Results for 'the identity of proofs'

995 found
Order:
  1.  31
    The Identity of Proofs and the Criterion for Admissible Reductions.Seungrak Choi - 2021 - Korean Journal of Logic 3 (24):245-280.
    Dag Prawitz (1971) put forward the idea that an admissible reduction process does not affect the identity of proofs represented by derivations in natural deduction. The idea relies on his conjecture that two derivations represent the same proof if and only if they are equivalent in the sense that they are reflexive, transitive and symmetric closure of the immediate reducibility relation. Schroeder-Heister and Tranchini (2017) accept Prawitz’s conjecture and propose the triviality test as the criterion for admissible reductions. (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  2.  37
    Formal Ontology and Mathematics. A Case Study on the Identity of Proofs.Matteo Bianchetti & Giorgio Venturi - 2023 - Topoi 42 (1):307-321.
    We propose a novel, ontological approach to studying mathematical propositions and proofs. By “ontological approach” we refer to the study of the categories of beings or concepts that, in their practice, mathematicians isolate as fruitful for the advancement of their scientific activity (like discovering and proving theorems, formulating conjectures, and providing explanations). We do so by developing what we call a “formal ontology” of proofs using semantic modeling tools (like RDF and OWL) developed by the computer science community. (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  3. Identity of proofs based on normalization and generality.Kosta Došen - 2003 - Bulletin of Symbolic Logic 9 (4):477-503.
    Some thirty years ago, two proposals were made concerning criteria for identity of proofs. Prawitz proposed to analyze identity of proofs in terms of the equivalence relation based on reduction to normal form in natural deduction. Lambek worked on a normalization proposal analogous to Prawitz's, based on reduction to cut-free form in sequent systems, but he also suggested understanding identity of proofs in terms of an equivalence relation based on generality, two derivations having the (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   33 citations  
  4. Meaning and identity of proofs in a bilateralist setting: A two-sorted typed lambda-calculus for proofs and refutations.Sara Ayhan - forthcoming - Journal of Logic and Computation.
    In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction system (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  5.  16
    On the equivalence of proofs involving identity.Glen Helman - 1987 - Notre Dame Journal of Formal Logic 28 (3):297-321.
  6.  17
    Towards an evaluation of the normalisation thesis on identity of proofs: The case of church-Turing thesis as Touchstone.Tiago de Castro Alves - 2020 - Manuscrito 43 (3):114-163.
    This article is a methodological discussion of formal approaches to the question of identity of proofs from a philosophical standpoint. First, an introduction to the question of identity of proofs itself is given, followed by a brief reconstruction of the so-called normalisation thesis, proposed by Dag Prawitz in 1971, in which some of its core mathematical and conceptual traits are presented. After that, a comparison between the normalisation thesis and the more well-known Church-Turing thesis on computability (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  7. Leibniz's principle of the identity of indiscernibles: A false principle.Alberto Cortes - 1976 - Philosophy of Science 43 (4):491-505.
    In considering the possibility that the fundamental particles of matter might violate Leibniz's Principle, one is confronted with logical proofs that the Principle is a Theorem of Logic. This paper shows that the proof of that theorem is not universal enough to encompass entities that might not be unique, and also strongly suggests that photons, for example, do violate Leibniz's Principle. It also shows that the existence of non-individuals would imply the breakdown of Quine's criterion of ontological commitment.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   32 citations  
  8.  41
    The Harmony of Identity.Ansten Klev - 2019 - Journal of Philosophical Logic 48 (5):867-884.
    The standard natural deduction rules for the identity predicate have seemed to some not to be harmonious. Stephen Read has suggested an alternative introduction rule that restores harmony but presupposes second-order logic. Here it will be shown that the standard rules are in fact harmonious. To this end, natural deduction will be enriched with a theory of definitional identity. This leads to a novel conception of canonical derivation, on the basis of which the identity elimination rule can (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  9. The Necessity of Identity.Jessica Leech - manuscript
    The aim of this chapter is to explore to some extent the relationship between identity and necessity in logic and metaphysics. First, I provide a historically-based summary of proofs of the necessity of identity, highlighting the importance of the role that self-identity plays. Second, I introduce two examples of metaphysical topics where the necessity of identity has played a pivotal role: the necessary a posteriori, and the coincidence of material objects. I argue that important aspects (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  10.  3
    Meaning is Use: the Case of Propositional Identity.Patrycja Kupś & Szymon Chlebowski - forthcoming - Bulletin of the Section of Logic:24 pp..
    We study natural deduction systems for a fragment of intuitionistic logic with propositional identity from the point of view of proof-theoretic semantics. We argue that the identity connective is a natural operator to be treated under the elimination rules as basic approach.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11. Arthur Prior's Proofs of the Necessities of Identity and Difference.Nils Kürbis - forthcoming - History and Philosophy of Logic:1-6.
    This paper draws attention to a proof of the necessity of identity given by Arthur Prior. In its simplicity, it is comparable to a proof of Quine's, popularised by Kripke, but it is slightly different. Prior's Polish notation is transcribed into a more familiar idiom. Prior's proof is followed by a proof of the necessity of difference, possibly the first such proof in the literature, which is also repeated here and transcribed. The paper concludes with a brief discussion of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  12.  50
    Generality of Proofs and Its Brauerian Representation.Kosta Došen & Zoran Petrić - 2003 - Journal of Symbolic Logic 68 (3):740 - 750.
    The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation if and only if they must remain occurrences of the same variable in every generalization of the derivation. The variables in question are propositional or of another type. A generalization of the derivation consists in diversifying variables without changing the rules of inference. This paper examines in the (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  13.  21
    On Synonymy in Proof-Theoretic Semantics: The Case of \(\mathtt{2Int}\).Sara Ayhan & Heinrich Wansing - 2023 - Bulletin of the Section of Logic 52 (2):187-237.
    We consider an approach to propositional synonymy in proof-theoretic semantics that is defined with respect to a bilateral G3-style sequent calculus \(\mathtt{SC2Int}\) for the bi-intuitionistic logic \(\mathtt{2Int}\). A distinctive feature of \(\mathtt{SC2Int}\) is that it makes use of two kind of sequents, one representing proofs, the other representing refutations. The structural rules of \(\mathtt{SC2Int}\), in particular its cut rules, are shown to be admissible. Next, interaction rules are defined that allow transitions from proofs to refutations, and vice versa, (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  14.  38
    Ontological Proof and the Critique of Religious Experience.Florin Lobont - 2010 - Journal for the Study of Religions and Ideologies 9 (27):157-174.
    Normal 0 false false false MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} Focusing mainly on a number of unpublished texts by Collingwood, especially his “Lectures on the Ontological Proof of the Existence of God,” the study examines the English philosopher’s innovative interpretation of the Anselm’s main contribution to the philosophical-theological tradition. Collingwood insightfully shows how the ontological argument can be used in (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  15.  48
    On the canonicity of Sahlqvist identities.Bjarni Jónsson - 1994 - Studia Logica 53 (4):473 - 491.
    We give a simple proof of the canonicity of Sahlqvist identities, using methods that were introduced in a paper by Jónsson and Tarski in 1951.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   17 citations  
  16. Logical Proof of Antinomy: A Trinitarian Interpretation of the Law of Identity.Michael C. Rhodes - 2005 - Theandros 2 (3).
     
    Export citation  
     
    Bookmark  
  17.  14
    Proof of the Prophethood of the Prophet Muhammad in the Context of the Bible in Shamsuddīn Al-Samarqandī.Tarık Tanribi̇li̇r & Esra Hergüner - 2020 - Kader 18 (2):617-641.
    Since the beginning of human history, there has been no society that did not have any religion. Man meets his need to believe, encoded in his nature by turning to God. God has not left humans alone in their journey on earth, and from time to time, He has intervened in the world through his prophets. The prophethood, which constitutes one of the main subjects of theology, is an important institution in God-human communication. The messengers chosen by God convey to (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  18.  46
    The Naturality of Natural Deduction.Luca Tranchini, Paolo Pistone & Mattia Petrolo - 2019 - Studia Logica 107 (1):195-231.
    Developing a suggestion by Russell, Prawitz showed how the usual natural deduction inference rules for disjunction, conjunction and absurdity can be derived using those for implication and the second order quantifier in propositional intuitionistic second order logic NI\. It is however well known that the translation does not preserve the relations of identity among derivations induced by the permutative conversions and immediate expansions for the definable connectives, at least when the equational theory of NI\ is assumed to consist only (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  19.  56
    Existence, freedom, identity, and the logic of abstractionist realism.Peter Milne - 2007 - Mind 116 (461):23-53.
    From the point of view of proof-theoretic semantics, we examine the logical background invoked by Neil Tennant's abstractionist realist account of mathematical existence. To prepare the way, we must first look closely at the rule of existential elimination familiar from classical and intuitionist logics and at rules governing identity. We then examine how well free logics meet the harmony and uniqueness constraints familiar from the proof-theoretic semantics project. Tennant assigns a special role to atomic formulas containing singular terms. This, (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  20.  23
    Harmony and Paradox: Intensional Aspects of Proof-Theoretic Semantics.Luca Tranchini - 2024 - Springer Verlag.
    This open access book investigates the role played by identity of proofs in proof-theoretic semantics. It develops a conception of proof-theoretic semantics as primarily concerned with the relationship between proofs (understood as abstract entities) and derivations (the linguistic representations of proofs). It demonstrates that identity of proof is a key both to clarify some —still not wholly understood— notions at the core of proof-theoretic semantics, such as harmony; and to broaden the range of the phenomena (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  21.  54
    Attention and seeing objects: The identity-crowding debate.Bradley Richards - 2016 - Philosophical Psychology 29 (5):743-758.
    Can unattended objects by seen? Ned Block has claimed they can on the basis of “identity-crowding.” This paper summarizes the ensuing debate with particular emphasis on the role of unconscious perception. Although unconscious perception plays an important role, it cannot support conscious object-seeing in identity-crowding. Nevertheless, unconscious perception assists in making successful judgments about unseen objects. Further, compelling conceptual evidence against seeing unattended objects places the burden of proof on Block. I argue that countability is necessary for seeing (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  22.  36
    Glivenko sequent classes in the light of structural proof theory.Sara Negri - 2016 - Archive for Mathematical Logic 55 (3-4):461-473.
    In 1968, Orevkov presented proofs of conservativity of classical over intuitionistic and minimal predicate logic with equality for seven classes of sequents, what are known as Glivenko classes. The proofs of these results, important in the literature on the constructive content of classical theories, have remained somehow cryptic. In this paper, direct proofs for more general extensions are given for each class by exploiting the structural properties of G3 sequent calculi; for five of the seven classes the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  23.  96
    Proof-relevance of families of setoids and identity in type theory.Erik Palmgren - 2012 - Archive for Mathematical Logic 51 (1-2):35-47.
    Families of types are fundamental objects in Martin-Löf type theory. When extending the notion of setoid (type with an equivalence relation) to families of setoids, a choice between proof-relevant or proof-irrelevant indexing appears. It is shown that a family of types may be canonically extended to a proof-relevant family of setoids via the identity types, but that such a family is in general proof-irrelevant if, and only if, the proof-objects of identity types are unique. A similar result is (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  24. Identity and Metaphysics in the Philosophy of Leibniz.Lois Elaine Frankel - 1980 - Dissertation, University of California, Berkeley
    I conclude that it is more accurate to say that, rather than trying to make logic metaphysical, Leibniz tries, in the context of a theistic system, to make metaphysics logical. ;I begin with a study of the principle of identity of indiscernibles, and show how it is best thought of as a principle which follows from a metaphysical interpretation of the principle of sufficient reason. It has been traditional to interpret the principle of identity of indiscernibles as primarily (...)
    No categories
     
    Export citation  
     
    Bookmark  
  25. The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   462 citations  
  26.  24
    “The Proof Is in the Pudding”: How Mental Health Practitioners View the Power of “Sex Hormones” in the Process of Transition.Jaye Cee Whitehead, Kath Bassett, Leia Franchini & Michael Iacolucci - 2015 - Feminist Studies 41 (3):623-650.
    In lieu of an abstract, here is a brief excerpt of the content:Feminist Studies 41, no. 3. © 2015 by Feminist Studies, Inc. 623 Jaye Cee Whitehead, Kath Bassett, Leia Franchini, and Michael Iacolucci “The Proof Is in the Pudding”: How Mental Health Practitioners View the Power of “Sex Hormones” in the Process of Transition In the United States today, popular discourse touts the power of “sex hormones” and hormone receptors in the brain to chemically produce gender expressions (manifested in (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  27.  36
    Leibniz's theory of proof.Mark Julian Cass - 2013 - Scientiae Studia 11 (2):267-279.
    Leibniz propôs que demonstrações fossem reformuladas como deduções a partir de identidades, e que proposições do tipo A = A fossem a fonte única de verdade. Neste artigo, procuro explicar essa teoria da prova (e do conhecimento), assim como seus conceitos elementares, ou seja, os conceitos de identidade, verdade (ou possibilidade) e proposição (inclusive a teoria leibniziana da redutibilidade a proposições sujeito-predicado). Leibniz proposed that demonstrations be reformulated as deductions from identities, and that propositions of the type A = A (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  28.  28
    Essential Structure of Proofs as a Measure of Complexity.Jaime Ramos, João Rasga & Cristina Sernadas - 2020 - Logica Universalis 14 (2):209-242.
    The essential structure of proofs is proposed as the basis for a measure of complexity of formulas in FOL. The motivating idea was the recognition that distinct theorems can have the same derivation modulo some non essential details. Hence the difficulty in proving them is identical and so their complexity should be the same. We propose a notion of complexity of formulas capturing this property. With this purpose, we introduce the notions of schema calculus, schema derivation and description complexity (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  29.  11
    On obdd-based algorithms and proof systems that dynamically change the order of variables.Dmitry Itsykson, Alexander Knop, Andrei Romashchenko & Dmitry Sokolov - 2020 - Journal of Symbolic Logic 85 (2):632-670.
    In 2004 Atserias, Kolaitis, and Vardi proposed $\text {OBDD}$ -based propositional proof systems that prove unsatisfiability of a CNF formula by deduction of an identically false $\text {OBDD}$ from $\text {OBDD}$ s representing clauses of the initial formula. All $\text {OBDD}$ s in such proofs have the same order of variables. We initiate the study of $\text {OBDD}$ based proof systems that additionally contain a rule that allows changing the order in $\text {OBDD}$ s. At first we consider a (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  30.  25
    The reception of Eduard Buchner's discovery of cell-free fermentation.Robert E. Kohler - 1972 - Journal of the History of Biology 5 (2):327-353.
    What general conclusions can be drawn about the reception of zymase, its relation to the larger shift from a protoplasm to an enzyme theory of life, and its status as a social phenomenon?The most striking and to me unexpected pattern is the close correlation between attitude toward zymase and professional background. The disbelief of the fermentation technologists, Will, Delbrück, Wehmer, and even Stavenhagen, was as sharp and unanimous as the enthusiasm of the immunologists and enzymologists, Duclaux, Roux, Fernback, and Bertrand, (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  31.  85
    Prior’s tonk, notions of logic, and levels of inconsistency: vindicating the pluralistic unity of science in the light of categorical logical positivism.Yoshihiro Maruyama - 2016 - Synthese 193 (11).
    There are still on-going debates on what exactly is wrong with Prior’s pathological “tonk.” In this article I argue, on the basis of categorical inferentialism, that two notions of inconsistency ought to be distinguished in an appropriate account of tonk; logic with tonk is inconsistent as the theory of propositions, and it is due to the fallacy of equivocation; in contrast to this diagnosis of the Prior’s tonk problem, nothing is actually wrong with tonk if logic is viewed as the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  32.  17
    Proofs of regular identities.Ewa Graczynska & Francis Pastijn - 1981 - Bulletin of the Section of Logic 10 (1):35-37.
    This is an abstract of the paper to be submitted to Houston Journal of Mathematics. Our nomenclature and notation will be basically those of [3]. We shall consider algebras of type : T ! N, where T is a nonempty set, and N the set of all positive integers. By V we denote the set of all variables occurring in a polynomial symbol p. An identity p = q is called strongly non-regular if it is of the form p (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  33.  6
    Permanent Temporality: Race, Time, and the Materiality of Romanian Identity Cards.Ildikó Zonga Plájás - 2023 - Science, Technology, and Human Values 48 (1):68-90.
    Documents, in particular identity cards, mediate relationships between individuals and institutions. Their materiality matters and actively impacts how states govern populations and their movements. In this paper, I examine one such object, the Romanian identity card. Focusing on its temporality and agency, I explore how objects and technological procedures enact race. In Romania, people without an address or proof of residence—many of them members of segregated Roma communities living in deep poverty—can only receive a temporary identity card, (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  34.  7
    Identity Theft, Deep Brain Stimulation, and the Primacy of Post‐trial Obligations.Joseph J. Fins, Amanda R. Merner, Megan S. Wright & Gabriel Lázaro-Muñoz - 2024 - Hastings Center Report 54 (1):34-41.
    Patient narratives from two investigational deep brain stimulation trials for traumatic brain injury and obsessive‐compulsive disorder reveal that injury and illness rob individuals of personal identity and that neuromodulation can restore it. The early success of these interventions makes a compelling case for continued post‐trial access to these technologies. Given the centrality of personal identity to respect for persons, a failure to provide continued access can be understood to represent a metaphorical identity theft. Such a loss recapitulates (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  35. The scrambling theorem: A simple proof of the logical possibility of spectrum inversion.Donald D. Hoffman - 2006 - Consciousness and Cognition 15 (1):31-45.
    The possibility of spectrum inversion has been debated since it was raised by Locke and is still discussed because of its implications for functionalist theories of conscious experience . This paper provides a mathematical formulation of the question of spectrum inversion and proves that such inversions, and indeed bijective scramblings of color in general, are logically possible. Symmetries in the structure of color space are, for purposes of the proof, irrelevant. The proof entails that conscious experiences are not identical with (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  36.  38
    Tableaux and Dual Tableaux: Transformation of Proofs.Joanna Golińska-Pilarek & Ewa Orłowska - 2007 - Studia Logica 85 (3):283-302.
    We present two proof systems for first-order logic with identity and without function symbols. The first one is an extension of the Rasiowa-Sikorski system with the rules for identity. This system is a validity checker. The rules of this system preserve and reflect validity of disjunctions of their premises and conclusions. The other is a Tableau system, which is an unsatisfiability checker. Its rules preserve and reflect unsatisfiability of conjunctions of their premises and conclusions. We show that the (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  37.  48
    The Liar Hypodox: A Truth-Teller’s Guide to Defusing Proofs of the Liar Paradox.Peter Eldridge-Smith - 2019 - Open Journal of Philosophy 9 (2):152-171.
    It seems that the Truth-teller is either true or false, but there is no accepted principle determining which it is. From this point of view, the Truth-teller is a hypodox. A hypodox is a conundrum like a paradox, but consistent. Sometimes, accepting an additional principle will convert a hypodox into a paradox. Conversely, in some cases, retracting or restricting a principle will convert a paradox to a hypodox. This last point suggests a new method of avoiding inconsistency. This article provides (...)
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  38.  11
    Brain wars: the scientific battle over the existence of the mind and the proof that will change the way we live our lives.Mario Beauregard - 2012 - New York: HarperOne.
    A Neuroscientist Offers Evidence of Where the Brain Ends and Consciousness Begins.
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  39.  9
    The Place of the Doctrine of Providence According to Maimonides.Leo Strauss - 2004 - Review of Metaphysics 57 (3):537-550.
    IN THE GUIDE OF THE PERPLEXED, Maimonides does not treat the doctrine of divine omniscience and divine providence in a strictly theological context. He arrives at this subject for the first time in the third section of the Guide, after he has concluded the thematic treatment of at least the following themes: the names and attributes of God ; the proof of the existence, unity, and incorporeality of God ; the separate intelligences and the order of the world ; the (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  40.  45
    The Commemoration of Slavery in France and the Emergence of a Black Political Consciousness.Jean-Yves Camus - 2006 - The European Legacy 11 (6):647-655.
    The abolition of slavery after the Revolution of 1789 has always been hailed by the French secular State as proof of the progressivist nature of the Republic. Nevertheless, there has never been any attempt to seriously confront the French involvement in the trade of slaves, which lasted for two centuries. France, a colonial power until the 1960s, which still retains several overseas possessions with an Afro-Caribbean population, has a large resident black population in the mainland which feels it has been (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  41.  26
    The Philosophy of Gottlob Frege.Richard L. Mendelsohn - 2005 - New York: Cambridge University Press.
    This analysis of Frege's views on language and metaphysics in On Sense and Reference, arguably one of the most important philosophical essays of the past hundred years, provides a thorough introduction to the function/argument analysis and applies Frege's technique to the central notions of predication, identity, existence and truth. Of particular interest is the analysis of the Paradox of Identity and a discussion of three solutions: the little-known Begriffsschrift solution, the sense/reference solution, and Russell's 'On Denoting' solution. Russell's (...)
    Direct download  
     
    Export citation  
     
    Bookmark   18 citations  
  42.  85
    Proof of a Sentient Knower: Utpaladeva’s Ajaḍapramātṛsiddhi with the Vṛtti of Harabhatta Shastri. [REVIEW]David Peter Lawrence - 2009 - Journal of Indian Philosophy 37 (6):627-653.
    Utpaladeva (c. 900–950 C.E.) was the chief originator of the Pratyabhijñā philosophical theology of monistic Kashmiri Śaivism, which was further developed by Abhinavagupta (c. 950–1020 C.E.) and other successors. The Ajaḍapramātṛsiddhi, “Proof of a Sentient Knower,” is one component of Utpaladeva’s trio of specialized studies called the Siddhitrayī, “Three Proofs.” This article provides an introduction to and translation of the Ajaḍapramātṛsiddhi along with the Vṛtti commentary on it by the nineteenth–twentieth century paṇḍit, Harabhatta Shastri. Utpaladeva in this work presents (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  43.  13
    The proof complexity of linear algebra.Michael Soltys & Stephen Cook - 2004 - Annals of Pure and Applied Logic 130 (1-3):277-323.
    We introduce three formal theories of increasing strength for linear algebra in order to study the complexity of the concepts needed to prove the basic theorems of the subject. We give what is apparently the first feasible proofs of the Cayley–Hamilton theorem and other properties of the determinant, and study the propositional proof complexity of matrix identities such as AB=I→BA=I.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  44.  18
    Listening to the Music of Reason: Nicolas Bourbaki and the Phenomenology of the Mathematical Experience.Till Düppe - 2015 - PhaenEx 10:38-56.
    Jean Dieudonné, the spokesman of the group of French mathematicians named Bourbaki, called mathematics the music of reason. This metaphor invites a phenomenological account of the affective, in contrast to the epistemic and discursive, nature of mathematics: What constitutes its charm? Mathematical reasoning is described as a perceptual experience, which in Husserl’s late philosophy would be a case of passive synthesis. Like a melody, a mathematical proof is manifest in an affective identity of a temporal object. Rather than an (...)
    No categories
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  45. The Origin of the Indirect Passions in the Treatise: An Analogy Between Books 1 and 2.Haruko Inoue - 2003 - Hume Studies 29 (2):205-221.
    In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume 29, Number 2, November 2003, pp. 205-221 The Origin of the Indirect Passions in the Treatise: An Analogy between Books 1 and 2 HARUKOINOUE 1. The Analogy Between Book 1 and Book 2 If the central design of the Treatise is to demonstrate that "the subjects of the Understanding and Passions make a complete chain of reasoning by themselves" (T 2; SBN xii), as Hume advertises, (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  46.  41
    The characterization of monadic logic.Leslie H. Tharp - 1973 - Journal of Symbolic Logic 38 (3):481-488.
    The first section of this paper is concerned with the intrinsic properties of elementary monadic logic (EM), and characterizations in the spirit of Lindström [2] are given. His proofs do not apply to monadic logic since relations are used, and intrinsic properties of EM turn out to differ in certain ways from those of the elementary logic of relations (i.e., the predicate calculus), which we shall call EL. In the second section we investigate connections between higher-order monadic and polyadic (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  47.  60
    Two Fallacies in Proofs of the Liar Paradox.Peter Eldridge-Smith - 2020 - Philosophia 48 (3):947-966.
    At some step in proving the Liar Paradox in natural language, a sentence is derived that seems overdetermined with respect to its semantic value. This is complemented by Tarski’s Theorem that a formal language cannot consistently contain a naive truth predicate given the laws of logic used in proving the Liar paradox. I argue that proofs of the Eubulidean Liar either use a principle of truth with non-canonical names in a fallacious way or make a fallacious use of substitution (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  48.  42
    Boolos and the Metamathematics of Quine's Definitions of Logical Truth and Consequence.Günther Eder - 2016 - History and Philosophy of Logic 37 (2):170-193.
    The paper is concerned with Quine's substitutional account of logical truth. The critique of Quine's definition tends to focus on miscellaneous odds and ends, such as problems with identity. However, in an appendix to his influential article On Second Order Logic, George Boolos offered an ingenious argument that seems to diminish Quine's account of logical truth on a deeper level. In the article he shows that Quine's substitutional account of logical truth cannot be generalized properly to the general concept (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  49.  6
    The Theory of an Arbitrary Higher \(\lambda\)-Model.Daniel Martinez & Ruy J. G. B. de Queiroz - 2023 - Bulletin of the Section of Logic 52 (1):39-58.
    One takes advantage of some basic properties of every homotopic \(\lambda\)-model (e.g. extensional Kan complex) to explore the higher \(\beta\eta\)-conversions, which would correspond to proofs of equality between terms of a theory of equality of any extensional Kan complex. Besides, Identity types based on computational paths are adapted to a type-free theory with higher \(\lambda\)-terms, whose equality rules would be contained in the theory of any \(\lambda\)-homotopic model.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  50.  27
    The Significance of Idealism For the Present Day.A. C. Ewing - 1971 - Idealistic Studies 1 (1):1-12.
    In Britain and, I think, America at least the “idealist movement” in philosophy is very widely regarded as a spent force, as a subject only for historical study. There are indeed different definitions of “idealism.” The term was defined explicitly by at least one distinguished British philosopher as covering “all those philosophies which agree in maintaining that spiritual values have a determining voice in the ordering of the universe.” This doctrine, though unfortunately less vocal than it was, has by no (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
1 — 50 / 995