Our research concerns a formal representation of Bolzano’s original concepts of Substanz and Adhärenz. The formalized intensional theory enables to articulate a question about the consistency of a part of Bolzano’s metaphysics and to suggest an answer to it in terms of contemporary model theory. The formalism is built as an extension of Zalta’s theory of abstract objects, describing two types of predication, viz. attribution and representation. Bolzano was aware about this distinction. We focus on the consistency of this formalism (...) and the description of its semantics. Firstly, we explore the possibility to reconstruct a Russellian antinomy based on the concept of the Bolzano’s Inbegriff of all adherences. Our aim is to show limitations of his theory that prevent a contradiction when the Inbegriff consists of non-self-referential adherences. Next, we discuss two competing semantics for the proposed theory: Scott’s and Aczel’s semantics. The first one yields a problematic result, that there are no models for the considered theory, containing a non-empty collection of all adherences. This is due to the fact that Scott’s structures verify the formula on reloading abstracts in extensional contexts. We show that Aczel’s semantics does not contain this difficulty. There are described Aczel’s models with a non-empty set of all adherences. The self-referentiality of such a collection becomes irrelevant here. Finally, we show that there are Aczel’s structures verifying the formula on reloading abstracts and we exclude them from the class of models intended for our theory. (shrink)

The topic of our analysis is the argument for the existence of substances given by Bernard Bolzano in Athanasia, where he essentially employs two ontological categories: substance and adherence. Bolzano considers the real and conditioned Inbegriff of all adherences, which are wirklich and nicht selbst bestehen. He claims that the formed collection is dependent on something external and non-adherential, which therefore is a substance. Bolzano’s argumentation turns out to be structurally similar to his argument for the existence of God from (...) Lehrbuch der Religionswissenschaft, but in each of these reasonings, we find different plausible interpretations of the key concept “Inbegriff”. The latter argumentation refers to the mereological totality of existentially conditioned objects. We propose the explication of the Bolzanian Inbegriff of all adherences using two types of predication: we consider its extension as composed of certain intensional counterparts of adherences. In our approach, we use a fragment of the theory of abstract objects formulated by E. Zalta, describing two different relations between individuals and properties: extensional exemplification and intensional encoding. We put our reconstruction in a wider context of Bolzano’s ontology, formulating the needed axioms with two primitive predicates of second order... is an adherence,... is conditioned by something real as well as the conditionally introduced first order predicate constant \ for Inbegriff of all adherential ideas. Finally, we sketch a model for our theory. (shrink)

Are there different sizes of infinity? That is, are there infinite sets of different sizes? This is one of the most natural questions that one can ask about the infinite. But it is of course generally taken to be settled by mathematical results, such as Cantor’s theorem, to the effect that there are infinite sets without bijections between them. These results settle the question, given an almost universally accepted principle relating size to the existence of functions. The principle is: for (...) any sets A and B, if A is the same size as B, then there is a bijection from A to B. The aim of the paper, however, is to argue that this question is in fact wide open: to argue that we are not in a position to know the answer, because we are not in one to know the principle. The aim, that is, is to argue that for all we know there is only one size of infinity. (shrink)

Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected . In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of (...) empty parts, in delivering a balanced and bounded metaphysics of naive space. (shrink)

Neo-Fregeanism contends that knowledge of arithmetic may be acquired by second-order logical reflection upon Hume's principle. Heck argues that Hume's principle doesn't inform ordinary arithmetical reasoning and so knowledge derived from it cannot be genuinely arithmetical. To suppose otherwise, Heck claims, is to fail to comprehend the magnitude of Cantor's conceptual contribution to mathematics. Heck recommends that finite Hume's principle be employed instead to generate arithmetical knowledge. But a better understanding of Cantor's contribution is achieved if it is supposed that (...) Hume's principle really does inform arithmetical practice. More generally, Heck's arguments misconceive the epistemological character of neo-Fregeanism. (shrink)

This volume contains an English translation of Edmund Husserl’s first major work, the Philosophie der Arithmetik, (Husserl 1891). As a translation of Husserliana XII (Husserl 1970), it also includes the first chapter of Husserl’s Habilitationsschrift (Über den Begriff der Zahl) (Husserl 1887) and various supplementary texts written between 1887 and 1901. This translation is the crowning achievement of Dallas Willard’s monumental research into Husserl’s early philosophy (Husserl 1984) and should be seen as a companion to volume V of the Husserliana: (...) Collected Works series (Husserl 1994b), which already contained selected translations from Hua XII. As Willard re- marks on the inner cover of the volume, it is “a window on a period of rich and illuminating philosophical activity”, to which I wholeheartedly agree. Willard’s two volumes of translations open this window on the beginnings of Husserl’s philosophy for the English-speaking world. This earliest period of Husserl’s philosophy has often been unjustly ignored and Willard provides the English reader with an excellent starting point. Husserl’s first steps into phenomenology and the philosophy of logic and mathematics contain many promising seeds that will flower later on, in the Logische Untersuchungen and beyond. (shrink)

Three principal varieties of mathematical structuralism are compared: set-theoretic structuralism (‘STS’) using model theory, Shapiro's ante rem structuralism invoking sui generis universals (‘SGS’), and the author's modal-structuralism (‘MS’) invoking logical possibility. Several problems affecting STS are discussed concerning, e.g., multiplicity of universes. SGS overcomes these; but it faces further problems of its own, concerning, e.g., the very intelligibility of purely structural objects and relations. MS, in contrast, overcomes or avoids both sets of problems. Finally, it is argued that the modality (...) of MS or a close cousin appears at crucial junctures in both STS and SGS, so that the above outcome is not obviously tendentious. (shrink)

Despite the often false impression that the analytic philosophy as an anti-metaphysical movement has nothing to do with metaphysics, there can be found good reasons to grant the metaphysical dispositions of analytic philosophers, and thereby, to minimize the anti-metaphysical nature of analytic philosophy in its all phases. Since analytic philosophy is a historical movement the main nature of which developed through several stages, the very kinds of metaphysical dispositions within each one of its various stages can be easily portrayed. In (...) the meantime, logical realism as the early stage of analytic philosophy contains plenty of metaphysical dispositions. Undoubtedly, one cannot say that analytic philosophy in this period was not committed to metaphysical theses about the plurality of entities, the ultimate nature of reality and the logical structure of the world. In this paper, then, after giving a relatively complete explanation of the logical realism, we claimed that although logical realists rejected the traditional speculative metaphysics of their predecessors, they also replaced it by the metaphysics of logic that pursues the metaphysical aims, this time, by logical means. So, we portrayed this kind of metaphysics as Bolzano’s Semantic Platonism, Frege’s and Russell’s Pluralistic Platonism, Russell’s Pluralistic Atomism, and Wittgenstein’s logical atomism. (shrink)

Since Peter van Inwagen in his book Material Beings raised The Special Composition Question, many lines have been written about the conditions for two or more material objects to compose a further object. This paper proposes a study of the relationship between composition and the notion of boundary. The question about composition entails drawing a boundary to determine when it occurs and when it does not. There are three traditional answers: restrictivism, universalism, and nihilism. While according to restrictivism, composition occurs (...) occasionally, according to universalism and nihilism, it occurs either always or never respectively. Nonetheless, despite the opposition of these two answers, both have a common target: to avoid the existence of ontologically vague boundaries for material composition. Thus, how a boundary is drawn will determinewhat kind of things we accept as components of the world. (shrink)

open journal of Philosophical Investigations (PI) is an international journal dedicated to the latest advancements in philosophy. The goal of this journal is to provide a platform for academicians all over the world to promote, share, and discuss various new issues and developments in different areas of philosophy. -/- All manuscripts to be prepared in English or Persian and are subject to a rigorous and fair peer-review process. Generally, accepted papers will appear online. The journal publishes papers including the following (...) fields: -/- · Analytic Philosophy · Ancient Greek and Roman Philosophy · Art Aesthetics · Comparative Philosophy West and Chinese · Eastern Philosophy . Islamic philosophy · Epistemology · Ethics · Hermeneutics · History of Religious Thought · History of Western Philosophy · Language Logic . (shrink)