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These findings of Gödel and Montague are closely related to the general study of computability, which is usually known as recursive function theory (see mathematics, foundations of: The crisis in foundations following 1900: Logicism, formalism, and the metamathematical method) and which is one of the most important branches of contemporary logic.
The subject of combinations of logics is still a young topic in contemporary logic.
In contemporary logic they are symbolized by function letters that are followed by the appropriate number of arguments, $f(x),g x,y $, etc.
Other references include, for example, the section on predicativism in the entry on philosophy of mathematics and the entry on paradoxes and contemporary logic.
*21 presents the "General Theory of Relations" (the theory of relations in extension; in contemporary logic these are treated as sets of ordered pairs, following Wiener).
For a detailed discussion and history of the paradoxes of self-reference in general, see the entry on paradoxes and contemporary logic.
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Those involved in state ritual are brought onstage only to be mocked, and the propositions of contemporary logic-choppers are drawn into the unending whirl of paradox, spun out to their conclusions, and so abolished.
Anyone remotely acquainted with contemporary symbolic logic, philosophy of logic, analytical metaphysics, philosophy of language, philosophy of mind, philosophy of science, and even modern theories of justice, will appreciate the motivation for according such philosophy the status of a science.
Of course, we need not and should not interpret Spinoza's following-from relation as the strict logical entailment of contemporary modal logic.
The interest of studying combinations of logics may thus be seen as a reflex of the pluralist view of contemporary logical research.
Perhaps his greatest achievement, as far as I am concerned, was to demonstrate beyond doubt the intellectual respectability of a fully-fledged philosophical position based on a contemporary heterodox logic.
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