Leśniewski’s Systems PrototheticJan J.T. Srzednicki, Z. Stachniak Springer Science & Business Media, 6 de des. 2012 - 310 pàgines Between the two world wars, Stanislaw Lesniewski (1886-1939), created the famous and important system of foundations of mathematics that comprises three deductive theories: Protothetic, Ontology, and Mereology. His research started in 1914 with studies on the general theory of sets (later named `Mereology'). Ontology followed between 1919 and 1921, and was the next step towards an integrated system. In order to combine these two systematically he constructed Protothetic - the system of `first principles'. Together they amount to what Z. Jordan called `... most thorough, original, and philosophically significant attempt to provide a logically secure foundation for the whole of mathematics'. The volume collects many of the most significant commentaries on, and contributions to, Protothetic. A Protothetic Bibliography is included. |
Continguts
| 1 | |
A Survey of Leśniewskis Logic | 23 |
ALFRED TAJTELBAUMTARSKI | 43 |
BOLESŁAW SOBOCIŃSKI | 69 |
JERZY SŁUPECKI | 84 |
BOLESŁAW SOBOCIŃSKI | 153 |
Axiomatic Inscriptional Syntax | 217 |
AUDOËNUS LE BLANC | 289 |
PROTOTHETIC BIBLIOGRAPHY | 299 |
| 309 | |
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abstract entities analogous assumption axiom of Protothetic axiom-system belong Bolesław Bolesław Sobociński category of propositions Collectanea Logica condition contains Dame Journal deductions defined definiendum definiens elementary protothetics equiform equivalence expressions Formal Logic formulated free variables functions functors Fundamenta Mathematicae ƒ q ƒ(Fl implication int(A Journal of Formal Kotarbiński law of extensionality law of substitution Lejewski Lemma Leśniewski 1929 Leśniewski's system Łukasiewicz mathematics Mereology metarule metatheorem Note obtained Ontology Ɔ 1 Ɔ Ɔ A ɛ Ɔ ƒ Ɔ q paper parentheses primitive term principle of bivalence proof proposition-forming functors propositional argument propositional calculus prove reism rule of extensionality rules of inference rules of procedure S₁ Section semantical category sentence SIII single axiom Słupecki Sobociński Stanisław Stanisław Leśniewski symbolism syntactical category system of protothetic Tarski theorem of S2 theory thesis truth-function variable functors verifiers vrb(A vrb(B