Syntax without Abstract Objects

In line with the nominalistic denial of the existence of abstract objects, a basic theory of syntax for formal languages is developed and shown to satisfy certain fundamental requirements

Abstract objects: Species, Kinds, Concepts

In the paper I present Kotarbiński’s approach to abstract objects and show some mistakes in his investigations. By formal ontology I try to explain Kotarbiński’s view and proffer a new solution, a formal solution that is – I hope – in the spirit of Lvov–Warsaw (Lwów–Warsaw) School

Knowledge of Abstract Objects in Physics and Mathematics

In this paper a parallel is drawn between the problem of epistemic access to abstract objects in mathematics and the problem of epistemic access to idealized systems in the physical sciences. On this basis it is argued that some recent and more traditional approaches to solving these problems are problematic

Abstract Objects in a Metaphysical Perspective

The article presents an unconventional although not absolutely unprecedented view on abstract objects defending the position of metaphysical realism. It is argued that abstract objects taken in purely ontological sense are the forms of objects. The forms possess some common characteristics of abstract objects, they can exist not in physical space and time and play a grounding role in their relation to concrete objects. It is stated that commonly discussed abstract objects – properties, kinds, mathematical objects – are forms

Abstracting object interactions using composition filters

It is generally claimed that object-based models are very suitable for building distributed system architectures since object interactions follow the client-server model. To cope with the complexity of today's distributed systems, however, we think that high-level linguistic mechanisms are needed to effectively structure, abstract and reuse object interactions. For example, the conventional object-oriented model does not provide high-level language mechanisms to model layered system architectures. Moreover, we consider the message passing model of the conventional object-oriented model as being too low-level because it can only specify object interactions that involve two partner objects at a time and its semantics cannot be extended easily. This paper introduces Abstract Communication Types (ACTs), which are objects that abstract interactions among objects. ACTs make it easier to model layered communication architectures, to enforce the invariant behavior among objects, to reduce the complexity of programs by hiding the interaction details in separate modules and to improve reusability through the application of object-oriented principles to ACT classes. We illustrate the concept of ACTs using the composition filters model