extensionality


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extensionality

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As we cannot aspire to a total overlapping between the criterion of the extensionality of propositions and the criterion of the extensionality of terms or names, we shall consider that any couple of factual propositions, or propositions with a fluctuating alethic nature, but conflicting with respect to meaning and informational content (and the class of such associations is practically infinite) reveal the matrix of the inter-propositional function Opq = F, improperly called "contradiction.
The second paragraph manifests comparatively higher portions of extensionality than the first paragraph.
Notice that no axiom of extensionality is used here, we just use syntactical replacements.
These recurring images suggest Kahneman, Ritov, and Schkade's concept of "attitude"--a "psychological tendency" to see and evaluate the world with a particular disposition, and consistent interpretation of data, without regard to "the logic of extensionality.
I would say that so retrieves intensional "type" referents (nonpresupposed propositional contents), whereas it prototypically has as potential referents ones that have extensionality, or are propositions that have been mutually validated by the discourse partners: they can be treated as (actual) facts for the purposes of the ensuing discourse, not as possible facts, which is, I believe, why Dik considers so to have this kind of reference.
Then [direct sum] satisfies success, inclusion, vacuity, commutation, and extensionality.
Equality between sets is regulated by the standard extensionality axiom (E).
We can then define t [is an element of] u by [exists]F(u = {x: Fx} & Ft) and derive comprehension and extensionality.
As we see it, the problem is that the game-theoretic quantifier rules seem to assume extensionality, since the outcome of a game should not depend on which name is picked for a object.
317-36; and at greater length in my "Content and the Subtle Extensionality of`.
Let's take the simplest possible example, the axiom of extensionality, which says that two sets are equivalent when they have the same elements.
Post-relational databases are distributed on many servers, which are flexible and easily extendable big data systems 'holding the traits of extensionality (can add new fields easily) and scalability (can expand rapidly) regardless of volume .