I LOGIC IN PHILOSOPHY— PHILOSOPHY OF LOGIC i. On the relation of logic to philosophy I n this book, the consequences of certain logical insights for ...

This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous (...) impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities. (shrink)

Most current work in epistemology deals with the evaluation and justification of information already acquired. In this book, Jaakko Hintikka instead discusses the more important problem of how knowledge is acquired in the first place. His model of information-seeking is the old Socratic method of questioning, which has been generalized and brought up-to-date through the logical theory of questions and answers that he has developed. Hintikka also argues that philosophers' quest for a definition of knowledge is ill-conceived and that the (...) entire notion of knowledge should be replaced by the concept of information. He offers an analysis of the different meanings of the concept of information and of their interrelations. The result is a new and illuminating approach to the field of epistemology. (shrink)

The papers collected in this volume were written over a period of some eight or nine years, with some still earlier material incorporated in one of them. Publishing them under the same cover does not make a con tinuous book of them. The papers are thematically connected with each other, however, in a way which has led me to think that they can naturally be grouped together. In any list of philosophically important concepts, those falling within the range of application (...) of modal logic will rank high in interest. They include necessity, possibility, obligation, permission, knowledge, belief, perception, memory, hoping, and striving, to mention just a few of the more obvious ones. When a satisfactory semantics (in the sense of Tarski and Carnap) was first developed for modal logic, a fascinating new set of methods and ideas was thus made available for philosophical studies. The pioneers of this model theory of modality include prominently Stig Kanger and Saul Kripke. Several others were working in the same area independently and more or less concurrently. Some of the older papers in this collection, especially 'Quantification and Modality' and 'Modes of Modality', serve to clarify some of the main possibilities in the semantics of modal logics in general. (shrink)

This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous (...) impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities. (shrink)

Is a genuine logic of scientific discovery possible? In the essays collected here, Hintikka not only defends an affirmative answer; he also outlines such a logic. It is the logic of questions and answers. Thus inquiry in the sense of knowledge-seeking becomes inquiry in the sense of interrogation. Using this new logic, Hintikka establishes a result that will undoubtedly be considered the fundamental theorem of all epistemology, viz., the virtual identity of optimal strategies of pure discovery with optimal deductive strategies. (...) Questions to Nature, of course, must include observations and experiments. Hintikka shows, in fact, how the logic of experimental inquiry can be understood from the interrogative vantage point. Other important topics examined include induction, explanation, the incommensurability of theories, theory-ladenness of observations, and identifiability. (shrink)

R. G. Collingwood saw one of the main tasks of philosophers and of historians of human thought in uncovering what he called the ultimate presuppositions of different thinkers, of different philosophical movements and of entire eras of intellectual history. He also noted that such ultimate presuppositions usually remain tacit at first, and are discovered only by subsequent reflection. Collingwood would have been delighted by the contrast that constitutes the overall theme of the essays collected in this volume. Not only has (...) this dichotomy ofviews been one ofthe mostcrucial watersheds in the entire twentieth-century philosophical thought. Not only has it remained largely implicit in the writings of the philosophers for whom it mattered most. It is a truly Collingwoodian presupposition also in that it is not apremise assumed by different thinkers in their argumentation. It is the presupposition of a question, an assumption to the effect that a certain general question can be raised and answered. Its role is not belied by the fact that several philosophers who answered it one way or the other seem to be largely unaware that the other answer also makes sense - if it does. This Collingwoodian question can be formulated in a first rough approximation by asking whether language - our actual working language, Tarski's "colloquiallanguage" - is universal in the sense of being inescapable. This formulation needs all sorts of explanations, however. (shrink)

In the last 25 years, the concept of information has played a crucial role in communication theory, so much so that the terms information theory and communication theory are sometimes used almost interchangeably. It seems to us, however, that the notion of information is also destined to render valuable services to the student of induction and probability, of learning and reinforcement, of semantic meaning and deductive inference, as~well as of scientific method in general. The present volume is an attempt to (...) illustrate some of these uses of information concepts. In 'On Semantic Information' Hintikka summarizes some of his and his associates' recent work on information and induction, and comments briefly on its philosophical suggestions. Jamison surveys from the sub jectivistic point of view some recent results in 'Bayesian Information Usage'. Rosenkrantz analyzes the information obtained by experimen tation from the Bayesian and Neyman-Pearson standpoints, and also from the standpoint of entropy and related concepts. The much-debated principle of total evidence prompts Hilpinen to examine the problem of measuring the information yield of observations in his paper 'On the Information Provided by Observations'. Pietarinen addresses himself to the more general task of evaluating the systematizing ('explanatory') power of hypotheses and theories, a task which quickly leads him to information concepts. Domotor develops a qualitative theory of information and entropy. His paper gives what is probably the first axiomatization of a general qualitative theory of information adequate to guarantee a numerical representation of the standard sort. (shrink)

Several of the so-called “fallacies” in Aristotle are not in fact mistaken inference-types, but mistakes or breaches of rules in the questioning games which were practiced in the Academy and in the Lyceum. Hence the entire Aristotelian theory of “fallacies” ought to be studied by reference to the author's interrogative model of inquiry, based on his theory of questions and answers, rather than as a part of the theory of inference. Most of the “fallacies” mentioned by Aristotle can in fact (...) be diagnosed by means of the interrogative model, including petitio principii, multiple questions, “babbling’, etc., and so can Aristotle's alleged anticipation of the fallacy of argumentum ad hominem. The entire Aristotelian conception of inquiry is an interrogative one. Deductive conclusions caught Aristotle's attention in the form of answers that every rational interlocutor must give, assuming only his own earlier answers. Several features of Aristotle's methodology can be understood by means of the interrogative model, including the role of endoxa in it. Theoretically, there is also considerable leeway as to whether “fallacies” are conceived of as mistakes in questioning or as breaches of the rules that govern questioning games. (shrink)

According to Kant, “mathematical knowledge is the knowledge gained by reason from the construction of concepts.” In this paper, I shall make a few suggestions as to how this characterization of the mathematical method is to be understood.

A word of warning concerning the aims of this volume is in order. Other wise some readers might be unpleasantly surprised by the fact that two of the chapters of an ostensibly historical book are largely topical rather than historical. They are Chapters 7 and 9, respectively entitled 'Are Logical Truths Analytic?' and 'A Priori Truths and Things-In-Them selves'. Moreover, the history dealt with in Chapter 11 is so recent as to have more critical than antiquarian interest. This mixture of (...) materials may seem all the more surprising as I shall myself criticize (in Chapter I) too facile assimilations of earlier thinkers' concepts and problems to later ones. There is no inconsistency here, it seems to me. The aims of the present volume are historical, and for that very purpose, for the purpose of understanding and evaluating earlier thinkers it is vital to know the conceptual landscape in which they were moving. A crude analogy may be helpful here. No military historian can afford to neglect the topo graphy of the battles he is studying. If he does not know in some detail what kind of pass Thermopylae is or on what sort of ridge the battle of Bussaco was fought, he has no business of discussing these battles, even if this topographical information alone does not yet amount to historical knowledge. (shrink)

Since the first chapter of this book presents an intro duction to the present state of game-theoretical semantics, there is no point in giving a briefer survey here. Instead, it may be helpful to indicate what this volume attempts to do. The first chapter gives a short intro duction to GTS and a survey of what is has accomplished. Chapter 2 puts the enterprise of GTS into new philo sophical perspective by relating its basic ideas to Kant's phi losophy of (...) mathematics, space, and time. Chapters 3-6 are samples of GTS's accomplishments in understanding different kinds of semantical phenomena, mostly in natural languages. Beyond presenting results, some of these chapters also have other aims. Chapter 3 relates GTS to an interesting line of logical and foundational studies - the so-called functional interpretations - while chapter 4 leads to certain important methodological theses. Chapter 7 marks an application of GTS in a more philo sophical direction by criticizing the Frege-Russell thesis that words like "is" are multiply ambiguous. This leads in turn to a criticism of recent logical languages, which since Frege have been based on the ambi guity thesis, and also to certain methodological sug gestions. In chapter 8, GTS is shown to have important implications for our understanding of Aristotle's doctrine of categories, while chapter 9 continues my earlier criticism of Chomsky's generative approach to linguistic theorizing. (shrink)

I n order to appreciate properly what we are doing in this book it is necessary to realize that our approach to linguistic theorizing differs from the prevailing views. Our approach can be described by indicating what distinguishes it from the methodological ideas current in theoretical linguistics, which I consider seriously misguided. Linguists typically construe their task in these days as that of making exceptionless generalizations from particular examples. This explanatory strategy is wrong in several different ways. It presupposes that (...) we can have "intuitions" about particular examples, usually examples invented by the linguist himself or herself, reliable and sharp enough to serve as a basis of sharp generalizations. It also presupposes that we cannot have equally reliable direct access to general linguistic regularities. Both assumptions appear to me extremely dubious, and the first of them has in effect been challenged by linguists like Dwight Bol inger. There is also some evidence that the degree of unanimity among linguists is fairly low when it comes to less clear cases, even in connection with such relatively simple questions as grammaticality. For this reason we have tried to rely more on quotations from contemporary fiction, newspapers and magazines than on linguists' and philosophers' ad hoc examples. I also find it strange that some of the same linguists as believe that we all possess innate ideas about general characteristics of humanly possible grammars assume that we can have access to them only via their particular consequences. (shrink)

The so-called New Theory of Reference (Marcus, Kripke etc.) is inspired by the insight that in modal and intensional contexts quantifiers presuppose nondescriptive unanalyzable identity criteria which do not reduce to any descriptive conditions. From this valid insight the New Theorists fallaciously move to the idea that free singular terms can exhibit a built-in direct reference and that there is even a special class of singular terms (proper names) necessarily exhibiting direct reference. This fallacious move has been encouraged by a (...) mistaken belief in the substitutional interpretation of quantifiers, by the myth of thede re reference, and a mistaken assimilation of direct reference to ostensive (perspectival) identification. Thede dicto vs.de re contrast does not involve direct reference, being merely a matter of rule-ordering (scope).The New Theorists' thesis of the necessity of identities of directly referred-to individuals is a consequence of an unmotivated and arbitrary restriction they tacitly impose on the identification of individuals. (shrink)

IF WITI'GENSTEIN COULD TALK, COULD WE UNDERSTAND HIM? Perusing the secondary literature on Wittgenstein, I have frequently experienced a perfect Brechtean Entfremdungseffekt. This is interesting, I have felt like saying when reading books and papers on Wittgenstein, but who is the writer talking about? Certainly not Ludwig Wittgenstein the actual person who wrote his books and notebooks and whom I happened to meet. Why is there this strange gap between the ideas of the actual philosopher and the musings of his (...) interpreters? Wittgenstein is talking to us through the posthumous publication of his writings. Why don't philosophers understand what he is saying? A partial reason is outlined in the first essay of this volume. Wittgenstein was far too impatient to explain in his books and book drafts what his problems were, what it was that he was trying to get clear about. He was even too impatient to explain in full his earlier solutions, often merely referring to them casually as it were in a shorthand notation. For one important instance, in The Brown Book, Wittgenstein had explained in some detail what name-object relationships amount to in his view. There he offers both an explanation of what his problem is and an account of his own view illustrated by means of specific examples of language-games. But when he raises the same question again in Philosophical Investigations I, sec. (shrink)

The notion of scope as it relates to a model of logical form is discussed. The inability of the accepted definition of scope to account for the contrast between priority scope - the logical priority of different quantifiers & other logical notions via rule ordering - & binding scope - the identification of the connection between variables of quantification & a particular quantifier - is demonstrated. The semantic ambiguity of this dichotomy of scope is explored via examination of donkey sentences. (...) A formal representation of this dichotomy is suggested. The government-binding approach & principle of compositionality that handle scope relations via the logical form is rejected due to the complexity of the mechanism by which syntactic form results in logical forms. A discourse representational approach is also rejected. It is concluded that the interaction of syntax & semantics is instead better represented by a game-theoretical treatment of scope & anaphora. 26 References. T. Rosenberg. (shrink)

The modern notion of the axiomatic method developed as a part of the conceptualization of mathematics starting in the nineteenth century. The basic idea of the method is the capture of a class of structures as the models of an axiomatic system. The mathematical study of such classes of structures is not exhausted by the derivation of theorems from the axioms but includes normally the metatheory of the axiom system. This conception of axiomatization satisfies the crucial requirement that the derivation (...) of theorems from axioms does not produce new information in the usual sense of the term called depth information. It can produce new information in a different sense of information called surface information. It is argued in this paper that the derivation should be based on a model-theoretical relation of logical consequence rather than derivability by means of mechanical (recursive) rules. Likewise completeness must be understood by reference to a model-theoretical consequence relation. A correctly understood notion of axiomatization does not apply to purely logical theories. In the latter the only relevant kind of axiomatization amounts to recursive enumeration of logical truths. First-order “axiomatic” set theories are not genuine axiomatizations. The main reason is that their models are structures of particulars, not of sets. Axiomatization cannot usually be motivated epistemologically, but it is related to the idea of explanation. (shrink)

The main currently unsolved problem in the theory of argumentation concerns the function of logic in argumentation and reasoning. The traditional view simply identified logic with the theory of reasoning. This view is still being echoed in older textbooks of formal logic. In a different variant, the same view is even codified in the ordinary usage of words such as ‘logic’, ‘deduction’, ‘inference’, etc. For each actual occurrence of these terms in textbooks of formal logic, there are hundreds of uses (...) of the same idioms to describe the feats of real or fictional detectives. I have called the idea reflected by this usage the “Sherlock Holmes conception of logic and deduction.” In the history of science, we find no less a thinker than Sir Isaac Newton describing his experimental method as one of analysis or resolution and claiming to have “deduced” at least some of his laws from the “phenomena.”. (shrink)