On Leśniewski’s Characteristica Universalis

Leśniewski's systems deviate greatly from standard logic in some basic features. The deviant aspects are rather well known, and often cited among the reasons why Leśniewski's work enjoys little recognition. This paper is an attempt to explain why those aspects should be there at all. Leśniewski built his systems inspired by a dream close to Leibniz's characteristica universalis: a perfect system of deductive theories encoding our knowledge of the world, based on a perfect language. My main claim is that Leśniewski built his characteristica universalis following the conditions of de Jong and Betti's Classical Model of Science (2008) to an astounding degree. While showing this I give an overview of the architecture of Leśniewski's systems and of their fundamental characteristics. I suggest among others that the aesthetic constraints Leśniewski put on axioms and primitive terms have epistemological relevance. © The Author(s) 2008

Pieces of a Theory

A survey of theories of part, whole and dependence from Aristotle to the Gestalt psychologists, with special attention to Husserl’s Third Logical Investigation “On the Theory of Parts and Wholes”

Philosophical reflection on mathematics in Poland in the interwar period

AbstractIn the paper the views and tendencies in the philosophical reflection on mathematics in Poland between the wars are analyzed. Views of most outstanding representatives of Lvov–Warsaw Philosophical School and of Polish Mathematical School are presented. Their influence on logical and mathematical researches is considered

Mereology and semiotics

This paper gives a fIrst overview over the role of mereology — the theory of parts and wholes — in semiotics. The mereology of four major semioticians — Husserl, Jakobson, Hjelmslev, and Peirce is presented briefly and its role in the overall architecture of each of their theories is outlined — with Brentano tradition as reference. Finally, an evaluation of the strength and weaknesses of the four is undertaken, and some guidelines for further research is proposed

Philosophy of exact sciences (logic and mathematics) in Poland in 1918–1939

This paper describes the philosophy of logic and mathematics in Poland in the years 1918‒1939. The special attention is attributed to the views developed in the Polish Mathematical School and the Warsaw School of Logic. The paper indicates various differences between mathematical circles in Warszawa, Lvov and Kraków

Some non-standard interpretations of the axiomatic basis of Leśniewski’s Ontology

We propose an intuitive understanding of the statement: ‘an axiom (or: an axiomatic basis) determines the meaning of the only specific constant occurring in it.’ We introduce some basic semantics for functors of the category s/n,n of Lesniewski’s Ontology. Using these results we prove that the popular claim that the axioms of Ontology determine the meaning of the primitive constants is false

On the Phases of Reism

Kotarbiński is one of the leading figures in the Lvov-Warsaw school of Polish philosophy. We summarize the development of Kotarbiński’s thought from his early nominalism and ‘pansomatistic reism’ to the later doctrine of ‘temporal phases’. We show that the surface clarity and simplicity of Kotarbiński’s writings mask a number of profound philosophical difficulties, connected above all with the problem of giving an adequate account of the truth of contingent (tensed) predications. The paper will examine in particular the attempts to resolve these difficulties on the part of Leśniewski. It will continue with an account of the relations of Kotarbińskian reism to the ontology of things or entia realia defended by the later Brentano. Kotarbiński’s identification of Brentano as a precursor of reism is, it will be suggested, at least questionable, and the paper will conclude with a more careful attempt to situate the Brentanian and Kotarbińskian ontologies within the spectrum of competing ontological views

Energy, structure, soil and self-regulation in plant/soil systems: a conceptual model

1989 Fall.Includes bibliographical references.Typescript (Photocopy).A new concept is presented which suggests that in stable plant/soil systems, plants control the soil environmental factors that affect plant growth and the interactions among those factors by controlling system structure. The concept is based on the plant-control hypothesis and rhizocentric model of soil structural development. The plant-control hypothesis declares that in plant/soil systems energy is the primary resource, and structure an essential regulator of energy flows. The rhizocentric model of soil structural development in grass-dominated plant/soil systems describes the process which results in plant-control of soil structure, and, consequently, of energy and nutrient flows for such systems. In conjunction, the plant-control hypothesis and rhizocentric model form a conceptual model of control in plant/soil systems. The conceptual model may help explain the self-regulatory capabilities of stable plant/soil systems, and the causes of instability in some agricultural plant/soil systems. Examination of published data from various sources has revealed no case in which application of the conceptual control model did not result in logically consistent, reliable prediction of experimental outcomes, plausible interpretation of previously uninterpretable results, and often, formulation of testable new hypotheses. It is concluded that the control model -- and the plant-control hypothesis and rhizocentric model which it implies -- has enough credibility to merit further critical examination as a potentially useful conceptual tool for soil and agricultural science, biology, and ecology