Results for 'diagonal lemma'

79 found
Order:
  1. The Diagonal Lemma: An Informal Exposition.Richard Kimberly Heck - manuscript
    This is a completely informal presentation of the ideas behind the diagonal lemma. One really can't see this important result from too many different angles. This one aims at getting the main idea across. (For the cognoscenti, it is in the spirit of Quine's treatment in terms of "appended to its own quotation".).
    Download  
     
    Export citation  
     
    Bookmark  
  2. Wittgenstein’s analysis on Cantor’s diagonal argument.Chaohui Zhuang - manuscript
    In Zettel, Wittgenstein considered a modified version of Cantor’s diagonal argument. According to Wittgenstein, Cantor’s number, different with other numbers, is defined based on a countable set. If Cantor’s number belongs to the countable set, the definition of Cantor’s number become incomplete. Therefore, Cantor’s number is not a number at all in this context. We can see some examples in the form of recursive functions. The definition "f(a)=f(a)" can not decide anything about the value of f(a). The definiton is (...)
    Download  
     
    Export citation  
     
    Bookmark  
  3. A Liar Paradox.Richard G. Heck - 2012 - Thought: A Journal of Philosophy 1 (1):36-40.
    The purpose of this note is to present a strong form of the liar paradox. It is strong because the logical resources needed to generate the paradox are weak, in each of two senses. First, few expressive resources required: conjunction, negation, and identity. In particular, this form of the liar does not need to make any use of the conditional. Second, few inferential resources are required. These are: (i) conjunction introduction; (ii) substitution of identicals; and (iii) the inference: From ¬(p (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  4. Operators in the paradox of the knower.Patrick Grim - 1993 - Synthese 94 (3):409 - 428.
    Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  5. This sentence does not contain the symbol X.Samuel Alexander - 2013 - The Reasoner 7 (9):108.
    A suprise may occur if we use a similar strategy to the Liar's paradox to mathematically formalize "This sentence does not contain the symbol X".
    Download  
     
    Export citation  
     
    Bookmark  
  6. Diagonal arguments and fixed points.Saeed Salehi - 2017 - Bulletin of the Iranian Mathematical Society 43 (5):1073-1088.
    ‎A universal schema for diagonalization was popularized by N. S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fit more theorems in the universal‎ ‎schema of diagonalization‎, ‎such as Euclid's proof for the infinitude of the primes and new proofs (...)
    Download  
     
    Export citation  
     
    Bookmark  
  7. Diagonalization & Forcing FLEX: From Cantor to Cohen and Beyond. Learning from Leibniz, Cantor, Turing, Gödel, and Cohen; crawling towards AGI.Elan Moritz - manuscript
    The paper continues my earlier Chat with OpenAI’s ChatGPT with a Focused LLM Experiment (FLEX). The idea is to conduct Large Language Model (LLM) based explorations of certain areas or concepts. The approach is based on crafting initial guiding prompts and then follow up with user prompts based on the LLMs’ responses. The goals include improving understanding of LLM capabilities and their limitations culminating in optimized prompts. The specific subjects explored as research subject matter include a) diagonalization techniques as practiced (...)
    Download  
     
    Export citation  
     
    Bookmark  
  8. Do Not Diagonalize.Cameron Kirk-Giannini - 2024 - In Ernie Lepore & Una Stojnic (eds.), The Oxford Handbook of Contemporary Philosophy of Language. Oxford University Press.
    Speakers assert in order to communicate information. It is natural, therefore, to hold that the content of an assertion is whatever information it communicates to its audience. In cases involving uncertainty about the semantic values of context-sensitive lexical items, moreover, it is natural to hold that the information an assertion communicates to its audience is whatever information audience members are in a position to recover from it by assuming that the proposition it semantically determines is true. This sort of picture (...)
    Download  
     
    Export citation  
     
    Bookmark  
  9. Minimal Sartre: Diagonalization and Pure Reflection.John Bova - 2012 - Open Philosophy 1:360-379.
    These remarks take up the reflexive problematics of Being and Nothingness and related texts from a metalogical perspective. A mutually illuminating translation is posited between, on the one hand, Sartre’s theory of pure reflection, the linchpin of the works of Sartre’s early period and the site of their greatest difficulties, and, on the other hand, the quasi-formalism of diagonalization, the engine of the classical theorems of Cantor, Gödel, Tarski, Turing, etc. Surprisingly, the dialectic of mathematical logic from its inception through (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  10. (1 other version)Natural Deduction for Diagonal Operators.Fabio Lampert - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. New York: Birkhäuser. pp. 39-51.
    We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  11. Operational axioms for diagonalizing states.Giulio Chiribella & Carlo Maria Scandolo - 2015 - EPTCS 195:96-115.
    In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that (...)
    Download  
     
    Export citation  
     
    Bookmark  
  12.  99
    A two-dimensional logic for diagonalization and the a priori.Melissa Fusco - 2020 - Synthese 198 (9):8307-8322.
    Two-dimensional semantics, which can represent the distinction between a priority and necessity, has wielded considerable influence in the philosophy of language. In this paper, I axiomatize the dagger operator of Stalnaker’s “Assertion” in the formal context of two-dimensional modal logic. The language contains modalities of actuality, necessity, and a priority, but is also able to represent diagonalization, a conceptually important operation in a variety of contexts, including models of the relative a priori and a posteriori often appealed to Bayesian and (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  13. Wittgenstein on Pseudo-Irrationals, Diagonal Numbers and Decidability.Timm Lampert - 2008 - In Lampert Timm (ed.), The Logica Yearbook 2008. pp. 95-111.
    In his early philosophy as well as in his middle period, Wittgenstein holds a purely syntactic view of logic and mathematics. However, his syntactic foundation of logic and mathematics is opposed to the axiomatic approach of modern mathematical logic. The object of Wittgenstein’s approach is not the representation of mathematical properties within a logical axiomatic system, but their representation by a symbolism that identifies the properties in question by its syntactic features. It rests on his distinction of descriptions and operations; (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  14. The Exotic – An example of a diagonal category.Mihai Nadin - 1976 - Revue Roumaine des Sciences Sociales 20 (1).
    Download  
     
    Export citation  
     
    Bookmark  
  15. Cantor's Illusion.Hudson Richard L. - manuscript
    This analysis shows Cantor's diagonal definition in his 1891 paper was not compatible with his horizontal enumeration of the infinite set M. The diagonal sequence was a counterfeit which he used to produce an apparent exclusion of a single sequence to prove the cardinality of M is greater than the cardinality of the set of integers N.
    Download  
     
    Export citation  
     
    Bookmark  
  16. Inférences traditionelles comme n-lemmes.Gheorghe-Ilie Farte - 2014 - Argumentum. Journal of the Seminar of Discursive Logic, Argumentation Theory and Rhetoric 12 (2):136-140.
    In this paper we propose to present from a new perspective some loci comunes of traditional logic. More exactly, we intend to show that some hypothetico-disjunctive inferences (i.e. the complex constructive dilemma, the complex destructive dilemma, the simple constructive dilemma, the simple destructive dilemma) and two hypothetico-categorical inferences (namely modus ponendo-ponens and modus tollendo-tollens) particularize two more abstract inferential structures: the constructive n-lemma and the destructive nlemma.
    Download  
     
    Export citation  
     
    Bookmark  
  17. A Two-Dimensional Logic for Two Paradoxes of Deontic Modality.Fusco Melissa & Kocurek Alexander - 2022 - Review of Symbolic Logic 15 (4):991-1022.
    In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  18. Gödel Incompleteness and Turing Completeness.Ramón Casares - manuscript
    Following Post program, we will propose a linguistic and empirical interpretation of Gödel’s incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make “infinite use of finite means”. The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in our (...)
    Download  
     
    Export citation  
     
    Bookmark  
  19. Modely chaotické dynamiky a problém reprezentace reálného systému.Lukáš Hadwiger Zámečník - 2015 - Teorie Vědy / Theory of Science 37 (3):253-277.
    Příspěvek přináší základní matematické zakotvení pojmů „teorie chaosu". Představuje klíčové vlastnosti modelů chaotického chování dynamického systému s ohledem na explanační a prediktivní sílu modelů. Z pozice filosofie vědy podrobuje analýze především reprezentační aspekty modelů chaotické dynamiky systému. Nejzajímavějším aspektem těchto modelů je přísné omezení jejich reprezentační úlohy s ohledem na splnění podmínky hyperbolicity nutné pro platnost stínového lemma.
    Download  
     
    Export citation  
     
    Bookmark  
  20. Cut-conditions on sets of multiple-alternative inferences.Harold T. Hodes - 2022 - Mathematical Logic Quarterly 68 (1):95 - 106.
    I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships between (...)
    Download  
     
    Export citation  
     
    Bookmark  
  21. On a Perceived Expressive Inadequacy of Principia Mathematica.Burkay T. Öztürk - 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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  22. On the Reality of the Continuum Discussion Note: A Reply to Ormell, ‘Russell's Moment of Candour’, Philosophy.Anne Newstead - 2008 - Philosophy 83 (1):117-127.
    In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In practice, this means excluding (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  23. The Algebraic Creativity in The Neutrosophic Square Matrices‏.Mohammad Abobala, Ahmed Hatip, A. A. Salama, Necati Olgun, Broumi Said & Huda E. Khaled - 2021 - Neutrosophic Sets and Systems 40:1-11.
    The objective of this paper is to study algebraic properties of neutrosophic matrices, where a necessary and sufficient condition for the invertibility of a square neutrosophic matrix is presented by defining the neutrosophic determinant. On the other hand, this work introduces the concept of neutrosophic Eigen values and vectors with an easy algorithm to compute them. Also, this article finds a necessary and sufficient condition for the diagonalization of a neutrosophic matrix.
    Download  
     
    Export citation  
     
    Bookmark  
  24. Wittgenstein And Labyrinth Of ‘Actual Infinity’: The Critique Of Transfinite Set Theory.Valérie Lynn Therrien - 2012 - Ithaque 10:43-65.
    In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of the concept (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  25. Sufficient Reason & The Axiom of Choice, an Ontological Proof for One Unique Transcendental God for Every Possible World.Assem Hamdy - manuscript
    Chains of causes appear when the existence of God is discussed. It is claimed by some that these chains must be finite and terminated by God. But these chains seem endless through our knowledge search. This endlessness for the physical reasons for any world event expresses the greatness and complexity of God’s creation and so the transcendence of God. So, only we can put our hands on physical reasons in an endless forage for knowledge. Yet, the endlessness of the physical (...)
    Download  
     
    Export citation  
     
    Bookmark  
  26. David Wolpert on impossibility, incompleteness, the liar paradox, the limits of computation, a non-quantum mechanical uncertainty principle and the universe as computer—the ultimate theorem in Turing Machine Theory.Michael Starks - manuscript
    I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv.org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, and even (...)
    Download  
     
    Export citation  
     
    Bookmark  
  27. Knowledge from Blindspots.Rhys Borchert, Juan Comesaña & Tim Kearl - 2023 - In Rodrigo Borges & Ian Schnee (eds.), Illuminating Errors: New Essays on Knowledge from Non-Knowledge. New York, NY: Routledge. pp. 76-91.
    No False Lemmas (NFL) says: necessarily, S’s belief that p is knowledge only if it is not inferred from any falsehood. Its proponents argue that alleged counterexamples to NFL are really cases of knowledge despite falsehood, wherein the false premise is inessential to the inference; perhaps some nearby truth does the justificatory heavy-lifting. We argue that there can be cases of inferential knowledge from a blindspot premise. Given that in such cases the relevant falsehood is essential to the inference, one (...)
    Download  
     
    Export citation  
     
    Bookmark  
  28. Actuality and the a priori.Fabio Lampert - 2018 - Philosophical Studies 175 (3):809-830.
    We consider a natural-language sentence that cannot be formally represented in a first-order language for epistemic two-dimensional semantics. We also prove this claim in the “Appendix” section. It turns out, however, that the most natural ways to repair the expressive inadequacy of the first-order language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  29. Ignorance, soundness, and norms of inquiry.Christopher Willard-Kyle - 2024 - Philosophical Studies 181 (6):1477-1485.
    The current literature on norms of inquiry features two families of norms: norms that focus on an inquirer’s ignorance and norms that focus on the question’s soundness. I argue that, given a factive conception of ignorance, it’s possible to derive a soundness-style norm from a version of the ignorance norm. A crucial lemma in the argument is that just as one can only be ignorant of a proposition if the proposition is true, so one can only be ignorant with (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  30. Deontic Modality and the Semantics of Choice.Melissa Fusco - 2015 - Philosophers' Imprint 15.
    I propose a unified solution to two puzzles: Ross's puzzle and free choice permission. I begin with a pair of cases from the decision theory literature illustrating the phenomenon of act dependence, where what an agent ought to do depends on what she does. The notion of permissibility distilled from these cases forms the basis for my analysis of 'may' and 'ought'. This framework is then combined with a generalization of the classical semantics for disjunction — equivalent to Boolean disjunction (...)
    Download  
     
    Export citation  
     
    Bookmark   22 citations  
  31. The negative theology of absolute infinity: Cantor, mathematics, and humility.Rico Gutschmidt & Merlin Carl - 2024 - International Journal for Philosophy of Religion 95 (3):233-256.
    Cantor argued that absolute infinity is beyond mathematical comprehension. His arguments imply that the domain of mathematics cannot be grasped by mathematical means. We argue that this inability constitutes a foundational problem. For Cantor, however, the domain of mathematics does not belong to mathematics, but to theology. We thus discuss the theological significance of Cantor’s treatment of absolute infinity and show that it can be interpreted in terms of negative theology. Proceeding from this interpretation, we refer to the recent debate (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  32. The Decision Problem for Effective Procedures.Nathan Salmón - 2023 - Logica Universalis 17 (2):161-174.
    The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong to mathematics proper (in a narrow sense)—and even if (as many have asserted) for that reason the Church–Turing thesis is unprovable. It is proved logically that the class of effective procedures is not decidable, i.e., that no effective procedure is possible for ascertaining whether a given procedure is effective. This (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  33. Completeness and Doxastic Plurality for Topological Operators of Knowledge and Belief.Thomas Mormann - 2023 - Erkenntnis: 1 - 34, ONLINE.
    The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  34. From Pictures to Employments: Later Wittgenstein on 'the Infinite'.Philip Bold - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    With respect to the metaphysics of infinity, the tendency of standard debates is to either endorse or to deny the reality of ‘the infinite’. But how should we understand the notion of ‘reality’ employed in stating these options? Wittgenstein’s critical strategy shows that the notion is grounded in a confusion: talk of infinity naturally takes hold of one’s imagination due to the sway of verbal pictures and analogies suggested by our words. This is the source of various philosophical pictures that (...)
    Download  
     
    Export citation  
     
    Bookmark  
  35. ‘Let No-One Ignorant of Geometry…’: Mathematical Parallels for Understanding the Objectivity of Ethics.James Franklin - 2023 - Journal of Value Inquiry 57 (2):365-384.
    It may be a myth that Plato wrote over the entrance to the Academy “Let no-one ignorant of geometry enter here.” But it is a well-chosen motto for his view in the Republic that mathematical training is especially productive of understanding in abstract realms, notably ethics. That view is sound and we should return to it. Ethical theory has been bedevilled by the idea that ethics is fundamentally about actions (right and wrong, rights, duties, virtues, dilemmas and so on). That (...)
    Download  
     
    Export citation  
     
    Bookmark  
  36. Self-reference and the languages of arithmetic.Richard Heck - 2007 - Philosophia Mathematica 15 (1):1-29.
    I here investigate the sense in which diagonalization allows one to construct sentences that are self-referential. Truly self-referential sentences cannot be constructed in the standard language of arithmetic: There is a simple theory of truth that is intuitively inconsistent but is consistent with Peano arithmetic, as standardly formulated. True self-reference is possible only if we expand the language to include function-symbols for all primitive recursive functions. This language is therefore the natural setting for investigations of self-reference.
    Download  
     
    Export citation  
     
    Bookmark   23 citations  
  37. A model of the ontology of time.Marian Călborean - manuscript
    I this paper I give minimal axioms for the ontology of time, especially A-theories and B-theories and I derive philosophically interesting lemmas. The exercise is set-theoretical, defining all notions and indicating assumptions and philosophical points of disagreement, while being easy to translate to other formal expressions . The issue of a logic for A-theories of time is treated towards the end, where I sketch ‘copresent’ operators for capturing the idea of temporal passage. The main conclusion will be that, while circularity (...)
    Download  
     
    Export citation  
     
    Bookmark  
  38. A new argument for evidentialism?Masahiro Yamada - 2010 - Philosophia 38 (2):399-404.
    In his “A new argument for evidentialism” (Shah, Philos Q 56(225): 481–498, 2006 ), Nishi Shah argues that the best explanation of a feature of deliberation whether to believe that p which he calls transparency entails that only evidence can be reason to believe that p. I show that his argument fails because a crucial lemma that his argument appeals to cannot be supported without assuming evidentialism to be true in the first place.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  39. (1 other version)What Paradoxes Depend on.Ming Hsiung - 2018 - Synthese:1-27.
    This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I prove (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  40. Notes on the Model Theory of DeMorgan Logics.Thomas Macaulay Ferguson - 2012 - Notre Dame Journal of Formal Logic 53 (1):113-132.
    We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's Collapsing (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  41. The Two-Dimensional Content of Consciousness.Simon Prosser - 2007 - Philosophical Studies 136 (3):319 - 349.
    In this paper I put forward a representationalist theory of conscious experience based on Robert Stalnaker's version of two-dimensional modal semantics. According to this theory the phenomenal character of an experience correlates with a content equivalent to what Stalnaker calls the diagonal proposition. I show that the theory is closely related both to functionalist theories of consciousness and to higher-order representational theories. It is also more compatible with an anti-Cartesian view of the mind than standard representationalist theories.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  42. Epistemicism without metalinguistic safety.Justin Khoo - 2023 - In Abrol Fairweather & Carlos Montemayor (eds.), Linguistic Luck: Safeguards and Threats to Linguistic Communication. Oxford, GB: Oxford University Press.
    Epistemicists claim that vague predicates have precise but unknow- able cutoffs. I argue against against the standard, Williamsonian, answer, that appeals to metalinguistic safety: we can know that p even if our true belief that p is metalinguistically lucky. I then propose that epistemicists should be diagonalized epistemicists and show how this alternative formulation of the view avoids the chal- lenge. However, in an M. Night Shyamalan-style twist, I then argue we should not be diagonalized epistemicists either.
    Download  
     
    Export citation  
     
    Bookmark  
  43. Verified completeness in Henkin-style for intuitionistic propositional logic.Huayu Guo, Dongheng Chen & Bruno Bentzen - 2023 - In Bruno Bentzen, Beishui Liao, Davide Liga, Reka Markovich, Bin Wei, Minghui Xiong & Tianwen Xu (eds.), Logics for AI and Law: Joint Proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, September 8-9 and 11-12, 2023, Hangzhou. College Publications. pp. 36-48.
    This paper presents a formalization of the classical proof of completeness in Henkin-style developed by Troelstra and van Dalen for intuitionistic logic with respect to Kripke models. The completeness proof incorporates their insights in a fresh and elegant manner that is better suited for mechanization. We discuss details of our implementation in the Lean theorem prover with emphasis on the prime extension lemma and construction of the canonical model. Our implementation is restricted to a system of intuitionistic propositional logic (...)
    Download  
     
    Export citation  
     
    Bookmark  
  44. Theoremizing Yablo's Paradox.Ahmad Karimi & Saeed Salehi - manuscript
    To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn Yablo's paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo's paradox comes in several varieties; and he showed in 2004 that there are other versions that are equally paradoxical. Formalizing these (...)
    Download  
     
    Export citation  
     
    Bookmark  
  45. (1 other version)Strong Completeness and Limited Canonicity for PDL.Gerard Renardel de Lavalette, Barteld Kooi & Rineke Verbrugge - 2008 - Journal of Logic, Language and Information 17 (1):69-87.
    Propositional dynamic logic is complete but not compact. As a consequence, strong completeness requires an infinitary proof system. In this paper, we present a short proof for strong completeness of $$\mathsf{PDL}$$ relative to an infinitary proof system containing the rule from [α; β n ]φ for all $$n \in {\mathbb{N}}$$, conclude $$[\alpha;\beta^*] \varphi$$. The proof uses a universal canonical model, and it is generalized to other modal logics with infinitary proof rules, such as epistemic knowledge with common knowledge. Also, we (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  46. The ethics of shareholding.B. Langtry - 2002 - Journal of Business Ethics 37 (2):175 - 185.
    The copy provided on ths site is a late draft. It provides a philosophical argument for the view that by and large it is morally wrong to buy shares in a company that is behaving badly unless you (if necessary acting together with others) are able and willing to prevent the misbehaviour. A key lemma in my argument concerns a chain of authorisation from the shareholders to the company's board to the CEO -- one in virtue of which shareholders (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  47. Graph of Socratic Elenchos.John Bova - manuscript
    From my ongoing "Metalogical Plato" project. The aim of the diagram is to make reasonably intuitive how the Socratic elenchos (the logic of refutation applied to candidate formulations of virtues or ruling knowledges) looks and works as a whole structure. This is my starting point in the project, in part because of its great familiarity and arguable claim to being the inauguration of western philosophy; getting this point less wrong would have broad and deep consequences, including for philosophy’s self-understanding. -/- (...)
    Download  
     
    Export citation  
     
    Bookmark  
  48. Linguistic Matrices.W. B. Vasantha Kandasamy, K. Ilanthenral & Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    In this book, the authors introduce the linguistic set associated with a linguistic variable and the structure of matrices, which they define as linguistic matrices. The authors build linguistic matrices only for those linguistic variables which yield a linguistic continuum or an ordered linguistic set. This book is organised into three chapters. The first chapter is introductory, in which we introduce all the basic concepts of linguistic variables and the associated linguistic set to make this book self-contained. Chapter two introduces (...)
    Download  
     
    Export citation  
     
    Bookmark  
  49. Grundgesetze and the Sense/Reference Distinction.Kevin C. Klement - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 142-166.
    Frege developed the theory of sense and reference while composing his Grundgesetze and considering its philosophical implications. The Grundgesetze is thus the most important test case for the application of this theory of meaning. I argue that evidence internal and external to the Grundgesetze suggests that he thought of senses as having a structure isomorphic to the Grundgesetze expressions that would be used to express them, which entails a theory about the identity conditions of senses that is relatively fine-grained, though (...)
    Download  
     
    Export citation  
     
    Bookmark  
  50. Explaining Away Kripke’s Wittgenstein.Derek Green - 2023 - Erkenntnis 88 (3):991-1011.
    The paradox of rule-following that Saul Kripke finds in Wittgenstein’s Philosophical Investigations purports to show that words and thoughts have no content—that there is no intentionality. This paper refutes the paradox with a dilemma. Intentional states are posited in rational explanations, which use propositional attitudes to explain actions and thoughts. Depending on which of the two plausible views of rational explanation is right, either: the paradox is mistaken about the a priori requirements for content; or, a fatal flaw in content (...)
    Download  
     
    Export citation  
     
    Bookmark  
1 — 50 / 79