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**These are excerpts and elaborations from my book "The Nature of Consciousness"**

Unlike Probability theory,
Fuzzy Logic represents the real world without any need to assume the existence
of randomness. For example, relative frequency is a measure of how a set is a
subset of another set. Many of Physics' laws are
not reversible because otherwise causality would be violated (after a
transition of state probability turns into certainty and cannot be rebuilt
working backwards). If they were expressed as "ambiguity", rather
than probability, they would be reversible, as the ambiguity of an event
remains the same before and after the event occurred. Fuzziness is pervasive in
nature (everything is a matter of degree), even if science does not admit
fuzziness. Even Probability Theory
still assumes that properties are crisp, while in nature they rarely are. Furthermore, Heisenberg's “uncertainty principle” (the more a quantity is accurately
determined, the less accurately a conjugate quantity can be determined) can be
reduced to the” Cauchy-Schwarz inequality”, which is related
to “Pythagoras’ theorem”, which is in turn
related to the “subsethood theorem”, i.e. to Fuzzy Logic. One is tempted to rewrite
Quantum Mechanics using Fuzzy Theory instead of Probability Theory. After all,
Quantum Mechanics, upon which our description of matter is built, uses
probabilities mainly for historical reasons: Probability Theory was the only
theory of uncertainty available at the time. The result is that Physics has a
standard interpretation of the world that is based on population thinking: we
cannot talk about a single particle, but only about sets of particles. We
cannot know whether a particle will end up here or there, but only how many
particles will end up here or there. The interpretation of
quantum phenomena would be slightly different if Quantum Mechanics were based
on Fuzzy Logic: probabilities deal with populations, whereas Fuzzy Logic deals
with individuals; probabilities entail uncertainty, whereas Fuzzy Logic entails
ambiguity. In a fuzzy universe a particle's position would be known at all
times, except that such a position would be ambiguous (a particle would be
simultaneously "here" to some degree and "there" to some
other degree). This might be viewed as
more plausible, or at least more in line with our daily experience that in
nature things are less clearly defined than they appear in a mathematical
representation of them.
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