** Bertrand Russell ( 1908a ) Mathematical logic as based on the theory of types, with commentary by Willard Quine, pages 150-182.

* Willard Van Orman Quine ( 1937 ) “ New Foundations for Mathematical Logic ,” American Mathematical Monthly 44, pp. 70 – 80.

Includes Frege's 1879 Begriffsschrift with commentary by van Heijenoort, Russell's 1908 Mathematical logic as based on the theory of types with commentary by Willard V. Quine, Zermelo's 1908 A new proof of the possibility of a well-ordering with commentary by van Heijenoort, letters to Frege from Russell and from Russel to Frege, etc.

Quine first proposed NF in a 1937 article titled " New Foundations for Mathematical Logic "; hence the name.

A notable exception to this generalization are the four editions of Quine's Methods of Logic, which discussed term logic ( which Quine called " Boolean term schemata ") and syllogisms at some length.

Indeed, Arthur Norman Prior warned his protégé Ruth Barcan to prepare well in the debates concerning Quantified Modal Logic with Willard Van Orman Quine, due to the biases against Modal Logic.

In Philosophy of Logic ( the chapter titled " Deviant Logics "), Quine rejects the idea that classical logic should be revised in response to the paradoxes, being concerned with " a serious loss of simplicity ", and " the handicap of having to think within a deviant logic ".

which both use the meaning of the quoted words to complete the sentence, and mention them as they are attributed to W. V. Quine, to argue against his teachers ' hard distinction.

Reprinted, pp. 185 – 196 in Quine ( 1976 ), Ways of Paradox.

( 1980 b ), " Reference and Modality ", pp. 139 – 159 in Quine ( 1980 a ), From a Logical Point of View.

In this respect second-order logic with standard semantics differs from first-order logic ; Quine ( 1970, pp. 90 – 91 ) pointed to the lack of a complete proof system as a reason for thinking of second-order logic as not logic, properly speaking.

This is philosophically unsatisfying to some and has motivated additional work in set theory and other methods of formalizing the foundations of mathematics such as New Foundations by Willard Van Orman Quine.

By contrast, in mainstream Analytical philosophy the topic is more confined to abstract investigation, in the work of such influential theorists as W. V. O. Quine, to name one of many.

Quine, Davidson and David Lewis published influential writings on the subject.

Dennett attended Phillips Exeter Academy and spent one year at Wesleyan University before receiving his Bachelor of Arts in philosophy from Harvard University in 1963, where he was a student of W. V. Quine.

The American philosopher W. V. O. Quine, in his " Two Dogmas of Empiricism ", famously challenged the distinction, arguing that the two have a blurry boundary.

Hold come what may is a phrase popularized by logician Willard Van Orman Quine.

Quine held ( on a perhaps simplistic construal ) that there are no beliefs that one ought to hold come what may — in other words, that all beliefs are rationally revisable.

Ultimately, it failed to solve many of the problems with which it was centrally concerned, and after the Second World War, its doctrines increasingly came under attack by thinkers such as Nelson Goodman, Willard Van Orman Quine, J. L. Austin, Peter Strawson, Hilary Putnam, and Richard Rorty.

Willard Van Orman Quine criticized the distinction between analytic and synthetic statements and the reduction of meaningful statements to immediate experience.

Key tenets of logical positivism, including its atomistic philosophy of science, the verifiability principle, and the fact-value distinction, came under attack after the Second World War by philosophers such as Nelson Goodman, Quine, J. L. Austin, and Peter Strawson.

) Decline and Obsolescence of Logical Empiricism: Carnap vs. Quine and the Critics.

Many current and recent philosophers — e. g., Daniel Dennett, Willard Van Orman Quine, Donald Davidson, John Rogers Searle, and Jerry Fodor — operate within a broadly physicalist or materialist framework, producing rival accounts of how best to accommodate mind — functionalism, anomalous monism, identity theory, and so on.

* D. H. Lehmer, " On the Maxima and Minima of Bernoulli Polynomials ", American Mathematical Monthly, volume 47, pages 533 – 538 ( 1940 )

The Search for Mathematical Roots 1870 – 1940.

In a demonstration to the American Mathematical Society conference at Dartmouth College on September 11, 1940, Stibitz was able to send the Complex Number Calculator remote commands over telephone lines by a teletype.

* Ivor Grattan-Guinness, The Search for Mathematical Roots 1870 – 1940.

* Mathematical Methods in Engineering, McGraw Hill, 1940 ( with M. A. Biot )

The Search for Mathematical Roots 1870 – 1940.

* 1940, " Polyadic groups ", Transactions of the American Mathematical Society 48: 208 – 350.

He was Instructor of Mathematics at Harvard University, 1930 – 31, 1933 – 35 ; NRC Fellow, Mathematics, 1931 – 33 ; Assistant Professor, 1935 – 40 ; Associate Professor, 1940 – 46, Professor, 1946 – 52 ; Professor Instructor, Institute for Advanced Study, Princeton University, 1952 – 77 ; Professor Emeritus, 1977 – 89 ; Chairman of the Mathematics Panel, National Science Foundation, 1953 – 56 ; Exchange Professor, Collège de France, 1957 ; Memorial Committee, Support of Research in Mathematical Sciences, National Research Council, 1966 – 67 ; President, International Commission of Mathematical Instruction, 1979 – 82 ; Research Mathematicians, National Defense Research Committee, 1943 – 45 ; Construction of the School of Mathematics.

The Search for Mathematical Roots 1870 – 1940.

In a demonstration to the American Mathematical Society conference at Dartmouth College on September 9, 1940, Stibitz used a teletype to send commands to the Complex Number Calculator in New York over telephone lines.

He married another mathematician and physicist, Bertha Swirles ( 1903 – 1999 ), in 1940 and together they wrote Methods of Mathematical Physics.

In 1980, all the contents of Mathematical Reviews since 1940 were integrated into an electronic searchable database.

The Search for Mathematical Roots 1870 – 1940: Logics, Set Theories, and the Foundations of Mathematics from Cantor through Russell to Gödel.

* Grattan-Guinness ' The Search for Mathematical Roots 1870 – 1940 is a sweeping study of the rise of mathematical logic during that critical period.

Rhodes held numerous positions involving mathematical computations before she joined the Mathematical Tables Project in 1940, where she worked under Gertrude Blanch, whom she would later credit as her mentor.

Donald Gene Saari ( born March 1940 in Houghton, Michigan ) is the Distinguished Professor of Mathematics and Economics and director of the Institute for Mathematical Behavioral Sciences at the University of California Irvine.

The Search for Mathematical Roots 1870 – 1940.

* Ivor Grattan-Guinness ( 2000 ) The Search for Mathematical Roots 1870 – 1940.

* Graham Higman ( 1940 ), " The units of group-rings ", Proceedings of the London Mathematical Society, ( 2 ) 46: 231 – 248.

* Grattan-Guinness, Ivor ( 2000 ), The Search for Mathematical Roots 1870 – 1940.