Online research in philosophy

The fundamental problem of what is explained in science should be considered and clarified since it determines the way of solving the problem of how something is explained as well as the entire view of explanation. In the first section after the introduction, Hempel's models of explanation are criticized for their narrow concern with logical reconstruction. In the next section a broader epistemological approach to explanation is presented, and in the last section an historical example of Newtonian explanation as epistemic activity is discussed.

In this paper we attempt to formulate logical foundations for a theory of actions or performance. Human beings act in various ways, and their actions are intimately interrelated with their use of language. But precisely how actions and the use of language are interrelated is not very clear. One of the reasons is perhaps that we have no precise vocabulary in terms of which such interrelations may be handled. There is need for developing a systematic theory in which different kinds of actions may be discussed, contrasted, and compared. Then the various interrelations between actions and linguistic usage may perhaps be discussed rather more carefully and thoroughly than heretofore. Although much important preliminary work has been done in the analysis of actions, no one it seems has attempted to develop a strict logical theory for such analysis. A few tentative and programmatic steps were taken in the author's Toward a Systematic Pragmatics. Let us attempt here to improve those and take a few more. Any first attempts of this kind are of course fraught with difficulties. There inevitably will be some oversimplification or some overelaboration here or there. Ultimately of course we are interested in interrelating performance with various notions from syntax, semantics, and quantitative pragmatics. But this is not easy and only a few tentative suggestions toward such a development can be given here. In section 1 the distinction between action-kinds and action-events is drawn, and the character of the primitive or primitives needed for the theory of performance is discussed. In section 2 some further notions are then defined. Certain Rules of Performance are suggested in section 3. In section 4 there is discussion of the somewhat tenuous notion of acceptance as a basis for action. In section 5 the fundamental notions required for Parsons and Shils' theory of social action is discussed briefly. In section 6 we attempt to define the two basic notions required in Leonard's recent papers concerning authorship and purpose. Finally, in section 7, the theory of performance is interrelated with von Wright's deontic logic, in which such notions as permission and obligation are considered.

We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures in contrast to the permissibility of classical first-order logic. We make a distinction between deductive and inductive inference via the notions of compactness and weak compactness. Connections with the arithmetical hierarchy and formal learning theory are explored. For the latter, we argue against the identification of inductive inference with the notion of learnable in the limit. Several results highlighting desirable properties of these hierarchies of generalized logical consequence are also presented.

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.

The paper shows how we can add a truth predicate to arithmetic (or formalized syntactic theory), and keep the usual truth schema Tr(A)A (understood as the conjunction of Tr(A)A and ATr(A)). We also keep the full intersubstitutivity of Tr(A)) with A in all contexts, even inside of an . Keeping these things requires a weakening of classical logic; I suggest a logic based on the strong Kleene truth tables, but with as an additional connective, and where the effect of classical logic is preserved in the arithmetic or formal syntax itself. Section 1 is an introduction to the problem and some of the difficulties that must be faced, in particular as to the logic of the ; Section 2 gives a construction of an arithmetically standard model of a truth theory; Section 3 investigates the logical laws that result from this; and Section 4 provides some philosophical commentary.

Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the material systems are, in several senses, formal as well. In section 1.2 variants as to language form (choices of logical constants and logical rules) are pointed out. Section 1.3 is concerned with options as to initial positions and the permissibility of attacks on elementary statements. The problem of ending a dialogue, and of infinite dialogues, is treated in section 1.4. Other options, e.g., as to the number of attacks allowed with respect to each statement, are listed in section 1.5. Section 1.6 explains the concept of a chain of arguments.From section 2 onward four types of dialectic systems are picked out for closer study: D, E, Di and Ei. After a preliminary section on dialogue sequents and winning strategies, the equivalence of derivability in intuitionistic logic and the existence of a winning strategy (for the Proponent) on the strength of Ei is shown by simple inductive proofs.

Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the material systems are, in several senses, formal as well. In section 1.2 variants as to language form (choices of logical constants and logical rules) are pointed out. Section 1.3 is concerned with options as to initial positions and the permissibility of attacks on elementary statements. The problem of ending a dialogue, and of infinite dialogues, is treated in section 1.4. Other options, e.g., as to the number of attacks allowed with respect to each statement, are listed in section 1.5. Section 1.6 explains the concept of a chain of arguments.From section 2 onward four types of dialectic systems are picked out for closer study: D, E, Di and Ei. After a preliminary section on dialogue sequents and winning strategies, the equivalence of derivability in intuitionistic logic and the existence of a winning strategy (for the Proponent) on the strength of Ei is shown by simple inductive proofs.

Our object is to study the interaction between mereology and David Lewis’ theory of subject-matters, elaborating his observation that not every subject matter is of the form: how things stand with such-and-such a part of the world. After an informal introduction to this point in Section 1, we turn to a formal treatment of the partial orderings arising in the two areas – the part-whole relation, on the one hand, and the relation of refinement amongst partitions of the set of worlds, on the other. (We follow Lewis – approximately – in identifying subject-matters with such partitions.) We emphasize a certain duality, formulated in (2.6) and (2.7) in Section 2, between the corresponding lattice operations – mereological joins with partition-lattice meets, mereological meets with partition-lattice joins. Section 3 presents some issues that are raised by consideration of the informally familiar idea of logical subtraction. These include, in particular, a problem about the need for a notion of independence different from the usual logical notion(s) going by that name. The apparatus of Section 2 promises to throw some light on this problem, as we indicate in Section 4. Section 5 ties up some loose ends and suggests an area in which further work would be desirable.

It is a fact of modern scientific thought that there is an enormous variety of logical systems - such as classical logic, intuitionist logic, temporal logic, and Hoare logic, to name but a few - which have originated in the areas of mathematical logic and computer science. In this book the author presents a systematic study of this rich harvest of logics via Tarski's well-known axiomatization of the notion of logical consequence. New and sometimes unorthodox treatments are given of the underlying principles and construction of many-valued logics, the logic of inexactness, effective logics, and modal logics. Throughout, numerous historical and philosophical remarks illuminate both the development of the subject and show the motivating influences behind its development. Those with a modest acquaintance of modern formal logic will find this to be a readable and not too technical account which will demonstrate the current diversity and profusion of logics. In particular, undergraduate and postgraduate students in mathematics, philosophy, computer science, and artificial intelligence will enjoy this introductory survey of the field.

What is the philosophical significance of the soundness and completeness theorems for first-order logic? In the first section of this paper I raise this question, which is closely tied to current debate over the nature of logical consequence. Following many contemporary authors' dissatisfaction with the view that these theorems ground deductive validity in model-theoretic validity, I turn to measurement theory as a source for an alternative view. For this purpose I present in the second section several of the key ideas of measurement theory, and in the third and central section of the paper I use these ideas in an account of the relation between model theory, formal deduction, and our logical intuitions.