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Definition Intensionality/Boer: is nowadays negative, defined as non-intensionality.
So we need a definition of "extensional sentence".
Denotation/denoting/Boer: Assuming, denotating terms are: names, indices, demonstrativa and mass terms.
Definition English +/Boer: be an extension of English by zero or more denotating expressions and predicates.
Definition extensional reading/Boer: (preliminary): E.g.: "A thing x is such that ... x ..." is unique, then it is an extensional reading S iff it fulfills the following extensional principles:
Definition strong principle of existential generalization/extensionality/Boer: for a denotating term D and variable v which does not belong to S if S has the form [... D ...], then one can conclude from S validly [an existing thing v is such that ... v ...].
Definition replacement principle for co-extensive predicates/Boer: ...from [for object x1,...xn, either P(x1, ... xn) or Q (x1, ... xn) or neither P nor Q], one can deduce every sentence by replacing one or more occurrences of P in S by Q. (DF). (LL).
Definition substituting principle for material-equivalent propositions/Boer: for every sentence P and Q in English +, if P is present in S, one can conclude from S and [Either P and Q, or neither P nor Q] every sentence one or several occurrences of P in S by Q.
Definition of the substitutability of the identity/Boer: for each denotating term D and E of English+: if S has the form [... D ...], one can deduce every sentence from S and an equation of the form [D = E] (or [E = D ] which is formed by replacing one or more occurrences of D by E in S.
Validity/everyday language/Boer: can only be asserted relatively to a particular reading.
English +/Boer: we need it to exclude the fact that the four principles are not trivially fulfilled by there being no counterexamples to the inferences in question simply because there are not enough names or predicates to formulate one._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Steven E. Boer
Thought-Contents: On the Ontology of Belief and the Semantics of Belief Attribution (Philosophical Studies Series) New York 2010
Steven E. Boer
Knowing Who Cambridge 1986