54 found
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  1.  13
    Consistent Truth.Hartley Slater - 2014 - Ratio 27 (3):247-261.
    Modern Logic has generated a lot of problems for itself through inattention to natural forms of speech. In particular it has had difficulties with a large group of ‘logical paradoxes’ through its preoccupation with the Predicate Calculus and related structures to the exclusion of other formal structures that represent natural language more fully, and thereby escape these paradoxes. In natural speech the unrecognized forms involved are principally individual referring terms with a non-specific or fictional reference. For, under the influence of (...)
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  2.  13
    Non‐Analytic Logic.Hartley Slater - 2014 - Philosophical Investigations 37 (3):195-207.
    A logic focusing on the analytic a priori and explicitly rejecting the synthetic a priori developed in the early decades of the 20th century, largely through the efforts of the Logical Empiricists. This group was very influenced by Wittgenstein's early work Tractatus Logico-Philosophicus. But Wittgenstein himself, later on, departed from the Tractatus in significant ways that the Logical Empiricists did not follow. Wittgenstein came later to accept the synthetic a priori, and out of this insight comes a non-analytic logic that (...)
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  3.  19
    What Priest (Amongst Many Others) has Been Missing.Hartley Slater - 2010 - Ratio 23 (2):184-198.
    It is shown that there are categorical differences between sentences and statements, which have the consequence in particular that there are no paradoxical cases of self-reference with the latter as there are with the former. The point corrects an extensive train of thought that Graham Priest has pursued over recent years, but also a much wider tradition in logic and the foundations of mathematics that has been dominant for over a century. That tradition might be broadly characterized as Formalist, or (...)
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  4.  9
    The Grammar of Platonism.Hartley Slater - 2016 - Logica Universalis 10 (4):533-541.
    In this paper, based on a critical analysis of ideas of Frege, Quine and Prior, we show how Lambda Calculus and Hilbert’s Epsilon Calculus are useful to give us a good understanding of Platonic objects.
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  5. Natural Language Consistency.Hartley Slater - 2011 - Logique Et Analyse 215:409-420.
  6.  6
    Tarski's Hidden Assumption.Hartley Slater - 2004 - Ratio 17 (1):84–89.
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  7.  19
    Choice and Logic.Hartley Slater - 2004 - Journal of Philosophical Logic 34 (2):207-216.
    There is a little known paradox the solution to which is a guide to a much more thoroughgoing solution to a whole range of classic paradoxes. This is shown in this paper with respect to Berry's Paradox, Heterologicality, Russell's Paradox, and the Paradox of Predication, also the Liar and the Strengthened Liar, using primarily the epsilon calculus. The solutions, however, show not only that the first-order predicate calculus derived from Frege is inadequate as a basis for a clear science, and (...)
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  8.  18
    Prior’s Individuals.Hartley Slater - 2016 - Synthese 193 (11):3497-3506.
    Criticisms have been aired before about the fear of certain Platonic abstract objects, propositions. That criticism extends to the widespread preference for an operator analysis of expressions like ‘It is true, known, obligatory that p’ as opposed to the predicative analysis in their equivalents ‘That p is true, known, obligatory’. The criticism in the present work also concerns Prior’s attitude to Platonic entities of a certain kind: not propositions, i.e., the referents of ‘that’-clauses, but individuals, i.e., the referents of Russell’s (...)
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  9.  18
    Logic is a Moral Science.Hartley Slater - 2015 - Philosophy 90 (4):581-591.
  10.  34
    Aggregate Theory Versus Set Theory.Hartley Slater - 2003 - Erkenntnis 59 (2):189 - 202.
    Maddy's (1990) arguments against Aggregate Theory were undermined by the shift in her position in 1997. The present paper considers Aggregate Theory in the light of this, and the recent search for `New Axioms for Mathematics'. If Set Theory is the part-whole theory of singletons, then identifying singletons with their single members collapses Set Theory into Aggregate Theory. But if singletons are not identical to their single members, then they are not extensional objects and so are not a basis for (...)
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  11. A Poor Concept Script.Hartley Slater - 2004 - Australasian Journal of Philosophy 2:44-55.
    The formal structure of Frege’s ‘concept script’ has been widely adopted in logic text books since his time, even though its rather elaborate symbols have been abandoned for more convenient ones. But there are major difficulties with its formalisation of pronouns, predicates, and propositions, which infect the whole of the tradition which has followed Frege. It is shown first in this paper that these difficulties are what has led to many of the most notable paradoxes associated with this tradition; the (...)
     
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  12.  57
    Fictions.Hartley Slater - 1987 - British Journal of Aesthetics 27 (2):145-155.
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  13.  23
    Epsilon Calculi.Hartley Slater - 2001 - Internet Encyclopedia of Philosophy.
    Epsilon Calculi are extended forms of the predicate calculus that incorporate epsilon terms. Epsilon terms are individual terms of the form ‘εxFx’, being defined for all predicates in the language. The epsilon term ‘εxFx’ denotes a chosen F, if there are any F’s, and has an arbitrary reference otherwise. Epsilon calculi were originally developed to study certain forms of Arithmetic, and Set Theory; also to prove some important meta-theorems about the predicate calculus. Later formal developments have included a variety of (...)
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  14.  60
    Wittgenstein's Aesthetics.Hartley Slater - 1983 - British Journal of Aesthetics 23 (1):34-37.
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  15.  29
    Logic is Not Mathematical.Hartley Slater - 2012 - Polish Journal of Philosophy 6 (1):69-86.
    I first show in this paper how twentieth century Set Theory got into its greatest tangle by, amongst other things, regarding relational remarks like ‘Rxy’ asbinary functions. I then show how the lack of indexicality, and of ‘that’-clauses, in Modern Logic led that subject into its intractable difficulties with the Theory of Truth. Both errors arose not only through a contempt for ordinary language, but also through the related failure to recognise that being logical is not a matter of being (...)
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  16.  57
    Harmonising Natural Deduction.Hartley Slater - 2008 - Synthese 163 (2):187 - 198.
    Prawitz proved a theorem, formalising 'harmony' in Natural Deduction systems, which showed that, corresponding to any deduction there is one to the same effect but in which no formula occurrence is both the consequence of an application of an introduction rule and major premise of an application of the related elimination rule. As Gentzen ordered the rules, certain rules in Classical Logic had to be excepted, but if we see the appropriate rules instead as rules for Contradiction, then we can (...)
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  17.  4
    Gödel's and Other Paradoxes.Hartley Slater - 2016 - Philosophical Investigations 39 (4):353-361.
    Francesco Berto has recently written “The Gödel Paradox and Wittgenstein's Reasons,” about a paradox first formulated by Graham Priest in 1971. The major reason for disagreeing with Berto's conclusions concerns his elucidation of Wittgenstein's understanding of Gödel's theorems. Seemingly, Wittgenstein was some kind of proto-paraconsistentist. Priest himself has also, though in a different way, tried to tar Wittgenstein with the same brush. But the resolution of other paradoxes is intimately linked with the resolution of the Gödel Paradox, and with understanding (...)
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  18.  51
    Art and Aesthetics.Hartley Slater - 1997 - British Journal of Aesthetics 37 (3):226-231.
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  19.  1
    Translatable Self-Reference.Hartley Slater - 2011 - Australasian Journal of Logic 10 (7):45-51.
    Stephen Read has advanced a solution of certain semantic paradoxes recently, based on the work of Thomas Bradwardine. One consequence of this approach, however, is that if Socrates utters only ‘Socrates utters a falsehood’ , while Plato says ‘Socrates utters a falsehood’ , then, for Bradwardine two different propositions are involved on account of being self-referential, while is not. Problems with this consequence are first discussed before a closely related analysis is provided that escapes it. Moreover, this alternative analysis merely (...)
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  20.  16
    Consistent Vagueness.Hartley Slater - 1989 - Noûs 23 (2):241-252.
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  21.  11
    Ellery Eells and Brian Skyrms (Eds.), Probability and Conditionals.Hartley Slater - 1997 - Erkenntnis 46 (2):273-276.
  22.  31
    The Central Error in the Tractatus Hartley Slater.Hartley Slater - manuscript
    Robert Fogelin claimed there was an error in the logic of the Tractatus. I first cover his point here before going on to show that any error in this area derived from an even more fundamental one. Correcting that further error, moreover, does more than correct the logic of the Tractatus : it has repercussions for the metaphysics and theory of value found there, in line with later developments in Wittgenstein’s philosophy. In what follows I use the Tractarian numbers to (...)
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  23.  24
    Frege's Hidden Assumption (El Supuesto Escondido de Frege).Hartley Slater - 2006 - Critica 38 (113):27 - 37.
    This paper is concerned with locating the specific assumption that led Frege into Russell's Paradox. His understanding of reflexive pronouns was weak, for one thing, but also, by assimilating concepts to functions he was misled into thinking one could invariably replace a two-place relation with a one-place property. /// Este trabajo se ocupa de localizar el supuesto específico que llevó a Frege a la Paradoja de Russell. Por una parte, su comprensión de los pronombres reflexivos era débil pero, por otra, (...)
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  24.  25
    Logic and Arithmetic.Hartley Slater - manuscript
    Since there are non-sortal predicates Frege’s attempt to derive Arithmetic from Logic stumbles at its very first step. There are properties without a number, so the contingency of that condition shows Frege’s definition of zero is not obtainable from Logic. But Frege made a crucial mistake about concepts more generally which must be remedied, before we can be clear about those specific concepts which are numbers.
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  25.  26
    1 Out of the Liar Tangle.Hartley Slater - manuscript
    There are some seemingly small points to be made, first of all, about usemention confusions in Stephen Read’s paper ‘The Truth Schema and the Liar’. But underlying them is a grammatical point that has much wider repercussions. For it generates, on its own, a more straightforward way of understanding what gets people into a tangle with Liar and Strengthened Liar sentences, and that leads to a much fuller, critical assessment of the line of approach to these matters that Read derives (...)
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  26.  17
    Completing Russell’s Logic.Hartley Slater - 2007 - Russell: The Journal of Bertrand Russell Studies 27 (1).
    The epsilon calculus improves upon the predicate calculus by systematically providing complete individual terms. Recent research has shown that epsilon terms are therefore the “logically proper names” Russell was not able to formalize, but their use improves upon Russell’s theory of descriptions not just in that way. This paper details relevant formal aspects of the epsilon calculus before tracing its extensive application not just to the theory of descriptions, but also to more general problems with anaphoric reference. It ends by (...)
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  27. The de-Mathematisation of Logic.Hartley Slater - manuscript
     
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  28.  8
    Paradoxes and Pragmatics.Hartley Slater - 2008 - Proceedings of the Xxii World Congress of Philosophy 13:87-104.
    Tarski’s assessment that natural language is inconsistent on account of the Liar Paradox is shown to be incorrect: what Tarski’s theorem in fact shows is that Truth is not a property of sentences but of propositions. By using propositions rather than sentences as the bearers of Truth, semantic closure within the same language is easily obtained. Tarski’s contrary assessment was partly based on confusions about propositions and their grammatical expression. But more centrally it arose through blindness to pragmatic factors in (...)
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  29.  21
    1 Ontological Discriminations.Hartley Slater - unknown
    Russell held that ‘a exists’, where ‘a’ is a logically proper name, was necessarily true. By contrast his account of ‘The K exists’ allowed this to be contingent, since, on his Theory of Descriptions, it did not assert the existence of an individual, but merely the instantiation of some uniquely identifying properties. The present paper refines Russell’s distinction in several ways, first by providing what Russell merely gestured at, namely explicit, formally defined logically proper names. But following from this it (...)
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  30.  18
    Logic and Grammar.Hartley Slater - 2007 - Ratio 20 (2):206–218.
    I have written a number of articles recently that have a rather remarkable character. They all point out trivial grammatical facts that, at great cost, have not been respected in twentieth century Logic. A major continuous strand in my previous work, with this same character, I will first summarise, to locate the kind of fact that is involved. But then I shall present an overview of the more recent, and more varied points I have made, which demonstrate the far larger (...)
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  31.  6
    Back to Aristotle!Hartley Slater - 2011 - Logic and Logical Philosophy 20 (4):275-283.
    There were already confusions in the Middle Ages with the reading of Aristotle on negative terms, and removing these confusions shows that the four traditional Syllogistic forms of statement can be readily generalised not only to handle polyadic relations (for long a source of difficulty), but even other, more measured quantifiers than just ‘all’, ‘some’, and ‘no’. But these historic confusions merely supplement the main confusions, which arose in more modern times, regarding the logic of singular statements. These main confusions (...)
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  32.  4
    Quine’s Other Way Out.Hartley Slater - 2014 - Philosophia Scientiæ 18:71-79.
    On montre que, avec la notion traditionnelle et grammaticale du prédicat comme ce qui reste de la phrase après l’enlèvement du sujet, le paradoxe de Russell, ou d’autres comparables comme le paradoxe de Grelling et le paradoxe de la prédication, ne posent aucun problème. L’interdit formel standard sur la substitution des prédicats impliquant des variables libres dans des schémas où ces variables deviendraient liées, suffit pour prévenir le développement des paradoxes standard. On discute ensuite des réarrangements requis dans les fondations (...)
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  33.  12
    Wittgenstein, Semantics and Connectionism.Laurence Goldstein & Hartley Slater - 1998 - Philosophical Investigations 21 (4):293–314.
  34.  7
    J. B. Paris, the Uncertain Reasoner's Companion.Hartley Slater - 1997 - Erkenntnis 46 (3):397-400.
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  35.  9
    Namely Riders: An Update.Hartley Slater - 2002 - Electronic Journal of Analytic Philosophy 7.
    I here recall Ryle's analysis of Heterologicality, but broaden the discussion to comparable analyses not only of Heterologicality but also other puzzles about self-reference. Such matters have a crucial bearing on the debate between representational and non-representational theories of mind, as will be explained.
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  36.  3
    2005 Annual Conference of the Australasian Association for Logic.Hartley Slater - 2006 - Bulletin of Symbolic Logic 12 (3):517-523.
  37.  5
    Scare Quoted Seeing.Hartley Slater - 1995 - American Philosophical Quarterly 32 (1):97-103.
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  38.  1
    Aggregate Theory Versus Set Theory.Hartley Slater - 2005 - Philosophia Scientae 9:131-144.
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  39. Motivation by de Se Beliefs B.H.Slater.Hartley Slater - unknown
    Such a misconception of grammar characterises a very popular approach to indexicality which has been current since the 1970s, stemming from the work of Casteñeda, and Kaplan. Gareth Evans was inclined to allow, for instance, that one could say ‘“To the left (I am hot)” is true, as uttered by x at t iff there is someone moderately near to the left of x such that, if he were to utter the sentence “I am hot” at t, what he would (...)
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  40.  4
    The System of the Arts.Hartley Slater - 1993 - Journal of Aesthetics and Art Criticism 51 (4):611-617.
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  41.  1
    The Grammar of the Attitudes.Hartley Slater - 2000 - In Klaus von Heusinger & Urs Egli (eds.), Reference and Anaphoric Relations. Kluwer Academic Publishers. pp. 183--190.
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  42. Art And Aesthetics.Hartley Slater - 1997 - British Journal of Aesthetics 37 (3):226-231.
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  43. A Poor Concept Script.Hartley Slater - 2004 - Australasian Journal of Logic 2 (2).
    The formal structure of Frege’s ‘concept script’ has been widely adopted in logic text books since his time, even though its rather elaborate symbols have been abandoned for more convenient ones. But there are major difficulties with its formalisation of pronouns, predicates, and propositions, which infect the whole of the tradition which has followed Frege. It is shown first in this paper that these difficulties are what has led to many of the most notable paradoxes associated with this tradition; the (...)
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  44. Aggregate Theory Versus Set Theory.Hartley Slater - 2005 - Philosophia Scientiae 9 (2):131-144.
    Maddy’s 1990 arguments against Aggregate Theory were undermined by the shift in her position in 1997. The present paper considers Aggregate Theory in the light this, and the recent search for ‘New Axioms for Mathematics’. If Set Theory is the part-whole theory of singletons, then identifying singletons with their single members collapses Set Theory into Aggregate Theory. But if singletons are not identical to their single members, then they are not extensional objects and so are not a basis for Science. (...)
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  45. Completing Russell’s Logic.Hartley Slater - 2014 - Russell: The Journal of Bertrand Russell Studies 27 (1).
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  46. Consistent Vagueness in 1989 APA Central Division Meetings.Hartley Slater - 1989 - Noûs 23 (2):241-252.
     
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  47. Frege's Hidden Assumption.Hartley Slater - 2006 - Crítica: Revista Hispanoamericana de Filosofía 38 (113):27-37.
    This paper is concerned with locating the specific assumption that led Frege into Russell's Paradox. His understanding of reflexive pronouns was weak, for one thing, but also, by assimilating concepts to functions he was misled into thinking one could invariably replace a two-place relation with a one-place property. /// Este trabajo se ocupa de localizar el supuesto específico que llevó a Frege a la Paradoja de Russell. Por una parte, su comprensión de los pronombres reflexivos era débil pero, por otra, (...)
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  48. Natural Language Sets.Hartley Slater - 2008 - Logique Et Analyse 201:29-48.
  49. Quine’s Other Way Out.Hartley Slater - 2014 - Philosophia Scientae 18:71-79.
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  50. Symbols and Their Meaning in Analysis.Hartley Slater - 2013 - Logique Et Analyse 222:211-225.
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