Formal ontology as a main branch of metaphysics investigates categories of being. In the formal ontological approach to metaphysics, these ontological categories are analysed by ontological forms. This analysis, which we illustrate by some category systems, provides a tool to assess the clarity, exactness and intelligibility of different category systems or formal ontologies. We discuss critically different accounts of ontological form in the literature. Of ontological form, we propose a character- neutral relational account. In this metatheory, ontological forms of entities (...) are their standings in internal relations whose holding is neutral on the character of their relata. These relations are “formal ontological relations”. Entities belong to ontological categories because they stand in the same formal ontological relations. We hold a nominalist relationalism about ontological categories and forms. We conclude by showing that our metatheory is useful for understanding categorial fundamentality/non- fundamentality, different formal ontologies, and for unifying metaphysical questions. (shrink)

I argue that normative formal epistemology (NFE) is best understood as modelling, in the sense that this is the reconstruction of its methodology on which NFE is doing best. I focus on Bayesianism and show that it has the characteristics of modelling. But modelling is a scientific enterprise, while NFE is normative. I thus develop an account of normative models on which they are idealised representations put to normative purposes. Normative assumptions, such as the transitivity of comparative credence, are characterised (...) as modelling idealisations motivated normatively. I then survey the landscape of methodological options: what might formal epistemologists be up to? I argue the choice is essentially binary: modelling or theorising. If NFE is theorising it is doing very poorly: generating false claims with no clear methodology for separating out what is to be taken seriously. Modelling, by contrast, is a successful methodology precisely suited to the management of useful falsehoods. Regarding NFE as modelling is not costless, however. First, our normative inferences are less direct and are muddied by the presence of descriptive idealisations. Second, our models are purpose-specific and limited in their scope. I close with suggestions for how to adapt our practice. (shrink)

We present a formal mechanical analysis using sweeping net methods to approximate surfacing singularities of saddle maps. By constructing densified sweeping subnets for individual vertices and integrating them, we create a comprehensive approximation of singularities. This approach utilizes geometric concepts, analytical methods, and theorems that demonstrate the robustness and stability of the nets under perturbations. Through detailed proofs and visualizations, we provide a new perspective on singularities and their approximations in analytic geometry.

This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) (...) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning. (shrink)

The formal sciences - mathematical as opposed to natural sciences, such as operations research, statistics, theoretical computer science, systems engineering - appear to have achieved mathematically provable knowledge directly about the real world. It is argued that this appearance is correct.

Formal principles governing best practices in classification and definition have for too long been neglected in the construction of biomedical ontologies, in ways which have important negative consequences for data integration and ontology alignment. We argue that the use of such principles in ontology construction can serve as a valuable tool in error-detection and also in supporting reliable manual curation. We argue also that such principles are a prerequisite for the successful application of advanced data integration techniques such as ontology-based (...) multi-database querying, automated ontology alignment and ontology-based text-mining. These theses are illustrated by means of a case study of the Gene Ontology, a project of increasing importance within the field of biomedical data integration. (shrink)

This paper examines two alleged limitations in the use of formal languages: on the one hand, the trade-offs between expressive and inferential power, and on the other, the phenomenon of system imprisonment. After reconceptualizing the issue, we consider the role played by modality in the understanding of certain aspects of mathematical structures and argue for its centrality.

Not focusing on the history of classical logic, this book provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and computational.

The central hypothesis of the collaboration between Language and Computing (L&C) and the Institute for Formal Ontology and Medical Information Science (IFOMIS) is that the methodology and conceptual rigor of a philosophically inspired formal ontology greatly benefits application ontologies. To this end r®, L&C’s ontology, which is designed to integrate and reason across various external databases simultaneously, has been submitted to the conceptual demands of IFOMIS’s Basic Formal Ontology (BFO). With this project we aim to move beyond the level of (...) controlled vocabularies to yield an ontology with the ability to support reasoning applications. Our general procedure has been the implementation of a meta-ontological definition space in which the definitions of all the concepts and relations in LinKBase® are standardized in a framework of first-order logic. In this paper we describe how this standardization has already led to an improvement in the LinKBase® structure that allows for a greater degree of internal coherence than ever before possible. We then show the use of this philosophical standardization for the purpose of mapping external databases to one another, using LinKBase® as translation hub, with a greater degree of success than possible hitherto. We demonstrate how this offers a genuine advance over other application ontologies that have not submitted themselves to the demands of philosophical scrutiny. LinKBase® is one of the world’s largest applications-oriented medical domain ontologies, and BFO is one of the world’s first philosophically driven reference ontologies. The collaboration of the two thus initiates a new phase in the quest to solve the so-called “Tower of Babel”. (shrink)

This book is a collection of articles dealing with criticisms of Robert S. Hartman’s theory of formal axiology. During his lifetime, Hartman wrote responses to many of his critics. Some of these were previously published but many are published here for the first time. In particular, published here are Hartman’s replies to such critics as Hector Neri Castañeda, Charles Hartshorne, Rem B. Edwards, Robert E. Carter, G. R. Grice, Nicholas Rescher, Robert W. Mueller, Gordon Welty, Pete Gunter, George Kimball Plochmann, (...) William Eckhardt, and Robert S. Brumbaugh. Crticial essays and responses to them developed by Rem B. Edwards, Frank G. Forrest, and Mark A. Moore after Hartman’s untimely death in 1973 are also included. (shrink)

This paper proposes a formal account of AI trustworthiness, connecting both intrinsic and perceived trustworthiness in an operational schematization. We argue that trustworthiness extends beyond the inherent capabilities of an AI system to include significant influences from observers' perceptions, such as perceived transparency, agency locus, and human oversight. While the concept of perceived trustworthiness is discussed in the literature, few attempts have been made to connect it with the intrinsic trustworthiness of AI systems. Our analysis introduces a novel schematization to (...) quantify trustworthiness by assessing the discrepancies between expected and observed behaviors and how these affect perceived uncertainty and trust. The paper provides a formalization for measuring trustworthiness, taking into account both perceived and intrinsic characteristics. By detailing the factors that influence trust, this study aims to foster more ethical and widely accepted AI technologies, ensuring they meet both functional and ethical criteria. (shrink)

This article presents a formal ontology which accounts for the general nature of artefacts. The objective is to help structure application ontologies in areas where specific artefacts are present - in other words, virtually any area of activity. The conceptualization relies on recent philosophical and psychological research on artefacts, having resulted in a largely consensual theoretical basis. Furthermore, this ontology of artefacts extends the foundational DOLCE ontology and supplements its axiomatization. The conceptual primitives are as follows: artificial entity, intentional production (...) of entities, (state of) capacity, capacity to play a role in actions of a given type, function and functional object. These primitives enable artefacts in general to be characterized as intentionally and successfully produced entities, and isolate an important subclass of “technical” artefacts to which a function is ascribed. Lastly, we emphasize the novelty of this ontology by comparing it with other works with similar objectives. (shrink)

This essay presents Husserl’s Formal and Transcendental Logic (1929) in three main sections following the layout of the work itself. The first section focuses on Husserl’s introduction where he explains the method and the aim of the essay. The method used in FTL is radical Besinnung and with it an intentional explication of proper sense of formal logic is sought for. The second section is on formal logic. The third section focuses on Husserl’s “transcendental logic,” which is needed to make (...) Husserl’s conception complete, i.e., to understand what makes Besinnung radical, how the proper sense of formal logic has been reached and how all this relates to transcendental constitution of an object in the world. Husserl’s work is connected to his context (in exact sciences) and the relevance of his views for the contemporary approaches is discussed. (shrink)

In my old manuscript “Formal Theology” that now is out as a preprint I show that science and theology can be founded upon the same set of basic assumptions. I now follow up this idea with the thought that Formal Theology may be used to ground also a religion. “Religion“, in this regard, as related to beliefs. I’m not going into any details, neither concerning the original manuscript, nor this new idea. The important thing, I think, is to explore if (...) this kind of “religion”, in any way, can be accommodated with “ordinary” religions. I leave more rigorous work to myself or to others for the future. (shrink)

Although formal thought disorder (FTD) has been for long a clinical label in the assessment of some psychiatric disorders, in particular of schizophrenia, it remains a source of controversy, mostly because it is hard to say what exactly the “formal” in FTD refers to. We see anomalous processing of terminological knowledge, a core construct of human knowledge in general, behind FTD symptoms and we approach this anomaly from a strictly formal perspective. More specifically, we present here a symbolic computational model (...) of storage in, and activation of, a human semantic network, or semantic memory, whose core element is logical form; this is normalized by description logic (DL), namely by CL, a DL-based language – Conception Language – designed to formalize conceptualization from the viewpoint of individual cognitive agency. In this model, disruptions in the rule-based implementation of the logical form account for the apparently semantic anomalies symptomatic of FTD, which are detected by means of a CL-based algorithmic assessment. (shrink)

I argue that Aristotle’s account of scientific demonstrations in the Posterior Analytics is centred upon formal causation, understood as a demonstration in terms of essence (and as innocent of the distinction between form and matter). While Aristotle says that all four causes can be signified by the middle term in a demonstrative syllogism, and he discusses at some length efficient causation, much of Aristotle’s discussion is foremost concerned with the formal cause. Further, I show that Aristotle had very detailed procedures (...) for identifying the formal cause, and that he is aware of several problems which might lead one to erroneously identify the wrong form as the cause of a property. Finally, I show that Aristotle’s account can easily be adapted to material causation, and through some modifications (introduction of process universals related through parthood), hinted at in II 11-12 and 16-17, to efficient and final causation. (shrink)

There are two fundamentally distinct kinds of biological theorizing. "Formal biology" focuses on the relations, captured in formal laws, among mathematically abstracted properties of abstract objects. Population genetics and theoretical mathematical ecology, which are cases of formal biology, thus share methods and goals with theoretical physics. "Compositional biology," on the other hand, is concerned with articulating the concrete structure, mechanisms, and function, through developmental and evolutionary time, of material parts and wholes. Molecular genetics, biochemistry, developmental biology, and physiology, which are (...) examples of compositional biology, are in serious need of philosophical attention. For example, the very concept of a "part" is understudied in both philosophy of biology and philosophy of science. ;My dissertation is an attempt to clarify the distinction between formal biology and compositional biology and, in so doing, provide a clear philosophical analysis, with case studies, of compositional biology. Given the social, economic, and medical importance of compositional biology, understanding it is urgent. For my investigation, I draw on the philosophical fields of metaphysics and epistemology, as well as philosophy of biology and philosophy of science. I suggest new ways of thinking about some classic philosophy of science issues, such as modeling, laws of nature, abstraction, explanation, and confirmation. I hint at the relevance of my study of two kinds of biological theorizing to debates concerning the disunity of science. (shrink)

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such (...) as Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: the (...) parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)

In this paper I try to answer four basic questions: (1) How the concept of God is to be represented? (2) Are there any logical principles governing it? (3) If so, what kind of logic lies behind them? (4) Can there be a logic of the concept of God? I address them by presenting a formal-logical account to the concept of God. I take it as a methodological desideratum that this should be done within the simplest existing logical formalism. I (...) start with first-order logic (FOL) with identity, and then show that its simplest modal extension (SQML, or the simplest quantified modal logic) is enough for us to formalize a minimally satisfactory theory of the concept of God. I focus exclusively on the monotheistic concept of God. (shrink)

This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These (...) acts are not propositions; they do not have truth-values. Our formalization is related to the input/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy. (shrink)

How does one formalize the structure of structures necessary for the foundations of physics? This work is an attempt at conceptualizing the metaphysics of pregeometric structures, upon which new and existing notions of quantum geometry may find a foundation. We discuss the philosophy of pregeometric structures due to Wheeler, Leibniz as well as modern manifestations in topos theory. We draw attention to evidence suggesting that the framework of formal language, in particular, homotopy type theory, provides the conceptual building blocks for (...) a theory of pregeometry. This work is largely a synthesis of ideas that serve as a precursor for conceptualizing the notion of space in physical theories. In particular, the approach we espouse is based on a constructivist philosophy, wherein ``structureless structures'' are syntactic types realizing formal proofs and programs. Spaces and algebras relevant to physical theories are modeled as type-theoretic routines constructed from compositional rules of a formal language. This offers the remarkable possibility of taxonomizing distinct notions of geometry using a common theoretical framework. In particular, this perspective addresses the crucial issue of how spatiality may be realized in models that link formal computation to physics, such as the Wolfram model. (shrink)

This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for (...) both BLE and LET J . The meanings of the connectives of BLE and LET J , from the point of view of preservation of evidence, is explained with the aid of an inferential semantics. A formalization of the notion of evidence for BLE as proposed by M. Fitting is also reviewed here. As a novel result, the paper shows that LET J is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed. (shrink)

Formal epistemology is just what it sounds like: epistemology done with formal tools. Coinciding with the general rise in popularity of experimental philosophy, formal epistemologists have begun to apply experimental methods in their own work. In this entry, I survey some of the work at the intersection of formal and experimental epistemology. I show that experimental methods have unique roles to play when epistemology is done formally, and I highlight some ways in which results from formal epistemology have been used (...) fruitfully to advance epistemically‐relevant experimental work. The upshot of this brief, incomplete survey is that formal and experimental methods often constitute mutually informative means to epistemological ends. (shrink)

In the era of “big data,” science is increasingly information driven, and the potential for computers to store, manage, and integrate massive amounts of data has given rise to such new disciplinary fields as biomedical informatics. Applied ontology offers a strategy for the organization of scientific information in computer-tractable form, drawing on concepts not only from computer and information science but also from linguistics, logic, and philosophy. This book provides an introduction to the field of applied ontology that is of (...) particular relevance to biomedicine, covering theoretical components of ontologies, best practices for ontology design, and examples of biomedical ontologies in use. After defining an ontology as a representation of the types of entities in a given domain, the book distinguishes between different kinds of ontologies and taxonomies, and shows how applied ontology draws on more traditional ideas from metaphysics. It presents the core features of the Basic Formal Ontology (BFO), now used by over one hundred ontology projects around the world, and offers examples of domain ontologies that utilize BFO. The book also describes Web Ontology Language (OWL), a common framework for Semantic Web technologies. Throughout, the book provides concrete recommendations for the design and construction of domain ontologies. (shrink)

Formal ontology as it is presented in Husserl`s Third Logical Investigation can be interpreted as a fundamental tool to describe objects in a formal sense. It is presented one of the main sources: chapter five of Carl Stumpf`s Ûber den psycholoogischen Ursprung der Raumovorstellung (1873), and then it is described how Husserlian Formal Ontology is applied in Fifth Logical Investigation. Finally, it is applied to dramatic structures, in the spirit of Roman Ingarden.

This special issue of the Logic Journal of the IGPL includes revised and updated versions of the best work presented at the fourth edition of the workshop Formal Ap- proaches to Multi-Agent Systems, FAMAS'09, which took place in Turin, Italy, from 7 to 11 September, 2009, under the umbrella of the Multi-Agent Logics, Languages, and Organisations Federated Workshops (MALLOW). -/- Just like its predecessor, research reported in this FAMAS 2009 special issue is very much inspired by practical concerns. This time (...) the authors of all the five selected papers are concerned with knowledge and beliefs in multi-agent settings: How to create a group belief in a fair way from individual plausibility orderings? How to close gaps and resolve ambiguities in a tractable way, when information comes from multiple sources? How to reason about a spatial environment? How to compare the strengths of an agent's beliefs in a principled way? How to decide as efficiently as possible whether a given formula concerning group beliefs is valid? These questions and their answers lead to a multi-faceted and at the same time coherent special issue. We concisely introduce the five articles. (shrink)

Inspired by impossibility theorems of social choice theory, many democratic theorists have argued that aggregative forms of democracy cannot lend full democratic justification for the collective decisions reached. Hence, democratic theorists have turned their attention to deliberative democracy, according to which “outcomes are democratically legitimate if and only if they could be the object of a free and reasoned agreement among equals” (Cohen 1997a, 73). However, relatively little work has been done to offer a formal theory of democratic deliberation. This (...) article helps fill that gap by offering a formal theory of three different modes of democratic deliberation: myopic discussion, constructive discussion, and debate. We show that myopic discussion suffers from indeterminacy of long run outcomes, while constructive discussion and debate are conclusive. Finally, unlike the other two modes of deliberation, debate is path independent and converges to a unique compromise position, irrespective of the initial status quo. (shrink)

Wittgenstein asks: “Now what do the words of this language signify?—What is supposed to shew what they signify, if not the kind of use they have?” Might one answer that rhetorical question by giving a compositional semantics for Wittgenstein’s builder language?

The purpose of this introduction is to give a rough overview of the discussion of the formalization of arguments, focusing on deductive arguments. The discussion is structured around four important junctions: i) the notion of support, which captures the relation between the conclusion and premises of an argument, ii) the choice of a formal language into which the argument is translated in order to make it amenable to evaluation via formal methods, iii) the question of quality criteria for such (...) formalizations, and finally iv) the choice of the underlying logic. This introductory discussion is supplemented by a brief description of the genesis of the special issue, acknowledgements, and summaries of each article. (shrink)

It is commonly said that some standards, such as morality, are ‘normatively authoritative’ in a way that other standards, such as etiquette, are not; standards like etiquette are said to be ‘not really normative’. Skeptics deny the very possibility of normative authority, and take claims like ‘etiquette is not really normative’ to be either empty or confused. I offer a different route to defeat skeptics about authority: instead of focusing on what makes standards like morality special, we should focus on (...) what makes standards like etiquette ‘not really normative’. I defend a fictionalist theory on which etiquette is ‘not really normative’ in roughly the same way that Sherlock is ‘not really a detective’, and show that fictionalism about some normative standards helps us explain the possibility of normative authority. (shrink)

A speculative exploration of the distinction between a relational formal ontology and a classical formal ontology for modelling phenomena in nature that exhibit relationally-mediated wholism, such as phenomena from quantum physics and biosemiotics. Whereas a classical formal ontology is based on mathematical objects and classes, a relational formal ontology is based on mathematical signs and categories. A relational formal ontology involves nodal networks (systems of constrained iterative processes) that are dynamically sustained through signalling. The nodal networks are hierarchically ordered and (...) exhibit characteristics of deep learning. (shrink)

In a first part, I defend that formal semantics can be used as a guide to ontological commitment. Thus, if one endorses an ontological view \(O\) and wants to interpret a formal language \(L\) , a thorough understanding of the relation between semantics and ontology will help us to construct a semantics for \(L\) in such a way that its ontological commitment will be in perfect accordance with \(O\) . Basically, that is what I call constructing formal semantics from an (...) ontological perspective. In the rest of the paper, I develop rigorously and put into practice such a method, especially concerning the interpretation of second-order quantification. I will define the notion of ontological framework: it is a set-theoretical structure from which one can construct semantics whose ontological commitments correspond exactly to a given ontological view. I will define five ontological frameworks corresponding respectively to: (i) predicate nominalism, (ii) resemblance nominalism, (iii) armstrongian realism, (iv) platonic realism, and (v) tropism. From those different frameworks, I will construct different semantics for first-order and second-order languages. Notably I will present different kinds of nominalist semantics for second-order languages, showing thus that we can perfectly quantify over properties and relations while being ontologically committed only to individuals. I will show in what extent those semantics differ from each other; it will make clear how the disagreements between the ontological views extend from ontology to logic, and thus why endorsing an ontological view should have an impact on the kind of logic one should use. (shrink)

One of the tasks of ontology in information science is to support the classification of entities according to their kinds and qualities. We hold that to realize this task as far as entities such as material objects are concerned we need to distinguish four kinds of entities: substance particulars, quality particulars, substance universals, and quality universals. These form, so to speak, an ontological square. We present a formal theory of classification based on this idea, including both a semantics for the (...) theory and a provably sound axiomatization. (shrink)

Formal views of autonomy rule out substantive rational capacities (reasons-responsiveness) as a condition of autonomous agency. I argue that such views face a number of underappreciated problems: they have trouble making sense of how autonomous agents could be robustly responsible for their choices, face the burden of explaining why there should be a stark distinction between the importance of factual and evaluative information within autonomous agency, and leave it mysterious why autonomy is the sort of thing that has value and (...) ought to be promoted. Moreover, I argue that the alternative view that includes substantive rational capacities need not have the unacceptable political implications it is sometimes thought to have. (shrink)

This paper introduces the special issue on Formal Approaches to the Ontological Argument of the Journal of Applied Logics (College Publications). The issue contains the following articles: Formal Approaches to the Ontological Argument, by Ricardo Sousa Silvestre and Jean-Yves Béziau; A Brief Critical Introduction to the Ontological Argument and its Formalization: Anselm, Gaunilo, Descartes, Leibniz and Kant, by Ricardo Sousa Silvestre; A Mechanically Assisted Examination of Begging the Question in Anselm’s Ontological Argument, by John Rushby; A Tractarian Resolution to (...) the Ontological Argument, by Erik Thomsen; On Kant’s Hidden Ambivalence Toward Existential Generalization in his Critique of the Ontological Argument, by Giovanni Mion; The Totality of Predicates and the Possibility of the Most Real Being, by Srećko Kovač; An Even More Leibnizian Version of Gödel’s Ontological Argument, by Kordula Świętorzecka and Marcin Łyczak; A Case Study On Computational Hermeneutics: E. J. Lowe’s Modal Ontological Argument, by David Fuenmayor. (shrink)

In this text I propose a formal framework for the study of phenomenal objectness - the distinction in an a priori undifferenciated experience of the phenomenal field of certain 'objects'. The purpose of this framework is to represent (even partially) the reality of phenomenal experience in its structure (which participates conceptually to consciousness as such) and at the same time to allow the production of a tractable formalism in order to search for a mathematical explanation for the fundamental phenomenon of (...) objectness. The constitution of this framework is based on intuitions from consciousness literature as well as the recent integrated information theory. Before coming to the framework's definition, I analyse this theory from the point of view of the discourse, through concepts that I introduce here (statical and dynamical phases of the discourse), and explain some severe epistemic difficulties it encounters. The definition of a general combination criterion for the inter-discourse between philosophy and mathematics (which is necessary for the project of explaining consciousness scientifically) in these terms leads in this text to disentangle this theory into the proposed framework. (shrink)

One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated differentials and a version of the multivariable chain rule which iterates to any desired level of derivative. We first present this material informally, and later discuss how to make it rigorous (a discussion which touches on formal foundations of calculus). We also suggest a finite calculus chain rule (contrary to Graham, Knuth (...) and Patashnik's claim that "there's no corresponding chain rule of finite calculus"). (shrink)

By separating the general concept of truth into syntactic truth and semantic truth, this article proposes a new theory of truth to explain several paradoxes like the Liar paradox, Card paradox, Curry’s paradox, etc. By revealing the relationship between syntactic /semantic truth and being-nothing-becoming which are the core concepts of dialectical logic, it is able to formalize dialectical logic. It also provides a logical basis for complexity theory by transferring all reasoning into a directed (cyclic/acyclic) graph which explains both paradoxical (...) and paradox-free reasoning. The different structure between cyclic graphs and acyclic graphs is the key to understanding paradoxes. By explaining the immanent between logic, paradox, and cellular automata, it also illustrates dialectical logic as ontology. (shrink)

Ontology and theology cannot be combined if ontology excludes non physical causes. This paper examines some possibilities for ontology to be combined with theology in so far as non physical causes are permitted. The paper builds on metaphysical findings that shows that separate ontological domains can interact causally indirectly via interfaces. As interfaces are not universes a first universe is allowed to be caused by an interface without violating the principle of causal closure of any universe. Formal theology can therefore (...) be based on the assumption that the (first) universe is caused by God if God is defined as the first cause. Given this, formal theology and science can have the same ontological base. (shrink)

A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements about a (...) quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics. (shrink)

The central hypothesis of the collaboration between Language and Computing (L&C) and the Institute for Formal Ontology and Medical Information Science (IFOMIS) is that the methodology and conceptual rigor of a philosophically inspired formal ontology will greatly benefit software application ontologies. To this end LinKBase®, L&C’s ontology, which is designed to integrate and reason across various external databases simultaneously, has been submitted to the conceptual demands of IFOMIS’s Basic Formal Ontology (BFO). With this, we aim to move beyond the level (...) of controlled vocabularies to yield an ontology with the ability to support reasoning applications. (shrink)

Recent debate about the error theory has taken a ‘formal turn’. On the one hand, there are those who argue that the error theory should be rejected because of its difficulties in providing a convincing formal account of the logic and semantics of moral claims. On the other hand, there are those who claim that such formal objections fail, maintaining that arguments against the error theory must be of a substantive rather than a formal kind. In this paper, we argue (...) that formal objections to the error theory cannot be eschewed but must be met head-on. (shrink)

This contribution unfolds an existential-ontological response to the question of sexual difference in the context of Heidegger’s formally indicative concept of “Dasein.” The question of Dasein’s “neutrality” concerns how formal indication formalizes, empties, and neutralizes the givenness of factical human existence. Ostensibly “given” biological and anthropological facts, such as sexual difference, are interpreted from an emptied and neutralized perspective that appears abstract and fictional to Heidegger’s critics. How, then, is the “neutrality” of formalizing emptying related to the “facticity” of in (...) each case factically existing as a sexual and gendered being? The answer lies in Heidegger’s elucidation of the existential-ontological structure of Dasein: Dasein is always relationally instituted in its factical entangled life through “being-with.” The sexual difference of human existence is not merely biologically or anthropologically given, but disclosed and enacted according to one’s relations with others, the environment, and oneself. The formally indicating concept “Dasein” indicates, accordingly, the concrete diversity and plurality of individuated sexual and gendered ways of being. (shrink)

When we ask ourselves about the meaning of life, two analyses are possible in principle: 1. that we are asking something about the purpose or the reason of being of life or of a life, or 2. that we are asking something the value of life or of a life. At the present article, I do not approach 1 neither the life as a whole, but I take the individual lives in the context of 2. I briefly explain what would (...) be to someone to have an objectivist conception of the meaning of life and what would be to someone to have a subjectivist one; and, then, I try to show how we can think in formulas that can capture the intuitions of those conceptions, without acquiring commitment with none of them. My way is to show that both objectivist and subjectivist conceptions think the meaning of life as related to projects or realizations that fulfill principles of value (the value can be objective or subjective according to the adopted conception), and ten I try to indicate that the projects or realizations from a person’s life come together through a simple sum to make the meaning of life of such a person’s life. The way I suggested for us to find the value of one of those realizations does not seem to present none theoretical problem. But the simple sum of realizations (and/or projects) to represent the value of the meaning of a person’s life simply did not work. That’s because it seems to lack some kind of index that is able to formalize the relations between realizations. Thus, although we couldn’t properly formalize the relation between the realizations that achieve the meaning of someone’s life at a certain moment, we get a good intuitive formalization of the value of a realization and we hope to have started an interesting investigation for future logicians, metaphysicians, mathematicians and theorists of value. (shrink)

This article outlines the basics of Robert S. Hartman's theory of formal axiology.

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

Two senses of ‘ontology’ can be distinguished in the current literature. First is the sense favored by information scientists, who view ontologies as software implementations designed to capture in some formal way the consensus conceptualization shared by those working on information systems or databases in a given domain. [Gruber 1993] Second is the sense favored by philosophers, who regard ontologies as theories of different types of entities (objects, processes, relations, functions) [Smith 2003]. Where information systems ontologists seek to maximize reasoning (...) efficiency even at the price of simplifications on the side of representation, philosophical ontologists argue that representational adequacy can bring benefits for the stability and resistance to error of an ontological framework and also for its extendibility in the future. In bioinformatics, however, a third sense of ‘ontology’ has established itself, above all as a result of the successes of the Gene Ontology (hereafter: GO), which is a tool for the representation and processing of information about gene products and their biological functions [Gene Ontology Consortium 2000]. We show how Basic Formal Ontology (BFO) has established itself as an overarching ontology drawing on all three of the strands distinguished above, and describe applications of BFO especially in the treatment of biological granularity. (shrink)

Etiquette and other merely formal normative standards like legality, honor, and rules of games are taken less seriously than they should be. While these standards are not intrinsically reason-providing in the way morality is often taken to be, they also play an important role in our practical lives: we collectively treat them as important for assessing the behavior of ourselves and others and as licensing particular forms of sanction for violations. This chapter develops a novel account of the normativity of (...) formal standards where the role they play in our practical lives explains a distinctive kind of reason to obey them. We have this kind of reason to be polite because etiquette is important to us. We also have this kind of reason to be moral because morality is important to us. This parallel suggests that the importance we assign to morality is insufficient to justify it being substantive. (shrink)

Cidadania Formal e Cidadania Real: Divergências e Direitos Infantis -/- 1 Introdução sobre o que seria cidadania -/- Para o clássico sociólogo francês Durkheim, a ideia de cidadania é questão de coesão social, isto é, essa coesão social nada mais é do que uma ideia de um Estado que mantém os indivíduos unidos (mais parecido com a ideia do fascismo em seus primórdios, que consistia basicamente na união do povo como um feixe), integrados a um grupo social, ou simplesmente, um (...) Estado de integração coesa do grupo social. Isso nos dá uma ideia genérica do que seria um cidadão para o pensador. -/- Na perspectiva de sociedade como um conjunto integrado, Dallari afirma que a sociedade humana é um conjunto de pessoas, ligadas entre si pela necessidade de se ajudarem umas às outras… a fim de que possam garantir a continuidade da vida e satisfazer seus interesses e desejos . -/- Já constitucionalmente, a cidadania está ligada ao direito, e a mesma é garantida e estabelecida em lei conforme a Constituição de um determinado país. O conceito, tal qual aceitado nas Ciências Sociais, é definido a partir dos conjuntos de direitos e deveres que foram conquistados ao longo de anos, mediante insistentes lutas para garantir e assegurar esses direitos. A cidadania também está ligada às condições sociais e locais dos indivíduos. Nessa perspectiva, a cidadania como estudo praxista, é dividida em duas esferas sociais divergenciadas em toda sua totalidade: Cidadania Formal e Cidadania Real. Logo, faz-se necessário desmembrar acerca de ambas para uma melhor análise e compreensão do texto. -/- 2 Breve divergência acerca das cidadanias formal e real -/- Sob um estudo superficial acerca do tema, podemos conceituar a cidadania formal como sendo a cidadania descrita em papel, isto é, a cidadania como ela deveria ser teoricamente, descrita sob lei universal onde descreve a igualdade entre todos, liberdade dos indivíduos e que garante a capacidade de lutar pelos direitos através do âmbito jurídico. Exemplo: o Estado deve priorizar proteção física, psicológica, etc a crianças e adolescentes, bem como outros direitos, como educação básica de qualidade conforme prescrita no ECA (Estatuto da Criança e do Adolescente). Uma vez que o Estado desobedeça tais regras constitucionais, o mesmo fere a universalidade dos direitos dos seus cidadãos que estão assegurados em lei. Então, pela cidadania formal, tais cidadãos negligenciados pelo governo, podem lutar pela proteção, educação, etc dos indivíduos que compõem a comunidade territorial, uma vez que a cidadania formal garante a possibilidade de luta pelos direitos no espaço jurídico. -/- Segundo Correa a cidadania formal nada mais é do que, conforme o direito universal, um indicativo de nacionalidade . Ainda ressalta que o termo ganha mais relevância no campo das Ciências Sociais e que se define mediante a posse dos direitos civis, políticos e sociais. A cidadania formal para a conformação infantil brasileira é platônica, isto é, está mais ligada a ideia utópica de teoria das ideias teóricas do que esperava-se da vida pragmática dessas crianças. -/- Em contrapartida, a cidadania real, por vezes alcunhada de substantiva, está ligada a vida tal qual ela é vivenciada; em termos sociais é concernente a vida pragmática dos indivíduos, em que os mesmos participam da arenga social, do debate de ideias, etc. Em contradição a formal que diz que todos os indivíduos são iguais, na vida real é observada uma sociedade estruturada sob uma divergência totalitária em diferentes ordens, seja a social, monetária, educacional, política, cultural, etc e, com isso, é levado ao grande problema social do Brasil e demais países, em que determinados grupos ditos “inferiores” sofrem os mais diversos tipos de preconceito. -/- É na cidadania real que se explicita todas as contradições sociais entre brancos e negros, ricos e pobres, homens e mulheres, etc. Por lei, todos esses indivíduos de diferentes classes e status social como elenca Marshall, são iguais e, por fim, são cidadãos aptos a receber os mesmos tratos, os mesmos privilégios, etc, só que no Brasil, como em demais países brancos agridem verbalmente e fisicamente os negros que todos os dias sofrem racismos e preconceitos; pobres ficam cada vez mais pobres, uma vez que o dinheiro cada vez se concentra nas mãos dos mais ricos e com maior poder e influência social e mulheres que trabalham igual ou até mais que os homens e não recebem o mesmo salário por serem “inferiores” dentro da cultura e sociedade machista e patriarcalista. -/- Exemplo claro: Um estudante de ensino público que não consegue pleitear uma competição em condições de igualdade com um estudante de ensino privado, tem sua cidadania “formal” conquistada, uma vez que a lei lhe garante acesso à educação de boa qualidade tal qual oferecida em escolas particulares, contudo, a cidadania “real” está bem longe de ser alcançada. E o mesmo acontece com negros e deficientes que conquistaram direitos formalmente, todavia tem um longo caminho para alcançar a cidadania real. Para que todos os indivíduos possam assegurar e garantir seus direitos na vida pragmática, direitos pelo qual encontram-se previstos em lei pela cidadania formal, é necessário uma “luta” entre os divergentes grupos sociais, como dizia Karl Marx, visando a justiça e a soberania social. -/- 3 Cidadania e Direitos Infantis -/- Para garantir e assegurar uma melhor faculdade de vida para as crianças -e também adolescentes-, bem como caucionar os direitos dos mesmos como cidadãos, a partir de 1990, pós Constituição brasileira, entrou em firmeza o ECA -Estatuto da Criança e do Adolescente-. Na produção e institucionalização do ECA, priorizou-se a ideia de que as crianças estão em processo de desenvolvimento e, com isso, demandam de mais necessidades específicas que demais camadas etárias, e que tais necessidades devem ser identificadas e respeitadas, sobretudo pelas leis. -/- Com toda essa institucionalização de direitos infantis, a camada etária de até 12 anos de idade -crianças-, passaram a ter adjutório integral reconhecida por lei como um direito. E que, a partir de tais prescritos, nenhuma criança pode sofrer violência das mais variadas possíveis, nenhum tipo de negligência, falta de cuidado, certo tipos de crueldade, discriminação, nenhum tipo de preconceito e nenhum tipo de exploração seja para trabalho ou demais áreas e que cabem aos adultos respeitar e fazer valer as regras estabelecidas pelo ECA. -/- O ECA, institucionalizou e definiu os direitos à vida, ao lazer, à nutrição, à liberdade, à altivez, à educação de boa qualidade, à profissionalização, ao respeito acima de tudo, à cultura e ao convívio e vivenciamento familiar e em comunhão. Não obstante, mesmo com todos esses direitos assegurados e garantidos em lei, crianças de todo os países sofrem por faltas de cuidados, sobretudo pelos pais e que gera um grande problema social que é o do suicídio; crianças são exploradas para labotar nos mais diversos ramos e até mesmo na prostituição; crianças são vítimas de violência e agressões físicas e verbais em casa ou na escola; crianças se envolvem com o tráfico e uso de drogas e entorpecentes; enfim, cabe aos familiares e ao Estado, garantir a integridade física e mental da camada infantil, com acompanhamento pedagógico, psicológico, etc, e que punam os responsáveis pela denigração física, motora e mental das crianças. -/- O que nos leva a questões de discussão social. As crianças gozam de todos os direitos essenciais inerentes à pessoa humana? “Menores drogados ameaçam quem passa pelo entorno da Rodoviária Laura Machado | Rio+ | 19/06/2011 10h33” -/- Esses menores, não têm direito real à cidadania? Como explanado anteriormente, a comunidade de infantes está amparada pelas leis e instituições do ECA em todo o país, no entanto, cabe aos adultos garantir a prioridade e o acompanhamento desses menores que, com toda a maldade do mundo e propriamente das pessoas, perdem o direito de gozar de sua infância. -/- . (shrink)