Online research in philosophy

In this paper, we discuss some formal properties of the model ofbidirectional Optimality Theory that was developed inBlutner (2000). We investigate the conditions under whichbidirectional optimization is a well-defined notion, and we give aconceptually simpler reformulation of Blutner's definition. In thesecond part of the paper, we show that bidirectional optimization can bemodeled by means of finite state techniques. There we rely heavily onthe related work of Frank and Satta (1998) about unidirectionaloptimization.

I will consider Armstrong's problems in trying to account for structural universals, i.e., a kind of complex universal whose instantiation by particulars involves different parts of those particulars instantiating several basic properties and relations, such as the property of being a molecule of methane. I present and criticise Armstrong's most recent attempt to explain structural properties by means of the identification of universals with types of states of affairs and I state my own solution to the problem by appealing to formal relations holding between particulars.

In this article I assess some results that purport to show the existence of a type of 'topological perception', i.e., perceptually based classification of topological features. Striking findings about perception in insects appear to imply that (1) configural, global properties can be considered as primitive perceptual features, and (2) topological features in particular are interesting as they are amenable to formal treatment. I discuss four interrelated questions that bear on any interpretation of findings about the perception of topological properties: what exactly are topological properties, what makes them global , in what sense the quoted findings makes them primitive, and what are the hopes of a formal theory of perception based upon them. I suggest that mathematical topology is not the correct model for cognition topological properties, hence that some other formalism ought to be used—a form of “internalized topology.” However, once the principles of this type of topology are spelled out, they may not be as globalistic as one may have expected.

Identity, existence, predication, necessity, and truth are vital concepts at the center of philosophy. Yet Colin McGinn believes that orthodox views of these topics are misguided in important ways. Philosophers and logicians have often distorted the nature of these concepts in an attempt to define them according to preconceived ideas. Logical Properties aims to respect the ordinary ways we talk and think when we employ these concepts, while at the same time showing that they are far more interesting and peculiar than some have assumed; these notions correspond to real properties--logical properties--that challenge naturalistic metaphysical views. Written with a minimum of formal terminology, this book deals with logico-linguistic issues as well as ontological ones. The focus is on trying to get to the essence of the concept concerned, not merely finding some established notation for providing formal interpretations.

Consider "Sam is sad" and "Sam exemplifies the property of being sad". The second sentence mentions a property and predicates the relation of exemplification. It belongs to a large class of sentences which mention such formal objects as propositions, states of affairs, facts, concepts and sets and predicate formal properties such as the truth of propositions, the obtaining of states of affairs and relations such as falling under concepts and being members of sets. The first sentence belongs to a distinct class of sentences in which only non-formal objects are mentioned and only non-formal properties and relations are predicated. We can, it seems, infer validly from the first sentence to the second. They are also equivalent. And Sam exemplifies the property of sadness because Sam is sad. What is the relation between inference, equivalence and explanation in the case of our two sentences and in analogous cases? What right have we to assume that there are formal objects?

Any discussion of the concept of “formal science” must acknowledge that the term is used in different ways, for different purposes, by different people. For some, the formal sciences are defined by the exclusive use of deductive methods for discovering, or reasoning about, the properties of formal, abstract systems. On this view, the formal sciences are synonymous with mathematics, formal logic, and certain branches of linguistics and computer science that emphasize the study of formal languages. For others, “formal science” means something like “exact science”, or “formalized science”. On this view, any scientific discipline that places heavy emphasis on mathematical or logical formalization of key theoretical concepts and theories, could be described as a formal science. This latter conception of formal science is much more liberal than the former, and would include all of physics, much of chemistry, and some parts of biology, ecology, psychology and economics, as well as newer computationoriented disciplines like artificial life and artificial intelligence that do not fit easily within the traditional classification of the sciences.

In this paper I present a formal language in which complex predicates stand for properties and relations, and assignments of denotations to complex predicates and assignments of extensions to the properties and relations they denote are both homomorphisms. This system affords a fresh perspective on several important philosophical topics, highlighting the algebraic features of properties and clarifying the sense in which properties can be represented by their extensions. It also suggests a natural modification of current logics of properties, one in which some complex predicates stand for properties while others do not.

John Hick uses a distinction between the formal and the substantial properties of the Real an sich, the noumenal God. Hick claims that substantial properties, such as 'being good' or 'being personal', cannot be ascribed to the Real an sich. On the other hand, according to Hick, formal properties -- such as 'being such that none of our concepts apply' -- can be predicated of the Real an sich. I argue, first of all, that many of the properties Hick ascribes to the Real an sich are hard to interpret as anything but substantial, unless we adopt a highly arbitrary substantial/formal distinction. Secondly, I argue that it is never possible to ascribe only formal properties to the Real an sich, since the correct framing and application of formal properties involves a prior knowledge of some substantial properties. I show that the predication of formal properties involves having more knowledge than we need for the application of substantial properties. I conclude that Hick's practice is better than his theory, and that by dispensing with the formal/substantial distinction, he would enable his doctrine of God to stand on more respectable and theological grounds.