> >>> Brent
> >>> You state: Physical laws are models we make up to explain and predict
> >>> the world.  Are properties of mathematics then dual, being both
> >>> representational (models) and encoded (rules) as instantiated brain
> >>> functions?
> >> Mathematics is a subset of language in which propositions are related by 
> >> rules of
> >> inference that preserve "truth".  We can use it to talk about all kinds of 
> >> things, both
> >> real and fictional.  We try to create mathematical models where possible 
> >> because then we
> >> have the rules of inference to make predictions that are precise.  Where 
> >> our models are
> >> not mathematical, e.g. in politics or psychology, it's never clear exactly 
> >> what the model
> >> predicts.
> >> I think the rules of inference are encoded in our brains.  See William S. 
> >> Coopers book
> >> "The Evolution of Reason".
> >>> In other words could the singularity in mathematics you refer to be
> >>> further divided?
> >> The singularity I was referring to is the hypersurface of infinite energy 
> >> density and
> >> curvature which general relativity predicts at the center of a black hole 
> >> and the Big
> >> Bang.  It is in the mathematical model - which only shows that the model 
> >> doesn't apply at
> >> these extreme conditions.  This was not a surprise to anyone, since it was 
> >> already known
> >> that general relativity isn't compatible with quantum mechanics and is 
> >> expected to
> >> breakdown at extremely high energies and short distances.
> >> Brent
> >   Brent
> > I was attempting to go down another layer of understanding as I see
> > it.  I will restate an abbreviated opinion:
> > Numerals (mathematics) and languages are themselves fundamental
> > instantiations of the laws/rules/inferences of truth abstract
> > mathematics representing the precise observed or discovered structure
> > and order of the universe and the semantically less precise languages
> > are used to interpret and communicate the mathematical models in
> > descriptions and predictions of the universe.
> I think it's a mistake to think mathematics has something to do with truth.  
> Truth is an
> attribute of a proposition that expresses a fact.  Mathematics consists of 
> relations of
> inference between propositions - which may or may not express anything at all 
> beyond the
> relations.
> > Mathematics...has multi faceted properties, being at least (1)
> > representational numbers as in descriptively enumerated models as well
> > as adjective position in spatiotemporal sequence (ordinals) and (2)
> > computable numbers as in counting and arithmetic.
> Mathematics doesn't exist in space and time; although it may be used to 
> describe them.

 Exactly, that is what I was attempting to state. You, and most other
contributors to this list are very knowledgeable but I believe that
some of the properties of numbers and mathematics may be overlooked as
to their relevance, but I may be wrong as I have only been observing
the “Everything” list for a short time.

Ordinal numbers are “descriptive adjectives” as to relational
position.  The relative position of an event in order being 1st, 2nd,
3rd etc. has describable meaning. The representational description of
mental events and external existent conditions are related as to their
position in the sequence of time. Time and place both exude conditions
that are describable and somewhat predictable. The representational
and descriptive conditional position of the earth to the sun, moon and
stars gives rise to conditions at a relational position in time.

The point is that numbers represent computation (counting and
arithmetic) and the ordinal attribute of numbers represent words that
communicate descriptive relational meaning. This appears to give dual
meaning to numbers that human brain/consciousness can distinguish,
represent, organize and compute.

An example: The mathematical “golden ratio” as observed in art and
nature appears to be pleasant in a geometrically way to the human
vision and brain/consciousness.

> > Your statement: I think the rules of inference are encoded in our
> > brains , This, I think, infers that primitive mathematics and
> > languages are instantiated in the biological brain and can,
> > *potentially*, represent or reflect any and all laws and rules
> > fundamental to the real (even abstract) and fictional universe.
> I don't think laws/rules are fundamental.  They are compact models we make up 
> to explain
> and predict facts.
> Brent
> > The
> > role of human embodied consciousness in any theory of everything is
> > established by this fact.
> > Mathematics may be a subset of language as you state or language
> > could also be an extension or instantiation (as a concrete verbal
> > idea) of what primitive mathematics represents (abstract rules/laws).
> > In either case it becomes circular as to what is more relevant
> > mathematics or the language to understand what the mathematics
> > represents or enumerates.
> > It is my opinion that there is no singularity but a duality which
> > roughly could be stated as both a state of being (quanta) and the
> > reason of being (qualia) (access to abstract primitive laws/rules or
> > as you state newer information ).
> > Perhaps monistic materialism and monistic idealism are semantically
> > created notions that lack newer information .
> > Thanks for your comments.

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