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Introduction to symbolic logic and its applications

New York,: Dover Publications (1958)

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  1. Nuel Belnap on Indeterminism and Free Action.Thomas Müller (ed.) - 2014 - Wien, Austria: Springer.
    This volume seeks to further the use of formal methods in clarifying one of the central problems of philosophy: that of our free human agency and its place in our indeterministic world. It celebrates the important contributions made in this area by Nuel Belnap, American logician and philosopher. Philosophically, indeterminism and free action can seem far apart, but in Belnap’s work, they are intimately linked. This book explores their philosophical interconnectedness through a selection of original research papers that build forth (...)
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  • Carnapian frameworks.Gabriel L. Broughton - 2021 - Synthese 199 (1-2):4097-4126.
    Carnap’s seminal ‘Empiricism, Semantics and Ontology’ makes important use of the notion of a framework and the related distinction between internal and external questions. But what exactly is a framework? And what role does the internal/external distinction play in Carnap’s metaontology? In an influential series of papers, Matti Eklund has recently defended a bracingly straightforward interpretation: A Carnapian framework, Eklund says, is just a natural language. To ask an internal question, then, is just to ask a question in, say, English. (...)
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  • The Epistemic Significance of Valid Inference – A Model-Theoretic Approach.Constantin C. Brîncuș - 2015 - In Sorin Costreie & Mircea Dumitru (eds.), Meaning and Truth. Pro Universitaria. pp. 11-36.
    The problem analysed in this paper is whether we can gain knowledge by using valid inferences, and how we can explain this process from a model-theoretic perspective. According to the paradox of inference (Cohen & Nagel 1936/1998, 173), it is logically impossible for an inference to be both valid and its conclusion to possess novelty with respect to the premises. I argue in this paper that valid inference has an epistemic significance, i.e., it can be used by an agent to (...)
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  • Formal Ontology and Conceptual Realism.Nino Barnabas Cocchiarella - 2007 - Dordrecht, Netherland: Springer.
    Theories about the ontological structure of the world have generally been described in informal, intuitive terms. This book offers an account of the general features and methodology of formal ontology. The book defends conceptual realism as the best system to adopt based on a logic of natural kinds. By formally reconstructing an intuitive, informal ontological scheme as a formal ontology we can better determine the consistency and adequacy of that scheme.
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  • New remarks on the cosmological argument.Gustavo E. Romero & Daniela Pérez - 2012 - International Journal for Philosophy of Religion 72 (2):103-113.
    We present a formal analysis of the Cosmological Argument in its two main forms: that due to Aquinas, and the revised version of the Kalam Cosmological Argument more recently advocated by William Lane Craig. We formulate these two arguments in such a way that each conclusion follows in first-order logic from the corresponding assumptions. Our analysis shows that the conclusion which follows for Aquinas is considerably weaker than what his aims demand. With formalizations that are logically valid in hand, we (...)
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  • Interconnection of the Lattices of Extensions of Four Logics.Alexei Y. Muravitsky - 2017 - Logica Universalis 11 (2):253-281.
    We show that the lattices of the normal extensions of four well-known logics—propositional intuitionistic logic \, Grzegorczyk logic \, modalized Heyting calculus \ and \—can be joined in a commutative diagram. One connection of this diagram is an isomorphism between the lattices of the normal extensions of \ and \; we show some preservation properties of this isomorphism. Two other connections are join semilattice epimorphims of the lattice of the normal extensions of \ onto that of \ and of the (...)
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  • Identity, Individuation and Substance.David Wiggins - 2012 - European Journal of Philosophy 20 (1):1-25.
    The paper takes off from the problem of finding a proper content for the relation of identity as it holds or fails to hold among ordinary things or substances. The necessary conditions of identity are familiar, the sufficient conditions less so. The search is for conditions at once better usable than the Leibnizian Identity of Indiscernibles (independently suspect) and strong enough to underwrite all the formal properties of the relation.It is contended that the key to this problem rests at the (...)
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  • Carnapian and Tarskian semantics.Pierre Wagner - 2017 - Synthese 194 (1):97-119.
    Many papers have been devoted to the semantic turn Carnap took in the late 1930s after Tarski had explained to him his method for defining truth and his work on the establishment of scientific semantics. Commentators have often argued that the major turn in Carnap’s approach to languages had already been taken in the Logical Syntax of Language, but they have usually assumed that Carnap was happy to subsequently follow Tarski and adopt Tarskian semantics. In this paper, it is argued (...)
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  • What Became of Russell's "Relation-Arithmetic"?Graham Solomon - 1989 - Russell: The Journal of Bertrand Russell Studies 9 (2):168.
  • Experimental Explication.Jonah N. Schupbach - 2017 - Philosophy and Phenomenological Research 94 (3):672-710.
    Two recently popular metaphilosophical movements, formal philosophy and experimental philosophy, promote what seem to be conflicting methodologies. Nonetheless, I argue that the two can be mutually supportive. I propose an experimentally-informed variation on explication, a powerful formal philosophical tool introduced by Carnap. The resulting method, which I call “experimental explication,” provides the formalist with a means of responding to explication's gravest criticism. Moreover, this method introduces a philosophically salient, positive role for survey-style experiments while steering clear of several objections that (...)
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  • Axioms in Mathematical Practice.Dirk Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.
    On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. The distinctions introduced aim at (...)
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  • Some problems concerning language and physics.Adonai Sant’Anna & Gabriel Guerrer - 2007 - Synthese 154 (3):467-484.
    We discuss three problems concerning the use of formal languages in theoretical physics: (i) the definability of time and spacetime in classical physical theories; (ii) how to cope with indistinguishable elementary particles in quantum mechanics without labeling them; and (iii) how to get a formal picture of quantum states jumping.
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  • The philosophy of Hans Reichenbach.Wesley C. Salmon - 1977 - Synthese 34 (1):5 - 88.
  • From Change to Spacetime: An Eleatic Journey.Gustavo E. Romero - 2013 - Foundations of Science 18 (1):139-148.
    I present a formal ontological theory where the basic building blocks of the world can be either things or events. In any case, the result is a Parmenidean worldview where change is not a global property. What we understand by change manifests as asymmetries in the pattern of the world-lines that constitute 4-dimensional existents. I maintain that such a view is in accord with current scientific knowledge.
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  • A Formal Ontological Theory Based on Timeless Events.Gustavo E. Romero - 2016 - Philosophia 44 (2):607-622.
    I offer a formal ontological theory where the basic building blocks of the world are timeless events. The composition of events results in processes. Spacetime emerges as the system of all events. Things are construed as bundles of processes. I maintain that such a view is in accord with General Relativity and offers interesting prospects for the foundations of classical and quantum gravity.
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  • François Recanati's Oratio Obliqua, Oratio Recta: An Essay on Metarepresentation. [REVIEW]Kirk Ludwig - 2003 - Philosophy and Phenomenological Research 66 (2):481-488.
    Among the entities that can be mentally or linguistically represented are mental and linguistic representations themselves. That is, we can think and talk about speech and thought. This phenomenon is known as metarepresentation. An example is "Authors believe that people read books." -/- In this book François Recanati discusses the structure of metarepresentation from a variety of perspectives. According to him, metarepresentations have a dual structure: their content includes the content of the object-representation (people reading books) as well as the (...)
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  • Can Church’s thesis be viewed as a Carnapian explication?Paula Quinon - 2019 - Synthese 198 (Suppl 5):1047-1074.
    Turing and Church formulated two different formal accounts of computability that turned out to be extensionally equivalent. Since the accounts refer to different properties they cannot both be adequate conceptual analyses of the concept of computability. This insight has led to a discussion concerning which account is adequate. Some authors have suggested that this philosophical debate—which shows few signs of converging on one view—can be circumvented by regarding Church’s and Turing’s theses as explications. This move opens up the possibility that (...)
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  • Plural descriptions and many-valued functions.Alex Oliver & Timothy Smiley - 2005 - Mind 114 (456):1039-1068.
    Russell had two theories of definite descriptions: one for singular descriptions, another for plural descriptions. We chart its development, in which ‘On Denoting’ plays a part but not the part one might expect, before explaining why it eventually fails. We go on to consider many-valued functions, since they too bring in plural terms—terms such as ‘4’ or the descriptive ‘the inhabitants of London’ which, like plain plural descriptions, stand for more than one thing. Logicians need to take plural reference seriously (...)
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  • Structuralism, model theory and reduction.Karl-Georg Niebergall - 2002 - Synthese 130 (1):135 - 162.
    In this paper, the (possible) role of model theory forstructuralism and structuralist definitions of ``reduction'' arediscussed. Whereas it is somewhat undecisive with respect tothe first point – discussing some pro's and con's ofthe model theoretic approach when compared with a syntacticand a structuralist one – it emphasizes that severalstructuralist definitions of ``reducibility'' do not providegenerally acceptable explications of ``reducibility''. This claimrests on some mathematical results proved in this paper.
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  • Michel Serres: Divergences.Marla Beth Morris - 2022 - Educational Philosophy and Theory 54 (4):362-374.
    In order to show how Michel Serres’s work diverges from traditional Western philosophy, this article explores a multitude of texts and contexts against which Serres might be better understood. Most starkly, Serres’s work diverges from the eighteenth and nineteenth century Germanic tradition of Bildung, meaning cultivation through introspection, apolitical thought and character building through education. Serres’s moves away from ego-centric thought to eco-centric thought more akin to what Gregory Bateson called an ecology of mind. That is, Serres’s integrates—in a more (...)
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  • Three paradoxes of medical diagnosis.G. William Moore & Grover M. Hutchins - 1981 - Metamedicine 2 (2):197-215.
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  • Three paradoxes of medical diagnosis.G. William Moore & Grover M. Hutchins - 1987 - Theoretical Medicine and Bioethics 2 (2):197-215.
    Sadegh-zadeh [23] has proposed a theory of the relativity of medical diagnosis in terms of the time at which a diagnosis is accepted, the patient to whom the diagnosis applies, the physician who renders the diagnosis, the medical knowledge used, the diagnostic method applied, and the set of patient observations. Use of classical formal logic as the diagnostic method may result in three paradoxes: the paradoxes of consistency, completeness, and justifiable ignorance. These paradoxes may be resolved by the addition of (...)
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  • François Recanati's Oratio Obliqua, Oratio Recta: An Essay on Metarepresentation[REVIEW]Kirk Ludwig - 2003 - Philosophy and Phenomenological Research 66 (2):481-488.
    The book is divided into twenty chapters, divided in turn into six parts. Parts I-III contain the main positive account of metarepresentations. The main semantic thesis of parts I-III is that metarepresentational sentences are not relational, but involve a metarepresentational operator applied to a sentence which functions in its usual way, but which is evaluated relative to a “shifted circumstance” in use. This is supposed to represent a novel account of the semantics of attitude sentences that preserves “semantic innocence” and (...)
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  • Frege, Carnap, and Explication: ‘Our Concern Here Is to Arrive at a Concept of Number Usable for the Purpose of Science’.Gregory Lavers - 2013 - History and Philosophy of Logic 34 (3):225-41.
    This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the (...)
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  • Carnap’s surprising views on the axiom of infinity.Gregory Lavers - 2016 - Metascience 25 (1):37-41.
  • Nondirected light signals and the structure of time.Robert W. Latzer - 1972 - Synthese 24 (1-2):236 - 280.
    Temporal betweenness in space-time is defined solely in terms of light signals, using a signalling relation that does not distinguish between the sender and the receiver of a light signal. Special relativity and general relativity are considered separately, because the latter can be treated only locally. We conclude that the (local) coherence of time can be described if we know only which pairs of space-time points are light-connected. Other consequences in the case of special relativity: (1) a categorical axiom system (...)
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  • Isomorphism in information-carrying systems.John Kulvicki - 2004 - Pacific Philosophical Quarterly 85 (4):380-395.
    For the information theorist, the lawful generalizations that subsume instantiations of properties in the environment and instantiations of properties of perceptual representations determine the latter's content. Perceptual representations are also commonly thought to be isomorphic to what they represent, which presents the information theorist with a puzzle. What role could isomorphism play in perceptual representation when lawful generalizations determine content? I show that in order for the information that they carry to be available to cognition, perceptual representations must be isomorphic (...)
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  • On reduction of theories.Andreas Kamlah - 1985 - Erkenntnis 22 (1-3):119 - 142.
  • Who's afraid of absolute space?John Earman - 1970 - Australasian Journal of Philosophy 48 (3):287-319.
  • Can the Pessimistic Induction be Saved from Semantic Anti-Realism about Scientific Theory?Greg Frost-Arnold - 2014 - British Journal for the Philosophy of Science 65 (3):521-548.
    Scientific anti-realists who appeal to the pessimistic induction (PI) claim that the theoretical terms of past scientific theories often fail to refer to anything. But on standard views in philosophy of language, such reference failures prima facie lead to certain sentences being neither true nor false. Thus, if these standard views are correct, then the conclusion of the PI should be that significant chunks of current theories are truth-valueless. But that is semantic anti-realism about scientific discourse—a position most philosophers of (...)
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  • Suppes predicates for space-time.Newton C. A. Costa, Otávio Bueno & Steven French - 1997 - Synthese 112 (2):271-279.
    We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field. Our approach was inspired by the work of Whitehead, though our (...)
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  • Kotarbiński’s reism and the vienna circle.Francesco Coniglione - 2000 - Axiomathes 11 (1 - 3):37-69.
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  • A Theory of Sentience.Austen Clark (ed.) - 2000 - New York: Oxford University Press.
    Drawing on the findings of neuroscience, this text proposes and defends the hypothesis that the various modalities of sensation share a generic form that the author, Austen Clark, calls feature-placing.
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  • Truth Diagrams Versus Extant Notations for Propositional Logic.Peter C.-H. Cheng - 2020 - Journal of Logic, Language and Information 29 (2):121-161.
    Truth diagrams are introduced as a novel graphical representation for propositional logic. To demonstrate their epistemic efficacy a set of 28 concepts are proposed that any comprehensive representation for PL should encompass. TDs address all the criteria whereas seven other existing representations for PL only provide partial coverage. These existing representations are: the linear formula notation, truth tables, a PL specific interpretation of Venn Diagrams, Frege’s conceptual notation, diagrams from Wittgenstein’s Tractatus, Pierce’s alpha graphs and Gardner’s shuttle diagrams. The comparison (...)
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  • Continuity in Semantic Theories of Programming.Felice Cardone - 2015 - History and Philosophy of Logic 36 (3):242-261.
    Continuity is perhaps the most familiar characterization of the finitary character of the operations performed in computation. We sketch the historical and conceptual development of this notion by interpreting it as a unifying theme across three main varieties of semantical theories of programming: denotational, axiomatic and event-based. Our exploration spans the development of this notion from its origins in recursion theory to the forms it takes in the context of the more recent event-based analyses of sequential and concurrent computations, touching (...)
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  • A reappraisal of the concept of 'culture'.Larry Brownstein - 1995 - Social Epistemology 9 (4):311 – 351.
    Abstract This investigation considers a number of approaches to the definition and analysis of ?culture?. It shows that although approaches to culture span a wide range of viewpoints, there are gems that can be distilled and developed. To that end, a definition of ?culture? is proposed that it is contended captures much of the positive character in what has preceded it and hopefully avoids the negative. This is followed by a discussion of some of the most important studies concerned with (...)
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  • On Gupta's book the logic of common nouns.Aldo Bressan - 1993 - Journal of Philosophical Logic 22 (4):335 - 383.
    Gupta's book [9] contains a theory of modal logic that is closely related to my modal language ML v [2], and his theory is used to treat some interesting philosophical problems. Hence, it is natural for me to review this valuable book and to concentrate on its logics, the more so as its use has already been spoken of and appreciated by Kapitan [10], although I cannot but share his appreciation.
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  • A Presuppositional Account of Causal and Temporal Interpretations of and.Joanna Blochowiak - 2016 - Topoi 35 (1):93-107.
    Despite extensive studies, the issue concerning the pragmatic mechanisms leading to causal and temporal interpretations of and remains problematic and has not yet been addressed in its totality within one framework. This paper proposes a solution based on presuppositional mechanisms built into a comprehensive analysis that accounts for both the various interpretations of and-sentences as well as those of other types of sentences involving similar interpretations. This account is a specific part of a unified solution to the knotty problem of (...)
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  • Temporally symmetric causal relations in Minkowski space-time.George Berger - 1972 - Synthese 24 (1-2):58 - 73.
  • Dispositional Essentialism and the Nature of Powerful Properties.William A. Bauer - 2013 - Disputatio 5 (35):1-19.
    Dispositional essentialism maintains that all sparse properties are essentially powerful. Two conceptions of sparse properties appear compatible with dispositional essentialism: sparse properties as pure powers or as powerful qualities. This paper compares the two views, criticizes the powerful qualities view, and then develops a new theory of pure powers, termed Point Theory. This theory neutralizes the main advantage powerful qualities appear to possess over pure powers—explaining the existence of powers during latency periods. The paper discusses the relation between powers and (...)
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  • Perceptual symbol systems.Lawrence W. Barsalou - 1999 - Behavioral and Brain Sciences 22 (4):577-660.
    Prior to the twentieth century, theories of knowledge were inherently perceptual. Since then, developments in logic, statis- tics, and programming languages have inspired amodal theories that rest on principles fundamentally different from those underlying perception. In addition, perceptual approaches have become widely viewed as untenable because they are assumed to implement record- ing systems, not conceptual systems. A perceptual theory of knowledge is developed here in the context of current cognitive science and neuroscience. During perceptual experience, association areas in the (...)
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  • Semantic holism in scientific language.Holger Andreas - 2010 - Philosophy of Science 77 (4):524-543.
    Whether meaning is compositional has been a major issue in linguistics and formal philosophy of language for the last 2 decades. Semantic holism is widely and plausibly considered as an objection to the principle of semantic compositionality therein. It comes as a surprise that the holistic peculiarities of scientific language have been rarely addressed in formal accounts so far, given that semantic holism has its roots in the philosophy of science. For this reason, a model-theoretic approach to semantic holism in (...)
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  • Semantic Challenges to Scientific Realism.Holger Andreas - 2011 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 42 (1):17 - 31.
    This paper is concerned with connections between scientific and metaphysical realism. It is not difficult to show that scientific realism, as expounded by Psillos (1999) clearly qualifies as a kind of metaphysical realism in the sense of Putnam (1980). The statement of scientific realism therefore must not only deal with underdetermination and the dynamics of scientific theories but also answer the semantic challenges to metaphysical realism. As will be argued, the common core of these challenges is the proposition that a (...)
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  • A modal view of the semantics of theoretical sentences.Holger Andreas - 2010 - Synthese 174 (3):367 - 383.
    Modal logic has been applied in many different areas, as reasoning about time, knowledge and belief, necessity and possibility, to mention only some examples. In the present paper, an attempt is made to use modal logic to account for the semantics of theoretical sentences in scientific language. Theoretical sentences have been studied extensively since the work of Ramsey and Carnap. The present attempt at a modal analysis is motivated by there being several intended interpretations of the theoretical terms once these (...)
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  • Quantifiers, Quantifiers, and Quantifiers. Themes in Logic, Metaphysics, and Language. (Synthese Library vol. 373).Alessandro Torza (ed.) - 2015 - Springer.
    This volume covers a wide range of topics that fall under the 'philosophy of quantifiers', a philosophy that spans across multiple areas such as logic, metaphysics, epistemology, and even the history of philosophy. It discusses the import of quantifier variance in the model theory of mathematics. It advances an argument for the uniqueness of quantifier meaning in terms of Evert Beth’s notion of implicit definition, and clarifies the oldest explicit formulation of quantifier variance: the one proposed by Rudolf Carnap. -/- (...)
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  • Space-time as a primitive for space and motion.Philippe Muller - 1998 - In Nicola Guarino (ed.), Formal Ontology in Information Systems. Ios Press. pp. 63-76.
  • Ontology and Information Systems (2004).Barry Smith - manuscript
    In a development that has still been hardly noticed by philosophers, a conception of ontology has been advanced in recent years in a series of extra-philosophical disciplines as researchers in linguistics, psychology, geography and anthropology have sought to elicit the ontological commitments (‘ontologies’, in the plural) of different cultures or disciplines. Exploiting the terminology of Quine, researchers in psychology and anthropology have sought to establish what individual human subjects, or entire human cultures, are committed to, ontologically, in their everyday cognition, (...)
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  • Mental imagery.Nigel J. T. Thomas - 2001 - Stanford Encyclopedia of Philosophy.
    Mental imagery (varieties of which are sometimes colloquially refered to as “visualizing,” “seeing in the mind's eye,” “hearing in the head,” “imagining the feel of,” etc.) is quasi-perceptual experience; it resembles perceptual experience, but occurs in the absence of the appropriate external stimuli. It is also generally understood to bear intentionality (i.e., mental images are always images of something or other), and thereby to function as a form of mental representation. Traditionally, visual mental imagery, the most discussed variety, was thought (...)
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  • Between abstraction and idealization: Scientific practice and philosophical awareness.Francesco Coniglione - 2004 - Poznan Studies in the Philosophy of the Sciences and the Humanities 82 (1):59-110.
    The aim of this essay is to emphasize a number of important points that will provide a better understanding of the history of philosophical thought concerning scientific knowledge. The main points made are: (a) that the principal way of viewing abstraction which has dominated the history of thought and epistemology up to the present is influenced by the original Aristotelian position; (b) that with the birth of modern science a new way of conceiving abstraction came into being which is better (...)
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  • Logical Truth / Logička istina (Bosnian translation by Nijaz Ibrulj).Nijaz Ibrulj & Willard Van Orman Quine - 2018 - Sophos 1 (11):115-128.
    Translated from: W.V.O.Quine, W. H. O. (1986): Philosophy of Logic. Second Edition. Harvard University Press. Cambridge, Massachusetts and London, England, 47-61.
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