>>> The universe is an hypersphere surface. The universe is the boundary
>>> of the 4th dimension. The universe came from nothing and is nowhere.
>>> There is no outside of the Hypersphere. There is only one hypersphere.
>>> There can be only one universe because this universe goes on forever.
>>> Mitch Raemsch Twice Nobel Laureate 2008
http://en.wikipedia.org/wiki/Semantics_of_logic
"The truth conditions of various sentences we may encounter in
arguments will depend upon their meaning, and so conscientious
logicians cannot completely avoid the need to provide some treatment
of the meaning of these sentences. The semantics of logic refers to
the approaches that logicians have introduced to understand and
determine that part of meaning in which they are interested; the
logician traditionally is not interested in the sentence as uttered
but in the proposition, an idealised sentence suitable for logical
manipulation.
Until the advent of modern logic, Aristotle's Organon, especially De
Interpretatione, provided the basis for understanding the significance
of logic. The introduction of quantification, needed to solve the
problem of multiple generality, rendered impossible the kind of
subject-predicate analysis that governed Aristotle's account, although
there is a renewed interest in term logic, attempting to find calculi
in the spirit of Aristotle's syllogistic but with the generality of
modern logics based on the quantifier.
The main modern approaches to semantics for formal languages are the
following:
Model-theoretic semantics is the archetype of Alfred Tarski's semantic
theory of truth, based on his T-schema, and is one of the founding
concepts of model theory. This is the most widespread approach, and is
based on the idea that the meaning of the various parts of the
propositions are given by the possible ways we can give a recursively
specified group of interpretation functions from them to some
predefined mathematical domains: an interpretation of first-order
predicate logic is given by a mapping from terms to a universe of
individuals, and a mapping from propositions to the truth values
"true" and "false". Model-theoretic semantics provides the foundations
for an approach to the theory of meaning known as Truth-conditional
semantics, which was pioneered by Donald Davidson. Kripke semantics
introduces innovations, but is broadly in the Tarskian mold.
Proof-theoretic semantics associates the meaning of propositions with
the roles that they can play in inferences. Gerhard Gentzen, Dag
Prawitz and Michael Dummett are generally seen as the founders of this
approach; it is heavily influenced by Ludwig Wittgenstein's later
philosophy, especially his aphorism "meaning is use".
Truth-value semantics (also commonly referred to as substitutional
quantification) was advocated by Ruth Barcan Marcus for modal logics
in the early 1960s and later championed by Dunn, Belnap, and Leblanc
for standard first-order logic. James Garson has given some results in
the areas of adequacy for intensional logics outfitted with such a
semantics. The truth conditions for quantified formulas are given
purely in terms of truth with no appeal to domains whatsoever (and
hence its name truth-value semantics).
Game-theoretical semantics has made a resurgence lately mainly due to
Jaakko Hintikka for logics of (finite) partially ordered
quantification which were originally investigated by Leon Henkin, who
studied Henkin quantifiers.
Probabilistic semantics originated from H. Field and has been shown
equivalent to and a natural generalization of truth-value semantics.
Like truth-value semantics, it is also non-referential in nature."
