's information wave mechanics is promising! I do
think that his work need to be generalized to be usefull to us. I guess
that that is my mission... :)

Later,

Stephen
> ben

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