List, Jeff:
> On Feb 9, 2019, at 3:08 PM, Jeffrey Brian Downard <[email protected]>
> wrote:
>
> For my part, I take the logical arguments for the categories to be based on
> the requirements for having valid arguments as well as meaningful
> propositions and terms. The question that he articulates in "On the Logic of
> Mathematics, an attempt to develop my categories from within" is: what are
> the elemental kinds of relations--both formal and material--that are
> necessary for logic?
Just several wandering thoughts about Jeff’s well-poised question.
Some questions this question raises:.
How do "elemental kinds of relations” differ?
If at all?
For example: One can assert that only one logical term exists for the concept
of “elemental kinds of relation”. All other linguistic terms are synonymous
with the concept of the unity of logic. (Could mathematicians, following
Quine, call such a relation a “variable”?)
Are “elemental kinds of relations” illated?
For example, One can assert that “All elemental kinds of of relations are
independent, interdependent and dependent.” because of th unity of nature and
the multiple languages for describing that (asserted) singularity.
Are formal and material kinds of elemental relations the only possible sorts of
elemental kinds of relations?
For example, in terms of antecedents and consequences and Aristotelian
causality, formal and material causes are necessary for efficient and final
causes.
Are (all?) elemental kinds of relations necessarily related by linguistic
sorities, however slender the thread of logic may become, as a consequence of
Tarski’s foundational assertion of the necessity of meta-languages for formal
human symbolic communication?
For example, the elemental physical relations must be expressed linguistic
terms of physical units of measure, the elemental chemical relations must be
expressed in the linguistic terms of chemical units of measure (atoms), the
elemental units of life must be expressed in linguistic terms of biological
measure (cells) (following A. Comte’s hierarchical reasoning.)
The noted physicist, John von Neumann, asserted that scientists had options:
> The basic idea of this approach to logic is that the system of logic which
> one uses should be derived from aggregates of experiences relative to the
> main application which one wishes to make-logics should be inspired by
> experience. (1937)
CSP's notion of an “identity” as in a “line of identity” seems to be ignored by
most modern logicians, perhaps because it can be so closely associated with the
logic of proper names. One wonders if the notion of identity is an “elemental
kind of relation” for CSP.
Cheers
Jerry
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