D.III.4 The Relations of Plato's Dialectic to modern logic and metaphysics

Reprise

10.1093/oso/9780198812722.003.0009 ◽

2018 ◽

Author(s):

Paul M. Pietroski

Keyword(s):

Modern Logic ◽

Theories Of Truth ◽

Theories Of Meaning

This chapter summarizes the main themes. Humans naturally acquire generative procedures that connect meanings with pronunciations. These meanings are neither concepts nor extensions. Meanings are composable instructions for how to access and assemble concepts of a special sort. In particular, phrasal meanings are instructions for how to build monadic (i.e., predicative) concepts that are massively conjunctive. Theories of meaning should not be confused with theories of truth. Lexicalization is a process of introducing concepts that can be combined via simple operations whose inputs must be monadic or dyadic. In theorizing about meanings, we can and should eschew much of the powerful typology and combinatorial operations that the founders of modern logic introduced for very different purposes.

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The Road to Modern Logic—An Interpretation

Bulletin of Symbolic Logic ◽

10.2307/2687794 ◽

2001 ◽

Vol 7 (4) ◽

pp. 441-484 ◽

Cited By ~ 30

Author(s):

José Ferreirós

Keyword(s):

Order Logic ◽

Point Of View ◽

First Order Logic ◽

Theoretical Point ◽

Primary Role ◽

Philosophical Discussion ◽

Modern Logic ◽

Core System ◽

First Order ◽

The Road

AbstractThis paper aims to outline an analysis and interpretation of the process that led to First-Order Logic and its consolidation as a core system of modern logic. We begin with an historical overview of landmarks along the road to modern logic, and proceed to a philosophical discussion casting doubt on the possibility of a purely rational justification of the actual delimitation of First-Order Logic. On this basis, we advance the thesis that a certain historical tradition was essential to the emergence of modern logic; this traditional context is analyzed as consisting in some guiding principles and, particularly, a set of exemplars (i.e., paradigmatic instances). Then, we proceed to interpret the historical course of development reviewed in section 1, which can broadly be described as a two-phased movement of expansion and then restriction of the scope of logical theory. We shall try to pinpoint ambivalencies in the process, and the main motives for subsequent changes. Among the latter, one may emphasize the spirit of modern axiomatics, the situation of foundational insecurity in the 1920s, the resulting desire to find systems well-behaved from a proof-theoretical point of view, and the metatheoretical results of the 1930s. Not surprisingly, the mathematical and, more specifically, the foundational context in which First-Order Logic matured will be seen to have played a primary role in its shaping.Mathematical logic is what logic, through twenty-five centuries and a few transformations, has become today. (Jean van Heijenoort)

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Syllogism and quantification

Journal of Symbolic Logic ◽

10.2307/2963679 ◽

1962 ◽

Vol 27 (1) ◽

pp. 58-72 ◽

Cited By ~ 14

Author(s):

Timothy Smiley

Keyword(s):

Predicate Logic ◽

Modern Logic ◽

First Order ◽

First Order Predicate Logic

Anyone who reads Aristotle, knowing something about modern logic and nothing about its history, must ask himself why the syllogistic cannot be translated as it stands into the logic of quantification. It is now more than twenty years since the invention of the requisite framework, the logic of many-sorted quantification.In the familiar first-order predicate logic generality is expressed by means of variables and quantifiers, and each interpretation of the system is based upon the choice of some class over which the variables may range, the only restriction placed on this ‘domain of individuals’ being that it should not be empty.

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