So far we have considered extensional arguments against internalism.
That extensional event was part of a much wider extensional province in north-central Africa.
However, a large debate remained unsettled, and that was the choice between the two versions of type theory that Martin-Löf presented: the earlier intensional theory, and the extensional theory first proposed in CMCP.
But an extensional theory is, of course, not thereby free of problems.
A very different variant of the Extensional approach was proposed by C.D.
Among the extensional logicians are George Boole, Augustus De Morgan, Charles Peirce, and John Venn.
Goodman eventually rejects intensional approaches and opts for an extensional theory for sameness of meaning.
Among the variety of objects in the extensional canon, sets are distinguished by their almost complete absence of structure.
Bolzano's system of extensional propositional logic is closely connected with his extensional logic of ideas.
Not necessarily, for the Extensional approach is perfectly compatible with version of Presentism which grant to the present a brief duration.
Section VII has as premises extensional relations between ideas, e.g., from A is included in B, we conclude to the equivalence of this premise with A is B.
A function concept may now be called extensional if and only if it requires functions that are extensionally equivalent at the actual world to be identical.
The notion of join semi-lattice is more general and far less constrained than classical extensional mereology (see Moltmann 1997, ch. 1, for other criticisms of the mereological extensional view).
(A correspondent of Lambert, Georg von Holland, had experimented with an extensional theory, and in 1839 the English writer Thomas Solly presented an extensional logic in A Syllabus of Logic, though not…
(A correspondent of Lambert, Georg von Holland, had experimented with an extensional theory, and in 1839 the English writer Thomas Solly presented an extensional logic in A Syllabus of Logic, though not an algebraic one.)
We label this stronger theory EM, for Extensional Mereology, the attribute ‘extensional’ being justified precisely by the exclusion of countermodels that, like the one in Figure 4, contain distinct objects with the same proper parts.
To distinguish the extensional concept of functions-as-sets from the non-extensional concept of functions-as-rules, the latter is often referred to as an ‘intensional’ function concept, in part because of the ostensibly intensional concept of a rule involved.
Since Extensional specious presents comprise earlier and later phases that are experienced together, in a single unified (albeit extended) state of consciousness, it may well be that Extensional models are incompatible with the Presentist conception of time, according to which only what is present is real.
Before leaving this overview of the quest for an extensional characterization of higher-order sequentiality, we should mention Bucciarelli & Ehrhard (1994) who introduced a refinement of the dI-domains of Berry supporting a notion of strongly stable function which allows them to build an extensional model of PCF, which is not fully abstract.
The idea of possible worlds raised the prospect of extensional respectability for modal logic, not by rendering modal logic itself extensional, but by endowing it with an extensional semantic theory — one whose own logical foundation is that of classical predicate logic and, hence, one on which possibility and necessity can ultimately be understood along classical Tarskian lines.
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The idea of possible worlds raised the prospect of extensional respectability for modal logic not by rendering modal logic itself extensional but by endowing it with an extensional semantic theory — one whose own logical foundation is that of classical predicate logic and hence one on which possibility and necessity can ultimately be understood along classical Tarskian lines