Online research in philosophy

The network theory of conceptual development is the theory that conceptual developmentmay be represented as a process of constructing a network of linked nodes. The nodes of such a network represent concepts and the links between nodes represent relations between concepts. The structure of such a network is not determined by experience alone but must evolve in accordance with abstraction heuristics, which constrain the varieties of network between which experience must decide. This paper criticizes the network theory on the grounds that current proposals regarding these abstraction heuristics all fail, and further, that, given certain plausible assumptions, no viable account of these abstraction heuristics will be possible. Abstraction heuristics cannot be universal principles of rational thought because virtually no concept is intrinsically unsuitable for use in a true and useful representation of reality. Nor can they be species-specific natural conventions because in that case, it is argued, we would not be able even in principle to learn to understand the language of creatures who used different ones.

Since the pioneering work by Kripke and Montague, the term possible world has appeared in most theories of formal semantics for modal logics, natural languages, and knowledge-based systems. Yet that term obscures many questions about the relationships between the real world, various models of the world, and descriptions of those models in either formal languages or natural languages. Each step in that progression is an abstraction from the overwhelming complexity of the world. At the end, nothing is left but a colorful metaphor for an undefined element of a set W called worlds, which are related by an undefined and undefinable primitive relation R called accessibility. For some purposes, the resulting abstraction has proved to be useful, but as a general theory of meaning, the abstraction omits too many significant features. So much information has been lost at each step that many philosophers, linguists, and psychologists have dismissed model-theoretic semantics as irrelevant to the study of meaning. This article examines the steps in the process of extractingthe pair (W,R) from the world and the way people talk about the world. It shows that the Kripke worlds can be reinterpreted as part of a Peircean semiotic theory, which can also include contributions from many other studies in cognitive science. Among them are Dunn’s semantics based on laws and facts, the lexical semantics preferred by manylinguists, psychological models of how the world is perceived, and philosophies of science that relate theories to the world. A full integration of all those sources is far beyond the scope of this article, but an outline of the approach suggests that Peirce’s vision is capable of relating and reconciling the competing sources.

A central element in neo-Fregean philosophy of mathematics is the focus on abstraction principles, and the use of abstraction principles to ground various areas of mathematics. But as is well known, not all abstraction principles are in good standing. Various proposals for singling out the acceptable abstraction principles have been presented. Here I investigate what philosophical underpinnings can be provided for these proposals; specifically, underpinnings that fit the neo-Fregean's general outlook. Among the philosophical ideas I consider are: general views on a priori justification; the idea of abstraction as reconceptualization, the idea that truth is prior to reference in the sense associated with Frege's context principle; and various broadly relativistic views. The conclusions are by and large negative.

The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those difficulties while still being able to put abstraction principles to a foundational use.

The proper statement and assessment of Russell's theory depends on one's semantic presuppositions. A semantic framework is provided, and Russell's theory formulated in terms of it. Referential uses of descriptions raise familiar problems for the theory, to which there are, at the most general level of abstraction, two possible Russellian responses. Both are considered, and both found wanting. The paper ends with a brief consideration of what the correct positive theory of definite descriptions might be, if it is not the Russellian theory.

Kit Fine develops a Fregean theory of abstraction, and suggests that it may yield a new philosophical foundation for mathematics, one that can account for both our reference to various mathematical objects and our knowledge of various mathematical truths. The Limits of Abstraction breaks new ground both technically and philosophically.

Ethicists of care have objected to traditional moral philosophy's reliance upon abstract universal principles. They claim that the use of abstraction renders traditional theories incapable of capturing morally relevant, particular features of situations. I argue that this objection sometimes conflates two different levels of moral thinking: the level of justification and the level of deliberation. Specifically, I claim that abstraction or attention to context at the level of justification does not entail, as some critics seem to think, a commitment to abstraction or attention to context at the level of deliberation. It follows that critics who reject a theory's use of abstraction at the level of justification have not shown that the theory recommends abstraction at the level of deliberation and that it, therefore, compels the deliberating agent to overlook morally salient details.

The process of abstraction and concretisation is a label used for an explicative theory of scientific model-construction. In scientific theorising this process enters at various levels. We could identify two principal levels of abstraction that are useful to our understanding of theory-application. The first level is that of selecting a small number of variables and parameters abstracted from the universe of discourse and used to characterise the general laws of a theory. In classical mechanics, for example, we select position and momentum and establish a relation amongst the two variables, which we call Newton’s 2nd law. The specification of the unspecified elements of scientific laws, e.g. the force function in Newton’s 2nd law, is what would establish the link between the assertions of the theory and physical systems. In order to unravel how and with what conceptual resources scientific models are constructed, how they function and how they relate to theory, we need a view of theory-application that can accommodate our constructions of representation models. For this we need to expand our understanding of the process of abstraction to also explicate the process of specifying force functions etc. This is the second principal level at which abstraction enters in our theorising and in which I focus. In this paper, I attempt to elaborate a general analysis of the process of abstraction and concretisation involved in scientific- model construction, and argue why it provides an explication of the construction of models of the nuclear structure.

A bracket abstraction algorithm is a means of translating λ-terms into combinators. Broda and Damas, in [1], introduce a new, rather natural set of combinators and a new form of bracket abstraction which introduces at most one combinator for each λ-abstraction. This leads to particularly compact combinatory terms. A disadvantage of their abstraction process is that it includes the whole Schonfinkel [4] algorithm plus two mappings which convert the Schonfinkel abstract into the new abstract. This paper shows how the new abstraction can be done more directly, in fact, using only 2n - 1 algorithm steps if there are n occurrences of the variable to be abstracted in the term. Some properties of the Broda-Damas combinators are also considered.