From Frege to Gödel. A source book in mathematical logic, 1879-1931.
Edited by Van Heijenoort Jean. Harvard: Harvard University Press 1967.
The rise of modern logic: from Leibniz to Frege. Edited by Gabbay Dov
and Woods John. Amsterdam: Elsevier 2004.
Handbook of the History of Logic: vol. 3.
Contents: Dov M. Gabbay and John Woods: Preface VII; List of Contributors IX-X;
Wolfgang Lenzen: Leibniz's logic 1; Mary Tiles: Kant: From General to
Transcendental Logic 85; John W. Burbidge: Hegel's logic 131; Paul Rusnock and
Rolf George; Bolzano as logician 177; Richard Tieszen: Husserl's logic 207;
Theodore Hailperin: Algebraical logic 1685-1900 323; Victor Sanchez Valencia:
The algebra of logic 389; Ivor Grattan-Guinness: The mathematical turn in logic
545; Volker Peckhaus: Schröder's logic 557; Risto Hilpinen: Peirce's logic 611;
Peter M. Sullivan: Frege's Logic 659; Index 751-770.
Logic from Russell to Church. Edited by Gabbay Dov and Woods John.
Amsterdam: Elsevier 2009.
Handbook of the History of Logic: vol. 5.
Contents: Dov M. Gabbay and John Woods: Preface VII; List of Contributors
XI-XII; Andrew D. Irvine: Bertrand Russell's logic 1; Dale Jacquette: Logic for
Meinongian object theory semantics 29; Joan Rand Moschovakis: The logic of
Brouwer and Heyting 77; Jens Erik Fenstad and Hao Wang: Thoralf Albert Skolem
127; Claus-Peter Wirth, Jörg Siekmann, Christoph Benzmüller and Serge Autexier:
Jacques Herbrand: life, logic, and automated deduction 195; Michael Potter: The
logic of the Tractatus 255; Peter M. Simons: Lesniewski's logic 305;
Wilfried Sieg: Hilbert's Proof Theory 321; Barry Hartley Slater: Hilbert'
Epsilon Calculus and its successors 385; Mark van Atten and Juliette Kennedy:
Gödel's logic 449; Keith Simmons: Tarski's logic 511; Alasdair Urquhart: Emil
Post 617; Jan von Plato: Gentzen's logic 667; Felice Cardone and J. Roger
Hindley: Lambda-calculus and Combinators in the 20th century 723; Jonathan P.
Seldin: The logic of Church and Curry 819; Andrea Cantini: Paradoxes,
self-reference and truth in the 20th century 875; Index 1015-1056.
Anderson Anthony C., "Some new axioms for the logic of sense and
denotation," Nous 14: 217-234 (1980).
Anellis Irving H., "From semantic tableaux to Smullyan trees: the history of
the falsifiability tree method," Modern Logic 1 (1): 36-69 (1990).
Anellis Irving H., "Forty years of "unnatural" natural deduction and
quantification: A history of first-order systems of natural deduction, from
Gentzen to Copi," Modern Logic 2 (2): 113-152 (1991).
Anellis Irving H., "Jean van Heijenoort's contributions to proof theory and
its history," Modern Logic 2: 312-335 (1992).
Anellis Irving H., "On the selection and use of sources in the history of
logic," Modern Logic 3 (1): 1-17 (1992).
Bochenski Joseph M. The general sense and character of modern logic. In
Modern logic - A survey. Edited by Agazzi Evandro. Dordrecht: Reidel 1981.
pp. 3-14
"By 'Modern Logic' (abridged as 'ML') the class of studies is meant which were
originated by Leibniz, developed, among others, by Boole, Peirce, Frege, Peano,
Lesniewski and their followers; in other term the class of studies listed in
Alonzo Church's Bibliography and in The Journal of Symbolic Logic. The expression 'ML' is sometimes used, it is true, in other ways, e.g. to
denote studies in Hegelian dialectics. Those uses are irrelevant for the sake of
the present paper which will be exclusively concerned with ML as described
above. It may be only said, that no other known sort of contemporary logic can
compare with the latter as far as standards of procedures and quality of results
are concerned.
The aim of the paper is to describe - as the title selected by the organizers of
the conference indicates - the general sense and character of ML thus
understood. In other terms an attempt will be made to find the fundamental
characteristics of ML-al studies.
The method used will be comparative. We are going to ask: How does ML compare
with three fields with which it is usually linked: logic, mathematics and
philosophy? Is ML Logic and, if so, how does it differ from other types of
logic? Is it a mathematical discipline and, if that is the case, what is the
difference between it and other mathematical sciences? Is it philosophy and,
this being admitted, what is its place among the other philosophical
disciplines?
The present paper will be mostly concerned with the first class of problems, the
comparison between ML and the other types of logic; the other two classes of
problems will be treated only marginally. As far as the main problems are
concerned, the method will necessarily be historical: for, contrary to
mathematics and philosophy, all other forms of logic with which ML may be
compared belong to the past." p. 3
Brady Geraldine. From Peirce to Skolem. A neglected chapter in the
history of logic. Amsterdam: Elsevier 2000.
Contents: Introduction 1; 1. The early work of Charles S. Peirce 9; 2. Peirce's
calculus of relatives: 1870 23; 3, Peirce on the algebra of logic: 1880 51; 4.
Mitchell on a new algebra of logic: 1883 75; 5. Peirce on the algebra of
relatives: 1883 95; 6. Peirce's logic of quantifiers: 1885 111; 7. Schröder's
calculus of relatives 143; 8. Löwenheim's contribution 169, 9. Skolem's
recasting 197; Appendices. 1. Schröder's Lecture I 207; 2. Schröder's Lecture II
223; 3. Schröder's Lecture III 251; 4. Schröder's Lecture V 257; 5. Schröder's
Lecture IX 295; 6. Schröder's Lecture XI 339; 7. Schröder's Lecture XII 379; 8.
Norbert Wiener's Thesis 429; Bibliography 445; Index 461-468.
"This book is an account of the important influence on the development of
mathematical logic of Charles S. Peirce and his student O. H. Mitchell, through
the work of Ernst Schröder, Leopold Löwenheim, and Thoralf Skolem. As far as we
know, this book is the first work delineating this line of influence on modern
mathematical logic.
Modern model theory began with the seminal papers of Löwenheim (1915) "On
possibilities in the calculus of relatives" and Skolem (1923) "Some remarks on
axiomatized set theory". They showed that in first-order logic, if a statement
has an infinite model, it also has a model with countable domain. They observed
that second-order logic fails to have this property; witness the axioms for the
real number field. Their papers focused the attention of a growing number of
logicians, starting with Kurt Gödel and Jacques Herbrand, on models of
first-order theories.(1) This became the main preoccupation of model theory and
a large component of mathematical logic as it developed over the rest of the
twentieth century. In addition, the work of Herbrand, based on the notion of
Skolem function, became, through J. Alan Robinson, the main basis of systems of
automated reasoning.
A careful examination of the contributions of Peirce, Mitchell, Schröder, and
Löwenheim sheds light on several questions: How did first-order logic as we know
it develop? What are the real contributions of Peirce, Mitchell and Schroder,
over and above the better known contributions of Gottlob Frege, Bertrand
Russell, and David Hilbert?
As a result of this investigation we conclude that, absent new historical
evidence, Lowenheim's and Skolem's work on what is now known as the downward
Lowenheim-Skolem theorem developed directly from Schroder's Algebra der Logik,
which was itself an avowed elaboration of the work of the American logician
Charles S. Peirce and his student O. H. Mitchell. We have been unable to detect
any direct influence of Frege, Russell, or Hilbert on the development of
Löwenheim and Skolem's seminal work, contrary to the commonly held perception.
This, in spite of the fact that Frege has undisputed priority for the discovery
and formulation of first-order logic.
This raises yet other intriguing questions. Why were the contributions of Peirce
and Schröder neglected by later authors? Was it because Peirce published in
American journals that were not easily available to Europeans? Was it because
Schröder had a verbose and sometimes obscure style as a writer? Was it because
the logical notations used by Peirce and Schröder were simply less readable than
those of Frege? After reading this book, the reader should be able to form his
or her own opinions." pp. 1-2
(1) We do not discuss here the Frege-Russell-Hilbert tradition leading to
first-order logic and Gödel, since this development has many excellent
treatments in the literature already, such as the beautiful book of the late
Jean van Heijenoort, From Frege to Gödel. Van Hejenoort's book treats
Frege, Löwenheim, and Skolem, but does not cover either Peirce's or Schröder's
work, which led to Löwenheim's paper. This omission is also present in the
historical papers of other otherwise very well-read logicians. There are
masterful accounts of the seminal papers of Löwenheim and Skolem in the late
Burton Dreben's introduction to Gödel's thesis in Collected Works of Kurt
Gödel and in the late Hao Wang's introduction to Skolem's Selected Works
in Logic. But Peirce and Schröder get no attention.
Church Alonzo. A formulation of the logic of sense and denotation. In
Structure method and meaning. Essays in honor of Henry M. Sheffer. Edited by
Henle Paul, Kallen Horace M., and Langer Susanne K. New York: Liberal Arts Press
1951. pp. 3-34
"The intensional aspects of Frege's logical doctrine, and his distinction
between the sense (Sinn) and the denotation (Bedeutung) of a name,
were explained by him informally in his paper, Uber Sinn und Bedeutung,
(1) and in incidental passages in a number of his other publications, including
the first volume of his book, Grundgesetze der Arithmetik (Jena, 1893).
In his more formal work, Frege's formalized language (Begriffsschrift, or
Formelsprache) has an entirely extensional interpretation, and it may even
be that his interest in intensional logic was primarily to clear up certain
difficulties regarding its relationship to extensional logic, (2) so as to be
able to proceed with development of the latter unhampered. Nevertheless, it
seems that Frege would agree that intensional logic also must ultimately receive
treatment by the logistic method. And it is the purpose of this paper to make a
tentative beginning toward such a treatment, along the lines of Frege's
doctrine.
While we preserve what we believe to be the important features of the theory of
Frege, we do make certain changes to which he would probably not agree. One of
these is the introduction of the simple theory of types as a means of avoiding
the logical antinomies. Another is the abandonment of Frege's notion of a
function (including propositional functions) as something ungesattigt, in
favor of a notion according to which the name of a function may be treated in
the same manner as any other name, provided that distinctions of type are
observed. (But it is even possible that Frege might accept this latter change,
on the basis of an understanding that what we call a function is the same thing
which he calls Werthverlauf einer Funktion.)" pp. 3-4
(1) In Zeitschrift fur Philosophie und philosophische Kritik, (1892),
25-50. See English translations of this paper by Black, in The Philosophical
Review, LVII (1948), 207-230, and by Feigl, in Readings in Philosophical
Analysis (New York, 1949); and also a discussion of Frege's doctrines by
Russell, in Appendix A of The Principles of Mathematics. In reading
these, it is necessary to make allowance for differences in the translations
that are adopted of some of Frege's terms. We shall here translate Frege's
ausdr?cken as "express" and Frege's bedeuten or bezeichnen as
"denote" or "be a name of," so that a name is said to express its sense and to
denote or to be a name of its denotation.
(2) We mention the doctrine of Frege's Begriffsschrift of 1879, according
to which the relation of identity or equality is a relation between names rather
than between the things named, apparently on the ground that identity construed
in the latter sense would be too trivial a relation to serve its intended
purpose. If use and mention are not to be confused, the idea of identity as a
relation between names renders a formal treatment of the logic of identity all
but impossible. Solution of this difficulty is made the central theme of Uber
Sinn und Bedeutung and is actually a prerequisite to Frege's treatment of
identity in Grundgesetze der Arithmetik.
Church Alonzo. The history of the question of existential import of
categorical propositions. In Logic, methodology and philosophy of science.
Proceedings of the 1964 International Congress. Edited by Bar-Hillel
Yehoshua. Amsterdam: North-Holland 1965. pp. 417-424
Church Alonzo, "Outline of a revised formulation of the logic of sense and
denotation (Part First)," Nous 7: 24-33 (1973).
Church Alonzo, "Outline of a revised formulation of the logic of sense and
denotation (Second First)," Nous 8: 135-156 (1974).
Church Alonzo, "A revised formulation of the logic of sense and denotation
Alternative (1)," Nous 27: 141-157 (1993).
Czezowski Tadeusz, "On certain peculiarities of singular propositions,"
Mind 64: 392-395 (1955).
Dawson John W.Jr., "The compactness of first-order logic: From Godel to
Lindström," History and Philosophy of Logic 14: 15-37 (1993).
Gandy Robin O. The simple theory of types. In Logic Colloquium 76.
Edited by Gandy Robin O. and Hyland John Martin. Amsterdam: North-Holland
Publishing Company 1977. pp. 173-181
Goldfard Warren, "Logic in the Twenties: the nature of the quantifier,"
Journal of Symbolic Logic 44 (3): 351-368 (1979).
Grattan-Guinness Ivor, "Notes on the fate of logicism from 'Principia
Mathematica' to Gödel incompletability," History and Philosophy of Logic
5: 67-78 (1984).
Hailperin Theodore, "Probability logic in the Twentieth Century," History
and Philosophy of Logic 11: 71-110 (1990).
Lewis Clarence Irving. Notes on the logic of intension. In Structure
method and meaning. Essays in honor of Henry M. Sheffer. Edited by Henle
Paul, Kallen Horace M., and Langer Susanne K. New York: Liberal Arts Press 1951.
pp. 25-34
Łukasiewicz Jan, "On the Principle of the Excluded Middle," History and
Philosophy of Logic 8: 67-69 (1987).
Moore Gregory H., "Beyond first-order logic: the historical interplay
between mathematical logic and axiomatic set theory," History and Philosophy
of Logic 1: 95-138 (1980).
"What has been the historical relationship between set theory and logic? on the
one hand, Zermelo and other mathematicians developed set theory as a
Hilbert-style axiomatic system. On the other hand, set theory influenced logic
by suggesting to Schr?der, L?wenheim and others the use of infinitely long
expressions. The question of which logic was appropriate for set theory --
first-order logic, second-order logic, or an infinitary logic -- culminated in a
vigorous exchange between Zermelo and G?del around 1930."
Mugnai Massimo. Alle origini dell'algebra della logica. In Atti del
convegno internazionale di storia della logica. Edited by Abrusci Michele,
Casari Ettore, and Mugnai Massimo. Bologna: CLUEB 1983. pp. 117-132
Murawski Roman and Bedürftig Thomas, "Die Entwicklung der Symbolik in der
Logik und ihr philosophischer Hintergrund," Mathematische Semesterberichte
42: 1-31 (1995).
Myhill John. On the ontological siginificance of the Löwenheim-Skolem
theorem. In Academic freedom, logic, and religion. Edited by White
Morton. Philadelpha: University of Pennsylvania Press 1953. pp. 57-70
Reprinted in: Irving M. Copi, James A. Gould (eds.) - Contemporary readings
in logical theory - New York, Macmillan, 1967, pp. 40-51
Nagel Ernest, "Impossible numbers: a chapter in the history of modern
logic," Studies in the History of Ideas 3: 429-474 (1935).
Reprinted in: E. Nagel - Teleology revisited and other essays in the
philosophy and history of science - New York, Columbia University Press,
1979
Peckhaus Volker, "The way of logic into mathematics," Theoria 12:
39-64 (1997).
"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 omnibus discipline logic into new
philosophical sub-disciplines and separate disciplines such as psychology,
epistemology, philosophy of science and formal (symbolic, mathematical) logic.
In the 19th century a growing foundational need in mathematics provoked the
emergence of a structural view on mathematics and the reformulation of logic for
mathematical means. As a result formal logic was taken over by mathematics in
the beginning of the 20th century as is shown by sketching the German example."
Peckhaus Volker, "19th century logic between philosophy and mathematics,"
Bulletin of Symbolic Logic 5: 433-450 (1999).
"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 Scholastic logic and in the rationalistic era,
its continuous development began with George Boole's The Mathematical Analysis
of Logic of 1847, and it became a mathematical subdiscipline in the early 20th
century. This style of presentation cuts off one eminent line of development,
the philosophical development of logic, although logic is evidently one of the
basic disciplines of philosophy. One needs only to recall some of the standard
19th century definitions of logic as, e.g., the art and science of reasoning
(Whateley) or as giving the normative rules of correct reasoning (Herbart). In
the paper the relationship between the philosophical and the mathematical
development of logic will be discussed. Answers to the following questions will
be provided:
1. What were the reasons for the philosophers' lack of interest in formal logic?
2. What were the reasons for the mathematicians' interest in logic?
3. What did "logic reform" mean in the 19th century? Were the systems of
mathematical logic initially regarded as contributions to a reform of logic?
4. Was mathematical logic regarded as art, as science or as both?"
Proust Joëlle. Questions of form. Logic and the analytic proposition from
Kant to Carnap. Minneapolis: University of Minnesota Press 1989.
Original French edition: Questions de forme. Logique et proposition analytique
de Kant à Carnap - Paris, Fayard, 1986.
Translated by Anastasios Albert Brenner.
See the Third Chapter: Bolzano's renovation of analiticity - pp. 49-108.
Pulkkinen Jarmo. The threat of logical mathematism. A study on the
critique of mathematical logic in Germany at the turn of the 20th century.
New York: Peter Lang 1994.
Contents: Acknowledgements 7; Introduction 9; 1. History of logic in Germany
1830-1920 15; 2. Logic and psychology 41; 3. Logic and linguistics 59; 4. Logic
and mathematics 71; 5. The reception of mathematical logic in Germany 91; 6.
Mauthner's critique 121; 7. Rickert's critique 139; 8. Ziehen's critique 153;
Conclusion 169; Bibliography 177-187.
"This work attempts to throw some light on an interesting feature in the
development of German logic which has not yet received the attention it
deserves. Almost a whole generation of German philosophers did not accept the
new mathematical logic at the turn of the 20th century. In this respect
development in Germany differs greatly from that in Britain where George Boole's
ideas received the attention of philosophers through the work of W.S. Jevons.
However, both Gottlob Frege and Ernst Schroder, the main representatives of
mathematical logic in Germany, remained isolated figures whose works were either
strongly criticized or completely neglected by philosophers. Schroder was able
to get some attention to his ideas but the influence of Frege remained very
limited for a long time. Frege's ideas started to have an impact in Germany only
through the Principia Mathematica by Russell and Whitehead.
The fate of mathematical logic in Germany cannot be explained away by saying
that German philosophers were not interested in logic. They were. In fact, the
landscape of German traditional logic is at that time so rich and varied that it
is difficult to give a coherent account of it. What makes the period
particularly interesting are the interrelationships between psychology, logic
and linguistics. All these disciplines came of age in Germany almost
simultaneously. Wilhelm Wundt founded modem experimental psychology during the
1870s. Frege did the same for modem mathematical logic at the end of the same
decade. As linguistics underwent a deep change at the turn of the 20th century,
the basic concepts of language and linguistics were studied not only by
linguists but also by philosophers and psychologists.
In the late 19th century linguistics, philosophy and psychology were seen to be
much closer to each other than nowadays. Linguists, philosophers and
psychologists alike wrote on logical questions. Particularly interesting is the
relationship between logic and psychology. In this period philosophers and
psychologists were involved in an intense struggle over the chairs of
philosophy. This struggle influenced deeply the logical discussion of the period
(the debate over the so-called 'psychologism'). One group of logicians believed
that their work could be made easier by the results of the new experimental
psychology. In other words, they believed that the new scientific psychology
could offer a solid foundation for the new scientific logic. Another group of
logicians criticized these attempts and tried to present logic as an independent
philosophical science. However, both groups had one thing in common: a negative
attitude towards mathematical logic.
The present survey of the critique of mathematical logic at the turn of the 20th
century attempts to answer several interesting questions: How did the
contemporary German philosophers see the role and significance of logic? What
kind of relationships did they claim to exist between logic, mathematics,
linguistics and psychology? What exactly were the arguments of the (now) almost
forgotten critics? I shall start by giving a historical survey of the
development of German logic 1830-1920 as it appears against the background of
German academic philosophy (chapter 1). Next I shall study the
interrelationships between logic and psychology (chapter 2), logic and
linguistics (chapter 3), and logic and mathematics (chapter 4). After this I
shall present the general features of the reception of mathematical logic in
Germany between 1880 and 1920 (chapter 5). This is followed by a more detailed
account of the arguments of three individual critics: Fritz Mauthner (chapter
6), Heinrich Rickert (chapter 7), and Theodor Ziehen (chapter 8). I have chosen
these three for several reasons. Firstly, each represents a different viewpoint:
Mauthner was mainly interested in the problems of language, Rickert was one of
the most prominent philosophers of the period, and Ziehen was originally a
psychologist. Secondly, I have wanted to bring forward previously unknown
figures (this is the reason why I did not choose Husserl, for instance, who
wrote much on the subject). Thirdly, I have tried to choose critics who
presented interesting ideas. And lastly, in order to have a large enough corpus
for study I have had to choose writers who wrote much on the subject."
Pulkkinen Jarmo. Thought and Logic. The debates between German-speaking
philosophers and symbolic logicians at the turn of the 20th century. New
York: Peter Lang 2005.
"The book deals with the reception and critique of symbolic logic among
German-speaking philosophers at the turn of the 20th century. The first part
discusses the period from the late 1870s up to the end of the 19th century. The
main issue is the arrival of the Boolean algebra of logic in Germany and
Austria. It examines also the reasons why Gottlob Frege was so unsuccessful in
his attempts to draw the attention of philosophers to his logicist programme.
The second part deals with the first two decades of the 20th century. Its main
topic of inquiry is the reception of Bertrand Russell's and Louis Couturat's
ideas in the German-speaking world. In particular, it concentrates on the
relationship between Russell and neo-Kantians."
Rao A.Pampapathy, "A survey of free logics," Modern Logic 6 (2):
123-191 (1996).
Salmon Nathan, "A problem in the Frege-Church theory of sense and
denotation," Nous 27: 158-166 (1993).
Schurz Gerhard, "Admissible versus valid rules: a case study of the modal
fallacy," Monist 77 (3): 376-388 (1994).
Thiel Christian. Some difficulties in the historiography of modern logic. In
Atti del convegno internazionale di storia della logica. Edited by Abrusci
Michele, Casari Ettore, and Mugnai Massimo. Bologna: CLUEB 1983. pp. 175-191
Thiel Christian. Research on the history of logic at Erlangen. In Studies
on the history of logic. Proceedings of the Third Symposium on the history of
logic. Edited by Angelelli Ignacio and Cerezo María. Berlin: Walter de
Gruyter 1996. pp. 397-401
Van Heijenoort Jean, "Historical development of modern logic," Modern
Logic 2 (3): 242-255 (1992).
Vega Reñón Luis, "La lógica en España (1890-1930): desencuentros,"
Teorema 20: 21-38 (2001).
"This paper is both a first step towards, and an invitation to go on with, the
study of the reception of modern -- symbolic, mathematical -- logic in Spain. I
examine the first and unsuccessful
introduction of modern logic in mathematical and philosophical circles, between
1890 and 1930. Such reception failures are usually attributed to external and/or
general circumstances, ranging from personal to institutional and cultural
conditions of Spanish learning.
But here we should also take into account the very working of the so-called
"sowers", i.e., introducing people, as well as some other internal factors and
frames of this non-reception case."
Wolenski Jan. Theories of reasoning in the Lvov-Warsaw School. In Topics
in philosophy and artificial intelligence. Edited by Albertazzi Liliana and
Poli Roberto. Bozen: Istituto Mitteleuropeo di Cultura 1991. pp. 91-101
Papers from the International Summer Schools in Bozen - 1989-1990
Wolenski Jan, "Mathematical logic in Poland 1900-1939: People, circles,
institutions, idea," Modern Logic 5 (4): 363-405 (1995).
Wolenski Jan. The achievements of the Polish School of logic. In The
Cambridge history of philosophy 1870-1945. Edited by Baldwin Thomas.
Cambridge: Cambridge University Press 2003. pp. 401-416
"In the most narrow sense, the Polish school of logic may be understood, as the
Warsaw school of mathematical logic with Jan Łukasiewicz, Stanislaw Lesniewski,
and Alfred Tarski as the leading figures. However, valuable contributions to
mathematical logic were also made outside Warsaw, in particular by Leon
Chwistek. Thus, the Polish school of logic sensu largo also comprises
logicians not belonging to the Warsaw school of logic. The third interpretation
is still broader. If logic is not restricted only to mathematical logic, several
Polish philosophers who were strongly influenced by formal logical results, for
example Kazimierz Ajdukiewicz and Tadeusz Kotarbinski, can be included in the
Polish school of logic sensu largissimo. Polish work on logic can
therefore encompass a variety of topics, from the 'hard' foundations of
mathematics (e.g. inaccessible cardinals, the structure of the real line, or
equivalents of the axiom of choice) through formal logic, semantics, and
philosophy of science to ideas in ontology and epistemology motivated by logic
or analysed by its tools. Since the development of logic in Poland is a
remarkable historical phenomenon, I shall first discuss its social history,
especially the rise of the Warsaw school. Then I shall describe the
philosophical views in question, the most important and characteristic formal
results of Polish logicians, their research in the history of logic, and
applications of logic to philosophy. My discussion will be selective: in
particular I will omit most results in the 'hard' foundations of mathematics."
p. 401
(click on the image to see the PDF file)