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In particular it has had difficulties with a large group of "logical paradoxes" through its preoccupation with the Predicate Calculus and related structures to the exclusion of other formal structures that represent natural language more fully, and thereby escape these paradoxes.
Bolzano's syntax is accordingly substantially different from both traditional Aristotelian logic and standard first-order predicate calculus.
Post and the development of logic, John von Neuman and the ideas of David Hilbert, the contribution of Polish logicians to decidability theory and predicate calculus, and the development of symbolism in logic and its philosophical background.
What is truly revolutionary about the Fregean predicate calculus in this context is the extension of mathematical function argument analysis to the logical analysis of statements.
The first is the worry that such interpretations commit Nagarjuna to the view--held, he says, by some disreputable continental semioticians--that the principles of the predicate calculus, including at least non-contradiction and excluded middle, are laws only of thought and not of reality; and that, as a result, Nagajuna's thought, if so read, would be open to the possibility that reality is such that it transcends, or in some other way does not abide by, those principles.
If common nouns in this grammatical subject position are indeed logical subject-terms, this should require a thorough reevaluation of the adequacy of Frege's predicate calculus as a tool for the analysis of the logic and semantics of natural language.
In representing a proposition undergoing irtifa, the predicate calculus is used.
But our standard formal languages, for example, the predicate calculus, feature only singular terms.