33,666 research outputs found
Willard Van Orman Quine's Philosophical Development in the 1930s and 1940s
As analytic philosophy is becoming increasingly aware of and interested in its own history, the study of that field is broadening to include, not just its earliest beginnings, but also the mid-twentieth century. One of the towering figures of this epoch is W.V. Quine (1908-2000), champion of naturalism in philosophy of science, pioneer of mathematical logic, trying to unite an austerely physicalist theory of the world with the truths of mathematics, psychology, and linguistics. Quine's posthumous papers, notes, and drafts revealing the development of his views in the forties have recently begun to be published, as well as careful philosophical studies of, for instance, the evolution of his key doctrine that mathematical and logical truth are continuous with, not divorced from, the truths of natural science. But one central text has remained unexplored: Quine's Portuguese-language book on logic, his 'farewell for now' to the discipline as he embarked on an assignment in the Navy in WWII. Anglophone philosophers have neglected this book because they could not read it. Jointly with colleagues, I have completed the first full English translation of this book. In this accompanying paper I draw out the main philosophical contributions Quine made in the book, placing them in their historical context and relating them to Quine's overall philosophical development during the period. Besides significant developments in the evolution of Quine's views on meaning and analyticity, I argue, this book is also driven by Quine's indebtedness to Russell and Whitehead, Tarski, and Frege, and contains crucial developments in his thinking on philosophy of logic and ontology. This includes early versions of some arguments from 'On What There Is', four-dimensionalism, and virtual set theory
Hilbert's Program Then and Now
Hilbert's program was an ambitious and wide-ranging project in the philosophy
and foundations of mathematics. In order to "dispose of the foundational
questions in mathematics once and for all, "Hilbert proposed a two-pronged
approach in 1921: first, classical mathematics should be formalized in
axiomatic systems; second, using only restricted, "finitary" means, one should
give proofs of the consistency of these axiomatic systems. Although Godel's
incompleteness theorems show that the program as originally conceived cannot be
carried out, it had many partial successes, and generated important advances in
logical theory and meta-theory, both at the time and since. The article
discusses the historical background and development of Hilbert's program, its
philosophical underpinnings and consequences, and its subsequent development
and influences since the 1930s.Comment: 43 page
The Behaviorisms of Skinner and Quine: Genesis, Development, and Mutual Influence
in april 1933, two bright young Ph.D.s were elected to the Harvard Society of Fellows: the psychologist B. F. Skinner and the philosopher/logician W. V. Quine. Both men would become among the most influential scholars of their time; Skinner leads the "Top 100 Most Eminent Psychologists of the 20th Century," whereas philosophers have selected Quine as the most important Anglophone philosopher after the Second World War.1 At the height of their fame, Skinner and Quine became "Edgar Pierce twins"; the latter obtaining the endowed chair at Harvard's department of philosophy, the former taking up the position at Harvard's psychology department.2Besides these biographical parallels, there also..
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
Several types of types in programming languages
Types are an important part of any modern programming language, but we often
forget that the concept of type we understand nowadays is not the same it was
perceived in the sixties. Moreover, we conflate the concept of "type" in
programming languages with the concept of the same name in mathematical logic,
an identification that is only the result of the convergence of two different
paths, which started apart with different aims. The paper will present several
remarks (some historical, some of more conceptual character) on the subject, as
a basis for a further investigation. The thesis we will argue is that there are
three different characters at play in programming languages, all of them now
called types: the technical concept used in language design to guide
implementation; the general abstraction mechanism used as a modelling tool; the
classifying tool inherited from mathematical logic. We will suggest three
possible dates ad quem for their presence in the programming language
literature, suggesting that the emergence of the concept of type in computer
science is relatively independent from the logical tradition, until the
Curry-Howard isomorphism will make an explicit bridge between them.Comment: History and Philosophy of Computing, HAPOC 2015. To appear in LNC
On the Syntax of Logic and Set Theory
We introduce an extension of the propositional calculus to include abstracts
of predicates and quantifiers, employing a single rule along with a novel
comprehension schema and a principle of extensionality, which are substituted
for the Bernays postulates for quantifiers and the comprehension schemata of ZF
and other set theories. We prove that it is consistent in any finite Boolean
subset lattice. We investigate the antinomies of Russell, Cantor, Burali-Forti,
and others, and discuss the relationship of the system to other set theoretic
systems ZF, NBG, and NF. We discuss two methods of axiomatizing higher order
quantification and abstraction, and then very briefly discuss the application
of one of these methods to areas of mathematics outside of logic.Comment: 34 pages, accepted, to appear in the Review of Symbolic Logi
- âŚ