: Usually, when studying schematism we devote almost exclusive attention to the study of the modifications that the categories suffer when combined with time. Instead, we have focused our attention on the determinations that time receives when combined with the categories. Departing from the definition of the transcendental schemata as “determinations of time”, an attempt is made to establish the various determinations that time receives from each one of the categories, as these perform the determination of (...) time in schematism. The categories of quantity allow us to think of time as a series of homogeneous unities; the categories of quality show each instant of time as a receptacle able to receive the different intensities of the real; the categories of relation establish a rule-dependent order on the flow of time; finally, the categories of modality determine the whole of time forming a collective unity that gathers or embraces each one of the instants of time preserving its specificity. (shrink)

Available for the first time in 20 years, here are two important works from the 1920s by the best-known representative of the Vienna Circle.

Available for the first time in 20 years, here are two important works from the 1920s by the best-known representative of the Vienna Circle.

We present a logically detailed case-study of Darwinian evolutionary explanation. Special features of Darwin’s explanatory schema made it an unusual theoretical breakthrough, from the point of view of the philosophy of science. The schema employs no theoretical terms, and puts forward no theoretical hypotheses. Instead, it uses three observational generalizations—Variability, Heritability and Differential Reproduction—along with an innocuous assumption of Causal Efficacy, to derive Adaptive Evolution as a necessary consequence. Adaptive Evolution in turn, with one assumption of scale (‘Deep Time’), (...) implies the observational generalization of Adaptation. It is a fascinating methodological task to regiment the premises and make the reasoning both rigorous and clear. Doing so reveals how surprisingly small an amount of mathematics is needed in order to carry out the argument. The investigation also reveals the crucial role played by heritability, and how heritability itself admits of Darwinian explanation. (shrink)

Ancient Chinese logicians presupposed no fixed order in the world. Things are changing all the time. Time, then, plays a crucial role in the structure of Chinese logic. This article uses the concept of "subjective time" and the Leibnizian concept of "possible worlds" to analyze the structure of logic in the Later Mohist Canon and in the logical reasoning of other early Chinese philosophers. The author argues that Chinese logic is structured in the time of (...) the now. This time is subjective and "spreads out" to more than one possible world. Chinese logicians had to deal with relationships in not only a single world but also more than one "possible world." The aim of Chinese logical reasoning is not to represent any universal truth but to point out (zhi ) a particular-world-related truth, or, in other words, the harmony of relations among particulars in a particular field at a single moment. Therefore, a valid Chinese logical argument represents only the beauty of harmony among possible worlds at a given moment. The harmony represented by Chinese logic brings to light a high level of aesthetic order in a world that is always changing. (shrink)

Originally published in 1938. This compact treatise is a complete treatment of Aristotle’s logic as containing negative terms. It begins with defining Aristotelian logic as a subject-predicate logic confining itself to the four forms of categorical proposition known as the A, E, I and O forms. It assigns conventional meanings to these categorical forms such that subalternation holds. It continues to discuss the development of the logic since the time of its founder and address traditional logic as it existed (...) in the twentieth century. The primary consideration of the book is the inclusion of negative terms - obversion, contraposition etc. – within traditional logic by addressing three questions, of systematization, the rules, and the interpretation. (shrink)

Originally published in 1938. This compact treatise is a complete treatment of Aristotle’s logic as containing negative terms. It begins with defining Aristotelian logic as a subject-predicate logic confining itself to the four forms of categorical proposition known as the _A, E, I _and_ O_ forms. It assigns conventional meanings to these categorical forms such that subalternation holds. It continues to discuss the development of the logic since the time of its founder and address traditional logic as it existed (...) in the twentieth century. The primary consideration of the book is the inclusion of negative terms - obversion, contraposition etc. – within traditional logic by addressing three questions, of systematization, the rules, and the interpretation. (shrink)

The paper is devoted to the role (function) of reflection in cognition and its modes (types) as part of the cognitive ability. Along with logical and transcendental reflection, Kant's transcendental shift (turn) is discussed, as well as the role of reflection in Kant's schematism (the ability to judge) and the formation of schemas. Particular attention is paid to another mode of reflection – reflexive switching, which underlies not only the formation of pure rational concepts and schemes (Kant's concept of (...) epigenesis; metaphysical deduction of categories), but the epigenesis of a priori forms of sensibility of space and (especially) time, connected with the Kantian synthesis of apprehension in the intuition. The article proposes an original conception of time, the so-called onion model of time, which is based on a reflexive (iterative) apperceptive ladder. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:JOSEPH MARGOLIS THE LOGIC AND STRUCTURES OF FICTIONAL NARRATIVE The fascination of fiction and narrative is plainly immense, sind current analyses are notably fresh and ingenious. But ifone were to venture a compendious account of die most strategic conceptual claims bearing on those notions, they might well be captured by the following three theses: (i) that fiction and narrative are logically quite distinct, without necessarily excluding one anodier; (...) (ii) that fictional worlds are no worlds at all; they are merely imagined to exist; and (iii) that events, whether actual or imagined, cannot be specified independently of the categories by which we identify them as the events they are, categories subject to change over time. What is intriguing about mese three claims is that they strike the ear as utterly commonplace and obvious. But that is dieir strength. For it would be a great convenience if the relevant puzzles generated by analytic philosophy, hermeneutics, the new narratology, semiotics and the like could be resolved, convincingly, by appeal to die implications of these diree homely trudis. In addition, diey affect one another in a rather complicated way, and, taken joindy, easily expose certain influential false starts. The import of (iii), for example, is notably ignored in die otherwise powerful analysis of narrative afforded by Gérard Genette. Its bearing on (i) utterly undermines the explicit dualism favored by Seymour Chatman, who is clearly influenced by Genette himself. The failure to mark die force of (i) and its analogue regarding poetry is most obvious in I. A. Richards's contrast between poetry and science, the work of the Prague circle, Northrop Frye's Anatomy of Criticism, and such recent speech-act theories of poetry and fiction as those proposed by Richard Ohmann, Monroe Beardsley, and Mary Louise Pratt. The corresponding failure widi respect to (ii) is clear in John Searle's theory of reference and in die ontological claims made by Nicholas Wolterstorff. The connection between (i) and (ii) is muddled most famously by G. E. Moore. These charges suggest die quarrelsome promise of the intended economy. But, as we shall see, they also lead in the direction of a more constructive theory of texts and their interpretation and of die constraints of narrative and style diat affect fiction. 162 Joseph Margolis163 Fiction, we say, differs from reality as well as from legend. But in speaking thus, we betray an understandable confidence that these three kinds of"world"— or, these three worlds — are conceptually well-behaved and open to straightforward demarcation. Once more, we slip altogether too easily between talking about certain worlds and about the narrative accounts by which we do so. What distinguishes fictional reference? we ask, and what is a fictional world? The best way to proceed here is to begin with strong intuitions and to trace dieir systematic consequences in order to test how far they are unassailable — or whether and where they must yield to others that are more accommodating. One particularly promising equivocation is the following. We speak of fictional worlds as possible (but not actual) worlds; but even if what is possible in a fictional world corresponds (in some sense) to what is possible in the actual world, it is not, as such, a possibility of or at the actual world. The "possible worlds" idiom is fundamentally and doubly equivocal. For, a "possible world" signifies either what is merely logically or conceptually compossible, or what (under suitably referential, predicative, causal, and similar constraints) is compossible specifically with respect to the actual world (or some part of it). Certainly, Balzac's La Cousine Bette "presents" an imaginary world that is internally coherent and compossible. One might even say, ignoring its fictive nature, diat such a world — or events very much like those of the story — is compossible with a certain portion of the actual world of nineteenth-century France. But Lewis Carroll's Alice in Wonderfond, though it scrupulously presents a coherent world of compossible events, does not present a world compossible with the actual world. And, on certain views at least, Thomas Mann's The Transposed Heads presents a possible world that is a conceptual impossibility. There is, however, no need to quarrel about particular cases... (shrink)

With this third edition of Nelson Goodman's The Structure of Appear ance, we are pleased to make available once more one of the most in fluential and important works in the philosophy of our times. Professor Geoffrey Hellman's introduction gives a sustained analysis and appreciation of the major themes and the thrust of the book, as well as an account of the ways in which many of Goodman's problems and projects have been picked up and developed by others. Hellman also (...) suggests how The Structure of Appearance introduces issues which Goodman later continues in his essays and in the Languages of Art. There remains the task of understanding Good man's project as a whole; to see the deep continuities of his thought, as it ranges from logic to epistemology, to science and art; to see it therefore as a complex yet coherent theory of human cognition and practice. What we can only hope to suggest, in this note, is the b. road Significance of Goodman's apparently technical work for philosophers, scientists and humanists. One may say of Nelson Goodman that his bite is worse than his bark. Behind what appears as a cool and methodical analysis of the conditions of the construction of systems, there lurks a radical and disturbing thesis: that the world is, in itself, no more one way than another, nor are we. It depends on the ways in which we take it, and on what we do. (shrink)

The central task of the book is to compare and contrast the model of time as comprised of discrete instants and the model of time as a continuum. The first half of the book develops axiomatic and algebraic interconnections between "point structures" and "period structures"; the second half explores the connections between propositional tense logics in the tradition of A.N. Prior and the associated point and period models. Both the author's fine style and the publisher's excellent (...) layout and typefaces contribute to making this a particularly pleasant, readable volume. The level of exposition is that of texts for beginning graduate students interested in logic or abstract algebra. (shrink)

We investigate the polynomial time isomorphic type structure of (the class of tally, polynomial time computable sets). We partition P T into six parts: D −, D^ − , C, S, F, F^, and study their p-isomorphic properties separately. The structures of , , and are obvious, where F, F^, and C are the class of tally finite sets, the class of tally co-finite sets, and the class of tally bi-dense sets respectively. The following results for the (...) structures of and will be proved, where D^ is the class of tally, co-dense, polynomial time computable sets and S is the class of tally, scatted (i.e., neither dense nor co-dense), polynomial time computable sets. 1. is a countable distributive lattice with the greatest element. 2. Infinitely many intervals in can be distinguished by first order formulas. 3. There exist infinitely many nontrivial automorphisms for . 4. is not distributive, but any interval in is a countable distributive lattice. RID=""ID="" Mathematics Subject Classification (2000): 03D15, 03D25, 03D30, 03D35, 06A06, 06B20 RID=""ID="" Key words or phrases: Computational complexity – Polynomial time – Degree structure – Lattice – Isomorphism RID=""ID="" Part of this work was done when the author was a PhD student at the University of Heidelberg under the direction of Professor Ambos-Spies. (shrink)

Stephen Jay Gould’s monumental The Structure of Evolutionary Theory ‘‘attempts to expand and alter the premises of Darwinism, in order to build an enlarged and distinctive evolutionary theory . . . while remaining within the tradition, and under the logic, of Darwinian argument.’’ The three branches or ‘‘fundamental principles of Darwinian logic’’ are, according to Gould: agency (natural selection acting on individual organisms), efficacy (producing new species adapted to their environments), and scope (accumulation of changes that through geological time (...) yield the living world’s panoply of diversity and morphological complexity). Gould’s efforts to contribute something important to each of these three fundamental components of Darwinian Theory are far from successful. (shrink)

The nrst of the people to be thanked for their help during the composition of this work is Professor I.M. Bochenski, under whom I had the good fortune to study for an extended period of time. Without his help, it is doubtful that this work would have been writt"l1 at all. Among the other professors who helped along the way, I would like to cite in particular Professors A.F. Utz, M.D. Philippe and N. Luyten of the University of Fribourg. (...) Many friends were present at the birth of the ideas contained in this book. By naming K.G. Ballestrem, T.l. Blakeley and M.F. Gagern, I do not want to slight any of the rest. It was A. Spiekermann in Hollinghofen who saw to it that other preoccupations did not rob me of all the time needed for the study of the subject-matter and to the composition of this treatise. Of particular help in getting sources from the libraries of the world were Miss Lifschitz of the Institute of East-European Studies and Mr. Uldry of the Cantonal Library in Fribourg, Switzerland. Finally, my patient typist, Mrs. Frey in Munster, deserves special mention for her beautiful work. (shrink)

Belief is the affirmation of reality, but not all affirmations of reality are beliefs, for if we have, or have had, perceptual experience of a reality, we do not say, “I believe,” but “I see, hear, perceive, or remember.” Similarly, of the realities involved in our inner experience, we say, “What I had in mind, desired, hoped, or felt was…” or else say, more simply, “I was much moved, was in pain, felt affection or hatred, longed for, was thinking about, (...) knew.” On the other hand, there are realities of the perceptual order in which we may express belief, as when we say, “I believe that New Zealand exists, that nitrogen is a gas, that the earth is round, that William the Conqueror crossed the Channel in 1066, that Jesus Christ suffered under Pontius Pilate, was crucified, died, was buried, and rose again.” The realities in which we thus express belief are not realities which we ourselves have observed, but are such that they could have been observed by a person appropriately situated in time and in place. Hence in this case it is not the nature of the realities affirmed that differentiates belief from experience of either the perceptual or the inner type. The difference lies elsewhere. When we affirm a reality of which we ourselves have, or have had, perceptual experience, it is the reality itself, present to our perceiving mind, which alike determines the content of our affirmation and justifies us in making it. (shrink)

Donald Davidson was one of the most famous and influential philosophers of the twentieth century. The Structure of Truth presents his 1970 Locke Lectures in print for the first time. They comprise an invaluable historical document which illuminates how Davidson was thinking about the theory of meaning, the role of a truth theory therein, the ontological commitments of a truth theory, the notion of logical form, and so on, at a pivotal moment in the development of his thought. (...) Unlike Davidson's previously published work, the lectures are written so as to be presented to an audience as a fully organized and coherent exposition of his program in the philosophy of language. Had they been widely available in the years following 1970, the reception of Davidson's work might have been very different. Given the systematic nature of their presentation of Davidson's semantic program, these lectures will be of interest to anyone working in the philosophy of language. (shrink)

We begin with a theory of thought as a biocognition not precisely situated in the individual, and still less in the brain alone, but deriving from a shared field of bioinformation. The structure of associations among elements of speech may reflect the structure of this field. Then we demonstrate that the analysis of the structure of the scientific discourse applied within this logic shows the fractal structure of the field of bioinformation. We also show that scientific culture can be interpreted (...) as a cultural model. So, scientific culture would be the elaboration of a cultural scenario in which each human being is another "myself" according to circumstances, an identification making a relationship of aid possible. This aid relationship is governed by an energy equilibrium defined by the cultural scenario, and may be calculated according to fractal theory. The result is a fractal model of consciousness and of the energies at work, whose equilibrium is necessary for the correct functioning of the human being. The consequences are determined concerning the reinsertion of the logic of the culture within the purely objective logic of medicine, in particular that of "giving-receiving" inherent in all cultures, even at the levels of giving birth in the context of modern medicine. We thank R. Ruiz-Banos for a long-time fruitful collaboration in the field of scientometrics. (shrink)

As Classical Propositional Logic finds its algebraic counterpart in Boolean algebras, the logic of Quantum Mechanics, as outlined within G. Birkhoff and J. von Neumann’s approach to Quantum Theory (Birkhoff and von Neumann in Ann Math 37:823–843, 1936) [see also (Husimi in I Proc Phys-Math Soc Japan 19:766–789, 1937)] finds its algebraic alter ego in orthomodular lattices. However, this logic does not incorporate time dimension although it is apparent that the propositions occurring in the logic of Quantum Mechanics are (...) depending on time. The aim of the present paper is to show that tense operators can be introduced in every logic based on a complete lattice, in particular in the logic of quantum mechanics based on a complete orthomodular lattice. If the time set is given together with a preference relation, we introduce tense operators in a purely algebraic way. We derive several important properties of such operators, in particular we show that they form dynamic pairs and, altogether, a dynamic algebra. We investigate connections of these operators with logical connectives conjunction and implication derived from Sasaki projections in an orthomodular lattice. Then we solve the converse problem, namely to find for given time set and given tense operators a time preference relation in order that the resulting time frame induces the given operators. We show that the given operators can be obtained as restrictions of operators induced by a suitable extended time frame. (shrink)

This chapter presents that our model is that of a network whose time is historically constructed by the events that occur within it – inter‐individual communications, intra‐individual categorization, forgetting by erasure or reinforcement – and not the other way around: far from being part of a temporal framework that is always there, these events produce time. The historical‐sociological register shows that the psychological and an historical determinations of the perceived acceleration of time thus interpreted have been over‐determined (...) by the primacy given to communication on cognition in our developed societies. The chapter proposes two complementary interpretations such as psychological interpretation and socio‐historical interpretation, both of which are logically in line with our model of the structure and evolution of our network of individual actors. It examines the meaning that macroscopic expression of entropy can have in our model of a complex socio‐cognitive network of individual actors. (shrink)

What formulas are tense-logically valid depends on the structure of time, for example on whether it has a beginning. Logicians have investigated what formulas correspond to what physical hypotheses about time. Analogously, we can investigate what formulas of modal logic correspond to what metaphysical hypotheses about necessity. It is widely held that physical hypotheses about time may be contingent. If so, tense-logical validity may be contingent. In contrast, validity in modal logic is typically taken to be (...) non-contingent, as reflected by the general acceptance of the so-called “rule of necessitation.” But as has been argued by various authors in recent years, metaphysical hypotheses may likewise be contingent. If, in particular, hypotheses about the extent of possibility are contingent, we should expect modal-logical validity to be contingent too. Let “contingentism” be the view that everything that is not ruled out by logic is possible. I shall investigate what the right system of modal logic is, if contingentism is true. Given plausible assumptions, the system contains the McKinsey principle, and is thus not even contained in S5. It also contains simple and elegant iteration principles for the contingency operator: something is contingent if and only if it is contingently contingent. (shrink)

This dissertation is about the structure of thought. Following Gottlob Frege, I define a thought as the sort of content relevant to determining whether an assertion is true or false. The historical component of the dissertation involves interpreting Frege’s actual views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in a variety of distinct ways. I (...) extend Frege’s position and use it to develop an account of the hierarchy of senses, the senses expressed by indexicals and demonstratives, and the distinction between logical and non-logical structure. I also discuss various connections with the nature of meta-representation, our capacity for reflective judgment, some aspects of the structure of conscious experience, the way we perceive regions of space and durations of time, and our conscious awareness of our own perceptions and events of thinking. (shrink)

For historical epistemology to succeed, it must adopt a defensible set of categories to characterise scientific activity over time. In historically orientated philosophy of science during the twentieth century, the original categories of theory and observation were supplemented or replaced by categories like paradigm, research program and research tradition. Underlying all three proposals was talk about conceptual systems and conceptual structures, attributed to individual scientists or to research communities, however there has been little general agreement on the nature (...) of these structures. Recent experimental research in cognitive science has considerably refined the theory of concepts. Drawing upon the results of that research, philosophers can construct more concrete and empirically defensible representations of conceptual systems. I will suggest that this research supports a modest and useful sense of both normal and revolutionary science, not as epistemological continuities or discontinuities, but as particular patterns of conceptual change. (shrink)

I call attention to the following theses concerning possibility. 1) Anything that has become actual must have been possible in the period of time immediately preceding its actualization. 2) The logically possible is a conception, and conceptions exist within the mind. 3) The possible is not a mere name. 4) The possible is not a mental entity and that alone. 5) Every possibility, whether mental entity or not must be, or image, an ontological entity, real although not actual. 6) (...) For all we know logical possibility is the sufficient condition of ontological possibility. 7) Philosophers who lack the category of ontological possibility nonetheless refer to it as an implicit, if hidden, feature of their systems. 8) In some part of the period of time preceding its actualization, an ontological possibility becomes a nascent actuality, and external consistency a necessary condition for nascency. 9) The rise or fall of energy level through directed energy vectors, on human and nonhuman levels, is the third condition for the actualizing of possibilities, or for their failure to actualize. (shrink)

This dissertation provides a systematic account of the metaphysics of transcendental idealism. According to the proposed theory, appearances are understood as intentional objects, while phenomena are considered as logical constructs that are grounded in noumena, whereby the grounding relation can be modelled by means of a coordinated multiple-domain supervenience relation. This framework is employed to provide a vindication of metaphysics, by giving dual-level explanations that explain how the world can have ontological structure, making intelligible the applicability of metaphysical concepts, (...) such as unity, persistence, causation and mind-body interaction, to the empirical realm. The key claim that is advanced in the dissertation is that in order to be realists we have to be transcendental idealists. In particular, transcendental arguments are provided that establish that if realism about science, metaphysics and ethics is to be possible, then the world must have a transcendental structure that integrates the fragmented perspective-dependent spatio-temporal frameworks into a unified perspective-independent space-time manifold, space and time must be forms of intuition that give rise to correspondences between appearances and phenomena, making it the case that we can have non-trivial scientific knowledge of the world, and we must have a priori concepts, namely the mathematical and dynamical categories, that allow us to cognise the empirical as well as ontological structure of the world. The ‘fact of experience’ as well as the ‘fact of reason’ are then brought in to strengthen the case for scientific, metaphysical and moral realism, thereby warding off the threat of nihilism. Moreover, a refutation of the more attractive versions of scepticism and idealism is provided, namely of those versions that claim that a subject’s representations or episodes of awareness can be temporally ordered even though they deny or doubt the existence of a law-governed external world. The conclusion then is that a realist stance is to be adopted and that we should consequently accept transcendental idealism and hold that the world has a transcendental structure. (shrink)

Two views of scientific theories dominated the philosophy of science during the twentieth century, the syntactic view of the logical empiricists and the semantic view of their successors. I show that neither view is adequate to provide a proper understanding of the connections that exist between theories at different times. I outline a new approach, a hybrid of the two, that provides the right structural connection between earlier and later theories, and that takes due account of the importance of (...) the mathematical models of a theory and of the various distinct formulations that pick out these models. (shrink)

According to logical theories of meaning, a meaning of an expression can be formalized and encoded in truth conditions. Vagueness of the language and individual differences between people are a challenge to incorporate into the meaning representations. In this paper, we propose a new approach to study truth-conditional representations of vague concepts. For a case study, we selected two natural language quantifiers most and more than half. We conducted two online experiments, each with 90 native English speakers. In the (...) first experiment, we tested between-subjects variability in meaning representations. In the second experiment, we tested the stability of meaning representations over time by testing the same group of participants in two experimental sessions. In both experiments, participants performed the verification task. They verified a sentence with a quantifier (e.g., “Most of the gleerbs are feezda.”) based on the numerical information provided in the second sentence, (e.g., “60% of the gleerbs are feezda”). To investigate between-subject and within-subject differences in meaning representations, we proposed an extended version of the Diffusion Decision Model with two parameters capturing truth conditions and vagueness. We fit the model to responses and reaction times data. In the first experiment, we found substantial between-subject differences in representations of most as reflected by the variability in the truth conditions. Moreover, we found that the verification of most is proportion-dependent as reflected in the reaction time effect and model parameter. In the second experiment, we showed that quantifier representations are stable over time as reflected in stable model parameters across two experimental sessions. These findings challenge semantic theories that assume the truth-conditional equivalence of most and more than half and contribute to the representational theory of vague concepts. The current study presents a promising approach to study semantic representations, which can have a wide application in experimental linguistics. (shrink)

We prove that for any finite deduction structure there exists a unique concise-widest chain-preserved split. Based on this result, we propose a logical splitting strategy which enables an agent to split its belief structure such that all the original inference chains can be preserved. The significance of such logical splitting at least is four-fold: It can be used by an agent to separate its concerns appropriately, or even create smaller and smarter clones which could save time and (...) efforts in their deliberation computing; It will enable an agent to adjust its concerns dynamically based on its recognition of the current situation, which may further enable the agent to make rapid and rational decisions when situation shifting occurs; In periodic team synchronization domains where agents can periodically synchronize their behaviors with no restriction on communication, it can be employed as a critical process for maintaining the shared mental models among a team of agents; and It is helpful in alleviating the complexity of reasoning about relevant information, and in better anticipating both explicit and implicit information needs based on the recognition of the current situation. (shrink)

The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.

When the original Dutch version of this book was presented in 1971 to the University of Leiden as a thesis for the Doctorate in philosophy, I was prevented by the academic mores of that university from expressing my sincere thanks to three members of the Philosophical Faculty for their support of and interest in my pursuits. I take the liberty of doing so now, two and a half years later. First and foremost I want to thank Professor G. Nuchelmans warmly (...) for his expert guidance of my research. A number of my most im portant sources were brought to my attention by him. During the whole process of composing this book his criticism and encouragement were carried out in a truly academic spirit. He thereby provided working conditions that are a sine qua non for every author who is attempting to approach controversial matters in a scientific manner, conditions which, however, were not easily available at that time. In a later phase I also came into contact with Professors L. M. de Rijk and J. B. Ubbink, with both of whom I had highly stimulating discussions and exchanges of ideas. The present edition contains some entirely new sections, viz. 1-9, IV-29, V-9, V-20, VII-14 (iii), (iv), VII-17 (i), VIII-22, IX-17, IX-19, X-9 and XI-8. Section X-9 was inspired by a remark made by Professor A. (shrink)

It is not an easy work to read, the phrasing being rather complicated, and the topics at times repetitious and intertwined; but great works do not have to be easy texts. It is the first of a proposed pair, its role being indicated by the sub-title: Problems in the Logic of Scientific Explanation. The next volume is to deal with the analysis of scientific concepts and inference. In the present work we may distinguish three groups of chapters. The first group (...) centers around certain structural concepts, particularly science, explanation and law. The second concerns problems of the physical sciences and the third is about social and biological sciences. It is entirely absurd to attempt a thorough review of the whole work in less than a work of comparable length particularly in view of the highly technical character of substantial parts of it. Another reviewer has already decided on the same grounds to restrict his attention to the second part. I shall concentrate on the first and third. I am particularly sensible that the comments which follow, when critical, are reflections of an alternative possible construal rather than objective demonstrations of error. (shrink)

The transformation of the relations between reflection and reality and between concepts and their correspondent objects into themes represents even in the present a field for most heated discussions. The joining of conceptual schemes corresponding to the intellect and reality represents a problem which is still to be solved. A solution to this problem was proposed by R. Carnap in his extremely ambitious project from Der logische Aufbau der Welt (1928). Overlooked for a long time, this work has returned (...) to the philosophical spotlight in recent years, because philosophers finally realized that Carnap’s project comprises almost allthe major themes of contemporary epistemology, such as the relation between theory and reality, between concepts and experience, the major lines of a phenomenology and of a “logic of experience” or the status of language and of the concepts of science. Situated at the confluence of some philosophical traditions such as neo-kantian philosophy, the logical analysis of Russell and Wittgenstein, but also phenomenology, Carnap’s program in Aufbau starts from some premises such: the need to control experience (= major stake of any scientific knowledge); the orientation towards form of the modern concept of scientific knowledge (under Kant’s direct influence); the assertion of a concept of knowledge mostly relational or structural (issue resulted in the orientation towards form of modern knowledge); the need for a methodology engaged in a constructive way and modelled on mathematical thinking; our reporting to the instance of sensitivity in the formation of experience (under E. Mach’s influence). (shrink)

Contemporary architecture is increasingly grounded in science and mathematics. Architectural discourse has shifted radically from the sometimes disorienting Derridean deconstruction, to engaging scientific terms such as fractals, chaos, complexity, nonlinearity, and evolving systems. That's where the architectural action is -- at least for cutting-edge architects and thinkers -- and every practicing architect and student needs to become conversant with these terms and know what they mean. Unfortunately, the vast majority of architecture faculty are unprepared to explain them to students, not (...) having had a scientific education themselves. Here is an architecture book by an architect/scientist, just in time to help architects in the new millennium. Alexander discusses many of the scientific terms arising in cutting-edge architecture, and explains them to those who don't have scientific training or advanced mathematical knowledge. We find discussions of the evolution of forms; the importance of process in design; iteration; genetic algorithms; sequences of transformations; different levels of scale (i.e. fractals); etc. They are explained here by an architect who is also a scientist, because he wants to change the way architects think and build. Alexander is not merely popularizing other scientists' results and making them accessible to architects: he is in fact presenting new and original scientific work that ties many of these concepts together in a way that will be useful to architects. (shrink)

To take a structural approach to genealogy means dealing with it as a story written in a language that is unknown and yet to be deciphered. It is the very language of time—individual and familial—in which a human being situates, often in a striking manner, the principal life and death events of his own destiny. Or better perhaps, it means discovering this in genealogies, which must first be exhumed from the dusty cabinets where a solid and excessively documentary tradition (...) has too long confined them, in order to consider them now, in a sense, as venerable “black boxes”, potentially containing secrets of the intimate functioning of families, capable of providing unknown information on this subject, with meaning and logic winning out over the apparent fantasy with which they have been coated. (shrink)

ABSTRACT This part of the series has a dual purpose. In the first place we will discuss two kinds of theories of proof. The first kind will be called a theory of linear proof. The second has been called a theory of suppositional proof. The term "natural deduction" has often and correctly been used to refer to the second kind of theory, but I shall not do so here because many of the theories so-called are not of the second kind--they (...) must be thought of either as disguised linear theories or theories of a third kind (see postscript below). The second purpose of this part is 25 to develop some of the main ideas needed in constructing a comprehensive theory of proof. The reason for choosing the linear and suppositional theories for this purpose is because the linear theory includes only rules of a very simple nature, and the suppositional theory can be seen as the result of making the linear theory more comprehensive. CORRECTION: At the time these articles were written the word ‘proof’ especially in the phrase ‘proof from hypotheses’ was widely used to refer to what were earlier and are now called deductions. I ask your forgiveness. I have forgiven Church and Henkin who misled me. (shrink)

On the basis of both logical and physical arguments, a majority of philosophers and physicists have opted for the Block View of time in which this ‘passage’ is purely subjective. However, the feeling of the ‘passage’ of time has been left principally unaccounted for in the Block View. It is argued that there are two ways by which the (apparent) ‘passage’ of time is perceived by human beings and it is the combination of these perceptions that (...) gives rise to the deep-seated impression on the conscious mind of a ‘dynamic’ nature of time. In postulating the existence of a specific kind of intrinsic structural difference between the two orientations of time within the Block View, a basis for these two perceptions may be provided. (shrink)

All the attempts to find the justification of the privileged evolution of phenomena exclusively in the external world need to refer to the inescapable fact that we are living in such an asymmetric universe. This leads us to look for the origin of the “arrow of time” in the relationship between the subject and the world. The anthropic argument shows that the arrow of time is the condition of the possibility of emergence and maintenance of life in the (...) universe. Moreover, according to Bohr’s, Poincaré’s and Watanabe’s analysis, this agreement between the earlier-later direction of entropy increase and the past-future direction of life is the very condition of the possibility for meaningful action, representation and creation. Beyond this relationship of logical necessity between the meaning process and the arrow of time the question of their possible physical connection is explored. To answer affirmatively to this question, the meaning process is modelled as an evolving tree-like structure, called “Semantic Time”, where thermodynamic irreversibility can be shown. (shrink)

Introduction. The technical art of cinematography is traditionally regarded as a synthetic unity of scientific and technological progress and creativity. The possibility of unlimited copying of movie plots makes it possible to extend the authority of cinema to broad areas of public attention and forms a mass man. At the same time, the fact that cinema is, first of all, an experiment with time, organized by technical means, remains behind the scenes. The purpose of the study. If the (...) core issues of humanity are centered on the problem of life and death, on the problem of mastering and overcoming time, then cinema clearly shows that humanity has a ready-made embodied model of its desire. Methods. The authors use a phenomenological method that allows one to see the temporal fabric behind the “opaque body” of cinema. The eidetic reduction to the foundations of the constructed film plot temporal reality is complemented by the structuralist method of analyzing technical devices and technological methods of the film industry. Scientific novelty of the research. The ontology of the technical art of cinema goes beyond rationality and pragmatics. By launching a special kind of experiment with time, cinema technologies allow the viewer to be present in the bifurcation moments of temporal metamorphoses that connect different temporal modes. The temporal fabric is subject to the plot logic. Results. In cinema, time is constructed by technical means. The nature of this construction allows us to see the layered structure of time, the intersections of time flows, influxes, reverse time orders and stops in time. The cinema technique clearly shows that time barriers are conditional. Conclusions. Cinema dissolves any empirical density, creating gaps in it and transitions to other worlds. The connection between the worlds is carried out by constructed time. Time is taken out of objects and, obeying the course of the narrative, expands the reality of the world. (shrink)

The article discusses the relation between two intuitive properties of time, namely its flow and branching. Both properties are introduced first in an informal way and compared. The conclusion of this informal analysis is that the two properties do not entail each other nor are they in contradiction. In order to verify this, we briefly introduced the branching temporal structures called branching space-time, branching continuation and their versions Minkowski branching structure and branching time with Instants. Two (...) possible ways how to formalize flow of time are given, one based on the definition of flow of time from temporal logics and the other based on relativistic physics. The latter is used to define flow of time with the use of linearly ordered points on worldines while respecting the ontological definiteness given by the difference of the past and the future. This is formalized in each of the branching models and it is concluded by comparing the resulting properties that branching and flow, even in the formal sense, do not entail each other. However, notions connected with flow of time represent a useful basis for semantics of the branching models. (shrink)

Central to Perelman and Olbrechts-Tyteca’s philosophical revival of rhetoric and dialectic is the importance given to the temporal character of argumentation. Unlike demonstration, situated within the “empty time” of a single instant, the authors of The New Rhetoric understand argumentation as an action that unfolds within the “full time” of meaningful human life. By taking a broader view of his work beyond The New Rhetoric, I first outline Perelman’s understanding of time and temporality and the challenge that (...) it poses for the study of argumentation. Next, I emphasize the distinction between argumentation’s internal and external temporal structures, and then show how Perelman problematizes a static view of a number of basic argumentative concepts by bringing out their essentially temporal character. Finally, in clarifying what is at stake in Perelman’s account, I conclude by drawing attention to a number of issues in contemporary argumentation studies that may benefit from a reconsideration of Perelman’s analysis of time. (shrink)

In addressing the problem of the compatibility of divine foreknowledge and human freedom, philosophers of religion encounter problems regarding the metaphysics and structure of time. Some models of temporal logic developed for completely independent reasons have proved especially appropriate for representing the temporal structure of the world as Molinism conceives it. In particular, some models of the Thin Red Line ) seem to imply that conditionals of freedom are true or false, as Molinists maintain. Noting the resemblance between Molinism (...) and \ models, Restall Molinism: the contemporary debate, pp 227–239, 2011) has advanced some criticisms of Molinism that have also been leveled against \ models. In particular, Restall believes that the implication \ is not true in \ models. Because Molinists must also accept that this implication is not true, this is a problem for them. We will show that Restall’s criticism is wide of the mark. Firstly, it will be demonstrated that in many open future models ) the implication \ is invalid. Secondly, while it is possible to account for this implication, some modifications are required in respect of the branching time semantics. In proposing one such modification, we show that this new semantics can be adopted by advocates of the \ and, as a consequence, by Molinists as well. We conclude that the principle stated by Restall is either a problem for many open future models or can be accounted for by these models and so is not a problem for Molinists either. (shrink)

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes (...) simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

In Ockhamist branching-time logic [Prior 67], formulas are meant to be evaluated on a specified branch, or history, passing through the moment at hand. The linguistic counterpart of the manifoldness of future is a possibility operator which is read as `at some branch, or history (passing through the moment at hand)'. Both the bundled-trees semantics [Burgess 79] and the $\langle moment, history\rangle$ semantics [Thomason 84] for the possibility operator involve a quantification over sets of moments. The Ockhamist frames are (...) (3-modal) Kripke structures in which this second-order quantification is represented by a first-order quantification. The aim of the present paper is to investigate the notions of modal definability, validity, and axiomatizability concerning 3-modal frames which can be viewed as generalizations of Ockhamist frames. (shrink)

In the early 1920s, Hans Reichenbach and Kurt Lewin presented two topological accounts of time that appear to be interrelated in more than one respect. Despite their different approaches, their underlying idea is that time order is derived from specific structural properties of the world. In both works, moreover, the notion of genidentity--i.e., identity through or over time--plays a crucial role. Although it is well known that Reichenbach borrowed this notion from Kurt Lewin, not much has been (...) written about their relationship, nor about the way Lewin implemented this notion in his own work in order to ground his topology. This paper examines these two early versions of the topology of time, and follows the extent of Lewin’s influence on Reichenbach’s proposal. (shrink)