Online research in philosophy

The present paper first shows that the validity of deductive-nomological (D-N) explanations (systematizations) depends in general on the interpretation context of the predicates involved in the explanation. Therefore, no logical-semantical model can be adequate. This problem is solved by relativisation of the validity criteria on both the confirmation context and the definition context of the premisses. Based upon this, a logical-pragmatical model of D-N explanation is developed. Thereby, especially explanations of laws and global explanations are taken into consideration, since these can be regarded as prototypes of scientific explanation.

Informational semantics were first developed as an interpretation of the model-theory of substructural (and especially relevant) logics. In this paper we argue that such a semantics is of independent value and that it should be considered as a genuine alternative explication of the notion of logical consequence alongside the traditional model-theoretical and the proof-theoretical accounts. Our starting point is the content-nonexpansion platitude which stipulates that an argument is valid iff the content of the conclusion does not exceed the combined content of the premises. We show that this basic platitude can be used to characterise the extension of classical as well as non-classical consequence relations. The distinctive trait of an informational semantics is that truth-conditions are replaced by information-conditions. The latter leads to an inversion of the usual order of explanation: Considerations about logical discrimination (how finely propositions are individuated) are conceptually prior to considerations about deductive strength. Because this allows us to bypass considerations about truth, an informational semantics provides an attractive and metaphysically unencumbered account of logical consequence, non-classical logics, logical rivalry and pluralism about logical consequence.

This paper deals with Popper's little-known work on deductive logic, published between 1947 and 1949. According to his theory of deductive inference, the meaning of logical signs is determined by certain rules derived from ?inferential definitions? of those signs. Although strong arguments have been presented against Popper's claims (e.g. by Curry, Kleene, Lejewski and McKinsey), his theory can be reconstructed when it is viewed primarily as an attempt to demarcate logical from non-logical constants rather than as a semantic foundation for logic. A criterion of logicality is obtained which is based on conjunction, implication and universal quantification as fundamental logical operations.

Abduction can be intended as a special kind of deductive consequence. In fact a general trend is to consider it as a backward deduction with some additional conditions. However, there can be more than one kind of deduction, so that any definition of abduction must take that into account. From a logical perspec-tive the problem is precisely the formalization of conditions when the deductive consequence is fixed. In this paper, we adopt Makinson’s method to define new consequence relations, hence abduction is defined as a reverse relation corresponding to each one of such relations.

We revive the idea that a deductive-nomological explanation of a scientific theory by its successor may be defensible, even in those common and troublesome cases where the theories concerned are mutually incompatible; and limiting, approximating and counterfactual assumptions may be required in order to define a logical relation between them. Our solution is based on a general characterization of limiting relations between physical theories using the method of nonstandard analysis.

Introduction -- The concept of logical consequence -- Tarski's characterization of the common concept of logical consequence -- The logical consequence relation has a modal element -- The logical consequence relation is formal -- The logical consequence relation is A priori -- Logical and non-logical terminology -- The meanings of logical terms explained in terms of their semantic properties -- The meanings of logical terms explained in terms of their inferential properties -- Model-theoretic and deductive-theoretic conceptions of logic -- Linguistic preliminaries : the language M -- Syntax of M -- The definition of a well formed formula of M -- Semantics for M -- The sentential connectives are defined -- The notion of satisfaction is introduced and the quantifiers are defined -- Model-theoretic consequence -- Truth in a structure -- Satisfaction revisited -- Formalized definition of truth -- Model-theoretic consequence defined -- The model-theoretic definition and the concept of logical consequence -- Does the model theoretic consequence relation reflect the salient features of the common concept of logical consequence? -- What is a logical constant? -- Deductive consequence -- Deductive system n -- The deductive theoretic definition and the concept of logical consequence -- Tarski's criticism of the deductive theoretic definition -- Is N a correct deductive system?

The notion of an algebraic semantics of a deductive system was proposed in [3], and a preliminary study was begun. The focus of [3] was the definition and investigation of algebraizable deductive systems, i.e., the deductive systems that possess an equivalent algebraic semantics. The present paper explores the more general property of possessing an algebraic semantics. While a deductive system can have at most one equivalent algebraic semantics, it may have numerous different algebraic semantics. All of these give rise to an algebraic completeness theorem for the deductive system, but their algebraic properties, unlike those of equivalent algebraic semantics, need not reflect the metalogical properties of the deductive system. Many deductive systems that don't have an equivalent algebraic semantics do possess an algebraic semantics; examples of these phenomena are provided. It is shown that all extensions of a deductive system that possesses an algebraic semantics themselves possess an algebraic semantics. Necessary conditions for the existence of an algebraic semantics are given, and an example of a protoalgebraic deductive system that does not have an algebraic semantics is provided. The mono-unary deductive systems possessing an algebraic semantics are characterized. Finally, weak conditions on a deductive system are formulated that guarantee the existence of an algebraic semantics. These conditions are used to show that various classes of non-algebraizable deductive systems of modal logic, relevance logic and linear logic do possess an algebraic semantics.

In the beginning, there was the DN (Deductive Nomological) model of explanation, articulated by Hempel and Oppenheim (1948). According to DN, scientific explanation is subsumption under natural law. Individual events are explained by deducing them from laws together with initial conditions (or boundary conditions), and laws are explained by deriving them from other more fundamental laws, as, for example, the simple pendulum law is derived from Newton's laws of motion.

This paper discusses the D-N model of scientific explanation. It is suggested that explanation is a part of assertive discourse where certain principles must be observed. Then use is made of the relation between the informative content and logical content of a sentence (as shown, for instance, by Popper) to draw some of the conditions necessary for a sound model. It is claimed that the conditions of the model proposed in the present paper exhaust the insights of the papers in the literature, solve the difficulties encountered by other authors, but have some damaging consequences on the D-N model of scientific explanation.

1 Logical empiricism: Hempel 1.1 Earlier criteria of significance 1.2 Significance as dependent on constitutive terms 1.3 Partially interpreted systems 2 Explanation 2.1 Background: deductive nomological explanation 2.2 Causal explanation 2.3 The pragmatics of explanation 2.4 Theoretical explanation 3 Confirmation 3.1 Hypothetico deductive model 3.2 The new riddle of induction 4 Scientific change 4.1 Kuhn's revolutions 4.2 Darwin's contribution 5 Realism 5.1 Constructive empiricism 5.2 Structural realism 6 Laws 6.1 Laws and mere regularities 6.2 Systems 6.3 Universals 7 Assignments..