A Study Of Le?niewski's Protothetic

Stanislaw Lesniewski belonged to the first-generation logicians of the Lvov-Warsaw School of Poland.His contribution in the field of logic is no less important than those of Frege,Pierce,and Whitehead-Russell,but his work is also least studied or even known.His logic is both technically and theoretically different from classical logic.He rejected Cantor's set theory and thus created his Mereology;he rejected Russell's type theory and thus created the theory of syntactic categories;he rejected the logicians' use of the copula"is" which goes against natural language intuition and thus created his Ontology based on the logical constant "?";he rejected Hilbert's axiomatization treatment which leads to epistemological closure,and thus introduced creative definitions;he rejected Principia Mathematica for its lack of exactness,and thus created Protothetic,the most exact logical system ever.In terms of logical hierarchy,Mereology assumes ontology,while Ontology assumes Protothetic.Ontology and Protothetic together form a logic that is approximately equivalent to classical first-order logic.Ontology is the ontological bearer of Lesniewski's logic.Protothetic is propositional logic plus general quantification.Besides general quantification,Protothetic is characterized by its inscriptionism,that is,the object of the entire system is limited to the language symbols used.Inscriptionism does not assume any extra-linguistic objects.In this sense,Protothetic is ontologically neutral.Although Lesniewski's three systems-Mereology,Ontology,and Protothetic-together as a whole form a foundation of mathematics,he possibly was the only logician who opposed the monopolization of logic by mathematicians and also the only philosopher who tried to take back the discourse(in the sense used by Michel Foucault)on logic from the hands of mathematicians.He opposed mathematicians'pragmatism or instrumentalism,that is,the consistency and feasibility of a system justify that system.As a philosopher,Lesniewski indeed suggested two concepts of foundational research.One is the concept of the foundations of mathematics,and logic is proposed as a whole or in part of a foundation of mathematics.In fact,since the nineteenth century,logic as a discipline had gradually fallen into the hands of mathematicians,so the issues related to logic are determined by mathematicians.Axiomatization,completeness,consistency,and proving various theorems dominated the study of logic.To a certain extent,these are questions affiliated with mathematics;but logic as a discipline was created by a philosopher or philosophers,and their thinking targeted problems that are philosophical or of scientific nature,not problems of mathematical systems,although the research scope of the philosophers and the mathematicians may overlap.This dissertation proposes another concept of foundational research as suggested by Lesniewski.If a logical language is not limited to being a tool of mathematics,but is more widely used as the basis of a language used to describe the world,in the sense of Leibniz's characteristic universalis,then we must answer the question of what kind of logical language is an appropriate(or even qualified!)language.Obviously,not that any "logical language" is acceptable.Lesniewski's Protothetic indirectly answers this philosophical question and is therefore significant.This is why Lesniewski constructed Protothetic:the linguistic base of a system of logic should be ontologically neutral.Protothetic is a blueprint for constructing a propositional calculus.One particular feature of this blueprint is that it has no extra-linguistic reference.For instance,a proposition refers only to an uttered string,and truth values are merely properties of language(propositions).Such a logical language base takes up the task of safeguarding the base from committing to any extra-linguistic reference.Another issue concerns epistemological openness.If we accept Hilbert's formalist axiomatization,the axiomatic system is a closed axiom system,and thus leads to epistemological closure.This is of course an absurd consequence from the perspective of science.Lesniewski was the first to question Hilbertian axiomatization and proposed a solution.In general,Lesniewski was probably the first modern logician to take ontological commitment as a major concern in constructing logical systems,and also the first philosopher to take back the discourse in logic from the hands of the mathematician.That said,the present thesis is a reconstruction of Lesniewski's Protothetic.Since most of his manuscripts were destroyed during the war,only two papers with actual discussions of Protothetic have survived.They are "Grundzuge eines neuen System der Grundlagen der Mathematik" and "Einleitende Bemerkungen zur Fortsetzung meiner Mitteilung u.d.T.'Grundzuge eines neuen System der Grundlagen der Mathematik'";the latter states 422 theorems whereas the former displays in sectyion 9 the technical elements,in 19 pages of basically unexplained symbols,required for the construction of any Protothetic system.These 19 pages constitute the main source of our reconstruction of Protothetic.