SUO: Re: Critique Of Non-Functional Reason
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| A. Automated Reasoning (AR)
|
| The standard will be suitable for automated logical inference
| to support knowledge-based reasoning applications.
| B. Inter-Operability (IO)
|
| The standard will provide a basis for achieving Inter-Operability
| among various software and database applications.
[A]
Examples to be used again:
| 9. "All men are mortal" implies "all white men are mortal"
|
| 11. All men are mortal implies all white men are mortal*
|
| 13. All men are mortal => all white men are mortal
We continue with Quine's treatment of "the relation of implication".
| A trivial analogue, 'material implication', may be said to hold whenever the
| truth-functional conditional which has the one statement as antecedent and
| the other as consequent is true. Thus one statement materially implies
| another provided merely that the first is false or the second true.
| This relation is so broad as not to deserve the name of implication
| at all except by analogy. But -- and this is the point usually
| missed -- "materially implies" is still a binary predicate, not
| a binary statement connective. It stands to "=>" precisely as
| "is false" stands to "~". Insertion of the connective "=>"
| between statements as in (13) amounts to inserting the verb
| "materially implies", not between the statements themselves,
| as in (11), but between their names as in (9).
|
| Quine, 'Mathematical Logic', page 29.
|
| If we were willing to reconstrue statements as names
| of some sort of entities, we might take implication as
| a relation between those entities rather than between the
| statements themselves; and correspondingly for equivalence,
| compatibility, etc. This procedure would dissolve the distinction
| between material implication and the truth-functional conditional, and
| likewise between other sorts of implication and other sorts of conditionals.
| "Implies" would come to enjoy simultaneously the status of a binary predicate
| and the status of a binary statement connective. Expressions such as (11) would
| be legitimized; and so also would the iterated use of implication, characteristic
| of Lewis and Smith. For thus construing statements as names some slight support
| can be adduced, indeed, by appeal to substantive clauses. The statement
| "All men are mortal" might be held to designate that abstract entity,
| whatever it is, which we ordinarily designate by the substantive
| "that all men are mortal". A deterring consideration,
| however, is the obscurity of these alleged entities. What
| are they like? and under what circumstances may the entities
| designated by two statements be said to be the same or different
| entities? Certain entities which are perhaps less obscure than these
| but no less abstract will indeed be countenanced at a later point (Section 22),
| viz. classes or properties, if only through ignorance of how to get on without them;
| but entities designated by statements are happily dispensable. It thus seems well
| to adhere to the common-sense view that statements are not names at all, though
| they may contain names along with verbs and adverbs and the rest. A statement
| remains meaningful, but meaningful by virtue of its structure together with
| the meanings of the constituent names and other words; its meaningfulness
| does not consist in its being a name of something.
|
| Quine, 'Mathematical Logic', page 32.
|
| Willard Van Orman Quine,
|'Mathematical Logic', Revised Edition,
| Harvard University Press, Cambridge, MA,
| 1940, 1951, 1981.
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