The Road to Modern Logic—An Interpretation

  title={The Road to Modern Logic—An Interpretation},
  author={Jos{\'e} Ferreir{\'o}s},
  journal={Bulletin of Symbolic Logic},
  pages={441 - 484}
  • J. Ferreirós
  • Published 1 December 2001
  • Philosophy
  • Bulletin of Symbolic Logic
Abstract This 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… 

Logic in the 1930s: Type Theory and Model Theory

It is argued that the move from type theory to first-order logic is better understood as a gradual transformation, and further, that the contributions to semantics made in the type-theoretic tradition should be seen as central to the evolution of model theory.

On Dedekind's Logicism

The place of Richard Dedekind in the history of logicism is a controversial matter. From the point of view of contemporary philosophy of mathematics, what is of interest is Dedekind’s contribution to

8 Logicism , Ontology , and the Epistemology of Second-Order Logic

At the basis of Frege’s logicism is his logic. And, although Frege does clearly distinguish firstfrom second-order quantification, at least in Grundgesetze,1 he never suggests that there might be any

Hilbert, logicism, and mathematical existence

David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following

Logicism, Ontology, and the Epistemology of Second-Order Logic

  • R. Heck
  • Philosophy
    Oxford Scholarship Online
  • 2018
In two recent papers, Bob Hale has attempted to free second-order logic of the “staggering existential assumptions” with which Quine famously attempted to saddle it. This chapter argues, first, that

A different approach to logic: absolute logic

The paper provides both the theoretical material and a fully documented example of deduction to obtain a general and unifying approach to logic and a faithful model of human mathematical deductive process.

A different approach to logic

The paper provides both the theoretical material and two fully documented examples of deduction to obtain a general and unifying approach to logic and a faithful model of human mathematical deductive process.

Notes on Substitution in First–Order Logic

The outcome for F OL is that substitution is simply string replacement of one constituent by another, and this substitution is also simpler than the standard one, raising the question why substitution is chosen for FOL.

Logical Axiomatizations of Space-Time. Samples from the Literature

The present paper gives samples from an ongoing broader research project which in turn is part of a research direction going back to Reichenbach and others in the 1920’s and tries to give some perspective on the literature related in a broader sense.

The Completion of the Emergence of Modern Logic from Boole's The Mathematical Analysis of Logic to Frege's Begriffsschrift

Both Boole and Frege mathematised logic, but Frege's goal was to logicise mathematics, however the emergence of modern logic in Frege should be detached from his logicism.



Notes on types, sets, and logicism, 1930-1950

The present paper is a contribution to the history of logic and its philosophy toward the mid-20th century. It examines the interplay between logic, type theory and set theory during the 1930s and

19th Century Logic Between Philosophy and Mathematics

Abstract The history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in

Hilbert and the emergence of modern mathematical logic

Hilbert's unpublished 1917 lectures on logic, analyzed here, are the beginning of modern metalogic. In them he proved the consistency and Post-completeness (maximal consistency) of propositional

The emergence of first-order logic

To most mathematical logicians working in the 1980s, first-order logic is the proper and natural framework for mathematics. Yet it was not always so. In 1923, when a young Norwegian mathematician

The way of logic into mathematics

Using a contextual method the specific development of logic between c. 1830 and 1930 is explained. A characteristic mark of this period is the decomposition of the complex traditional philosophical

The Formation of Modern Conceptions of Formal Logic in the Development of Geometry

In this division of mathematics " all axioms expressing spatial intuitions would be entirely lacking" and the foundations of this science would thereby become as evident as those of arithmetic, while the restriction that it be limited to the study of a threedimensional manifold would be dropped.

The Structure of Scientific Revolutions

A good book may have the power to change the way we see the world, but a great book actually becomes part of our daily consciousness, pervading our thinking to the point that we take it for granted,

From a Logical Point of View

It is the wish of the author to keep general terms distinct from abstract singular terms, so that the over-all dis­ pensability of some assumption that has always rankled as ad hoc and unintuitive is discovered.

A formulation of the simple theory of types

  • A. Church
  • Mathematics
    Journal of Symbolic Logic
  • 1940
A formulation of the simple theory oftypes which incorporates certain features of the calculus of λ-conversion into the theory of types and is offered as being of interest on this basis.

A System of Axiomatic Set Theory