Most of my work is on logic, philosophy of mathematics and related areas.
"Kosta Došen" (in print, in Serbian),
Srpska enciklopedija, Vol. III (2019), Matica srpska i Srpska akademija nauka i umetnosti.
"Gödel on deduction" (with Kosta Došen),
Studia Logica, 107, Issue 1 (2019), 31–51.
Abstract,
This is an examination, a commentary, of links between some philosophical views ascribed to Gödel and general proof theory. In these views deduction is of central concern not only in predicate logic, but in set theory too, understood from an infinitistic ideal perspective. It is inquired whether this centrality of deduction could also be kept in the intensional logic of concepts whose building Gödel seems to have taken as the main task of logic for the future.
arXiv,
DOI.
"Gödel’s natural deduction" (with Kosta Došen),
Studia Logica, 106, Issue 2 (2018), 397–415.
Abstract,
This is a companion to a paper by the authors entitled "Gödel on deduction", which examined the links between some philosophical views ascribed to Gödel and general proof theory. When writing that other paper, the authors were not acquainted with a system of natural deduction that Gödel presented with the help of Gentzen's sequents, which amounts to Jaśkowski's natural deduction system of 1934, and which may be found in Gödel's unpublished notes for the elementary logic course he gave in 1939 at the University of Notre Dame. Here one finds a presentation of this system of Gödel accompanied by a brief reexamination in the light of the notes of some points concerning his interest in sequents made in the preceding paper. This is preceded by a brief summary of Gödel's Notre Dame course, and is followed by comments concerning Gödel's natural deduction system.
arXiv,
DOI.
"Is natural deduction natural?" (extended abstract) (with Ana Došen, Kosta Došen, Jovana Kostić, Katarina Maksimović and Senka Milošević),
Empirical Studies in Psychology, Laboratory of experimental psychology and the Institute of psychology, Faculty of Philosophy, University of Belgrade (2017).
Abstract,
Natural deduction, a formalization of hypothetical reasoning, is found in a particular kind of formal systems of logic, which have attracted some attention from cognitive psychologists rather recently. The formal systems envisaged here were not dominant in textbooks of logic. The aim of this work is to answer the question in the title by dealing with such systems of natural deduction, which do not seem to have been envisaged up to now in experimental cognitive psychology. This version of natural deduction is simpler, and stands a chance of being found more natural. We do not present results of experiments, but seek cooperation from psychologists in designing them. The experiments envisaged are to deal with the early growth of logic among children, which are expected to have an at least implicit knowledge of the simple natural deduction rules we would investigate. These are rules concerning first the connectives of conjunction and negation, and also the connectives of implication and disjunction of propositional logic.
Preprint.
Logic Lectures: Gödel’s basic logic course at Notre Dame (edited with Kosta Došen),
Dosije, Logical society, Belgrade (2017).
Abstract,
An edited version is given of the text of Gödel's unpublished manuscript of the notes for a course in basic logic he delivered at the University of Notre Dame in 1939. Gödel's notes deal with what is today considered as important logical problems par excellence, completeness, decidability, independence of axioms, and with natural deduction too, which was all still a novelty at the time the course was delivered. Full of regards towards beginners, the notes are not excessively formalistic. Gödel presumably intended them just for himself, and they are full of abbreviations. This together with some other matters (like two versions of the same topic, and guessing the right order of the pages) required additional effort to obtain a readable edited version. Because of the quality of the material provided by Gödel, including also important philosophical points, this effort should however be worthwhile. The edited version of the text is accompanied by another version, called the source version, which is quite close to Gödel's manuscript. It is meant to be a record of the editorial interventions involved in producing the edited version (in particular, how the abbreviations were disabridged), and a justification of that later version.
arXiv. (Review by Jan von Plato in: History and Philosophy of Logic, 39 (2018), 396-401, DOI; and by Johannes Stern in: Dialectica, 72 (2018), 617-622, DOI.)
"Gödel’s Notre Dame course" (with Kosta Došen),
The Bulletin of Symbolic Logic, 22 (2016), 469-481.
Abstract,
This is a companion to a paper by the authors entitled "Gödel's natural deduction", which presented and made comments about the natural deduction system in Gödel's unpublished notes for the elementary logic course he gave at the University of Notre Dame in 1939. In that earlier paper, which was itself a companion to a paper that examined the links between some philosophical views ascribed to Gödel and general proof theory, one can find a brief summary of Gödel's notes for the Notre Dame course. In order to put the earlier paper in proper perspective, a more complete summary of these interesting notes, with comments concerning them, is given here.
arXiv,
DOI.
"Gödel on the absolute proof and the logic of concepts" (abstract), in: General Proof Theory: Celebrating 50 Years of Dag Prawitz's "Natural Deduction", Proceedings of the Conference held in Tübingen, 27-29 November 2015, edited by Thomas Piecha and Peter Schroeder-Heister, University of Tübingen (2016), 12.
Abstract,
To be added.
Proceedings.
"On demons (and) bankers" (in Serbian),
in: U sećanje na Svetlanu Knjazev-Adamović, edited by Miloš Arsenijević and Živan Lazović, Faculty of Philosophy, University of Belgrade and Serbian Philosophical Society, Belgrade (2016), 35-39.
Abstract.
To be added.
"Gunkology and Pointilism: Two Mutually Supervening Models of the Region Based and the Point-Based Theory of the Infinite Two-Dimensional Continuum" (with Miloš Arsenijević),
in: Space and Time: A Priori and A Posteriori Studies, edited by Vincenzo Fano, Francesco Orilia and Giovanni Macchia, De Gruyter, Berlin (2014), 137-170.
Abstract,
First, in a pure Hilbertian manner, the Neo-Aristotelian Region-Based and the Cantorian Point-Based theory of the infinite two-dimensional continuum are formulated in the extended first-order language $L_{\omega_{1}\omega_{1}}$ through a selection of two appropriate sets of axioms. Then, it is proved that the two theories are only trivially different amongst themselves in the sense defined by Arsenijević 2003, where what matters is not the question of the isomorphism of the basic sets of their models but the sameness of their truth-expressive power. Namely, contrary to the received view, according to which the two theories represent interesting alternatives to each other, it turns out that any of them can be used to express all the truths about its basic and supervening entities and their relations as well as all the truths about its rival's basic and supervening entities and their relations. Consequently, from a metaontological point of view, Gunkology and Pointillism, at least at the two-dimensional level, are just mutually supervening models of the two formal theories that have the same truth-expressive power.
DOI.
"On pitfals of naturalism" (in Serbian),
Theoria, 3 (2012), 33-44.
Abstract,
This note examines some arguments directed against naturalism in the philosophy of mathematics. These arguments are formulated from the platonistic standpoint with the intention to show that we can coherently describe the faculty of mathematical intuition, which is unacceptable to every kind of naturalism.
DOI.
"Of older Serbian logic" (in Serbian) (with Senka Milošević),
Kultura, 134 (2012), 237-245.
Abstract,
In this paper we aim to pinpoint some of the key markers of the development of logic in Serbia, starting from the founding of the Lyceum in 1836 until the end of the 19th century. Our main goal is to underline the role that Ljubomir Nedić, a philosopher and literary critic, had in this context. Although he did not leave any original contributions in logic, Nedić played a significant part by exposing contemporary results in symbolic logic, which were to lead, through Frege’s later work, to the creation of modern logic.
DOI.
"Algorithms, categories and proofs: some topics in modern Serbian logic" (in Serbian) (with Senka Milošević),
Kultura, 134 (2012), 366-387.
Abstract,
In this paper we focus on two branches of modern logic, computability theory and proof theory, tracing their development in Serbia from the end of World War II to this day. Owing to the unfortunate set of circumstances, computability theory did not give birth to a school in Serbia. Proof theory, on the other hand, found a base in Belgrade as one of the few places in the world promoting Gentzen’s ideas, especially in the field of categorial proof theory which will be our sole interest in this work.
DOI.
"Philosophical set theory" (in Serbian),
Theoria, 2 (2010), 127-132.
Abstract.
To be added.
"Ontological and epistemological dimensions of Gödel’s Platonism" (in Serbian),
Theoria, 2 (2010), 39-50.
Abstract,
Kurt Gödel is certainly one of the biggest names of logic and mathematics of the last century. Besides that, he is also the most famous proponent of mathematical Platonism. The aim of this work is to investigate different aspects of Gödel’s Platonism as well as arguments he put forward in its support. We shall see that despite the problems Platonism faces, there is a lot to cite that promotes it as the only viable position in the philosophy of mathematics.
DOI.
Gödel’s Introduction to Deduction: Logic Lectures at Notre Dame, "Celebrating 90 Years of Gödel's Incompleteness Theorems", Carl Friedrich von Weizsäcker Center & Kurt Gödel Society, Nürtingen, 9/7/2021.
From recursion to deduction, two strands of modern logic in Serbia (with Jovana Kostić and Katarina Maksimović), "The Third Conference of East European Network for Philosophy of Science", Faculty of Philosophy, University of Belgrade, Belgrade, 9/6/2021.
Logic and the paradoxes (in Serbian, by title), "Philosophy and Science", Serbian Academy of Sciences and Arts, Belgrade, 21/10/2020.
Gödel’s lectures on logic (in Serbian), Seminar for Mathematical Logic, Mathematical Institute, Belgrade, 27/12/2019.
Gödel’s conceptual realism (in Serbian), Seminar for Probability Logic, Mathematical Institute, Belgrade, 26/12/2019.
Ludwig Wittgenstein (in Serbian), Serbian Philosophical Society, Belgrade, 14/12/2019.
Gödel’s basic logic course at Notre Dame (in Serbian) (with Kosta Došen), Seminar for General Proof Theory, Mathematical Institute, Belgrade, 15/5/2017.
Kurt Gödel and modern logic (in Serbian), Seminar for Constructive Mathematics, Faculty of Mechanical Engineering, Niš, 27/4/2017.
Is natural deduction natural? (in Serbian) (with Ana Došen, Kosta Došen, Jovana Kostić, Katarina Maksimović and Senka Milošević), "Empirical Studies in Psychology", Belgrade, 26/3/2017.
Gödel and deduction (in Serbian), Seminar for General Proof Theory, Mathematical Institute, Belgrade, 24/10/2016.
Gödel on the intensional logic of concepts, Oberseminar Logik und Sprachtheorie, Tübingen, 5/7/2016.
Gödel on absolute proof and the logic of concepts (in Serbian) Seminar for General Proof Theory, Mathematical Institute, Belgrade, 28/12/2015.
Gödel on proofs and axioms, "Second Belgrade Graduate Conference in Philosophy and Logic", Belgrade, 26/4/2015.
Infinite abacus: Lambek's calculating machine (in Serbian), Seminar for General Proof Theory, Mathematical Institute, Belgrade, 15/12/2014.
Gödel on axioms and proofs (in Serbian), Seminar for General Proof Theory, Mathematical Institute, Belgrade, 18/3/2013.
Platonistic explanation of mathematical knowledge (in Serbian), "Structure of Explanation", Belgrade, 17/11/2012.
The life and work of Vladeta Vučković (in Serbian) (with Kosta Došen), Seminar for General Proof Theory, Mathematical Institute, Belgrade, 29/10/2012.
Notes on Logic: Incompleteness and Undecidability (in Serbian), Belgrade, 2022.
"Geach on Dummett's Frege: A Ruinous Confusion?"
"A Note on Reflexive Paradoxes"
"Paradoxical Facts of the Matter"
E-mail: mradzic@f.bg.ac.rs
Mail: Faculty of Philosophy, University of Belgrade, Čika Ljubina 18-20, 11000 Belgrade, Serbia.