Results for 'Structural proof theory'

953 found
Order:
  1. Stoic Sequent Logic and Proof Theory.Susanne Bobzien - 2019 - History and Philosophy of Logic 40 (3):234-265.
    This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  2. Topics in the Proof Theory of Non-classical Logics. Philosophy and Applications.Fabio De Martin Polo - 2023 - Dissertation, Ruhr-Universität Bochum
    Chapter 1 constitutes an introduction to Gentzen calculi from two perspectives, logical and philosophical. It introduces the notion of generalisations of Gentzen sequent calculus and the discussion on properties that characterize good inferential systems. Among the variety of Gentzen-style sequent calculi, I divide them in two groups: syntactic and semantic generalisations. In the context of such a discussion, the inferentialist philosophy of the meaning of logical constants is introduced, and some potential objections – mainly concerning the choice of working with (...)
    Download  
     
    Export citation  
     
    Bookmark  
  3. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value.John Corcoran - 1971 - Journal of Structural Learning 3 (2):1-16.
    1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  4. Algorithmic Structuring of Cut-free Proofs.Matthias Baaz & Richard Zach - 1993 - In Börger Egon, Kleine Büning Hans, Jäger Gerhard, Martini Simone & Richter Michael M. (eds.), Computer Science Logic. CSL’92, San Miniato, Italy. Selected Papers. Springer. pp. 29–42.
    The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB ( LK where blocks of quantifiers can be introduced in one step) is investigated, where a distinction is made between linear proofs and proofs in tree form. In this framework, structuring coincides with the introduction of cuts into a proof. The algorithmic solvability of this problem can be reduced to the question of k-l-compressibility: "Given a proof of length k , and l ≤ k (...)
    Download  
     
    Export citation  
     
    Bookmark  
  5. Discourse Grammars and the Structure of Mathematical Reasoning III: Two Theories of Proof,.John Corcoran - 1971 - Journal of Structural Learning 3 (3):1-24.
    ABSTRACT This part of the series has a dual purpose. In the first place we will discuss two kinds of theories of proof. The first kind will be called a theory of linear proof. The second has been called a theory of suppositional proof. The term "natural deduction" has often and correctly been used to refer to the second kind of theory, but I shall not do so here because many of the theories so-called (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  6. From Display to Labelled Proofs for Tense Logics.Agata Ciabattoni, Tim Lyon & Revantha Ramanayake - 2013 - In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science (Lecture Notes in Computer Science 7734). Springer. pp. 120 - 139.
    We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  7. Display to Labeled Proofs and Back Again for Tense Logics.Agata Ciabattoni, Tim Lyon, Revantha Ramanayake & Alwen Tiu - 2021 - ACM Transactions on Computational Logic 22 (3):1-31.
    We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is translatable to (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  8. Beyond semantic pollution: Towards a practice-based philosophical analysis of labelled calculi.Fabio De Martin Polo - 2024 - Erkenntnis:1-30.
    This paper challenges the negative attitudes towards labelled proof systems, usually referred to as semantic pollution, by arguing that such critiques overlook the full potential of labelled calculi. The overarching objective is to develop a practice-based philosophical analysis of labelled calculi to provide insightful considerations regarding their proof-theoretic and philosophical value. To achieve this, successful applications of labelled calculi and related results will be showcased, and comparisons with other relevant works will be discussed. The paper ends by advocating (...)
    Download  
     
    Export citation  
     
    Bookmark  
  9. Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics.Tim Lyon & Kees van Berkel - 2019 - In M. Baldoni, M. Dastani, B. Liao, Y. Sakurai & R. Zalila Wenkstern (eds.), PRIMA 2019: Principles and Practice of Multi-Agent Systems. Springer. pp. 202-218.
    This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  10. A theory of presumption for everyday argumentation.David M. Godden & Douglas N. Walton - 2007 - Pragmatics and Cognition 15 (2):313-346.
    The paper considers contemporary models of presumption in terms of their ability to contribute to a working theory of presumption for argumentation. Beginning with the Whatelian model, we consider its contemporary developments and alternatives, as proposed by Sidgwick, Kauffeld, Cronkhite, Rescher, Walton, Freeman, Ullmann-Margalit, and Hansen. Based on these accounts, we present a picture of presumptions characterized by their nature, function, foundation and force. On our account, presumption is a modal status that is attached to a claim and has (...)
    Download  
     
    Export citation  
     
    Bookmark   32 citations  
  11. Refining Labelled Systems for Modal and Constructive Logics with Applications.Tim Lyon - 2021 - Dissertation, Technischen Universität Wien
    This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  12. An analytical framework-based pedagogical method for scholarly community coaching: A proof of concept.Ruining Jin, Giang Hoang, Thi-Phuong Nguyen, Phuong-Tri Nguyen, Tam-Tri Le, Viet-Phuong La, Minh-Hoang Nguyen & Quan-Hoang Vuong - 2023 - MethodsX 10:102082.
    Working in academia is challenging, even more so for those with limited resources and opportunities. Researchers around the world do not have equal working conditions. The paper presents the structure, operation method, and conceptual framework of the SM3D Portal's community coaching method, which is built to help Early Career Researchers (ECRs) and researchers in low-resource settings overcome the obstacle of inequality and start their career progress. The community coaching method is envisioned by three science philosophies (cost-effectiveness, transparency spirit, and proactive (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  13. Fermat’s last theorem proved in Hilbert arithmetic. II. Its proof in Hilbert arithmetic by the Kochen-Specker theorem with or without induction.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (10):1-52.
    The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The (...)
    Download  
     
    Export citation  
     
    Bookmark  
  14. Causality and attribution in an Aristotelian Theory.Srećko Kovač - 2015 - In Arnold Koslow & Arthur Buchsbaum (eds.), The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziauvol. 1, Cham, Heidelberg, etc.: Springer-Birkhäuser. Springer-Birkhäuser. pp. 327-340.
    Aristotelian causal theories incorporate some philosophically important features of the concept of cause, including necessity and essential character. The proposed formalization is restricted to one-place predicates and a finite domain of attributes (without individuals). Semantics is based on a labeled tree structure, with truth defined by means of tree paths. A relatively simple causal prefixing mechanism is defined, by means of which causes of propositions and reasoning with causes are made explicit. The distinction of causal and factual explanation are elaborated, (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  15. The Basics of Display Calculi.Tim Lyon, Christian Ittner, Timo Eckhardt & Norbert Gratzl - 2017 - Kriterion - Journal of Philosophy 31 (2):55-100.
    The aim of this paper is to introduce and explain display calculi for a variety of logics. We provide a survey of key results concerning such calculi, though we focus mainly on the global cut elimination theorem. Propositional, first-order, and modal display calculi are considered and their properties detailed.
    Download  
     
    Export citation  
     
    Bookmark  
  16. All science as rigorous science: the principle of constructive mathematizability of any theory.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal 12 (12):1-15.
    A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it (...)
    Download  
     
    Export citation  
     
    Bookmark  
  17. (I can’t get no) antisatisfaction.Pablo Cobreros, Elio La Rosa & Luca Tranchini - 2020 - Synthese 198 (9):8251-8265.
    Substructural approaches to paradoxes have attracted much attention from the philosophical community in the last decade. In this paper we focus on two substructural logics, named ST and TS, along with two structural cousins, LP and K3. It is well known that LP and K3 are duals in the sense that an inference is valid in one logic just in case the contrapositive is valid in the other logic. As a consequence of this duality, theories based on either logic (...)
    Download  
     
    Export citation  
     
    Bookmark   16 citations  
  18. Reale Möglichkeit: Eine allgemeine Theorie des Werdens.Wolfgang Sohst - 2016 - Berlin: Xenomoi.
    (For the English version, see below) Dieser Band schließt an die "Prozessontologie" von Wolfgang Sohst an. In vorliegenden Buch entwickelt er den Begriff der Emergenz auf der Grundlage einer Schichtenontologie. Kern dieser Theorie ist der Nachweis, dass die Struktur alles Gegebenen (also nicht nur des physischen Universums, sondern auch der irdischen Biosphäre und der aus ihr hervorgegangenen psychischen, sozialen und abstrakten Existenzformen) offen ist; es gibt keine absolute Entwicklungsgrenze der Weltstruktur. Alles Gegebene ist allerdings in Schichten gegliedert, beginnend mit den (...)
    Download  
     
    Export citation  
     
    Bookmark  
  19. Galileo's Letter to the Grand Duchess Christina: Genre, Coherence, and the Structure of Dispute.Joseph Zepeda - 2019 - Galilaeana 1 (XVI):41-75.
    This paper proposes a reading of Galileo’s Letter to the Grand Duchess Christina as analogous to a legal brief submitted to a court en banc. The Letter develops a theory of the general issues underlying the case at hand, but it is organized around advocacy for a particular judgment. I have drawn two architectonic implications from this framework, each of which helps to resolve an issue still standing in the literature. First, the Letter anticipates varying degrees of acquiescence to (...)
    Download  
     
    Export citation  
     
    Bookmark  
  20. ‘Risk in a Simple Temporal Framework for Expected Utility Theory and for SKAT, the Stages of Knowledge Ahead Theory’, Risk and Decision Analysis, 2(1), 5-32. selten co-author.Robin Pope & Reinhard Selten - 2010/2011 - Risk and Decision Analysis 2 (1).
    The paper re-expresses arguments against the normative validity of expected utility theory in Robin Pope (1983, 1991a, 1991b, 1985, 1995, 2000, 2001, 2005, 2006, 2007). These concern the neglect of the evolving stages of knowledge ahead (stages of what the future will bring). Such evolution is fundamental to an experience of risk, yet not consistently incorporated even in axiomatised temporal versions of expected utility. Its neglect entails a disregard of emotional and financial effects on well-being before a particular risk (...)
    Download  
     
    Export citation  
     
    Bookmark  
  21. On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems.Tim Lyon - 2013 - In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science (Lecture Notes in Computer Science 7734). Springer. pp. 177-194.
    This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  22. (1 other version)Wolpert, Chaitin and Wittgenstein on impossibility, incompleteness, the liar paradox, theism, the limits of computation, a non-quantum mechanical uncertainty principle and the universe as computer—the ultimate theorem in Turing Machine Theory (revised 2019).Michael Starks - 2019 - In Suicidal Utopian Delusions in the 21st Century -- Philosophy, Human Nature and the Collapse of Civilization-- Articles and Reviews 2006-2019 4th Edition Michael Starks. Las Vegas, NV USA: Reality Press. pp. 294-299.
    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 dot org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, (...)
    Download  
     
    Export citation  
     
    Bookmark  
  23. Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof (...)
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  24. On the Correspondence between Nested Calculi and Semantic Systems for Intuitionistic Logics.Tim Lyon - 2021 - Journal of Logic and Computation 31 (1):213-265.
    This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  25. Takeuti's proof theory in the context of the Kyoto School.Andrew Arana - 2019 - Jahrbuch Für Philosophie Das Tetsugaku-Ronso 46:1-17.
    Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  26. Proof Theory and Semantics for a Theory of Definite Descriptions.Nils Kürbis - 2021 - In Anupam Das & Sara Negri (eds.), TABLEAUX 2021, LNAI 12842.
    This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown to (...)
    Download  
     
    Export citation  
     
    Bookmark  
  27. Non-reflexive Nonsense: Proof-Theory for Paracomplete Weak Kleene Logic.Bruno Da Ré, Damian Szmuc & María Inés Corbalán - forthcoming - Studia Logica:1-17.
    Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are attached; and (iii) (...)
    Download  
     
    Export citation  
     
    Bookmark  
  28. Questions about proof theory vis-à-vis natural language semantics (2007).Anna Szabolcsi - manuscript
    Semantics plays a role in grammar in at least three guises. (A) Linguists seek to account for speakers‘ knowledge of what linguistic expressions mean. This goal is typically achieved by assigning a model theoretic interpretation in a compositional fashion. For example, *No whale flies* is true if and only if the intersection of the sets of whales and fliers is empty in the model. (B) Linguists seek to account for the ability of speakers to make various inferences based on semantic (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  29. (1 other version)Subatomic Inferences: An Inferentialist Semantics for Atomics, Predicates, and Names.Kai Tanter - 2021 - Review of Symbolic Logic:1-28.
    Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material (...)
    Download  
     
    Export citation  
     
    Bookmark  
  30. What Structural Injustice Theory Leaves Out.Daniel Butt - 2021 - Ethical Theory and Moral Practice 24 (5):1161-1175.
    Alasia Nuti’s recent book Injustice and the Reproduction of History: Structural Inequalities, Gender and Redress puts forward a compelling vision of contemporary duties to redress past wrongdoing, grounded in the idea of “historical-structural-injustice”, constituted by the “structural reproduction of an unjust history over time and through changes”. Such an approach promises to transcend the familiar scholarly divide between “backward-looking” and “forward-looking” models, and allow for a reparative approach that focuses specifically on those past wrongs that impact the (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  31. Hypersequents and the proof theory of intuitionistic fuzzy logic.Matthias Baaz & Richard Zach - 2000 - In Clote Peter G. & Schwichtenberg Helmut (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Springer. pp. 187– 201.
    Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and complete, (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  32. Uniform and Modular Sequent Systems for Description Logics.Tim Lyon & Jonas Karge - 2022 - In Ofer Arieli, Martin Homola, Jean Christoph Jung & Marie-Laure Mugnier (eds.), Proceedings of the 35th International Workshop on Description Logics (DL 2022).
    We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be obtained for extensions of description logics with special formulae that we call "role relational axioms." All sequent systems are sound, complete, and possess favorable properties such as height-preserving admissibility of common structural rules and height-preserving invertibility of rules.
    Download  
     
    Export citation  
     
    Bookmark  
  33. Jin Yuelin zhi shi lun bi jiao yan jiu.Zhizhong Cui - 2015 - Beijing: Zhi shi chan quan chu ban she.
    This book researches the thought of Jin Yuelin’s epistemology with some notions and methods of contemporary epistemology as the frame of reference. There are two kinds of academical significance in this book, one is that author has accurately comprehended the specific content, inadequacies and contradictions in Jin’ s epistemology, recognized the methods by which Jin Yuelin built his theory of knowledge. The other is that author has known about the differences in research objects and methods between Jin’s theory (...)
    Download  
     
    Export citation  
     
    Bookmark  
  34. Pregeometry, Formal Language and Constructivist Foundations of Physics.Xerxes D. Arsiwalla, Hatem Elshatlawy & Dean Rickles - manuscript
    How does one formalize the structure of structures necessary for the foundations of physics? This work is an attempt at conceptualizing the metaphysics of pregeometric structures, upon which new and existing notions of quantum geometry may find a foundation. We discuss the philosophy of pregeometric structures due to Wheeler, Leibniz as well as modern manifestations in topos theory. We draw attention to evidence suggesting that the framework of formal language, in particular, homotopy type theory, provides the conceptual building (...)
    Download  
     
    Export citation  
     
    Bookmark  
  35. Szemerédi’s theorem: An exploration of impurity, explanation, and content.Patrick J. Ryan - 2023 - Review of Symbolic Logic 16 (3):700-739.
    In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  36. Stegmuller on the structure of theories.Mario Alai - 1985 - Scientia 79:105-115.
    A discussion of Wolfgang's Stegmüller's ideas on the structuralist conception of theories, especially as presented in his book The Structure and Dynamics of Theories (Springer, 1976).
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  37. A Categorical Characterization of Accessible Domains.Patrick Walsh - 2019 - Dissertation, Carnegie Mellon University
    Inductively defined structures are ubiquitous in mathematics; their specification is unambiguous and their properties are powerful. All fields of mathematical logic feature these structures prominently: the formula of a language, the set of theorems, the natural numbers, the primitive recursive functions, the constructive number classes and segments of the cumulative hierarchy of sets. -/- This dissertation gives a mathematical characterization of a species of inductively defined structures, called accessible domains, which include all of the above examples except the set of (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  38. Because I Believe It’s the Right Thing to Do.Joshua May - 2013 - Ethical Theory and Moral Practice 16 (4):791-808.
    Our beliefs about which actions we ought to perform clearly have an effect on what we do. But so-called “Humean” theories—holding that all motivation has its source in desire—insist on connecting such beliefs with an antecedent motive. Rationalists, on the other hand, allow normative beliefs a more independent role. I argue in favor of the rationalist view in two stages. First, I show that the Humean theory rules out some of the ways we ordinarily explain actions. This shifts the (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  39. Mutual translatability, equivalence, and the structure of theories.Thomas William Barrett & Hans Halvorson - 2022 - Synthese 200 (3):1-36.
    This paper presents a simple pair of first-order theories that are not definitionally (nor Morita) equivalent, yet are mutually conservatively translatable and mutually 'surjectively' translatable. We use these results to clarify the overall geography of standards of equivalence and to show that the structural commitments that theories make behave in a more subtle manner than has been recognized.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  40. starting rational reconstruction of Spinoza's metaphysics by "a formal analogy to elements of 'de deo' (E1)".Friedrich Wilhelm Grafe - 2020 - Archive.Org.
    We aim to compile some means for a rational reconstruction of a named part of the start-over of Baruch (Benedictus) de Spinoza's metaphysics in 'de deo' (which is 'pars prima' of the 'ethica, ordine geometrico demonstrata' ) in terms of 1st order model theory. In so far, as our approach will be judged successful, it may, besides providing some help in understanding Spinoza, also contribute to the discussion of some or other philosophical evergreen, e.g. 'ontological commitment'. For this text (...)
    Download  
     
    Export citation  
     
    Bookmark  
  41. P≠NP, By considering time as a fuzzy concept.Didehvar Farzad - manuscript
    Here, we try to build the structure of a Theory of computation based on considering time as a fuzzy concept. Actually, there are some reasons to consider time as a fuzzy concept. In this article, we don’t go to this side but we remind that Brower and Husserl ideas about the concept of time were similar [14]. Throughout this article, we present the Theory of Computation with Fuzzy Time. Considering the classical definition of Turing Machine we change and (...)
    Download  
     
    Export citation  
     
    Bookmark  
  42. Balloons on a String: A Critique of Multiverse Cosmology.Bruce Gordon - 2011 - In Bruce Gordon & William A. Dembski (eds.), The nature of nature: examining the role of naturalism in science. Wilmington, DE: ISI Books. pp. 558-601.
    Our examination of universal origins and fine-tuning will begin with a discussion of infl ationary scenarios grafted onto Big Bang cosmology and the proof that all infl ationary spacetimes are past-incomplete. After diverting into a lengthy critical examination of the “different physics” offered by quantum cosmologists at the past-boundary of the universe, we will proceed to dissect the inadequacies of infl ationary explanations and string-theoretic constructs in the context of three cosmological models that have received much attention: the Steinhardt-Turok (...)
    Download  
     
    Export citation  
     
    Bookmark  
  43. P≠NP.Didehvar Farzad - manuscript
    Here, the author tries to build the structure of the Theory of computation based on considering time as a fuzzy concept. In fact, there are reasons to consider time as a fuzzy concept. In this article, the author doesn’t go to this side but note that Brower and Husserl views on the concept of time were similar [8]. Some reasons have been given for it in [3]. Throughout this article, the author presents the Theory of Computation with Fuzzy (...)
    Download  
     
    Export citation  
     
    Bookmark  
  44. Some Highs and Lows of Hylomorphism: On a Paradox about Property Abstraction.Teresa Robertson Ishii & Nathan Salmón - 2020 - Philosophical Studies 177 (6):1549-1563.
    We defend hylomorphism against Maegan Fairchild’s purported proof of its inconsistency. We provide a deduction of a contradiction from SH+, which is the combination of “simple hylomorphism” and an innocuous premise. We show that the deduction, reminiscent of Russell’s Paradox, is proof-theoretically valid in classical higher-order logic and invokes an impredicatively defined property. We provide a proof that SH+ is nevertheless consistent in a free higher-order logic. It is shown that the unrestricted comprehension principle of property abstraction (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  45. A Unified Explanation of Quantum Phenomena? The Case for the Peer‐to‐Peer Simulation Hypothesis as an Interdisciplinary Research Program.Marcus Arvan - 2014 - Philosophical Forum 45 (4):433-446.
    In my 2013 article, “A New Theory of Free Will”, I argued that several serious hypotheses in philosophy and modern physics jointly entail that our reality is structurally identical to a peer-to-peer (P2P) networked computer simulation. The present paper outlines how quantum phenomena emerge naturally from the computational structure of a P2P simulation. §1 explains the P2P Hypothesis. §2 then sketches how the structure of any P2P simulation realizes quantum superposition and wave-function collapse (§2.1.), quantum indeterminacy (§2.2.), wave-particle duality (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  46. Il relativismo etico fra antropologia culturale e filosofia analitica.Sergio Volodia Marcello Cremaschi - 2007 - In Ilario Tolomio, Sergio Cremaschi, Antonio Da Re, Italo Francesco Baldo, Gian Luigi Brena, Giovanni Chimirri, Giovanni Giordano, Markus Krienke, Gian Paolo Terravecchia, Giovanna Varani, Lisa Bressan, Flavia Marcacci, Saverio Di Liso, Alice Ponchio, Edoardo Simonetti, Marco Bastianelli, Gian Luca Sanna, Valentina Caffieri, Salvatore Muscolino, Fabio Schiappa, Stefania Miscioscia, Renata Battaglin & Rossella Spinaci (eds.), Rileggere l'etica tra contingenza e principi. Ilario Tolomio (ed.). Padova: CLUEP. pp. 15-46.
    I intend to: a) clarify the origins and de facto meanings of the term relativism; b) reconstruct the reasons for the birth of the thesis named “cultural relativism”; d) reconstruct ethical implications of the above thesis; c) revisit the recent discussion between universalists and particularists in the light of the idea of cultural relativism.. -/- 1.Prescriptive Moral Relativism: “everybody is justified in acting in the way imposed by criteria accepted by the group he belongs to”. Universalism: there are at least (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  47. Skolem’s “paradox” as logic of ground: The mutual foundation of both proper and improper interpretations.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (19):1-16.
    A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. (...)
    Download  
     
    Export citation  
     
    Bookmark  
  48. Vagueness And The Sorites Paradox.Kirk Ludwig & Greg Ray - 2002 - Noûs 36 (s16):419-461.
    A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of this paper. (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  49. A defense of Isaacson’s thesis, or how to make sense of the boundaries of finite mathematics.Pablo Dopico - 2024 - Synthese 203 (2):1-22.
    Daniel Isaacson has advanced an epistemic notion of arithmetical truth according to which the latter is the set of truths that we grasp on the basis of our understanding of the structure of natural numbers alone. Isaacson’s thesis is then the claim that Peano Arithmetic (PA) is the theory of finite mathematics, in the sense that it proves all and only arithmetical truths thus understood. In this paper, we raise a challenge for the thesis and show how it can (...)
    Download  
     
    Export citation  
     
    Bookmark  
  50. MODIFIED STRUCTURE-NOMINATIVE RECONSTRUCTION OF PRACTICAL PHYSICAL THEORIES AS A FRAME FOR THE PHILOSOPHY OF PHYSICS.Vladimir Kuznetsov - forthcoming2021 - Epistemological studies in Philosophy, Social and Political Sciences 4 (1):20-28.
    Physical theories are complex and necessary tools for gaining new knowledge about their areas of application. A distinction is made between abstract and practical theories. The last are constantly being improved in the cognitive activity of professional physicists and studied by future physicists. A variant of the philosophy of physics based on a modified structural-nominative reconstruction of practical theories is proposed. Readers should decide whether this option is useful for their understanding of the philosophy of physics, as well as (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
1 — 50 / 953