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This essay proposes to differentiate between science and philosophy on the evidence that the truth of scientific, or, more generally, empirical, statements is perspectival wlereas the truth of a philosophical statement is not. A perspectival truth depends upon a perspective in the sense that it may no longer be acceptable after the point of view which determines a perspective has been changed to another. Accordingly, the admission of perspectival truth requires the existence of alternative perspectives. The existence of alternative perspectives does not mean that every statement which is true in one of them is false in another. Some statements, to be called perspectivally invariant, remain true regardless of the perspective. But the admission of perspectival truth requires at least one statement to be true in one perspective but false in an alternative perspective. Two perspectives, no matter how different in other respects, will not be called alternative unless they involve perspectival truth. The point is important. For no one denies that perspectives differ with regard to their heuristic value, i.e. no one would deny that a certain point of view may lead us to findings which from a different point of view might remain indiscernible and therefore undiscovered. But the opponents of perspectival truth and of alternative perspectives argue, with W. R. Dennes, that once a truth has been established the same finding can be acknowledged by a true statement in any other perspective although the acknowledgment may call for a restatement in a different idiom or language (1). The issue is between the admission of perspectival truth, on the one hand, and the contention of interperspectival translatability of truth, on the other. 1. Perspectival Truth. An examination of the disagreement between the proponent and the opponent of perspectival truth requires an extention of the term "perspective" from the literal sense of a visual, or perceptual, perspective to include ideological or interpretive perspectives, i.e. ways of cognition which are, in part, determined by a point of view in the metaphorical sense of a set of basic concepts or principles. The extension of the term is required because the opponents of perspectival truth have been preoccupied with interpretive perspectives and it is not clear whether they would object to perspectival truth in the literal sense of the adjective "perspectival." Let me explain the point by means of an illustration. Consider the following situation. A railroad connects two stations. An observer on the platform of one of the stations looks in the direction of the other and describes his visual datum by the statement "The rails of the track converge and meet at the horizon". Another observer, the pilot of an airoplane hovering above the railroad, disagrees: "The rails of the track run parallel all the way from one station to the other." We may conclude that each statement is a perspectival truth, in the literal sense, because it is true in one visual perspective but false in another. And this conclusion seems to be indisputable so long as the admissible evidence for a statement is confined to visual data, i.e. so long as any interpretation of the situation is excluded.

A survey of the outstanding developments in Soviet philosophical logic shows that the formal and dialectical logicians have resolved most of the issues that divided them in the early 1950s. In orientation they are both converging on the avant‐garde of English‐speaking logicians who regard formalization as irrelevant for solving the essential problems of philosophical logic. Soviet dialecticians consider their logic to be a rapprochement with epistemology that will result in a logic that is concerned with the content and genetic development of concepts. Such a logic will provide a methodology of science that can encompass the creative growth of science, in contrast to the positivists’ fixation on the ‘logic of the finished research report’.

The problem of the relationship between formal logic and philosophy, which arose when formal logic arose, continues to concern both Soviet and foreign philosophers and logicians. Interest in this problem is traceable to a number of factors, among which, it should be noted at the outset, is the appearance of dialectical, logic. With the emergence of dialectical logic, the question of the relationship of formal logic to philosophy is posed anew. No matter how we approach the question of the subject matter of dialectical logic, there is no doubt of the fact that, being logic, it is concerned with the investigation of philosophical problems. It follows that logic (or part of logic, some form of logic) is at the same time philosophy or, at least, a portion of philosophy.

We show that Leitgeb’s dependence operator of Leitgeb (Journal of Philosophical Logic, 34, 155–192, 2005) is a \({{\Pi }^{1}_{1}}\)-operator and that this is best possible.

If we take a look, even a superficial one, at the literature of logic, pure and/or applied, extending, for example, from model theory to linguistics, from proof theory to deontic logic or intensional logics in general; if, in short, we reflect on the logical works developing in close contact with either mathematics or completely different disciplines, arriving finally at so-called ‘philosophical logic’, we can well ask ourselves to what extent all this can qualify as logic. One way to answer this question (considered by some as the way) is to indicate the entire historical course leading up to the formation of contemporary logical practice: the ‘necessity’ of recent developments should result from the interrelation of themes and techniques which have led to them historically. Certainly an argument of this kind is plausible; in fact, the understanding, let’s say, of the categorical approach to logic would be inconceivable without taking into account the concrete development of mathematical practice.

At first sight it might seem strange to devote in a handbook of philosophical logic a chapter to algorithms. For, algorithms are traditionally the concern of mathematicians and computer scientists. There is a good reason, however, to treat the material here, because the study of logic presupposes the study of languages, and languages are by nature discrete inductively defined structures of words over an alphabet. Moreover, the derivability relation has strong algorithmic features. In almost any (finitary) logical system, the consequences of a statement can be produced by an algorithm. Hence questions about derivability, and therefore also underivability, ask for an analysis of possible algorithms. In particular, questions about decidability (is there an algorithm that automatically decides if ψ is derivable from φ?) boil down to questions about all algorithms. This explains the interest of the study of algorithms for logicians.

“Reflexivity” is the generic name for all kinds and species of circularity. It includes the self-reference of signs, the self-appplication of principles and predicates, the self-justification and self-refutation of propositions and inferences, the self-fulfillment and self-falsification of predictions, the self-creation and self-destruction of logical and legal entities, the self-augmentation and self-limitation of powers, circular reasoning, circular causation, cyclic and spiral recurrence, feedback systems, mutuality, reciprocity, and organic form. It includes the fallacious, the vicious, the trivial, and the question begging, but also the sound, the benign, the useful, and the inescapable. It ranges from the prosaic to the numinous, from the paradoxical to the self-evident, from science to religion. It is reality and appearance, native to the processes of the world and to our knowledge and discourse about them.

The most influential semanticist in the recent history of logic and of philosophy of language did not believe in semantics and consequently left the most important part of his semantical ideas unexpressed. In the last hundred years, most of philosophical logic and of philosophical analysis has been deeply influenced, often virtually dominated, by the ideas of Gottlob Frege (in most cases as propagated by Russell; cf. e.g. [85]). Yet Frege left many of his own semantical assumptions undefended, unless the success of his overall approach is supposed to be its defense.

Georg Henrik von Wright’s work on the logic of preference represented in its time the most thorough treatment of this area of twentieth century philosophy. Without question, von Wright performed the invaluable task of carefully defining the range of a logic of preference, considered in an intrinsic sense, demarcating the extent and limits of its scope. His understanding of the complexity of the theoretical issues with which this logic deals introduced a wholly philosophical attitude to the enterprise of developing such a logic, in marked contrast to prior efforts which relied heavily upon techniques developed in economics and related areas. Von Wright’s early effort was to affect almost every subsequent attempt in this particular area of philosophical logic.

In his paper 'What is Referential Opacity?' (Journal of Philosophical Logic 2 (1973), 155-180), Bell argues that the answer to this question is to be found in Donnellan's familiar referential/attributive distinction (henceforth R/A D). Bell treats the latter as an ambiguity which should be represented at the level of logical structure. He then accounts for Quine's transparent/ opaque distinction in terms of the R/A D. That is, the (generally accepted) ambiguity in a sentence like (1) follows automatically, in Bell's view, from the presence of an ambiguity in the embedded sentence (2).

The semantics of tense has received a great deal of attention in the contemporary linguistics, philosophy and logic literatures. This is probably due partly to a renewed appreciation for the fact that issues involving tense touch on certain issues of philosophical importance (viz., determinism, causality, and the nature of events, of time and of change). It may also be due partly to neglect. Tense was noticeably omitted from the theories of meaning advanced in previous generations. In the writings of both Russell and Frege there is the suggestion that tense would be absent altogether from an ideal or scientifically adequate language. (Tense was not the only blemish of natural language to be removed, of course, but tense is a more serious omission than, say, pronouns because it is present in every sentence of the language.) Finally, in recent years there has been a greater recognition of the important role that all of the so-called “indexical” expressions must play in an explanation of mental states and human behavior. Tense is no exception. Knowing that our friend died is cause for mourning, knowing that he dies is just another confirmation of a familiar syllogism.

Reseñas de tres libros de lógica matemática, En estas tres reseñas se discuten sendos libros de lógica que encierran interés desde el punto de vista filosófico, principalmente el de Haack, autora que había pretendido abordar en su libro (publicado en inglés en 1975) los temas que juzgó esenciales relativos a las lógicas no-clásicas, o lógicas desviacionistas; era una desmesurada pretensión para un libro de modestísimo volumen; pecaba de superficialidad y hasta de ligereza en ciertos casos, a la vez que ni siquiera mencionaba muchas motivaciones filosóficamente relevantes para optar por lógicas desviacionistas. Así y todo, el libro, al que no faltaban méritos, fue útil porque aportó razones para cuestionar la intangibilidad filosófica de la lógica clásica.

The semantical paradoxes are not a scientific subject like Inductive Definitions, Algebraic Geometry or Plasma Physics. At least not yet. On the other hand the paradoxes exert a strong fascination and many a philosopher or logician has spent some thought on them, mostly in relative isolation. The literature on the paradoxes is vast but scattered, repetitive and disconnected. This made it impossible to give a presentation in which all ideas in the literature receive their due.

The purpose of this paper is to discuss the transitivity paradoxes of (qualitative) confirmation (or support) by connecting the concept of confirmation with that of explanation. We cannot here discuss in any detail the general philosophical reasons for making this connection. But let it be said that even a brief consultation of scientific examples should convince one of ‘facts’ such as that when a theory explains some statements (explananda) it gives confirmatory credence to these statements, and these explananda can also be taken to support or confirm the theory. What we shall do below is to spell out this in some detail and show that even by means of such small, intuitively obvious, observations one can show that many of the transitivity paradoxes of confirmation can be avoided or blocked. In other words, the main idea in our paper is, so to speak, to ‘localize’ some general principles of confirmation in the sense of restricting their range of applicability to nomological explanation situations.

A computer program capable of acting intelligently in the world must have a general representation of the world in terms of which its inputs are interpreted. Designing such a program requires commitments about what knowledge is and how it is obtained. Thus, some of the major traditional problems of philosophy arise in artificial intelligence. More specifically, we want a computer program that decides what to do by inferring in a formal language that a certain strategy will achieve its assigned goal. This requires formalizing concepts of causality, ability, and knowledge. Such formalisms are also considered in philosophical logic. The first part of the paper begins with a philosophical point of view that seems to arise naturally once we take seriously the idea of actually making an intelligent machine. We go on to the notions of metaphysically and epistemo-logically adequate representations of the world and then to an explanation of can, causes, and knows in terms of a representation of the world by a system of interacting automata. A proposed resolution of the problem of freewill in a deterministic universe and of counterfactual conditional sentences is presented. The second part is mainly concerned with formalisms within which it can be proved that a strategy will achieve a goal. Concepts of situation, fluent, future operator, action, strategy, result of a strategy and knowledge are formalized. A method is given of constructing a sentence of first-order logic which will be true in all models of certain axioms if and only if a certain strategy will achieve a certain goal. The formalism of this paper represents an advance over McCarthy (1963) and Green (1969) in that it permits proof of the correctness of strategies that contain loops and strategies that involve the acquisition of knowledge; and it is also somewhat more concise. The third part discusses open problems in extending the formalism of part 2. The fourth part is a review of work in philosophical logic in relation to problems of artificial intelligence and a discussion of previous efforts to program ‘general intelligence’ from the point of view of this paper.

In striking contrast to the influential streams of his time, Roman Ingarden’s philosophy of language and logic is clearly anti-positivistic in its nature. While the syntactic ideology of the Vienna Circle was achieving its high peak and the successful mathematical logic of Russell, Hilbert, Godel and Tarski did not even admit a dissenting voice in the traditional field of philosophical logic, Ingarden published his masterpiece, The Literary Work of Art,1 which contains a full-blooded theory of language, and he also launched an attack against a positivistic interpretation or misrepresentation of logic and its role in philosophy.2 Moreover, his criticisms of the contemporary mathematical logic were supplemented by his pioneering work in the theory (and logic) of questions,3 and by his treatments of hypothetical propositions,4 among other of his positive contributions. It is true — and the inspection of his bibliography reveals it — that Ingarden was not primarily a logician, not even a philosopher of language. His concerns with logic and language are part of a greater plan: the phenomenological reconstruction of philosophy via ontological structural analysis — in particular the analysis of works of art. Such a tremendous task asks for an analogue of Aristotle’s Organon. Ingarden inherited portions of a phenomenological Organon from his teacher, Husserl, and other leading members of the phenomenological movement, especially A. Pfander.5

Definition has been unpopular amongst philosophers since Wittgenstein’s Philosophical Investigations. His invitation, to bring back words and concepts from their philosophical to their everyday use, his cautionary maxims against the danger of hasty generalisation, in which the human mind so effortlessly indulges, tended to be strictures on defining, certainly, but also on theorising as well. But ordinary language is not perfectly in order as it is. There is a genuine need, not only in science, for stipulative definitions, a need which Wittgenstein acknowledged and philosophers have long turned their backs on in linguistic philosophy. Theorising is once more the order of the day. There is a saying that if you can’t define x in a single sentence, then use as many sentences as you need and then you have a theory, rather than a definition, of x. Theorising in philosophy tends to mean books, not articles. If we turn, for example, to two areas of current philosophical endeavour, Philosophical Logic/Philosophy of Language and Philosophy of Mind, we can see how true this is. In both fields, books and more books, theory upon theory, engulf the philosopher in ever-increasing tides. Where, for example, in Philosophical Logic, Russell’s Theory of Definite Descriptions held sway for nearly half-a-century, theories of meaning and reference now supercede one another within a few years. The same is true of the Philosophy of Mind.

It may be that Wittgenstein’s influence on the philosophy of religion has aroused more hostility than any other aspect of his work. The years since the Second World War have been described as ‘a sorry time for the philosophy of religion in English-speaking countries’, and this, it is said, has been due not least to the disastrous influence of Wittgenstein.1 During the period referred to, the influence of Wittgenstein has been far-reaching in almost every branch of philosophy: philosophical logic, philosophy of mathematics, theory of knowledge, philosophy of mind, ethics, aesthetics, philo sophy of the social sciences, and so on. Adverse comments on his influence on the philosophy of religion, however, are not confined to those who think that Wittgenstein’s philosophical influence in general has been a disaster. On the contrary, they are made, as in the instance quoted, by sympathetic commen tators. Unfortunately, it cannot be denied that a philosophy by innuendo has grown up by which it is hinted, rather than argued, that what Wittgenstein is said to have said about religion and ritual is not closely related to the rest of his work. It has been suggested also that those influenced by him in the philosophy of religion have imposed alien features on Wittgenstein’s work, and made use of certain of his terms, such as ‘language-games’, in ways of which he would not have approved.

Physics should have helped us to realise that a temporal theory of a phenomenon X is, in general, more than a simple combination of two components: the statics of X and the ordered set of temporal instants. The case in which all functions from times to world-states are allowed is uninteresting; there are too many such functions, and the theory has not begun until we have begun to restrict them. And often the principles that emerge from the interaction of time with the phenomena seem new and surprising. The most dramatic example of this, perhaps, is the interaction of space with time in relativistic space-time.

For some time, one of the most typical (and emphasized) characteristics of ‘modern’ logic was that of qualifying as ‘scientific’, in contradistinction to traditional logic, which was meant to be simply ‘philosophical’. We shall not be interested in analysing the hidden meaning underlying that distinction, which surely expressed, at an initial stage, a kind of mistrust of traditional logic: those times — which go back to the early stages of logical positivism — are quite far away by now, and a number of distinguished scholars openly declare themselves concerned with problems of ‘philosophical logic’. What might still be worth remembering are rather the reasons why modern logic claimed to be ‘scientific’, and these are essentially twofold. On the one hand, the characteristic of scientificity appeared to be the fact that the new logic had adopted the configuration of a respectable mathematical discipline, including the feature of having been explicity axiomatized. On the other hand, its appurtenance to the family of sciences was evidenced by the fact that its aim was assume to be, among others, that of providing an exact (and also practical) analysis of the processes or ideally to be adopted in scientific investigation and theory building. It is, obviously, the second aspect that made modern logic relevant to the methodology of science, with particular emphasis upon the methodology of formal sciences, i.e., mathematics.

Many researchers in Computer Science, Linguistics, Logic, and Philosophy have been discovering in various ways that analogues of the Liar paradox pose deep foundational problems for intensional semantics. In this survey paper I state my own view of what the problems are, and try to provide a broad perspective on the issues, with many references to the literature. Although the paper concentrates on developments in Philosophical Logic, I hope that the paper will help all researchers concerned with these problems to locate their concerns in a broad, interdisciplinary framework.

Illocutionary logic is the branch of philosophical logic that is concerned with the study of the illocutionary acts (assertions, questions, requests, promises, orders, declarations…) that are performed by the utterance of sentences of natural or formal languages. The analytic philosophers (especially J. L. Austin and J. R. Searle) have shown the philosophical importance of a logical analysis of the forms of such speech acts. Illocutionary force is indeed one essential and irreducible component of the sense of a sentence of a natural language. One cannot understand the sense of a sentence without understanding that its literal utterance in a given context of use constitutes the performance of illocutionary acts of such and such forms. Thus for example, in order to understand the sense of the English sentence (1) “Are you going to the theater tonight?” one must not only understand that in a context of use where this sentence is uttered literally, the speaker expresses a proposition that is true in the world of utterance iff the hearer in that world goes to a theater the evening of the day of the utterance. One must also understand that this utterance in that context of use constitutes the asking of a question.

I am going to be as brief and as clear as I can, and in the attempt to do so may seem provocative, though that is not my main intention. Besides commenting on certain issues raised by Mr Dearden’s and Miss Telfer’s papers, I shall say some things which are relevant to Mrs Warnock’s and Mr Norman’s; for it is thought by many people (perhaps rightly) that autonomy and neutrality are two sides of the same coin. And indeed I shall be saying things which have a bearing on a lot of the other topics of the conference.

This chapter relates our approach to semantics and pragmatics described in the previous chapter to traditional theories of philosophical logic and model theory. This discussion is relevant for two reasons. Logical semantics in general, and predicate calculus in particular, have become the main paradigm for analyzing meaning in natural language. At the same time, predicate calculus plays an important role in Artificial Intelligence, including automatic theorem proving, rule based deductions, and planning. Therefore, this chapter may be read as an investigation of the ontological assumptions of model-theoretic semantics, and as a study of the “epistemological problems” of Artificial Intelligence (in the sense of McCarthy (1977)).

For about 80 years logicians have participated in a research programme called “solve the paradox”. The immediate cause of the existence of the research programme was the proliferation of logical paradoxes around the turn of the century. The central assumption or “hard core” of the programme is the assumption that no contradiction is true, and hence that the reasonings which result in the contradictions must be fallacious. The aim has been to locate the fallacies and to articulate a theory which explains the data: the fallacious, yet highly plausible reasoning. Some time later, which might conventionally be dated at the publication of Ramsey’s essay “The Foundations of Mathematics” [1926], the programme bifurcated into one for solving the set theoretic paradoxes and one for solving the semantic paradoxes. The strategy of divide and conquer is a familiar enough one, and often successful. Yet in this case it was a retrograde, or at least defeatist, step: the original aim of the founding fathers, such as Russell, to find a unified solution to the problem had to be given up. If one now considers the semantic branch of the program, it is difficult to avoid the conclusion that it has been somewhat less than successful. (I think that the same is true of the set theoretic branch. However in virtue of the general acceptance-at least by mathematicians-of the cumulative hierarchy, the case is much more difficult to make and I shall not address it here.)

One of the principal analytical tools of contemporary philosophical logic is the concept of a possible world. It has becomc commonplace to identify necessary truth with truth in all possible worlds. Possible worlds are also employed in the analysis of counterfactual conditions and law statements, in probability theory, in providing a foundation for modal and intensional logics, and so forth. But it is not entirely clear just what possible worlds arc supposed to be, or precisely how they arc related to other notions. David Lewis says that possible worlds arc “ways things could have been”.1 Kripke describes possible worlds as “counterfactual situations”.2 There is a great deal of intuitive appeal to some such notion, but there is not a great deal of agreement about how the concept of a possible world is to be defined or analysed. One might insist that the notion is primitive and unanalysable,3 but that makes it quite mysterious and of questionable utility in the clarification of other concepts. Plantinga has been one of the principal figures involved in the attempt to clarify and understand the metaphysics of possible worlds. His book. The Nature of Necessity, together with a series of subsequent articles, constitutes what is perhaps the most sophisticated theory of possible worlds yet to be constructed. A number of questions remain, however, and I propose to take up some of them here.