Results for 'completeness'

127 found
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  1. The Completeness of Kant’s Metaphysical Exposition of Space.Henny Blomme - 2012 - Kant-Studien 103 (2):139-162.
    In the first edition of his book on the completeness of Kant’s table of judgments, Klaus Reich shortly indicates that the B-version of the metaphysical exposition of space in the Critique of pure reason is structured following the inverse order of the table of categories. In this paper, I develop Reich’s claim and provide further evidence for it. My argumentation is as follows: Through analysis of our actually given representation of space as some kind of object (the formal intuition (...)
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  2. Completeness of an Ancient Logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.
    In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...)
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  3.  98
    Post Completeness in Congruential Modal Logics.Peter Fritz - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic Volume 11. College Publications. pp. 288-301.
    Well-known results due to David Makinson show that there are exactly two Post complete normal modal logics, that in both of them, the modal operator is truth-functional, and that every consistent normal modal logic can be extended to at least one of them. Lloyd Humberstone has recently shown that a natural analog of this result in congruential modal logics fails, by showing that not every congruential modal logic can be extended to one in which the modal operator is truth-functional. As (...)
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  4. Completeness and Correspondence in Chellas–Segerberg Semantics.Matthias Unterhuber & Gerhard Schurz - 2014 - Studia Logica 102 (4):891-911.
    We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg – Chellas–Segerberg (CS) semantics – plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) non-trivial frame conditions in CS semantics which correspond to the 30 principles.
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  5. Laws and the Completeness of the Fundamental.Martin Glazier - 2016 - In Mark Jago (ed.), Reality Making. Oxford, UK: Oxford University Press. pp. 11-37.
    Any explanation of one fact in terms of another will appeal to some sort of connection between the two. In a causal explanation, the connection might be a causal mechanism or law. But not all explanations are causal, and neither are all explanatory connections. For example, in explaining the fact that a given barn is red in terms of the fact that it is crimson, we might appeal to a non-causal connection between things’ being crimson and their being red. Many (...)
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  6. Explanatory Completeness and Idealization in Large Brain Simulations: A Mechanistic Perspective.Marcin Miłkowski - 2016 - Synthese 193 (5):1457-1478.
    The claim defended in the paper is that the mechanistic account of explanation can easily embrace idealization in big-scale brain simulations, and that only causally relevant detail should be present in explanatory models. The claim is illustrated with two methodologically different models: Blue Brain, used for particular simulations of the cortical column in hybrid models, and Eliasmith’s SPAUN model that is both biologically realistic and able to explain eight different tasks. By drawing on the mechanistic theory of computational explanation, I (...)
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  7. Emergence, Downwards Causation and the Completeness of Physics.David Yates - 2009 - Philosophical Quarterly 59 (234):110 - 131.
    The 'completeness of physics' is the key premise in the causal argument for physicalism. Standard formulations of it fail to rule out emergent downwards causation. I argue that it must do this if it is tare in a valid causal argument for physicalism. Drawing on the notion of conferring causal power, I formulate a suitable principle, 'strong completeness'. I investigate the metaphysical implications of distinguishing this principle from emergent downwards causation, and I argue that categoricalist accounts of properties (...)
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  8. Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic.Richard Zach - 1999 - Bulletin of Symbolic Logic 5 (3):331-366.
    Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, (...)
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  9.  39
    Continuity and Completeness of Strongly Independent Preorders.David McCarthy & Kalle Mikkola - 2018 - Mathematical Social Sciences 93:141-145.
    A strongly independent preorder on a possibly in finite dimensional convex set that satisfi es two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfi es two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii') mixture continuity; and (iii') completeness. (...)
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  10.  16
    Algorithmic Correspondence and Completeness in Modal Logic. IV. Semantic Extensions of SQEMA.Willem Conradie & Valentin Goranko - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):175-211.
    In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several extensions (...)
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  11.  33
    Aggregation for General Populations Without Continuity or Completeness.David McCarthy, Kalle Mikkola & Teruji Thomas - 2017 - MPRA Paper No. 80820.
    We generalize Harsanyi's social aggregation theorem. We allow the population to be infi nite, and merely assume that individual and social preferences are given by strongly independent preorders on a convex set of arbitrary dimension. Thus we assume neither completeness nor any form of continuity. Under Pareto indifference, the conclusion of Harsanyi's theorem nevertheless holds almost entirely unchanged when utility values are taken to be vectors in a product of lexicographic function spaces. The addition of weak or strong Pareto (...)
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  12. The Completeness of Physics.David Spurrett - 1999 - Dissertation, University of Natal, Durban
    The present work is focussed on the completeness of physics, or what is here called the Completeness Thesis: the claim that the domain of the physical is causally closed. Two major questions are tackled: How best is the Completeness Thesis to be formulated? What can be said in defence of the Completeness Thesis? My principal conclusions are that the Completeness Thesis can be coherently formulated, and that the evidence in favour if it significantly outweighs that (...)
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  13. On the Causal Completeness of Physics.Agustín Vicente - 2006 - International Studies in the Philosophy of Science 20 (2):149 – 171.
    According to an increasing number of authors, the best, if not the only, argument in favour of physicalism is the so-called 'overdetermination argument'. This argument, if sound, establishes that all the entities that enter into causal interactions with the physical world are physical. One key premise in the overdetermination argument is the principle of the causal closure of the physical world, said to be supported by contemporary physics. In this paper, I examine various ways in which physics may support the (...)
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  14. Hypothetical Arguments and the Completeness of the Syllogistic.Tal Glezer - 2007 - Ancient Philosophy 27 (2):323-334.
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  15.  47
    Completeness of a First-Order Temporal Logic with Time-Gaps.Matthias Baaz, Alexander Leitsch & Richard Zach - 1996 - Theoretical Computer Science 160 (1-2):241-270.
    The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.
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  16. Completeness in the Theory of Properties, Relations, and Propositions.George Bealer - 1983 - Journal of Symbolic Logic 48 (2):415-426.
    Higher-order theories of properties, relations, and propositions are known to be essentially incomplete relative to their standard notions of validity. It turns out that the first-order theory of PRPs that results when first-order logic is supplemented with a generalized intensional abstraction operation is complete. The construction involves the development of an intensional algebraic semantic method that does not appeal to possible worlds, but rather takes PRPs as primitive entities. This allows for a satisfactory treatment of both the modalities and the (...)
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  17.  23
    Algorithmic Correspondence and Completeness in Modal Logic. V. Recursive Extensions of SQEMA.Willem Conradie, Valentin Goranko & Dimitar Vakarelov - 2010 - Journal of Applied Logic 8 (4):319-333.
    The previously introduced algorithm \sqema\ computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend \sqema\ with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of modal formulae in the extension of first-order logic with monadic least fixed-points \mffo. This computation operates by transforming input formulae into locally frame equivalent ones in the pure fragment of the hybrid mu-calculus. In particular, we prove that (...)
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  18.  27
    Completeness of a Hypersequent Calculus for Some First-Order Gödel Logics with Delta.Matthias Baaz, Norbert Preining & Richard Zach - 2006 - In 36th International Symposium on Multiple-valued Logic. May 2006, Singapore. Proceedings. Los Alamitos: IEEE Press.
    All first-order Gödel logics G_V with globalization operator based on truth value sets V C [0,1] where 0 and 1 lie in the perfect kernel of V are axiomatized by Ciabattoni’s hypersequent calculus HGIF.
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  19.  83
    Modal Logic with Names.George Gargov & Valentin Goranko - 1993 - Journal of Philosophical Logic 22 (6):607 - 636.
    We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ ⍯φ (...)
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  20. Physics and Fundamentality.Ney Alyssa - manuscript
    What justifies the allocation of funding to research in physics when many would argue research in the life and social sciences may have more immediate impact in transforming our world for the better? Many of the justifications for such spending depend on the claim that physics enjoys a kind of special status vis-a-vis the other sciences, that physics or at least some branches of physics exhibit a form of fundamentality. The goal of this paper is to articulate a conception of (...)
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  21. Variable Binding Term Operators.John Corcoran, William Hatcher & John Herring - 1972 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (12):177-182.
    Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic (...)
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  22.  35
    Hierarchies of Modal and Temporal Logics with Reference Pointers.Valentin Goranko - 1996 - Journal of Logic, Language and Information 5 (1):1-24.
    We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and (...)
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  23. Frege's Begriffsschrift is Indeed First-Order Complete.Yang Liu - 2017 - History and Philosophy of Logic 38 (4):342-344.
    It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, the standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively sufficient as far as the first-order completeness (...)
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  24. Can Physics Ever Be Complete If There is No Fundamental Level in Nature?Markus Schrenk - 2009 - Dialectica 63 (2):205-208.
    In their recent book Every Thing Must Go Ladyman and Ross (Ladyman et al. 2007) claim: (1) Physics is analytically complete since it is the only science that cannot be left incomplete (cf. Ladyman et al. 2007, 283). (2) There might not be an ontologically fundamental level (cf. Ladyman et al. 2007, 178). (3) We should not admit anything into our ontology unless it has explanatory and predictive utility (cf. Ladyman et al. 2007, 179). In this discussion note I aim (...)
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  25. Models for Modal Syllogisms.Fred Johnson - 1989 - Notre Dame Journal of Formal Logic 30 (2):271-284.
    A semantics is presented for Storrs McCall's separate axiomatizations of Aristotle's accepted and rejected polysyllogisms. The polysyllogisms under discussion are made up of either assertoric or apodeictic propositions. The semantics is given by associating a property with a pair of sets: one set consists of things having the property essentially and the other of things having it accidentally. A completeness proof and a semantic decision procedure are given.
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  26.  65
    The Basic Algebra of Game Equivalences.Valentin Goranko - 2003 - Studia Logica 75 (2):221-238.
    We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities. En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways game identities into modal formulae. The completeness proof is based on reduction of game terms to (...)
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  27.  35
    Modal Logics for Parallelism, Orthogonality, and Affine Geometries.Philippe Balbiani & Valentin Goranko - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):365-397.
    We introduce and study a variety of modal logics of parallelism, orthogonality, and affine geometries, for which we establish several completeness, decidability and complexity results and state a number of related open, and apparently difficult problems. We also demonstrate that lack of the finite model property of modal logics for sufficiently rich affine or projective geometries (incl. the real affine and projective planes) is a rather common phenomenon.
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  28. McKinsey Algebras and Topological Models of S4.1.Thomas Mormann - manuscript
    The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The construction of these models is based on the fact that every space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1. It is shown that the class of topological models based on McKinsey algebras contains a canonical model that can be used to (...)
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  29. The Logic of Phenomenal Transparency.Kenneth Williford - 2007 - Soochow Journal of Philosophical Studies 2007 (16):181-195.
    This paper explores the logical consequences of the the thesis that all of the essential properties of consciousness can be known introspectively (Completeness, called "Strong Transparency" in the paper, following D.M. Armstrong's older terminology). It is argued that it can be known introspectively that consciousness does not have complete access to its essential properties; and it is show how this undermines conceivability arguments for dualism.
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  30.  70
    Axiomatizations with Context Rules of Inference in Modal Logic.Valentin Goranko - 1998 - Studia Logica 61 (2):179-197.
    A certain type of inference rules in modal logics, generalizing Gabbay's Irreflexivity rule, is introduced and some general completeness results about modal logics axiomatized with such rules are proved.
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  31. Categorical Consequence for Paraconsistent Logic.Fred Johnson & Peter Woodruff - 2002 - In Walter Carnielli (ed.), Paraconsistency:the logical way to the inconsistent. pp. 141-150.
    Consequence rleations over sets of "judgments" are defined by using "overdetermined" as well as "underdetermined" valuations. Some of these relations are shown to be categorical. And generalized soundness and completeness results are given for both multiple and single conclusion consequence relations.
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  32.  15
    A General Tableau Method for Propositional Interval Temporal Logics: Theory and Implementation.V. Goranko, A. Montanari, P. Sala & G. Sciavicco - 2006 - Journal of Applied Logic 4 (3):305-330.
    In this paper we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's \cdt\ logic interpreted over partial orders (\nsbcdt\ for short). It combines (...)
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  33.  68
    Identity Logics.John Corcoran & Stanley Ziewacz - 1979 - Notre Dame Journal of Formal Logic 20 (4):777-784.
    In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include (...)
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  34.  23
    Aristotelian Assertoric Syllogistic.Mohamed A. Amer - manuscript
    Abstract. Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced later on. These approaches (with few exceptions) are here discussed, developed and interrelated. Among other things, di-erent facets of soundness, completeness, decidability and independence are investigated. Speci/cally arithmetization (Leibniz), algebraization (Leibniz and Boole), and Venn models (Euler and Venn) are closely examined. All proofs are simple. In (...)
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  35.  78
    Lógica positiva : plenitude, potencialidade e problemas (do pensar sem negação).Tomás Barrero - 2004 - Dissertation, Universidade Estadual de Campinas
    This work studies some problems connected to the role of negation in logic, treating the positive fragments of propositional calculus in order to deal with two main questions: the proof of the completeness theorems in systems lacking negation, and the puzzle raised by positive paradoxes like the well-known argument of Haskel Curry. We study the constructive com- pleteness method proposed by Leon Henkin for classical fragments endowed with implication, and advance some reasons explaining what makes difficult to extend this (...)
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  36. A Note on Harmony.Nissim Francez & Roy Dyckhoff - 2012 - Journal of Philosophical Logic 41 (3):613-628.
    In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion . We propose (...)
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  37. The Semantics of Entailment.Richard Routley & Robert K. Meyer - 1973 - In Hughes Leblanc (ed.), Truth, Syntax, and Modality: Proceedings Of The Temple University Conference On Alternative Semantlcs. Amsterdam: North-Holland Publishing Company. pp. 199-243.
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  38. Closing in on Causal Closure.Robert K. Garcia - 2014 - Journal of Consciousness Studies 21 (1-2):96-109.
    I examine the meaning and merits of a premise in the Exclusion Argument, the causal closure principle that all physical effects have physical causes. I do so by addressing two questions. First, if we grant the other premises, exactly what kind of closure principle is required to make the Exclusion Argument valid? Second, what are the merits of the requisite closure principle? Concerning the first, I argue that the Exclusion Argument requires a strong, “stringently pure” version of closure. The latter (...)
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  39.  47
    Analytic Tableaux for All of SIXTEEN 3.Stefan Wintein & Reinhard Muskens - 2015 - Journal of Philosophical Logic 44 (5):473-487.
    In this paper we give an analytic tableau calculus P L 1 6 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t, ⊧ f, ⊧ i, and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment (...)
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  40. Gott Würfelt Nicht. Einsteins Immer Noch Aktuelle Kritik der Quantenmechanik.Gregor Schiemann - 2005 - In J. Renn (ed.), Albert Einstein. Ingenieur des Universums. 100 Autoren für Einstein.
    Kaum eine Äußerung Einsteins ist so bekannt wie sein Wort, dass Gott nicht würfelt. In ähnlicher Weise, wie Einstein dies unerläutert gelassen hat, ist seine gesamte Position zur Quantenmechanik, auf die es sich bezieht, von Uneindeutigkeiten nicht frei geblieben. Für seine Würfelmetapher ergibt sich ein Spielraum von gegensätzlichen Sichtweisen. Sie lässt sich zum einen mit jüngeren Forschungsresultaten verbinden und weist zum anderen auf rückschrittliche Elemente in Einsteins Denken hin. Ich wende mich zuerst diesen Elementen zu und betrachte dann eine dazu (...)
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  41. Categoricity.John Corcoran - 1980 - History and Philosophy of Logic 1 (1):187-207.
    After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those (...)
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  42.  68
    Some Concerns Regarding Ternary-Relation Semantics and Truth-Theoretic Semantics in General.Ross T. Brady - 2017 - IfCoLog Journal of Logics and Their Applications 4 (3):755--781.
    This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment.
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  43. A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
    In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...)
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  44. SEPTEMBER 2015 UPDATE CORCORAN ARISTOTLE BIBLIOGRAPHY.John Corcoran - forthcoming - Aporia 5.
    This presentation includes a complete bibliography of John Corcoran’s publications relevant on Aristotle’s logic. The Sections I, II, III, and IV list respectively 23 articles, 44 abstracts, 3 books, and 11 reviews. Section I starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article—from Corcoran’s Philadelphia period that antedates his discovery of Aristotle’s natural deduction system—and the Journal of Symbolic Logic article—from his Buffalo period first reporting his original results. It ends with works published in 2015. (...)
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  45.  9
    Computation Tree Logics and Temporal Logics with Reference Pointers.V. Goranko - 2000 - Journal of Applied Non-Classical Logics 10 (3-4):221-242.
    A complete axiomatic system CTL$_{rp}$ is introduced for a temporal logic for finitely branching $\omega^+$-trees in a temporal language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL* into CTL$_{rp}$. In particular, that yields a complete axiomatization for the translations of all valid CTL*-formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive medium for reasoning (...)
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  46. CORCORAN'S 27 ENTRIES IN THE 1999 SECOND EDITION.John Corcoran - 1999 - In Robert Audi (ed.), The Cambridge Dictionary of Philosophy. CAMBRIDGE UP. pp. 65-941.
    Corcoran’s 27 entries in the 1999 second edition of Robert Audi’s Cambridge Dictionary of Philosophy [Cambridge: Cambridge UP]. -/- ancestral, axiomatic method, borderline case, categoricity, Church (Alonzo), conditional, convention T, converse (outer and inner), corresponding conditional, degenerate case, domain, De Morgan, ellipsis, laws of thought, limiting case, logical form, logical subject, material adequacy, mathematical analysis, omega, proof by recursion, recursive function theory, scheme, scope, Tarski (Alfred), tautology, universe of discourse. -/- The entire work is available online free at more than (...)
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  47. Einige Bemerkungen zum Prinzip der kausalen Abgeschlossenheit des Physischen.Andreas Hüttemann - 2013 - In Jan Michel & Gernot Münster (eds.), Die Suche nach dem Geist. mentis.
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  48. The Use of Axiomatic Rejection.Piotr Kulicki - 2000 - In Logica yearbook 1999. Filosophia.
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  49.  66
    On a Perceived Inadequacy of Principia Mathematica.Burkay Ozturk - 2011 - Florida Philosophical Review 12 (1):83-92.
    This paper deploys a Cantor-style diagonal argument which indicates that there is more possible mathematical content than there are propositional functions in Russell and Whitehead's Principia Mathematica and similar formal systems. This technical result raises a historical question: "How did Russell, who was himself an expert in diagonal arguments, not see this coming?" It turns out that answering this question requires an appreciation of Russell's understanding of what logic is, and how he construed the relationship between logic and Principia Mathematica.
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  50.  46
    Refutation Systems in Modal Logic.Valentin Goranko - 1994 - Studia Logica 53 (2):299 - 324.
    Complete deductive systems are constructed for the non-valid (refutable) formulae and sequents of some propositional modal logics. Thus, complete syntactic characterizations in the sense of Lukasiewicz are established for these logics and, in particular, purely syntactic decision procedures for them are obtained. The paper also contains some historical remarks and a general discussion on refutation systems.
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