Artykuł w całości poświęcony jest rozważaniom nad pytaniem Bogusława Wolniewicza postawionym w je... more Artykuł w całości poświęcony jest rozważaniom nad pytaniem Bogusława Wolniewicza postawionym w jego nocie <i>A question about join-semilattices</i> ("Bulletin of the Section of Logic" 1990, T. 19, nr 3). Część pierwsza artykułu dotyczy oryginalnego sformułowania tego pytania, w którym chodzi o podanie warunków dostatecznych na to, by w pewnej określonej rodzinie BM podzbiorów półkraty górnej z jednością istniały elementy minimalne. W kolejnych czterech częściach pytanie roztrząsane jest w odniesieniu do innych analogicznych rodzin zbiorów, których elementami są: dowolne zbiory (abstrakcyjne), zbiory gęste w przestrzeni topologicznej; filtry w algebrze Boole'a oraz zbiory domknięte względem operacji konsekwencji.
W eseju przedstawione zostały wybrane kontakty naukowe Jacka Hawranka i Jana Zygmunta z Profesore... more W eseju przedstawione zostały wybrane kontakty naukowe Jacka Hawranka i Jana Zygmunta z Profesorem Bogusławem Wolniewiczem w okresie od końca lat osiemdziesiątych XX w. do początku XXI w. Kontakty dotyczyły algebraicznych aspektów ontologii sytuacji, a od pewnego momentu – jednego tylko pytania sformułowanego w nocie <i>A question about join-semilattices</i> (Wolniewicz 1990). Esej streszcza dyskusję naukową między B. Wolniewiczem a J. Hawrankiem i J. Zygmuntem, w rezultacie której powstał artykuł <i>Wokół pewnego zagadnienia z dziedziny półkrat górnych z jednością</i> (Hawranek, Zygmunt 1993), zawierający próbę odpowiedzi na pytanie Wolniewicza. Artykuł Hawranka i Zygmunta jest niżej przedrukowany, a niniejszy esej jest też pomyślany jako wstęp historyczno-analityczny do jego lektury. Historia kontaktów: Wolniewicz – Hawranek & Zygmunt została ukazana za pomocą zachowanej korespondencji, która jest dość obficie cytowana. W listach Profesor Wolniewicz jawi si...
<jats:p>The term 'Polish logic' was coined by McCall to signal the important contri... more <jats:p>The term 'Polish logic' was coined by McCall to signal the important contributions to modern logic by logicians from Poland between the wars. There were several centres of research, of which the Warsaw school, which grew out of the earlier Lwów–Warsaw philosophical movement, was the most significant. Its development was closely connected with the Warsaw school of mathematics, which gave it its characteristic mathematical bent.</jats:p> <jats:p>Polish logic took as its point of departure the main trends in logical research of the time and it has influenced both subsequent logical research and subsequent work in the Western analytic tradition of philosophy. Its chief contributions were: (1) an enrichment of existing logical theory (including work on Boolean algebras, the sentential calculus, set theory, the theory of types); (2) new logical theories (for example, Leśniewski's systems, Łukasiewicz's many-valued logics, Tarski's theory of truth, theory of the consequence operation and the calculus of systems); (3) new methods and tools as well as improvements of existing methods (for example, the matrix method of constructing sentential calculi, axiomatizability of logical matrices, algebraic and topological interpretations of deductive systems, permutation models for set theory, the application of quantifier elimination to decidability and definability problems); and (4) the application of formal methods to the study of the history of logic, resulting in a new understanding of the logics of Aristotle, the Stoics and the medievals.</jats:p>
... vol. 32 (1939), pp. 201–252.[JSL 4, pp. 129–130 (AA Ben-nett); ZMG 22, pp. 120–121 (L. Egyed)... more ... vol. 32 (1939), pp. 201–252.[JSL 4, pp. 129–130 (AA Ben-nett); ZMG 22, pp. 120–121 (L. Egyed); JFM 65.1164. 01 (Th. Skolem).] (1) On the independence of the well-ordering theorem from the ordering principle, in [79b], pp. ...
This paper revisits the life of Adolf Lindenbaum in light of new research findings, then looks at... more This paper revisits the life of Adolf Lindenbaum in light of new research findings, then looks at two areas among many—metric spaces, and decompositions of point sets—where his work has been underappreciated.
The paper makes some methodological and historical comments on Tarski&#39;s first published c... more The paper makes some methodological and historical comments on Tarski&#39;s first published contribution to the theory of conseguence of consegience operations &quot;Remarques sur les notions fondamentales de la Méthodologie des Mathématique&quot; (1928). [An English translation of the French original follows the text of the paper.]
The life and work of Mojżesz Presburger (1904–1943?) are summarised in this article. Although his... more The life and work of Mojżesz Presburger (1904–1943?) are summarised in this article. Although his production in logic was small, it had considerable impact, both his own researches and his editions of lecture notes of Adjukiewicz and Łukasiewicz. In addition, the surviving records of his student time at Warsaw University provide information on a little-studied topic.
The purpose of this article is to highlight a selected few of Alfred Tarski's career achievem... more The purpose of this article is to highlight a selected few of Alfred Tarski's career achievements. The choice of these achievements is subjective. Section 1 is a general sketch of his life and work, emphasizing his role as researcher, teacher, organizer and founder of a scientific school. Section 2 discusses his contributions to set theory. Section 3 discusses his contributions to the foundations of geometry and to measure theory. Section 4 looks at his metamathematical work, and especially the decision problem for formalized theories. Section 5 is a selected bibliography to illustrate Sects. 1–4.
<jats:p>The term 'Polish logic' was coined by McCall to signal the important contri... more <jats:p>The term 'Polish logic' was coined by McCall to signal the important contributions to modern logic by logicians from Poland between the wars. There were several centres of research, of which the Warsaw school, which grew out of the earlier Lwów–Warsaw philosophical movement, was the most significant. Its development was closely connected with the Warsaw school of mathematics, which gave it its characteristic mathematical bent.</jats:p> <jats:p>Polish logic took as its point of departure the main trends in logical research of the time and it has influenced both subsequent logical research and subsequent work in the Western analytic tradition of philosophy. Its chief contributions were: (1) an enrichment of existing logical theory (including work on Boolean algebras, the sentential calculus, set theory, the theory of types); (2) new logical theories (for example, Leśniewski's systems, Łukasiewicz's many-valued logics, Tarski's theory of truth, theory of the consequence operation and the calculus of systems); (3) new methods and tools as well as improvements of existing methods (for example, the matrix method of constructing sentential calculi, axiomatizability of logical matrices, algebraic and topological interpretations of deductive systems, permutation models for set theory, the application of quantifier elimination to decidability and definability problems); and (4) the application of formal methods to the study of the history of logic, resulting in a new understanding of the logics of Aristotle, the Stoics and the medievals.</jats:p>
Artykuł w całości poświęcony jest rozważaniom nad pytaniem Bogusława Wolniewicza postawionym w je... more Artykuł w całości poświęcony jest rozważaniom nad pytaniem Bogusława Wolniewicza postawionym w jego nocie <i>A question about join-semilattices</i> ("Bulletin of the Section of Logic" 1990, T. 19, nr 3). Część pierwsza artykułu dotyczy oryginalnego sformułowania tego pytania, w którym chodzi o podanie warunków dostatecznych na to, by w pewnej określonej rodzinie BM podzbiorów półkraty górnej z jednością istniały elementy minimalne. W kolejnych czterech częściach pytanie roztrząsane jest w odniesieniu do innych analogicznych rodzin zbiorów, których elementami są: dowolne zbiory (abstrakcyjne), zbiory gęste w przestrzeni topologicznej; filtry w algebrze Boole'a oraz zbiory domknięte względem operacji konsekwencji.
W eseju przedstawione zostały wybrane kontakty naukowe Jacka Hawranka i Jana Zygmunta z Profesore... more W eseju przedstawione zostały wybrane kontakty naukowe Jacka Hawranka i Jana Zygmunta z Profesorem Bogusławem Wolniewiczem w okresie od końca lat osiemdziesiątych XX w. do początku XXI w. Kontakty dotyczyły algebraicznych aspektów ontologii sytuacji, a od pewnego momentu – jednego tylko pytania sformułowanego w nocie <i>A question about join-semilattices</i> (Wolniewicz 1990). Esej streszcza dyskusję naukową między B. Wolniewiczem a J. Hawrankiem i J. Zygmuntem, w rezultacie której powstał artykuł <i>Wokół pewnego zagadnienia z dziedziny półkrat górnych z jednością</i> (Hawranek, Zygmunt 1993), zawierający próbę odpowiedzi na pytanie Wolniewicza. Artykuł Hawranka i Zygmunta jest niżej przedrukowany, a niniejszy esej jest też pomyślany jako wstęp historyczno-analityczny do jego lektury. Historia kontaktów: Wolniewicz – Hawranek & Zygmunt została ukazana za pomocą zachowanej korespondencji, która jest dość obficie cytowana. W listach Profesor Wolniewicz jawi si...
<jats:p>The term 'Polish logic' was coined by McCall to signal the important contri... more <jats:p>The term 'Polish logic' was coined by McCall to signal the important contributions to modern logic by logicians from Poland between the wars. There were several centres of research, of which the Warsaw school, which grew out of the earlier Lwów–Warsaw philosophical movement, was the most significant. Its development was closely connected with the Warsaw school of mathematics, which gave it its characteristic mathematical bent.</jats:p> <jats:p>Polish logic took as its point of departure the main trends in logical research of the time and it has influenced both subsequent logical research and subsequent work in the Western analytic tradition of philosophy. Its chief contributions were: (1) an enrichment of existing logical theory (including work on Boolean algebras, the sentential calculus, set theory, the theory of types); (2) new logical theories (for example, Leśniewski's systems, Łukasiewicz's many-valued logics, Tarski's theory of truth, theory of the consequence operation and the calculus of systems); (3) new methods and tools as well as improvements of existing methods (for example, the matrix method of constructing sentential calculi, axiomatizability of logical matrices, algebraic and topological interpretations of deductive systems, permutation models for set theory, the application of quantifier elimination to decidability and definability problems); and (4) the application of formal methods to the study of the history of logic, resulting in a new understanding of the logics of Aristotle, the Stoics and the medievals.</jats:p>
... vol. 32 (1939), pp. 201–252.[JSL 4, pp. 129–130 (AA Ben-nett); ZMG 22, pp. 120–121 (L. Egyed)... more ... vol. 32 (1939), pp. 201–252.[JSL 4, pp. 129–130 (AA Ben-nett); ZMG 22, pp. 120–121 (L. Egyed); JFM 65.1164. 01 (Th. Skolem).] (1) On the independence of the well-ordering theorem from the ordering principle, in [79b], pp. ...
This paper revisits the life of Adolf Lindenbaum in light of new research findings, then looks at... more This paper revisits the life of Adolf Lindenbaum in light of new research findings, then looks at two areas among many—metric spaces, and decompositions of point sets—where his work has been underappreciated.
The paper makes some methodological and historical comments on Tarski&#39;s first published c... more The paper makes some methodological and historical comments on Tarski&#39;s first published contribution to the theory of conseguence of consegience operations &quot;Remarques sur les notions fondamentales de la Méthodologie des Mathématique&quot; (1928). [An English translation of the French original follows the text of the paper.]
The life and work of Mojżesz Presburger (1904–1943?) are summarised in this article. Although his... more The life and work of Mojżesz Presburger (1904–1943?) are summarised in this article. Although his production in logic was small, it had considerable impact, both his own researches and his editions of lecture notes of Adjukiewicz and Łukasiewicz. In addition, the surviving records of his student time at Warsaw University provide information on a little-studied topic.
The purpose of this article is to highlight a selected few of Alfred Tarski's career achievem... more The purpose of this article is to highlight a selected few of Alfred Tarski's career achievements. The choice of these achievements is subjective. Section 1 is a general sketch of his life and work, emphasizing his role as researcher, teacher, organizer and founder of a scientific school. Section 2 discusses his contributions to set theory. Section 3 discusses his contributions to the foundations of geometry and to measure theory. Section 4 looks at his metamathematical work, and especially the decision problem for formalized theories. Section 5 is a selected bibliography to illustrate Sects. 1–4.
<jats:p>The term 'Polish logic' was coined by McCall to signal the important contri... more <jats:p>The term 'Polish logic' was coined by McCall to signal the important contributions to modern logic by logicians from Poland between the wars. There were several centres of research, of which the Warsaw school, which grew out of the earlier Lwów–Warsaw philosophical movement, was the most significant. Its development was closely connected with the Warsaw school of mathematics, which gave it its characteristic mathematical bent.</jats:p> <jats:p>Polish logic took as its point of departure the main trends in logical research of the time and it has influenced both subsequent logical research and subsequent work in the Western analytic tradition of philosophy. Its chief contributions were: (1) an enrichment of existing logical theory (including work on Boolean algebras, the sentential calculus, set theory, the theory of types); (2) new logical theories (for example, Leśniewski's systems, Łukasiewicz's many-valued logics, Tarski's theory of truth, theory of the consequence operation and the calculus of systems); (3) new methods and tools as well as improvements of existing methods (for example, the matrix method of constructing sentential calculi, axiomatizability of logical matrices, algebraic and topological interpretations of deductive systems, permutation models for set theory, the application of quantifier elimination to decidability and definability problems); and (4) the application of formal methods to the study of the history of logic, resulting in a new understanding of the logics of Aristotle, the Stoics and the medievals.</jats:p>
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