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Lectures on Jacques Herbrand as a Logician [article]

Claus-Peter Wirth, Joerg Siekmann, Christoph Benzmueller, Serge Autexier
2014 arXiv   pre-print
We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving.  ...  The intended audience ranges from students interested in logic over historians to logicians.  ...  Acknowledgements 58 Bibliography of Jacques Herbrand 59 Acknowledgements We would like to thank Irving H. Anellis, Paolo Bussotti, and Lawrence C.  ... 
arXiv:0902.4682v5 fatcat:pgxxo7vjcbeyvhjej4svsv6lqe

BERNARD LINSKY. The Evolution of Principia Mathematica: Bertrand Russell's Manuscripts and Notes for the Second Edition. Cambridge: Cambridge University Press, 2011. ISBN 978-1-107-00327-9. Pp. vii + 407

N. Griffin
2013 Philosophia Mathematica  
† I am grateful to Erik Curiel for discussions that led to a co-authored contribution to a book symposium and for comments on an earlier version and to Gordon Belot for his willingness to participate in  ...  the book symposium, his careful replies to various questions and objections, and comments on an earlier version of this review.  ...  In high school, young Albert became a close friend of Jacques Herbrand, the future logician.  ... 
doi:10.1093/phimat/nkt011 fatcat:vob35zrqcfa4vgwefzswc7uwlq

RUSSELL AND GÖDEL

ALASDAIR URQUHART
2016 Bulletin of Symbolic Logic  
After a description of Russell's influence on Gödel, it concludes with a discussion of Russell's reaction to the incompleteness theorems.  ...  It is well known that Jacques Herbrand found inspiration in one of the oddest and most idiosyncratic passages in PM, namely * 9.  ...  Yet, as we have seen, they suggested new ideas to both Gödel and Herbrand.  ... 
doi:10.1017/bsl.2016.35 fatcat:3ga6ea7tbnfthhkr4vsfpktdvy

Computational Logic: Memories of the Past and Challenges for the Future [chapter]

John Alan Robinson
2000 Lecture Notes in Computer Science  
The rapid growth of the field and its proliferation into a wide variety of subfields is noted and is attributed to a proliferation of subject matter rather than to a proliferation of logic itself.  ...  Kurt Gödel received his degree on February 6, 1930 at the University of Vienna, aged 23, and Jacques Herbrand received his at the Sorbonne on 11 June, 1930, aged 22 ([4] , pp. 582 ff., and pp 525 ff.)  ...  Just as had Herbrand in 1930, and Prawitz in 1960, Colmerauer in 1980 saw unification itself as a constraint problem, of satisfying a system of equations in a domain of terms.  ... 
doi:10.1007/3-540-44957-4_1 fatcat:jsmzjkrbancv3lutfe35mgpcba

Why Gödel didn't have church's thesis

Martin Davis
1982 Information and Control  
Later in the same lectures, G6del (1934 G6del ( , Davis, 1965 , following up on a suggestion of Jacques Herbrand, proposed an answer to the question of "what one would mean by 'every recursive function  ...  Following a suggestion of Herbrand, but modifying it in an important respect, G6del has proposed (in a set of lectures at Princeton, N.  ... 
doi:10.1016/s0019-9958(82)91226-8 fatcat:qajogh5tdnhjhgbz2mdvj6k5dy

1936: Post, Turing and 'a kind of miracle' in mathematical logic

G. T. Q. Hoare
2004 Mathematical Gazette  
Loosely, recursion is a process of defining a function by specifying each of its values in terms of previously defined values.  ...  (A function from natural numbers to natural numbers is effectively calculable if there is some finite rule or mechanism which will calculate the value of the function for any natural number.)  ...  Acknowledgements I am indebted to the referee for making helpful suggestions on the first draft and to Becky Carter who typed it.  ... 
doi:10.1017/s0025557200174170 fatcat:echz27tckzegjf52yco6b5izna

How Peircean was the "'Fregean' Revolution" in Logic? [article]

Irving H. Anellis
2012 arXiv   pre-print
I also consider the extent to which Peirce and Frege were aware of, and may have influenced, one another's logical writings.  ...  The historiography of logic conceives of a Fregean revolution in which modern mathematical logic (also called symbolic logic) has replaced Aristotelian logic.  ...  Herbrand (1908 Herbrand ( -1931 , in his [1930] Recherches sur la théorie des démonstration.  ... 
arXiv:1201.0353v1 fatcat:akg6yyefyvgszjx23qnpaolwwy

Cut as Consequence

Curtis Franks
2010 History and Philosophy of Logic  
between a system as a whole and its 'semantics').  ...  ', and (2) the structure of the sequent calculi li and lk allowed Gentzen to conceptualize completeness as a question about the relationships among a system's individual rules (as opposed to the relationship  ...  Graham Leach-Krouse, Neil Tennant, and two anonymous referees for History and Philosophy of Logic offered helpful suggestions on an earlier draft of the paper.  ... 
doi:10.1080/01445340.2010.522365 fatcat:dnibzkfrlfapjkdfxfpaj4d2bm

HILBERT, BOURBAKI AND THE SCORNING OF LOGIC [chapter]

A. R. D. Mathias
2013 Infinity and Truth  
A C K N O W L E D G M E N T S The author is much indebted to those friends, mathematicians, logicians, philosophers and historians who proffered encouraging, helpful, informative and in many cases detailed  ...  comments on earlier versions: Joan  ...  Herbrand in a mountaineering accident.  ... 
doi:10.1142/9789814571043_0003 fatcat:rahlrt2ffrgtrkjb3mfvyupby4

A Most Interesting, but Revoked Draft for Hilbert and Bernays' "Grundlagen der Mathematik" that never found its way into any publication, and 2 CV of Gisbert Hasenjaeger [article]

Claus-Peter Wirth
2021 arXiv   pre-print
In May 2017, we identified an incorrectly filed text in Bernays scientific legacy at the archive of the ETH Zurich as a candidate for the beginning of the revoked draft for the 1st edn. or of a revoked  ...  We document that - even after the need for a complete reorganization had become obvious - this joint work went on to a considerable extent.  ...  Lectures on Jacques Herbrand as a Logician. SEKI-Report SR-2009-01 (ISSN 1437-4447). SEKI Publications, Bremen. Rev. edn.  ... 
arXiv:1803.01386v4 fatcat:ai5itqzjnzddpnum2shh5johua

Gödel's incompleteness theorems, free will and mathematical thought [chapter]

SOLOMON FEFERMAN
2011 Free Will and Modern Science  
Some have claimed that Gödel's incompleteness theorems on the formal axiomatic model of mathematical thought can be used to demonstrate that mind is not mechanical, in opposition to a Formalist-Mechanist  ...  Both arguments are subject to a number of critiques.  ...  Early in the 1930s, two proposals were made by the logicians Alonzo Church and Jacques Herbrand, respectively, to define the concept of effective computation procedure in precise mathematical terms  ... 
doi:10.5871/bacad/9780197264898.003.0007 fatcat:6tz5s6axenadpj6ndb3ra53j6i

On Rereading van Heijenoort's Selected Essays

Solomon Feferman
2012 Logica Universalis  
Among the topics discussed are absolutism and relativism in logic, mass terms, the idea of a rational dictionary, and sense and identity of sense in Frege.  ...  This is a critical reexamination of several pieces in van Heijenoort's Selected Essays that are directly or indirectly concerned with the philosophy of logic or the relation of logic to natural language  ...  And within a year after the publication of From Frege to Gödel [51] that had taken almost a decade of effort to bring to completion, he edited and published Jacques Herbrand.  ... 
doi:10.1007/s11787-012-0058-5 fatcat:yucp7jrvu5aqlawafwt2f5bwpu

The Emergence of Cognitive Science in France:

Brigitte Chamak
1999 Social Studies of Science  
This paper can be considered as a study in how the differing contexts in France and the USA shaped the history of the construction of cognitive science in each of these two countries.  ...  The influence of new practices and tools developed during World War II and the Cold War appears to be of crucial importance in understanding the development of this new field, as well as that of cybernetics  ...  The first contingent reason includes the untimely death of logicians such as Jean Nicod and Jacques Herbrand , and philosophers interested in logic such as Jean Cavaillès and Albert Lautman .  ... 
doi:10.1177/030631299029005001 pmid:11624503 fatcat:smfvymbpgbhclapablf6t2utaq

Methodological Frames: Paul Bernays, Mathematical Structuralism, and Proof Theory [chapter]

Wilfried Sieg
2020 The Prehistory of Mathematical Structuralism  
Drawing on broadened meta-mathematical experience, this chapter proposes a more general characterization of frames that has ontological and epistemological significance.  ...  That aim was to be reached on the basis of finitist mathematics. Gödel's second incompleteness theorem forced a step from absolute finitist to relative constructivist proof-theoretic reductions.  ...  As to (1), John von Neumann and Jacques Herbrand believed that Gödel's results spelled the definite impossibility of the program for strong formal theories like analysis or even full number theory.  ... 
doi:10.1093/oso/9780190641221.003.0014 fatcat:qjhvjruv2bbxplabx6qn6cl3rm

Never mind mind, essence is not essential, and matter does not matter [chapter]

2014 Nelson Goodman  
with presentation of slides of Las Meninas by Velazquez and of Picasso's painted variations on it. ), Harvard's younger generation was soon familiar with the work by Carnap, Kurt Gödel, Jacques Herbrand  ...  When Whitehead then started to lecture at Harvard, he had his debut as a philosopher.  ... 
doi:10.4324/9781315712178-15 fatcat:dhahdxjyovegrjaxkgvhabs3hi
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