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Alonzo Church

[author unknown]
Bulletin of Symbolic Logic 3 (2):153-153 (1997)

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  1. Ernst Mally’s Anticipation of Encoding.Bernard Linsky - 2014 - Journal for the History of Analytical Philosophy 2 (5).
    Ernst Mally’s Gegenstandstheoretische Grundlagen der Logik und Logistik proposes that the abstract object “the circle” does not satisfy the properties of circles, but instead “determines” the class of circles. In this he anticipates the notion of “encoding” that Edward Zalta proposes for his theory ofObjects. It is argued that Mally did anticipate the notion of “encoding”, but sees it as a way of taking the concept as the subject of a proposition, rather than as a primitive notion in the theory (...)
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  • Sets, Logic, Computation. An Open Introduction to Metalogic.Richard Zach - 2017
    An introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic.
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  • Incompleteness and Computability. An Open Introduction to Gödel's Theorems.Richard Zach - 2019
    Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.
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  • Fixed-Point Models for Theories of Properties and Classes.Greg Restall - 2017 - Australasian Journal of Logic 14 (1).
    There is a vibrant community among philosophical logicians seeking to resolve the paradoxes of classes, properties and truth by way of adopting some non-classical logic in which trivialising paradoxical arguments are not valid. There is also a long tradition in theoretical computer science|going back to Dana Scott's fixed point model construction for the untyped lambda-calculus of models allowing for fixed points. In this paper, I will bring these traditions closer together, to show how these model constructions can shed light on (...)
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  • The Philosophy of Computer Science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.
  • Can Concepts Be Defined in Terms of Sets?Marie Duží & Pavel Materna - 2010 - Logic and Logical Philosophy 19 (3):195-242.
    The goal of this paper is a philosophical explication and logical rectification of the notion of concept. We take into account only those contexts that are relevant from the logical point of view. It means that we are not interested in contexts characteristic of cognitive sciences, particularly of psychology, where concepts are conceived of as some kind of mental objects or representations. After a brief recapitulation of various theories of concept, in particular Frege’s and Church’s ones, we propose our own (...)
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  • Intensional Logic.Melvin Fitting - 2008 - Stanford Encyclopedia of Philosophy.
    There is an obvious difference between what a term designates and what it means. At least it is obvious that there is a difference. In some way, meaning determines designation, but is not synonymous with it. After all, “the morning star” and “the evening star” both designate the planet Venus, but don't have the same meaning. Intensional logic attempts to study both designation and meaning and investigate the relationships between them.
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  • Concepts as Hyperintensional Objects.Pavel Materna - 2014 - Logic and Logical Philosophy (2):133-170.
    The author defends the view that the notion of concept, if used in the logical tradition, should be explicated procedurally . He argues that Tichý’s Transparent Intensional Logic is an apt tool for such an explication and derives the respective definition. Some consequences of this definition concern the notions of emptiness, simple concepts, empirical concepts and algorithmic concepts.
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  • On Designating.Nathan Salmon - 2005 - Mind 114 (456):1069-1133.
    A detailed interpretation is provided of the ‘Gray's Elegy’ passage in Russell's ‘On Denoting’. The passage is suffciently obscure that its principal lessons have been independently rediscovered. Russell attempts to demonstrate that the thesis that definite descriptions are singular terms is untenable. The thesis demands a distinction be drawn between content and designation, but the attempt to form a proposition directly about the content (as by using an appropriate form of quotation) inevitably results in a proposition about the thing designated (...)
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  • Strong Types for Direct Logic.Carl Hewitt - unknown
    This article follows on the introductory article “Direct Logic for Intelligent Applications” [Hewitt 2017a]. Strong Types enable new mathematical theorems to be proved including the Formal Consistency of Mathematics. Also, Strong Types are extremely important in Direct Logic because they block all known paradoxes[Cantini and Bruni 2017]. Blocking known paradoxes makes Direct Logic safer for use in Intelligent Applications by preventing security holes. Inconsistency Robustness is performance of information systems with pervasively inconsistent information. Inconsistency Robustness of the community of professional (...)
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  • The Principle of Wholistic Reference.John Corcoran - 2004 - Manuscrito 27 (1):159-171.
    In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a slightly (...)
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  • Diagonalisation and Church's Thesis: Kleene's Homework.Enrique Alonso & Maria Manzano - 2005 - History and Philosophy of Logic 26 (2):93-113.
    In this paper we will discuss the active part played by certain diagonal arguments in the genesis of computability theory. 1?In some cases it is enough to assume the enumerability of Y while in others the effective enumerability is a substantial demand. These enigmatical words by Kleene were our point of departure: When Church proposed this thesis, I sat down to disprove it by diagonalizing out of the class of the ??definable functions. But, quickly realizing that the diagonalization cannot be (...)
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  • Emil Post.Alasdair Urquhart - 2009 - In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier. pp. 5--617.
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  • Paradoxes of Intensionality.Dustin Tucker & Richmond H. Thomason - 2011 - Review of Symbolic Logic 4 (3):394-411.
    We identify a class of paradoxes that is neither set-theoretical nor semantical, but that seems to depend on intensionality. In particular, these paradoxes arise out of plausible properties of propositional attitudes and their objects. We try to explain why logicians have neglected these paradoxes, and to show that, like the Russell Paradox and the direct discourse Liar Paradox, these intensional paradoxes are recalcitrant and challenge logical analysis. Indeed, when we take these paradoxes seriously, we may need to rethink the commonly (...)
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  • Formalizing the Semantics of Derived Words.Richmond H. Thomason - unknown
    I believe that this approach leads to a wider problem that brings together elements of linguistics and philosophy in an illuminating way. But the single case study that I provide here, while it may be suggestive, does not go far enough to make a good case for the more general point. This paper is extracted from a larger collection of documents, and is intended to motivate and illustrate the ideas.
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