Alfred Tarski: Semantic Shift, Heuristic Shift In Metamathematics

  title={Alfred Tarski: Semantic Shift, Heuristic Shift In Metamathematics},
  author={Hourya Sinaceur},
With his proof theory, Hilbert created one of the three fundamental trends of metamathematical research which, along with recursion theory and model theory, nowadays constitute the scope of mathematical logic. I shall not look at recursion theory here. Rather, I will examine how Tarski developed Hilbertian metamathematics in order to create the basis of a new domain of mathematical logic, i.e., model theory. 
Tarski's Conceptual Analysis of Semantical Notions
Tarski is famous for his widely accepted conceptual analysis (or, in his terms, “explication”) of the notion of truth for formal languages and the allied notions of satisfaction, definability, and
Tarski's Practice and Philosophy: Between Formalism and Pragmatism
Considering works by Tarski, the author claims that Tarski’s fundamental aim was to establish formal semantics as a new branch of mathematics.
The role of universal language in the early work of Carnap and Tarski
It is argued that by assuming the existence of a universal language, one prohibits oneself from conducting semantical investigations, and in Carnap’s case, axiom systems are not closed under derivation rules, which enables him to adopt a substitutional concept of models.
Tarski ’ s Intuitive Notion of Set
Tarski did research on set theory and also used set theory in many of his emblematic writings. Yet his notion of set from the philosophical viewpoint was almost unknown. By studying mostly the
Metamathematical fixed points
This thesis concerns the concept of metamathematical fixed points. After an introduction, we survey the field of metamathematics, from la fin du siècle to present. We are especially interested in the
The Gödelian Inferences
I attribute an ‘intensional reading’ of the second incompleteness theorem to its author, Kurt Gödel. My argument builds partially on an analysis of intensional and extensional conceptions of
From Hypocomputation to Hypercomputation
This paper will briefly survey the known landmarks both inside and outside the borders of computational theory, and focuses on what the structure of formal theory looks like, moving from hypocomputational, through traditional computational theories, and then beyond to hypercomputational theories.
Tarski on Definition, Meaning and Truth
  • D. Patterson
  • Philosophy
    The Golden Age of Polish Philosophy
  • 2009
Tarski’s conception of truth in its relation to Polish philosophy and other developments of the time is set out and a response is responded to in the hope of vindicating Tarski and the tradition to which he belonged.
From Mereology to Boolean Algebra: The Role of Regular Open Sets in Alfred Tarski’s Work
Can the content of a whole paper be explained by a single footnote In 1956 Alfred Tarski made an effort in this direction in his chapter ‘On the Foundations of Boolean Algebra’ (Tarski, 1956c). This
Polish Axiomatics and Its Truth - On Tarski’s Leśniewskian Background and the Ajdukiewicz Connection
Leśniewski used to say that he had 100 percent genius doctoral students, his only student being Alfred Tarski (Wolenski 1995, 68 note 11). According to unwritten sources,1 however, when Tarski’s The


Logic, Semantics, Metamathematics: Papers from 1923 to 1938
This edition of The Concept of Truth in Formalized Languages includes a new preface and a new analytical index for use by philosophers and linguists as well as by historians of mathematics and philosophy.
Alfred Tarski's Work on General Metamathematics
This essay discusses Tarski's work on what he called the methodology of the deductive sciences, or more briefly, borrowing the terminology of Hilbert, metamathematics, and characteristic feature is his broad view of what constitutes the domain of metam athematical investigations.
Some Current Problems in Metamathematics1
In this article the author first described the developments which brought to focus the importance of consistency proofs for mathematics, and which led Hilbert to promote the science of
What are logical notions
In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those
Tarski on Truth and Logical Consequence
The influence of Tarski's writings on truth and logical consequence has been equally pervasive, extending not only to work in semantics and the philosophies of logic and language, but to less obviously allied areas such as epistemology and the philosophy of science as well.
On Tarski’s Background
Let me start with the following quotation from Mostowski: Tarski, in oral discussions, has often indicated his sympathies with nominalism. While he never accepted the ‘reism’ of Tadeusz Kotarbinski,
Semantic Revolution Rudolf Carnap, Kurt Gödel, Alfred Tarski
According to a common opinion, the word ‘semantics’ (precisely: its French counterpart semantique’), derived from the Greek word semantikos (=having meaning, denoting), appeared for the first time,
On the development of the model-theoretic viewpoint in logical theory
The most important background factor in the development of twentieth-century logic has received insufficient attention in the literature. This factor is a largely tacit contrast between ways of
The Semantic Conception of Truth and the Foundations of Semantics
X is true if, and only if, p. [...] we shall call a definition of truth “adequate” if all these equivalences follow from it. [...] The definition of truth which was outlined above [...] implies all
This paper explores such questions as who actually discovered non-euclidean geometry, who actually believed in its consistency and why, and who can be said to have proved it to be free of