In this 1992 book, Professor Koslow advances an account of the basic concepts of logic. A central feature of the theory is that it does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple, but insightful way. The study has four parts. In the first two parts the various sources of the general (...) concept of an implication structure and its forms are illustrated and explained. Part 3 defines the various logical operations and systematically explores their properties. A generalized account of extensionality and dual implication is given, and the extensionality of each of the operators, as well as the relation of negation and its dual, are given substantial treatment because of the novel results they yield. Part 4 considers modal operators and studies their interaction with logical operators. By obtaining the usual results without the usual assumptions this new approach allows one to give a very simple account of modal logic minus the excess baggage of possible world semantics. (shrink)
We shall try to defend two non-standard views that run counter to two well-entrenched familiar views. The standard views are the universal and existential quantifiers of first-order logic are not modal operators, and the quantifiers are extensional. If that is correct then the counterclaims create genuine problems for some traditional philosophical doctrines.
Carnap in the 1930s discovered that there were non-normal interpretations of classical logic - ones for which negation and conjunction are not truth-functional so that a statement and its negation could have the same truth value, and a disjunction of two false sentences could be true. Church ar-gued that this did not call for a revision of classical logic. More recent writers seem to disa-gree. We provide a definition of "non-normal interpretation" and argue that Church was right, and in fact, (...) the existence of non-normal interpretations tells us something important about the condi-tions of extensionality of the classical logical operators. (shrink)
. On a structuralist account of logic, the logical operators, as well as modal operators are defined by the specific ways that they interact with respect to implication. As a consequence, the same logical operator (conjunction, negation etc.) can appear to be very different with a variation in the implication relation of a structure. We illustrate this idea by showing that certain operators that are usually regarded as extra-logical concepts (Tarskian algebraic operations on theories, mereological sum, products and negates of (...) individuals, intuitionistic operations on mathematical problems, epistemic operations on certain belief states) are simply the logical operators that are deployed in different implication structures. That makes certain logical notions more omnipresent than one would think. (shrink)
The original motivation of D. Gabbay’s concept of Fibring concerned the combination of logics, and initially it involved the syntactic introduction of modals into formulations of intuitionistic logic in which modals are syntactically absent. We show, using the notion of structural modals that there are many modals of intuitionism, and logics for subjunctive and epistemic conditionals which are not syntactically evident in our best formulations of them. We discuss some cases when the attempt to make them syntactically evident can have (...) undesirable consequences. (shrink)
The initial part of this paper explores and rejects three standard views of how scientific laws might be systematically connected with physical necessity or possibility. The first concerns laws and their consequences, the second concerns the so‐called counterfactual connection, and the third concerns a possible worlds construction of physical necessity. The remaining part introduces a neglected notion of possibility, and, with the aid of some examples, illustrates the special way in which laws reduce or narrow down possibilities.
A description is given of the quantitative-qualitative distinction for terms in theories of measurable attributes, and, adjoined to that account, a suggestion is made concerning the sense in which empirical relational systems have an empirical attribute as their topic or focus. Since this characterization of quantitative terms, relative to a partition, makes no explicit reference to numbers, concatenation operations, or ordering relations, we show how our results are related to some standard theorems in the literature. Analogs of representation and uniqueness (...) theorems are proved, and the notions of exact quantitative term and the underlying attribute of a quantitative term, are described and studied. (shrink)