In (1991), Meinwald initiated a major change of direction in the study of Plato’s Parmenides and the Third Man Argument. On her conception of the Parmenides , Plato’s language systematically distinguishes two types or kinds of predication, namely, predications of the kind ‘x is F pros ta alla’ and ‘x is F pros heauto’. Intuitively speaking, the former is the common, everyday variety of predication, which holds when x is any object (perceptible object or Form) and F is a property (...) which x exemplifies or instantiates in the traditional sense. The latter is a special mode of predication which holds when x is a Form and F is a property which is, in some sense, part of the nature of that Form. Meinwald (1991, p. 75, footnote 18) traces the discovery of this distinction in Plato’s work to Frede (1967), who marks the distinction between pros allo and kath’ hauto predications by placing subscripts on the copula ‘is’. (shrink)

Zalta's notion of encoding which lies at the core of his theory of abstract objects is refined so that it can capture cognitive dynamic phenomena such as multiple object-tracking in particular intentional contexts; namely hypothetical stipulation concerning abstract objects and counter-essential conceivability about ordinary ones. Zalta's Modal Axiom of Encoding is weakened and the notion of 'quasi-encoding' is spelt out.

The appeal to possible worlds in the semantics of modal logic and the philosophical defense of possible worlds as an essential element of ontology have led philosophers and logicians to introduce other kinds of `worlds' in order to study various philosophical and logical phenomena. The literature contains discussions of `non-normal worlds', `non-classical worlds', `non-standard worlds', and `impossible worlds'. These atypical worlds have been used in the following ways: (1) to interpret unusual modal logics, (2) to distinguish logically equivalent propositions, (3) (...) to solve the problems associated with propositional attitude contexts, intentional contexts, and counterfactuals with impossible antecedents, and (4) to interpret systems of relevant and paraconsistent logic. However, those who have attempted to develop a genuine metaphysical theory of such atypical worlds tend to move too quickly from philosophical characterizations to formal semantics. (shrink)

In this paper, the author derives the Dedekind-Peano axioms for number theory from a consistent and general metaphysical theory of abstract objects. The derivation makes no appeal to primitive mathematical notions, implicit definitions, or a principle of infinity. The theorems proved constitute an important subset of the numbered propositions found in Frege's *Grundgesetze*. The proofs of the theorems reconstruct Frege's derivations, with the exception of the claim that every number has a successor, which is derived from a modal axiom that (...) (philosophical) logicians implicitly accept. In the final section of the paper, there is a brief philosophical discussion of how the present theory relates to the work of other philosophers attempting to reconstruct Frege's conception of numbers and logical objects. (shrink)

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)