The basic theory of scientific understanding presented in Sections 1–2 exploits three main ideas.First, that to understand a phenomenonP (for a given agent) is to be able to fitP into the cognitive background corpusC (of the agent).Second, that to fitP intoC is to connectP with parts ofC (via arguments in a very broad sense) such that the unification ofC increases.Third, that the cognitive changes involved in unification can be treated as sequences of shifts of phenomena inC. How the theory fits (...) typical examples of understanding and how it excludes spurious unifications is explained in detail. Section 3 gives a formal description of the structure of cognitive corpuses which contain descriptive as well as inferential components. The theory of unification is then refined in the light of so called puzzling phenomena, to enable important distinctions, such as that between consonant and dissonant understanding. In Section 4, the refined theory is applied to several examples, among them a case study of the development of the atomic model. The final part contains a classification of kinds of understanding and a discussion of the relation between understanding and explanation. (shrink)
Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term itself. The essays in this collection explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. Amongst the applications on offer are those to the analysis of existence statements, to definite descriptions and to partial functions. The volume contains a proof that (...) free logics of any kind are non-extensional and then uses that proof to show that Quine's theory of predication and referential transparency must fail. The purpose of this collection is to bring an important body of work to the attention of a new generation of professional philosophers, computer scientists and mathematicians. (shrink)
Free logic, an alternative to traditional logic, has been seen as a useful avenue of approach to a number of philosophical issues of contemporary interest. In this collection, Karel Lambert, one of the pioneers in, and the most prominent exponent of, free logic, brings together a variety of published essays bearing on the application of free logic to philosophical topics ranging from set theory and logic to metaphysics and the philosophy of religion. The work of such distinguished philosophers as Bas (...) van Fraassen, Dana Scott, Tyler Burge, and Jaakko Hintikka is represented. Lambert provides an introductory essay placing free logic in the logical tradition beginning with Aristotle, developing it as the natural culmination of a trend begun in the Port Royal logic of the 1600s, and continuing through current predicate logic--the trend to rid logic of existence assumptions. His Introduction also provides a useful systematic overview of free logic, including both a standard syntax and some semantical options. (shrink)
The authors contend that most contemporary logic textbooks fail the average student because they emphasize the evaluation of arguments over their clarification, assuming that the student already understands what motivations underlie logic.
The essays in this volume are based on addresses presented during a colloquium on free logic, modal logic and related areas held at the University of California at Irvine, in May of 1968. With the single exception of Dagfinn F011esdal, whose revised address is included in a recent issue of Synthese honoring W. V. Quine, all of the speakers at the Irvine colloquium are contributors to this volume. Thanks are due to Professor A. I. Melden, Chairman of the Department of (...) Philosophy at Irvine, for his enthusiastic support of the colloquium, and to Drs. Gordon Brittan and Daniel Dennett for their help in the administration of the colloquium. Finally. I should also like to thank Professor Ralph W. Gerard, Dean of the Graduate Division of the University of California at Irvine, for the financial support which made the colloquium possible. KAREL LAMBERT Laguna Beach, California, 1969 TABLE OF CONTENTS PREFACE V KAREL LAMBERT and BAS C. VAN FRAASSEN/ Meaning Relations, Possible Objects, and Possible Worlds 1 JAAKKO HINTIKKA / Existential Presuppositions and Uniqueness Presuppositions 20 RICHMOND H. THOMASON / Some Completeness Results for Modal Predicate Calculi 56 H. LEBLANC and R. K. MEYER / Truth-Value Semantics for the Theory of Types 77 J. M. VICKERS / Probability and Non Standard Logics 102 PETER W. WOODRUFF / Logic and Truth Value Gaps 121 DANA SCOTT / Advice on Modal Logic 143 INDEX OF NAMES 175 KAREL LAMBER T AND BAS C. (shrink)
The essay outlines the character of free logic, and motivation for its construction and development. It details some technical achievements of high philosophical interest, but urges that the role of existence assumptions in logic is still not fully understood, that unresolved old problems, both technical and philosophical, abound, and presents some new problems of considerable philosophical import in free logic.
The authors contend that most contemporary logic textbooks fail the average student because they emphasize the evaluation of arguments over their clarification, assuming that the student already understands what motivations underlie logic.
This paper deals with the Meinong-Russell controversy on nonsubsistent objects. The first part notes the similarity of certain contemporary semantical developments to Meinonj;'s theory of nonsubsistent objects. Then it lays out the major features of Meinong's famous theory, considers Russell's objections to same and Meinong's counter-objections to Russell, and argues that Russell's well-known argument fails. However, it is possible to augment Russell's argument against Meinong with sound Russellian principles in such a way that it presents at least a strong inclining (...) reason against Meinong's theory of impossible objects. (shrink)
The essays in this volume are based on addresses presented during a colloquium on free logic, modal logic and related areas held at the University of California at Irvine, in May of 1968. With the single exception of Dagfinn F011esdal, whose revised address is included in a recent issue of Synthese honoring W. V. Quine, all of the speakers at the Irvine colloquium are contributors to this volume. Thanks are due to Professor A. I. Melden, Chairman of the Department of (...) Philosophy at Irvine, for his enthusiastic support of the colloquium, and to Drs. Gordon Brittan and Daniel Dennett for their help in the administration of the colloquium. Finally. I should also like to thank Professor Ralph W. Gerard, Dean of the Graduate Division of the University of California at Irvine, for the financial support which made the colloquium possible. KAREL LAMBERT Laguna Beach, California, 1969 TABLE OF CONTENTS PREFACE V KAREL LAMBERT and BAS C. VAN FRAASSEN/ Meaning Relations, Possible Objects, and Possible Worlds 1 JAAKKO HINTIKKA / Existential Presuppositions and Uniqueness Presuppositions 20 RICHMOND H. THOMASON / Some Completeness Results for Modal Predicate Calculi 56 H. LEBLANC and R. K. MEYER / Truth-Value Semantics for the Theory of Types 77 J. M. VICKERS / Probability and Non Standard Logics 102 PETER W. WOODRUFF / Logic and Truth Value Gaps 121 DANA SCOTT / Advice on Modal Logic 143 INDEX OF NAMES 175 KAREL LAMBER T AND BAS C. (shrink)
It is an historical fact that one of Russell's greatest philosophical contributions was to highlight the role that premises about logical form play in ontological arguments. A pair of quotations will introduce his point that great metaphysical systems are often not only based on, but are debased by, the belief that certain statements of philosophical discourse are logically subject-predicate in form.Speaking of Hegel's Absolute Idealism, Russell wrote in Our Knowledge of The Extemal World:Mr. Bradley has worked out a theory according (...) to which, in all judgment, we are ascribing a predicate to Reality as a whole; and this theory is derived from Hegel. Now the traditional logic holds that every proposition ascribes a predicate to a subject, and from this it easily follows that there can be only one subject, the Absolute, for if there were two, the proposition that there were two would not ascribe a predicate to either. Thus Hegel's doctrine, that philosophical propositions must be of the form, “the Absolute is such and such,” depends on the traditional belief in the universality of the subject-predicate form. This belief, being traditionaL scarcely self-conscious, and not supposed to be important, operates underground, and is assumed in arguments which, like the refutation of relations, appear at first sight to e;tablish its truth. (shrink)
A 'free logic' for singular terms with restrictions on existential generalization and universal instantiation is set out and argued for. Weaker logics, Such as lambert's fd and fd1 are held incapable of proving instances of tarski's truth schema for languages containing non-Denoting terms. Stronger logics, Such as scott's and lambert's fd2, Are held to yield false theorems when given natural interpretations. The logic defended conforms essentially to russell's semantical intuitions. Some consequences are drawn for the theory of identity.
This essay lays out the leading principles of the theories of definite descriptions advocated by Frege, Russell, and Hilbert and Bernays, and discusses various difficulties, philosophical and otherwise, with each treatment, fixing especially on the treatment of singular existence claims. Then the leading principles of free (definite) description theory are presented and it is shown how it resolves difficulties confronting the more traditional approaches. Finally, a pair of technical problems in free (definite) description theory are addressed. They help to show (...) the fecundity of this treatment of definite descriptions. (shrink)
This paper offers an explanation of the maj or traditions in the logical treatment of definite descriptions as reactions to paradoxical naive definite descriptiontheory. The explanation closely parallels that of various set theories as reactions to paradoxical naive set theory. Indeed, naive set theory is derivable from naive definite description theory given an appropriate definition of set abstracts in terms of definite descriptions.
Regimentation of an intuitively plausible distinction enhances understanding of that distinction. In Carnap’s words, it is an explication. Properly employed, it is, in the case to be considered, and in almost all others, an indispensable aid to good philosophizing.
This essay argues for the importance of developing theories of nonexistent objects. The grounds are utility and smoothness of logical theory. In the latter case a parallel with the theory of negative and imaginary numbers is exploited. The essay concludes with a counterexample to a general argument against the enterprise of developing theories of nonexistent objects, and outlining the foremost problem an adequate theory of nonexistent objects must solve.
