This paper explores some variants and aspects of multi-quantificational criteria of existence, examining these in the context of the debate between monism and pluralism in analytical philosophy. Assuming familiarity with the findings to date, we seek to apply to these the newly introduced concepts of “substitution” and “substitutional model”. Possible applications of formal theories involving multiple types of existential quantifier are highlighted, together with their methods of construction. These considerations then lead to a thesis asserting the irrelevance of both multi-quantificational (...) criteria and assumptions involving quantificational ontology to the debate between monism and pluralism in ontology. Many quantifiers cannot properly distinguish different modes of existence–as we aim to show by furnishing a general method for constructing counter-examples to any theory that assumes that different types of existential quantifier correspond to different modes of existence. (shrink)

This paper seeks to determine the intuitive meaning of the concept of information by indicating its essential (definitional) features and relations with other concepts, such as that of knowledge. The term “information” – as with many other concepts, such as “process”, “force”, “energy” and “matter” – has a certain established meaning in natural languages, which allows it to be used, in science as well as in everyday life, without our possessing any somewhat stricter definition of it. The basic aim here (...) is thus to explicate what it amounts to in the context of its intuitive meaning as encountered in natural languages, what the subject of cognition implicitly presumes when using the term, and to which ontological situations it can be applied. I demonstrate that the essential features of the notion of information include the presence of a material medium, its transformation, the recording and reading of information encoded in the medium, and the grasp of what is recorded, coded and transmitted as an intentional object, where the latter is construed in terms broadly in line with the ontologies of Husserl and Ingarden. Along the way, a number of issues relating to the notion of information are also pointed out: the problem of informational identity, of the existence of virtual objects, and of the choice of an adequate information carrier, as well as formal-ontological problems, including those which concern relations between information carriers and intentional objects. (shrink)

This paper is devoted to the reconstruction of the implicit logic of Plato’s Par-menides. The reconstructed logic, F, makes it possible to form a new semi-intuitionistic system of logic of predicates, FN. The axioms of Peano Arithmetic (PA) and an axiom of infinity follow from FN. Therefore, FN can be seen as a new attempt at the realization of Frege’s logicist program. Some very strong systems can be seen as other variants of FN, e.g. Leśniewski’s ontology. The hypothesis from Parmenides (...) II contains proof of the existence of the two highest principles, i.e. the One and the Dyad, their mutual relationship, their relations to other things, and the reasoning regarding the mutual relationship follows some exact formal rules. Six types of Plato’s negation of a predicate are defined. The system is a first-order logic with non-classical negation of a predicate (local negation) that is non-definable by classical sentential negation. Therefore, the implicit logic of Plato’s Parmenides differs from classical syllogistics (formed in the Łukasiewicz’s style) as well as from the classical predicate calculus. (shrink)

We aim to show from a new perspective that Quine’s ontological relativity, based largely on his so-called “proxy-function argument”, falls short of being a rigorously coherent philosophical conception, as it exhibits significant formal defects. This new perspective enables exposing the shortcomings of Quine's position and suggests a possible reformulation of the original position. Moreover, we argue that his ontological relativity is inconsistent with the empirical data associated with some of our best physical theories, such as quantum mechanics. We refer to (...) fundamental concepts of philosophy and the foundations of mathematics in order to clarify our critique of Quine’s position concerning the relation between formalized theories and both what we can know about the real world and how we come to know it. (shrink)

The paper is devoted to the reconstruction of some stage of the proces leading to the emergence in modern science the concept of Infinite „Euclidean” space to geometry of the Elements in late antiquity and the Middle Ages. Some historical medieval sources and views concerning Archytas, Cleomedes, Proclus, Simplicius, Aganis, al-Nayrizi and the Arabs, Boetius, Gerard of Cremona, Albertus Magnus et al., are described analyzed and compared. The small changes in the understanding of geometry in the Elements during the ages (...) are reconstructed up to the first explicit use of the concept of infinity in geometry by Nicole Oresme. (shrink)

This article presents some modern philosophical reasons that lay behind the introduction of the concept of the hermeneutical horizon to explain scientific change; cf. [1], chapter 17. These reasons reveal arbitrariness of sociological variabilism following from its elimination of the objective intellectual factors, essential in knowledge creation.

In this paper the final stages of the historical process of the emergence of actual infinity in mathematics are considered. The application of God’s point of view – i.e. the possibility to create mathematics from a divine perspective, i.e. from the point of view of an eternal, timeless, omniscience and unlimited subject of cognition – is one of the main factors in this process. Nicole Oresme is the first man who systematically used actual infinity in mathematical reasoning, constructions and proofs (...) in geometry. (shrink)

This paper presents sources pertinent to the transmission of Euclid’s Elements in Western medieval civilization. Some important observations follow from the pure description of the sources concerning the development of mathematics, e.g., the text of the Elements was supplemented with new axioms, proofs and theorems as if an “a priori skeleton” lost in Dark Ages was reconstructed and rediscovered during the late Middle Ages. Such historical facts indicate the aprioricity of mathematics.

This paper presents sources pertinent to the transmission of Euclid’s Elements in Western medieval civilization. Some important observations follow from the pure description of the sources concerning the development of mathematics, e.g., the text of the Elements was supplemented with new axioms, proofs and theorems as if an “a priori skeleton” lost in Dark Ages was reconstructed and rediscovered during the late Middle Ages. Such historical facts indicate the aprioricity of mathematics.

The greatest challenge with which the Readers of my book had to cope with was the problem of ontological presence. In Srzednicki’s conception ontological presence has two dimensions: a logical and an onto-factual one.Every cognitive perspective is always contingent but this contingency must be limited somehow. Srzednicki restores the ontological dimension of cognition (crossed out by traditional epistemology and philosophy), but avoids ontological fundamentalism. His conception gives rise to a new model of metaphysics understood not as the most general theory (...) of being or a general theory of cognition but as the non-epistemic closure of all epistemological projects and theoretical discourses.The main parameters of the epistemic closure can only be reconstructed theoretically in the logical space of the observer. This non-epistemic closure is marked by three categorical constraints: ontological, formative and normative.Srzednicki overcomes Wittgenstein’s skepticism by understanding transcendentalism much more deeply. (shrink)

This paper is devoted to the reconstruction of the development of ancient theories of proportion. I argue that the development of ancient theories of proportion was motivated by the quest for one general mathematical theory and by inquiries of the mutual relations between the highest principles of Plato’s protology: the One and the Dyad . Six main types of the theory of proportion are analyzed, with a historical, mathematical and philosophical background.

Braddon-Mitchell and Miller put forward the claim that the relation of being-the-same-person is gradable: a person can be the same person tomorrow as today, but only half the same. To justify their thesis, they propose a model of persons that is intended to be metaphysically neutral. This article sets out to show that such a model implicitly contains strong metaphysical assumptions that run contrary to the authors’ own statements. Using Roman Ingarden’s phenomenological ontology, we aim to demonstrate that within the (...) model in question persons exist intentionally, where this leads to a caricature rather than an adequate account of persons. In opposition to Braddon-Mitchell and Miller, we argue that the justification presented for the thesis of the gradability of the relation of being-the-same-person in fact makes it reasonable to demand that an adequate model of persons be posited. We present Kurt Lewin’s holistic topological-dynamic model, and show that in this context it is not being-the-same-person that is gradable, but rather the characteristic (of persons) that is dimension. Thus, we reject the thesis of the gradability of the relation of being-the-same-person involved in personal identity. (shrink)