This volume collects the papers presented at the 9th edition of the Formal Ontology in Information Systems conference, FOIS 2016, held July 6–9, 2016, in Annecy, France. As in the previous editions, FOIS 2016 included keynote addresses, full paper presentations, an Ontology Competition, an Early Career Symposium in its scientific program and was preceded by the Interdisciplinary Summer School on Ontological Analysis, now at its third edition and held June 27–July 1 in Bolzano-Bozen, Italy.

This article accomplishes two goals. First, the paper clarifies Edmund Husserl’s investigation of the historical inception of the number system from his early works, Philosophy of Arithmetic and, “On the Logic of Signs (Semiotic)”. The article explores Husserl’s analysis of five historical developmental stages, which culminated in our ancestor’s ability to employ and enumerate with number signs. Second, the article reveals how Husserl’s conclusions about the history of the number system from his early works opens up a fusion (...) point with his investigations from his mature texts, The Crisis of the European Sciences and “The Origin of Geometry”. On the one hand, the essay shows that Husserl’s methodology was similar, as he sought in both his early and late writings to uncover the essence of the history of the formal sciences and was not executing mere intellectual history. On the other hand, the article discloses that Husserl’s insights from both time periods are strikingly analogous. Already in his early texts, Husserl saw that the sciences emerged from pre-theoretical experiences of the world and that the sciences are the result of a historical process, which involves the psychic activities of past individuals and the maintaining of discoveries over time by intersubjective communities. I conclude by showing how, in light of the analysis of this paper, we can rethink the evolution of Husserl’s philosophy. (shrink)

A generative grammar for a language L generates one or more syntactic structures for each sentence of L and interprets those structures both phonologically and semantically. A widely accepted assumption in generative linguistics dating from the mid-60s, the Generative Grammar Hypothesis , is that the ability of a speaker to understand sentences of her language requires her to have tacit knowledge of a generative grammar of it, and the task of linguistic semantics in those early days was taken to (...) be that of specifying the form that the semantic component of a generative grammar must take. Then in the 70s linguistic semantics took a curious turn. Without rejecting GGH, linguists turned away from the task of characterizing the semantic component of a generative grammar to pursue instead the Montague-inspired project of providing for natural languages the same kind of model-theoretic semantics that logicians devise for the artificial languages of formal systems of logic, and “formal semantics” continues to dominate semantics in linguistics. This essay argues that the sort of compositional meaning theory that would verify GGH would not only be quite different from the theories formal semanticists construct, but would be a more fundamental theory that supersedes those theories in that it would explain why they are true when they are true, but their truth wouldn’t explain its truth. Formal semantics has undoubtedly made important contributions to our understanding of such phenomena as anaphora and quantification, but semantics in linguistics is supposed to be the study of meaning. This means that the formal semanticist can’t be unconcerned that the kind of semantic theory for a natural language that interests her has no place in a theory of linguistic competence; for if GGH is correct, then the more fundamental semantic theory is the compositional meaning theory that is the semantic component of the internally represented generative grammar, and if that is so, then linguistic semantics has so far ignored what really ought to be its primary concern. (shrink)

Derrida's key concepts or pseudo-concepts of différance, the trace, and the undecidable suggest analogies to some of the most significant results of formal, symbolic logic and metalogic. As early as 1970, Derrida himself pointed out an analogy between his use of ‘undecidable’ and Gödel's incompleteness theorems, which demonstrate the existence, in any sufficiently complex and consistent system, of propositions which cannot be proven or disproven (i.e., decided) within that system itself. More recently, Graham Priest has interpreted différance as (...) an instance of the general metalogical procedure of diagonalisation. In this essay, I consider the extent to which Derrida's key terms and the essential operations of deconstruction can be formalised. I argue that, if formalisation is indeed the technique of writing par excellence, then the formalisation of deconstructive concepts tends to show how the auto-deconstruction of total systems arises from the problematic possibility of writing itself. For instance, since diagonalisation permits the ‘arithmetisation of syntax’ whereby a formal system is able to formulate claims about its own logico-grammatical properties, we can understand its potential to inscribe the undecidable within the systematicity of language as simply one instance of the potential of writing, in figuring itself, to render inscrutable the trace of its own origin. (shrink)

It has been accepted since the early part of the Century that there is no problem formalizing mathematics in standard formal systems of axiomatic set theory. Most people feel that they know as much as they ever want to know about how one can reduce natural numbers, integers, rationals, reals, and complex numbers to sets, and prove all of their basic properties. Furthermore, that this can continue through more and more complicated material, and that there is never (...) a real problem. (shrink)

Fichte’s Foundations of the Entire Wissenschaftslehre 1794 is one of the most fundamental books in classical German philosophy. The use of laws of thought to establish foundational principles of transcendental philosophy was groundbreaking in the late eighteenth and early nineteenth century and is still crucial for many areas of theoretical philosophy and logic in general today. Nevertheless, contemporaries have already noted that Fichte’s derivation of foundational principles from the law of identity is problematic, since Fichte lacked the tools to (...) correctly present the formal parts of Foundations. In this paper, however, we argue that Fichte’s approach intuitively offers an important contribution to transcendental philosophy, and especially to philosophy of logic. We first point out the difficulties of Fichte’s logic in the Foundations and improve it in a second part on the basis of a formal system in which both propositional logic and syllogistic are combined. (shrink)

It has been accepted since the early part of the Century that there is no problem formalizing mathematics in standard formal systems of axiomatic set theory. Most people feel that they know as much as they ever want to know about how one can reduce natural numbers, integers, rationals, reals, and complex numbers to sets, and prove all of their basic properties. Furthermore, that this can continue through more and more complicated material, and that there is never (...) a real problem. (shrink)

A generative grammar for a language L generates one or more syntactic structures for each sentence of L and interprets those structures both phonologically and semantically. A widely accepted assumption in generative linguistics dating from the mid-60s, the Generative Grammar Hypothesis, is that the ability of a speaker to understand sentences of her language requires her to have tacit knowledge of a generative grammar of it, and the task of linguistic semantics in those early days was taken to be (...) that of specifying the form that the semantic component of a generative grammar must take. Then in the 70s linguistic semantics took a curious turn. Without rejecting GGH, linguists turned away from the task of characterizing the semantic component of a generative grammar to pursue instead the Montague-inspired project of providing for natural languages the same kind of model-theoretic semantics that logicians devise for the artificial languages of formal systems of logic, and “formal semantics” continues to dominate semantics in linguistics. This essay argues that the sort of compositional meaning theory that would verify GGH would not only be quite different from the theories formal semanticists construct, but would be a more fundamental theory that supersedes those theories in that it would explain why they are true when they are true, but their truth wouldn’t explain its truth. Formal semantics has undoubtedly made important contributions to our understanding of such phenomena as anaphora and quantification, but semantics in linguistics is supposed to be the study of meaning. This means that the formal semanticist can’t be unconcerned that the kind of semantic theory for a natural language that interests her has no place in a theory of linguistic competence; for if GGH is correct, then the more fundamental semantic theory is the compositional meaning theory that is the semantic component of the internally represented generative grammar, and if that is so, then linguistic semantics has so far ignored what really ought to be its primary concern. (shrink)

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical (...) philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato's Theory of Forms and Aristotle's metaphysics and logic. Plato's and Aristotle's systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a principle of contradiction is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing "space" as the seat of stability, and "time" as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion `separable system', related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of `non-locality' as related to it, indicating the need to re-think the notions `system', `entity', as well as the implications of the operation `measurement', which is seen here as an application of classical logic on the material world. (shrink)

A chronicled approach to the notion of computer simulations shows that there are two predominant interpretations in the specialized literature. According to the first interpretation, computer simulations are techniques for finding the set of solutions to a mathematical model. I call this first interpretation the problem-solving technique viewpoint. In its second interpretation, computer simulations are considered to describe patterns of behavior of a target system. I call this second interpretation the description of patterns of behavior viewpoint of computer simulations. This (...) article explores these two interpretations of computer simulations from three different angles. First, I collect a series of definitions of computer simulation from the historical record. I track back definitions to the early 1960s and show how each viewpoint shares similar interpretations of computer simulations—ultimately clustering into the two viewpoints aforementioned. This reconstruction also includes the most recent literature. Second, I unpack the philosophical assumptions behind each viewpoint, with a special emphasis on their differences. Third, I discuss the philosophical implications of each viewpoint in the context of the recent discussion on the logic of scientific explanation for computer simulations. (shrink)

A chronicled approach to the notion of computer simulations shows that there are two predominant interpretations in the specialized literature. According to the first interpretation, computer simulations are techniques for finding the set of solutions to a mathematical model. I call this first interpretation the problem-solving technique viewpoint. In its second interpretation, computer simulations are considered to describe patterns of behavior of a target system. I call this second interpretation the description of patterns of behavior viewpoint of computer simulations. This (...) article explores these two interpretations of computer simulations from three different angles. First, I collect a series of definitions of computer simulation from the historical record. I track back definitions to the early 1960s and show how each viewpoint shares similar interpretations of computer simulations—ultimately clustering into the two viewpoints aforementioned. This reconstruction also includes the most recent literature. Second, I unpack the philosophical assumptions behind each viewpoint, with a special emphasis on their differences. Third, I discuss the philosophical implications of each viewpoint in the context of the recent discussion on the logic of scientific explanation for computer simulations. (shrink)

The epistemic arrow of time is the fact that our knowledge of the past seems to be both of a different kind and more detailed than our knowledge of the future. Just like with the other arrows of time, it has often been speculated that the epistemic arrow arises due to the second law of thermodynamics. In this paper, we investigate the epistemic arrow of time using a fully formal framework. We begin by defining a memory system as any (...) physical system whose present state can provide information about the state of the external world at some time other than the present. We then identify two types of memory systems in our universe, along with an important special case of the first type, which we distinguish as a third type of memory system. We show that two of these types of memory systems are time-symmetric, able to provide knowledge about both the past and the future. However, the third type of memory systems exploits the second law of thermodynamics, at least in all of its instances in our universe that we are aware of. The result is that in our universe, this type of memory system only ever provides information about the past. We also argue that human memory is of this third type, completing the argument. We end by scrutinizing the basis of the second law itself. This uncovers a previously unappreciated formal problem for common arguments that try to derive the second law from the “Past Hypothesis”, i.e., from the claim that the very early universe was in a state of extremely low entropy. Our analysis is indebted to prior work by one of us but expands and improves upon this work in several respects. (shrink)

Scientific research in the formal sciences comes in multiple degrees of formality: fully formal work; rigorous proofs that practitioners know to be formalizable in principle; and informal work like rough proof sketches and considerations about the advantages and disadvantages of various formal systems. This informal work includes informal and semi-formal debates between formal scientists, e.g. about the acceptability of foundational principles and proposed axiomatizations. In this paper, we propose to use the methodology of structured (...) argumentation theory to produce a formal model of such informal and semi-formal debates in the formal sciences. For this purpose, we propose ASPIC-END, an adaptation of the structured argumentation framework ASPIC+ which can incorporate natural deduction style arguments and explanations. We illustrate the applicability of the framework to debates in the formal sciences by presenting a simple model of some arguments about proposed solutions to the Liar paradox, and by discussing a more extensive—but still preliminary—model of parts of the debate that mathematicians had about the Axiom of Choice in the early twentieth century. (shrink)

“The Craft of Formal Logic” is Arthur Prior’s unpublished textbook, written in 1950–51, in which he developed a theory of modality as quantification over possible worlds-like objects. This theory predates most of the prominent pioneering texts in possible worlds semantics and anticipates the significance of its basic concept in modal logic. Prior explicitly defines modal operators as quantifiers of ‘entities’ with modal character. Although he talks about these ‘entities’ only informally, and hesitates how to name them, using alternately the (...) phrases ‘possible states of affairs’, ‘chances’, ‘cases’ or ‘peculiar objects’, he is nevertheless very clear that they should be the fundamental concept of any theory of modality as a form of quantity. Without the assumption that modal operators quantify over such modal objects, the modal system will be incapable of distinguishing an actually true proposition from a necessarily true one. Due to the fact that Prior never made any direct reference to this theory in his subsequently published papers, it remained largely unknown. The comparison of “The Craft” with some of his papers on tense logic suggests that this early theory of modality underlies his later work on temporality. (shrink)

This paper analyses the Australian Values Education Program (VEP) within the framework of late-classical political economy. Using analytical methods from systemic functional linguistics and critical discourse analysis, we demonstrate that the VEP is an unwitting restatement of the principles of ideology as developed by the likes of Destutt de Tracy and the Young Hegelians. We conclude that the sudden shock of globalisation and the post-national cultures this has entailed is in many ways similar to the shock of formal nationalism (...) that emerged in the late-Seventeenth and early-Eighteenth centuries. The overall result of the VEP for the Australian school system is a massive procedural burden that is unlikely to produce the results at which the program is aimed. (shrink)

Both the constructive and predicative approaches to mathematics arose during the period of what was felt to be a foundational crisis in the early part of this century. Each critiqued an essential logical aspect of classical mathematics, namely concerning the unrestricted use of the law of excluded middle on the one hand, and of apparently circular \impredicative" de nitions on the other. But the positive redevelopment of mathematics along constructive, resp. predicative grounds did not emerge as really viable alternatives (...) to classical, set-theoretically based mathematics until the 1960s. Now we have a massive amount of information, to which this lecture will constitute an introduction, about what can be done by what means, and about the theoretical interrelationships between various formal systems for constructive, predicative and classical analysis. (shrink)

The object of this paper is to reply to Morrison's ([2000]) claim that while ‘structural unity’ was achieved at the level of the mathematical models of population genetics in the early synthesis, there was explanatory disunity. I argue to the contrary, that the early synthesis effected by the founders of theoretical population genetics was unifying and explanatory both. Defending this requires a reconsideration of Morrison's notion of explanation. In Morrison's view, all and only answers to ‘why’ questions which (...) include the ‘cause or mechanism’ for some phenomenon count as explanatory. In my view, mathematical demonstrations that answer ‘how possibly’ and ‘why necessarily’ questions may also count as explanatory. The authors of the synthesis explained how evolution was possible on a Mendelian system of inheritance, answered skepticism about the sufficiency of selection, and thus explained why and how a Darwinian research program was warranted. While today we take many of these claims as obvious, they required argument, and part of the explanatory work of the formal sciences is providing such arguments. Surely, Fisher and Wright had competing views as to the optimal means of generating adaptation. Nevertheless, they had common opponents and a common unifying and explanatory goal that their mathematical demonstrations served. Introduction: Morrison's challenge Fisher v. Wright revisited The early synthesis Conclusion: unification and explanation reconciled. (shrink)

G. Schiemer has recently ascribed to Carnap the so-called domains-as-fields conception of models, which he subsequently used to defend Carnap’s treatment of extremal axioms against J. Hintikka’s criticism that the number of tuples in a relation, and not the domain of discourse, is optimised in Carnap’s treatment. We will argue by a careful textual analysis, however, that this domains-as-fields conception cannot be applied to Carnap’s early semantics, because it includes a notion of submodel and subrelation that is not only (...) absent from Carnap’s work at that time, but even contradicts it. As a consequence, Schiemer’s defense of Carnap’s extremal axioms against Hintikka’s criticism fails. We will reconcile Carnap’s treatment of extremal axioms and Hintikka’s observation by taking into account the practice of axiomatics in the early twentieth century. If one realises that, in Carnap’s time, a predicate for the domain of discourse was often introduced in the formal theory, and that Carnap defined such predicates from the basic relations of an axiom system, the apparent disagreement between optimising relations and optimising domains disappears. (shrink)

The word buddhi is an important term of Indian philosophical discourse, but some aspects of its use have caused confusion and continue to occasion difficulties. This paper undertakes a survey of the usage of the word buddhi in general Sanskrit literature from its earliest late Vedic occurrences up to the middle of the first millennium CE. Signifying fundamentally “awareness,” the word “buddhi” is shown to refer often to a being’s persisting capacity or faculty of awareness and also, often, to the (...) content of a being’s awareness. There are also instances where it is hard to determine which of these two kinds of reference are intended in our written sources, and there are other instances where both senses seem present simultaneously. Various examples attest to the use of the word to refer to an affective and volitional capacity in a being—and to affective and volitional content—as well as to a cognitive faculty and cognitive content. One feature that occurs frequently in the word’s use is that this faculty and, or, its content, regularly describe alterations of a subject’s knowledge of the surrounding situation, the transformation of surrounding complexity or multiplicity into a simpler and more manageable mental construct—an understanding, an interpretation, a decision, a plan, etc. As the word buddhi is related to the primary Sanskrit word-family used to describe the concrete experience of awakening—moving from no awareness to clear awareness—it is not surprising that its more abstract usage would often incorporate a similar dynamic, a transition from less clear to more clear knowledge, a rendering of early knowledge to better and more useful knowledge, in short, a faculty of “intellect” that produces refined decisions, resolutions, and determinations. It is suggested that this element of its semantic profile contributed to the word’s eventually becoming the preferred word for the most important of the mental functions of beings in one of the most widespread philosophical psychologies of ancient India, that which ultimately became formally enshrined in the philosophical system “Sāṃkhya.”. (shrink)

The word buddhi is an important term of Indian philosophical discourse, but some aspects of its use have caused confusion and continue to occasion difficulties. This paper undertakes a survey of the usage of the word buddhi in general Sanskrit literature from its earliest late Vedic occurrences up to the middle of the first millennium CE. Signifying fundamentally “awareness,” the word “buddhi” is shown to refer often to a being’s persisting capacity or faculty of awareness and also, often, to the (...) content of a being’s awareness. There are also instances where it is hard to determine which of these two kinds of reference are intended in our written sources, and there are other instances where both senses seem present simultaneously. Various examples attest to the use of the word to refer to an affective and volitional capacity in a being—and to affective and volitional content—as well as to a cognitive faculty and cognitive content. One feature that occurs frequently in the word’s use is that this faculty and, or, its content, regularly describe alterations of a subject’s knowledge of the surrounding situation, the transformation of surrounding complexity or multiplicity into a simpler and more manageable mental construct—an understanding, an interpretation, a decision, a plan, etc. As the word buddhi is related to the primary Sanskrit word-family used to describe the concrete experience of awakening—moving from no awareness to clear awareness—it is not surprising that its more abstract usage would often incorporate a similar dynamic, a transition from less clear to more clear knowledge, a rendering of early knowledge to better and more useful knowledge, in short, a faculty of “intellect” that produces refined decisions, resolutions, and determinations. It is suggested that this element of its semantic profile contributed to the word’s eventually becoming the preferred word for the most important of the mental functions of beings in one of the most widespread philosophical psychologies of ancient India, that which ultimately became formally enshrined in the philosophical system “Sāṃkhya.”. (shrink)

The main purpose of this paper is to present a formal systemPin which we enjoy a smooth-running technique and which countenances a universe of classes which is symmetrical as between large and small. More exactly,Pis a system which differs from the inconsistent system of [1] only in the introduction of a rather natural new restrictive condition on the defining formulas of the elements. It will be proved that if the weaker system of [2] is consistent, thenPis also consistent.After the (...) discovery of paradoxes, it may be recalled, Russell and Zermelo in the same year proposed two different ways of safeguarding logic against contradictions. Since then various simplifications and refinements of these systems have been made. However, in the resulting systems of Zermelo set theory, generation of classes still tends to be laborious and uncertain; and in the systems of Russell's theory of types, complications in the matter of reduplication of classes and meaningfulness of formulas remain. In [2], Quine introduced a system which seems to be free from all these complications. But later it was found out that in it there appears to be an unavoidable difficulty connected with mathematical induction. Indeed, we encounter the curious situation that although we can prove in it the existence of a class V of all classes, and we can also prove particular existence theorems for each of infinitely many classes, nobody has so far contrived to prove in it that V is an infinite class or that there exists an infinite class at all. (shrink)

Formal systems of fuzzy logic are well-established logical systems and respected members of the broad family of the so-called substructural logics closely related to the famous logic BCK. The study of fragments of logical systems is an important issue of research in any class of non-classical logics. Here we study the fragments of nine prominent fuzzy logics to all sublanguages containing implication. However, the results achieved in the paper for those nine logics are usually corollaries of (...) theorems with much wider scope of applicability. In particular, we show how many of these fragments are really distinct and we find axiomatic systems for most of them. In fact, we construct strongly separable axiomatic systems for eight of our nine logics. We also fully answer the question for which of the studied fragments the corresponding class of algebras forms a variety. Finally, we solve the problem how to axiomatize predicate versions of logics without the lattice disjunction. (shrink)

This book presents a systematic philosophical and historical analysis of operating systems (0S). The discussion starts with the evolution of OSs since before their birth. It continues with a comprehensive philosophical analysis grounded in technical aspects. Coverage looks at software and (where appropriate) hardware as well as their historical developments. The authors not only offer historical and philosophical reflections on operating systems. They also explore the programs they coordinate and trace the epsitemic and ontological consequences of their designs. (...) Each chapter investigates one or more overlapping fragments of this fascinating history. These include: the birth of the UNIX system and the development of early systems and prototypes; a conceptual analysis of the plurality of systems; an investigation into business, ethical, and aesthetics aspects related to operating systems; and logical principles of formal languages. This book will interest researchers from a diversity of backgrounds. It will appeal to historians, philosophers, as well as logicians and computer scientists who want to engage with topics relevant to the history and philosophy of programming and more specifically that of operating systems. (shrink)

We present a formal system, E, which provides a faithful model of the proofs in Euclid's Elements, including the use of diagrammatic reasoning.

Miloš Forman began his career as a filmmaker at the Barrandov Studios in Prague in the 1960s and films Amadeus with Barrandov in the early 1980s. The contrast between the high budget historical spectacle of Amadeus and the gently ironic realism of his 1960s films could not be more pronounced. I will explore here the changes that mark both Forman’s own development as a filmmaker between the 1960s and the 1980s as well as considering the impact of normalisation on (...) the Barrandov Studios following the events of August 1968. During the 1960s, aside from its relationship with the young filmmakers of the New Wave, Barrandov supported an extraordinary range of films from popular to historical epics. Under the directorship of Josef Veselý, Barrandov turned out to be an environment that produced films that were successful with the public, formally experimental and politically challenging. The situation at Barrandov after 1968 quickly changed and Forman decided not to return to Czechoslovakia. Forman’s films during the 1970s in the USA brought him a level of international fame and popularity that is unrivalled in the history of Czech cinema but showed a radical departure from the films of the 1960s. This change culminates with Amadeus and his return to Barrandov. Even as his budgets increased massively, there was a loss of quality in the films of the 1970s and beyond and we can see in Amadeus, both as film and as production, a parable of exploitation and decadence that mourns the creative possibilities of the 1960s. (shrink)

This paper explores one aspect of the political in the early Hegel, that of criminal action and its relationship to the concept of recognition in the System of Ethical Life. While it is clear that in this work Hegel thinks that criminal action plays an important role in the transformation of simple ethical communities, it is not clear that, for Hegel, the formal character of crime in the struggle for recognition is anything but negative. I attempt to show (...) how this role for crime leads Hegel to a legalistic conception of Right that has no solid connection with recognition as a social force. (shrink)

Note?takers in early modern Europe mixed a number of scribal practices. Not only did they write down extracts of texts, they also collected data from observation or from accounting. Practices such as commonplacing were part of sometimes communal, rather informal personal practices that laid the foundations for personal diaries. Other note?taking was prescriptive, fact?establishing technical data entry. Yet both the personal, sentimental and technical forms of note?taking were interrelated. It was during this period that merchants, administrators, scholars and scientists (...) sought methods to transform raw information such as notes into formalized knowledge for practical use. Notes had formed a part of larger writing and archival projects since the dawn of writing and literacy, but during the seventeenth and eighteenth centuries, figures such as Bacon, Boyle and Pepys not only mixed note?taking practices from both scholarly and mercantile traditions; they also thought about the very act of note?taking and how to transform it into a tool for the management of large?scale government, industry and research. Most of all, in the seventeenth century, scholars, merchants and naturalists began thinking in formal terms about how to use notes as part of larger information systems which they called collections, compilations and even archives. (shrink)

The advance of mechanism in science and philosophy in the 17th century created a great interest to machines or automata. Leibniz was no exception - in an early memoir Drôle de pensée he wrote admiringly about a machine that could walk on water, exhibited in Paris. The idea of automatic processing in general had a large role in his thought, as can be seen, for example, in his invention of the binary code and the so-called Calculemus!-model for solving controversies. (...) In metaphysics, the idea of an automata was expressed most clearly in the 1695 article New System of the Nature of Substances and their Communication, and the ensuing correspondence with, among others, Foucher, Bayle, Lamy, Jaquelot and Masham. In the article Leibniz discusses the soul as a spiritual machine in the context of pre-established harmony, arguing that God can "give to a substance at the outset a nature or internal force which could produce in it an orderly way (as in spiritual or formal automaton; but a free one, in the case of a substance which is endowed with a share of reason) everything that is going to happen to it, that is to say, all the appearances or expressions it is going to have, and all without the help of any created thing." The basic idea of Leibniz's spiritual machine is that the soul or entelechy is an autonomous and spontaneous unity, consisting of internal active force and producing its own perceptions (both confused and distinct). It is a self-moving machine, driven by its perceptions and appetites, but it follows (without being conscious of it) a lawful series or programme created by God. The entelechy remains the same despite undergoing an infinite number of changes. To Foucher he explained that each state of the individual substance is a consequence of its preceding one, "as if there were only God and the substance in the world". Despite this, the spiritual machine is related not only to God, but through the pre-established harmony to bodies or natural machines. However, as it is not dependent on them, the spiritual machine is superiot to natural machines. In this paper I concentrate on three moral themes related to the spiritual machine: moral deliberation, moral identity and the goal of moral action. All these themes are more or less implicit in the New System, but are discussed in more detail in the ensuing correspondence after the publication of the article. Finally, the themes are given an extended discussion especially in the second book of New Essays on Human Understanding (1704, published 1765), written partly at the same time as some of the correspondence and unpublished related material. I will first give an overview of Leibniz's position concerning the spiritual machine or automaton in the New System and then go on to explore the three moral themes one by one, as they feature in the subsequent correspondence and in the New Essays. I will show that the three topics are essential to the function of the spiritual machine – to Sophie Charlotte Leibniz wrote: "...let us say that everything in bodies happens mechanically, or in accordance with laws of motion, and that everything in the soul happens morally, or in accordance with perceived good or evil." There are many texts that anticipate the views in the New System (notably the unpublished memoir De Affectibus of 1679) and Leibniz continued to discuss its themes later on (in addition to correpondence, for example, in Theodicy of 1710 and Monadology and Principles of Nature and Grace of 1714). Here I focus on the short-term development of Leibniz's views on the topic (around 1695-1705), but I argue that his basic view of the spiritual machine did not change much after finishing the dialogue with Locke in 1704. (shrink)

This paper traces a relatively linear sequence of early research approaches to the formal verification of concurrent programs. It does so forwards and then backwards in time. After briefly outlining the context, the key insights from three distinct approaches from the 1970s are identified (Ashcroft/Manna, Ashcroft (solo) and Owicki). The main technical material in the paper focuses on a specific program taken from the last published of the three pieces of research (Susan Owicki’s): her own verification of her (...) _Findpos_ example is outlined followed by attempts at verifying the same example using the earlier approaches. Reconsidering the prior approaches on the basis of Owicki’s useful example illuminates similarities and differences between the proposals. Along the way, observations about interactions between researchers (and some “blind spots”) are noted. (shrink)

Recent historical studies have investigated the first proponents of methodological structuralism in late nineteenth-century mathematics. In this paper, I shall attempt to answer the question of whether Peano can be counted amongst the early structuralists. I shall focus on Peano’s understanding of the primitive notions and axioms of geometry and arithmetic. First, I shall argue that the undefinability of the primitive notions of geometry and arithmetic led Peano to the study of the relational features of the systems of (...) objects that compose these theories. Second, I shall claim that, in the context of independence arguments, Peano developed a schematic understanding of the axioms which, despite diverging in some respects from Dedekind’s construction of arithmetic, should be considered structuralist. From this stance I shall argue that this schematic understanding of the axioms anticipates the basic components of a formal language. (shrink)

Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the material systems are, in several senses, formal as well. In section 1.2 variants as to language form (choices of logical constants and logical rules) are pointed out. Section 1.3 is concerned with options as to initial positions and the permissibility of attacks on elementary statements. (...) The problem of ending a dialogue, and of infinite dialogues, is treated in section 1.4. Other options, e.g., as to the number of attacks allowed with respect to each statement, are listed in section 1.5. Section 1.6 explains the concept of a chain of arguments.From section 2 onward four types of dialectic systems are picked out for closer study: D, E, Di and Ei. After a preliminary section on dialogue sequents and winning strategies, the equivalence of derivability in intuitionistic logic and the existence of a winning strategy (for the Proponent) on the strength of Ei is shown by simple inductive proofs. (shrink)

Wilfried Sieg. Formal Systems, Church Turing Thesis, and Gödel's Theorems: Three Contributions to The MIT Encyclopedias of Cognitive Science.

Adopting a different method from the previous scholars, this article deduces the remaining 23 valid syllogisms just taking the syllogism AEE-4 as the basic axiom. The basic idea of this study is as follows: firstly, make full use of the trichotomy structure of categorical propositions to formalize categorical syllogisms. Then, taking advantage of the deductive rules in classical propositional logic and the basic facts in the generalized quantifier theory, we deduce the remaining 23 valid categorical syllogisms by taking just one (...) syllogism (that is, AEE-4) as the basic axiom. This article not only reveals the reducible relations between the syllogism AEE-4 and the other 23 valid syllogisms, but also establishes a concise formal axiomatic system for categorical syllogistic logic. We hope that the results and methods will provide a good mathematical paradigm for studying other kinds of syllogistic logics, and that the project will appeal to specialists in logic, linguistic semantics, computational semantics, cognitive science and artificial intelligence. (shrink)

Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the material systems are, in several senses, formal as well. In section 1.2 variants as to language form (choices of logical constants and logical rules) are pointed out. Section 1.3 is concerned with options as to initial positions and the permissibility of attacks on elementary statements. (...) The problem of ending a dialogue, and of infinite dialogues, is treated in section 1.4. Other options, e.g., as to the number of attacks allowed with respect to each statement, are listed in section 1.5. Section 1.6 explains the concept of a chain of arguments.From section 2 onward four types of dialectic systems are picked out for closer study: D, E, Di and Ei. After a preliminary section on dialogue sequents and winning strategies, the equivalence of derivability in intuitionistic logic and the existence of a winning strategy (for the Proponent) on the strength of Ei is shown by simple inductive proofs. (shrink)

The study of the autonomic nervous system (ANS) function has shown to provide useful indicators for risk stratification and early detection on a variety of cardiovascular pathologies. However, data gathered during different tests of the ANS are difficult to analyse, mainly due to the complex mechanisms involved in the autonomic regulation of the cardiovascular system (CVS). Although model-based analysis of ANS data has been already proposed as a way to cope with this complexity, only a few models coupling the (...) main elements involved have been presented in the literature. In this paper, a new model of the CVS, representing the ventricles, the circulatory system and the regulation of the CVS activity by the ANS, is presented. The models of the vascular system and the ventricular activity have been developed using the Bond Graph formalism, as it proposes a unified representation for all energetic domains, facilitating the integration of mechanic and hydraulic phenomena. In order to take into account the electro-mechanical behaviour of both ventricles, an electrophysiologic model of the cardiac action potential, represented by a set of ordinary differential equations, has been integrated. The short-term ANS regulation of heart rate, cardiac contractility and peripheral vasoconstriction is represented by means of continuous transfer functions. These models, represented in different continuous formalisms, are coupled by using a multi-formalism simulation library. Results are presented for two different autonomic tests, namely the Tilt Test and the Valsalva Manoeuvre, by comparing real and simulated signals. (shrink)

This article is a brief formulation of a radical thesis. We start with the formalist doctrine that mathematical objects have no meanings; we have marks and rules governing how these marks can be combined. That's all. Then I go further by arguing that the signs of a formal system of mathematics should be considered as physical objects, and the formal operations as physical processes. The rules of the formal operations are or can be expressed in terms of (...) the laws of physics governing these processes. In accordance with the physicalist understanding of mind, this is true even if the operations in question are executed in the head. A truth obtained through (mathematical) reasoning is, therefore, an observed outcome of a neuro-physiological (or other physical) experiment. Consequently, deduction is nothing but a particular case of induction. (shrink)

After the initial formulation of the concept of reification in Georg Lukács’s History and Class Consciousness (HCC, 1923), a series of confusing uses of it within critical theory have contributed to blurring its contours. In his pre-Marxist work, while analyzing the social rationalization process, Lukács located the modern form of mediation between subject and object and connected it with certain effects on the level of human consciousness and behavior. This very scheme is repeated and refined in HCC. In the Reification (...) essay, Lukács uses the neo-Kantian concept of the “form of objectivity” to grasp the central constitutive form of all kinds of objects in bourgeois society. He interprets Marx’s commodity form as the “archetype” of all capitalist objectivity, which consists in converting qualitative contents into quantitative categories. Thus, the formal/calculative rationality of exchange penetrates all kinds of objectification in modern society. In Lukács’s view, only in its modern, universalized form does rational objectification bring about the phenomenon of reification, i.e. the de-historicization and political neutralization of the social relations that constitute the social system and the dominant forms of consciousness. This systemic, cultural, and political understanding of reification can prove to be fruitful in the context of contemporary discussions on democratic transformative praxis. (shrink)

In the history of Newtonian Mechanics physicists and astronomers did not rely on so-called inertial frames, indeed they were not able to identify such frames. So the usual neo-Newtonian formalism of Newtonian Mechanics contains some superfluous components. In the present paper I will formulate a formal system for classical particle mechanics in Leibnizian space-time, where a relation, a counterpart of the second law of motion, between force on bodies and derivative of their momentum will be defined relative to every, (...) inertial or not, reference frame. And I will present a view that in the research process under Newtonian mechanics the accumulation of those models of the relation that satisfied some realistic conditions determined an additional structure of non-rotating frames to Leibnizian space-time. (shrink)

This article is a brief formulation of a radical thesis. We start with the formalist doctrine that mathematical objects have no meanings; we have marks and rules governing how these marks can be combined. That's all. Then I go further by arguing that the signs of a formal system of mathematics should be considered as physical objects, and the formal operations as physical processes. The rules of the formal operations are or can be expressed in terms of (...) the laws of physics governing these processes. In accordance with the physicalist understanding of mind, this is true even if the operations in question are executed in the head. A truth obtained through (mathematical) reasoning is, therefore, an observed outcome of a neuro-physiological (or other physical) experiment. Consequently, deduction is nothing but a particular case of induction. (shrink)

This chapter uncovers a less investigated aspect of the relationship between the two most important scholastic schools of the Renaissance, Thomism and Scotism: the influence of Scotist literature on distinctions as seen in some sixteenth-century Thomists. The chapter has a primary focus on Chrysostomus Javelli’s engagement in his discussion of divine attributes with the Scotist doctrine of distinctions, but also considers other Thomist sources. First, the beginnings of the highly specialised Scotist literature on distinctions are traced back to the start (...) of the fourteenth century; I show how some early followers of Duns Scotus, in particular Francis of Meyronnes and Petrus Thomae, systematised Scotus’ ontology of the various grades of being by compiling lists of subtle distinctions to be applied to various levels of reality. I give some indications as to the later reception of these models of distinctions in the Scotist school. Special attention is paid to Étienne Brulefer, since his summary of Petrus Thomae’s model of seven distinctions was Javelli’s source for the Scotist doctrine. I then investigate how Javelli worked with Brulefer’s summary, and how he sought to integrate the Scotist doctrine into his own discussion of divine attributes. Thomists traditionally allowed only a rational or mental kind of distinction among divine attributes, and between them and the divine essence. Javelli, however, endeavours to show how the Thomist position may be reconciled with the Scotist doctrine of a formal or ex natura rei distinction. He did not always endorse this conciliatory approach; I hypothesise that he changed his mind on the subject over time. Finally, I show how other Renaissance Thomists reacted to the Scotist system of distinctions; in particular, I draw attention to the Thomists Andreas Bodenstein von Karlstadt, Bartolomeo Manzoli, and Mattia Gibboni da Aquario, who all wrote treatises on Thomist distinction theory modelled on the Scotist system of distinctions. In some of this literature, lists of distinctions based on Thomist metaphysics were compiled in order to replace the Scotist system. I argue that Javelli’s approach is more conciliatory and, in fact, has some overlap with the concordist thought of Giovanni Pico della Mirandola, who himself considered Scotus and Aquinas to be in fundamental agreement as regards the distinction between divine attributes. (shrink)

A formal system for Ł ${}_{\infty}$ , based on a "game-theoretic" analysis of the Łukasiewicz propositional connectives, is defined and proved to be complete. An "Herbrand theorem" for the Ł ${}_{\infty}$ predicate calculus (a variant of some work of Mostowski) and some corollaries relating to its axiomatizability are proved. The predicate calculus with equality is also considered.

A formal system for , based on a game-theoretic analysis of the ukasiewicz prepositional connectives, is defined and proved to be complete. An Herbrand theorem for the predicate calculus (a variant of some work of Mostowski) and some corollaries relating to its axiomatizability are proved. The predicate calculus with equality is also considered.