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  1. Hartley Slater, The de-Mathematisation of Logic.
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  2. Hartley Slater, A Poor Concept Script.
    Throughout the study of what have come to be known as first-, second-, and higher-order languages, what has been primarily overlooked is that these languages are abstractions. Many well known paradoxes, we shall see, arose because of the elementary level of simplification which has been involved in the abstract languages studied. Straightforward resolutions of the paradoxes immediately appear merely through attention to languages of greater sophistication, notably natural language, of course. The basic problem has been exclusive attention to a theory (...)
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  3. Hartley Slater, 1 Completing Russell's Logic.
    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 formalise, 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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  4. Hartley Slater, Logic and Arithmetic.
    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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  5. Hartley Slater, Motivation by de Se Beliefs B.H.Slater.
    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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  6. Hartley Slater, Namely-Riders: An Update.
    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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  7. Hartley Slater, 1 Ontological Discriminations.
    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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  8. Hartley Slater, 1 Out of the Liar Tangle.
    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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  9. Hartley Slater, The Central Error in the Tractatus Hartley Slater.
    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 (...)
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  10. Hartley Slater (2014). Consistent Truth. 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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  11. Hartley Slater (2014). Non‐Analytic Logic. 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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  12. Hartley Slater (2013). Symbols and Their Meaning in Analysis. Logique Et Analyse 222:211-225.
     
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  13. Hartley Slater (2012). Logic is Not Mathematical. 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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  14. Hartley Slater (2012). The Right Square. In. In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser. 139--145.
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  15. Hartley Slater (2011). Back to Aristotle! 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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  16. Hartley Slater (2011). Natural Language Consistency. Logique Et Analyse 215:409-420.
     
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  17. Hartley Slater (2010). What Priest (Amongst Many Others) has Been Missing. 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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  18. Hartley Slater (2008). Harmonising Natural Deduction. 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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  19. Hartley Slater (2008). Natural Language Sets. Logique Et Analyse 201:29-48.
     
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  20. Hartley Slater (2008). Paradoxes and Pragmatics. 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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  21. Hartley Slater (2007). Logic and Grammar. 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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  22. Hartley Slater (2006). 2005 Annual Conference of the Australasian Association for Logic. Bulletin of Symbolic Logic 12 (3):517-523.
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  23. Hartley Slater (2006). Frege's Hidden Assumption (El Supuesto Escondido de Frege). 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. Hartley Slater (2005). Choice and Logic. 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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  25. Hartley Slater (2004). Tarski's Hidden Assumption. Ratio 17 (1):84–89.
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  26. Hartley Slater (2003). Aggregate Theory Versus Set Theory. 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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  27. Hartley Slater, Epsilon Calculi. 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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  28. Hartley Slater (2000). The Grammar of the Attitudes. In. In Klaus von Heusinger & Urs Egli (eds.), Reference and Anaphoric Relations. Kluwer. 183--190.
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  29. Laurence Goldstein & Hartley Slater (1998). Wittgenstein, Semantics and Connectionism. Philosophical Investigations 21 (4):293–314.
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  30. Hartley Slater (1997). Art and Aesthetics. British Journal of Aesthetics 37 (3):226-231.
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  31. Hartley Slater (1997). Ellery Eells and Brian Skyrms (Eds.), Probability and Conditionals. Erkenntnis 46 (2):273-276.
  32. Hartley Slater (1997). J. B. Paris, the Uncertain Reasoner's Companion. Erkenntnis 46 (3):397-400.
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  33. Hartley Slater (1995). Scare Quoted Seeing. American Philosophical Quarterly 32 (1):97-103.
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  34. Hartley Slater (1993). The System of the Arts. Journal of Aesthetics and Art Criticism 51 (4):611-617.
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  35. Hartley Slater (1989). Consistent Vagueness. Noûs 23 (2):241-252.
  36. Hartley Slater (1989). Consistent Vagueness in 1989 APA Central Division Meetings. Noûs 23 (2):241-252.
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  37. Hartley Slater (1987). Fictions. British Journal of Aesthetics 27 (2):145-155.
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  38. Hartley Slater (1983). Wittgenstein's Aesthetics. British Journal of Aesthetics 23 (1):34-37.
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