re:RE: SUO: RE: First piece of 4D ontology
>### You and others use KIF to specify axioms, rather than an
>"accepted" syntax such as mathematics ("accepted" = "universally"
>semantically agreed, at least since Hilbert and consorts --and
>pardon the many quotes) in which, incidentally, the 4 axioms could
>be written much more concisely.
The use of KIF syntax is one choice among many, and is of little
significance in itself. There is no 'standard' syntax for logic or
mathematics ; there are prefix, postfix, infix and many other
syntactic variations (not to mention graphical notations), and the
choice between them is only an aesthetic or pragmatic issue.
Offer a silent prayer of thanks that we arent writing it all in XML,
which is rapidly becoming the 'standard' for a new generation.
>Clearly this is done with a certain
>form of future computer processing in mind, i.e. interpretation by
>a program for purposes of storage, validation, reasoning, ... by
>computers. This requires a formal definition of the syntax used --in
>the case at hand this likely involves an (the!) ontology itself we
>are trying to define. So, in order to avoid infinite regress, we
>have no alternative but to axiomatically define (= agree on) the
>basic predicates such as "exists ?x ?y".
Exists is not a predicate, it is the existential quantifier, as used
throughout logic for about a century now. Its meaning is not (cannot)
be given axiomatically, but is properly expressed by the rules of
interperation for the formal language. In this case, (exists (?x)
PHI[?x] ) is true in an interpretation I if there is something in the
universe of I such that if ?x is interpreted as denoting that thing,
then PHI[?x] denotes True in that interpretation. (This is a sketch
of the precise definition.)
>E.g. if this merely involves
>finite sets, one "only" has to agree on the definition of the extension
>of ?x and on the lookup of ?y in this extension --but one assumes there
>is more at play here, otherwise the whole SUO becomes an exercise
>in triviality.
There is no requirement that a universe of interpretation be finite.
>I believe thick volumes of logic have been written on
>this subject of "exists" alone (cfr. the Intuitionists, ...) so a
>proper initial agreement seems required. Of course I don't doubt that
>[the interpreter for] KIF++ has/will "prescribe" this; my point is
>that it will be required at every step and needs to be performed
>explicitly.
If this means that the formalism being used should be given a clear
semantics, I agree wholeheartedly. I would however point out that
this requirement seems to be at odds with a Peircian emphasis on
meaning depending on the circumstances of use of a symbol by an agent.
Pat Hayes
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