20 found
Order:
  1.  76
    Semantics for Pure Theories of Connexive Implication.Yale Weiss - 2022 - Review of Symbolic Logic 15 (3):591-606.
    In this article, I provide Urquhart-style semilattice semantics for three connexive logics in an implication-negation language (I call these “pure theories of connexive implication”). The systems semantically characterized include the implication-negation fragment of a connexive logic of Wansing, a relevant connexive logic recently developed proof-theoretically by Francez, and an intermediate system that is novel to this article. Simple proofs of soundness and completeness are given and the semantics is used to establish various facts about the systems (e.g., that two of (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  2.  45
    A Note on the Relevance of Semilattice Relevance Logic.Yale Weiss - 2019 - Australasian Journal of Logic 16 (6):177-185.
    A propositional logic has the variable sharing property if φ → ψ is a theorem only if φ and ψ share some propositional variable. In this note, I prove that positive semilattice relevance logic and its extension with an involution negation have the variable sharing property. Typical proofs of the variable sharing property rely on ad hoc, if clever, matrices. However, in this note, I exploit the properties of rather more intuitive arithmetical structures to establish the variable sharing property for (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  3.  52
    Connexive Extensions of Regular Conditional Logic.Yale Weiss - 2019 - Logic and Logical Philosophy 28 (3):611-627.
    The object of this paper is to examine half and full connexive extensions of the basic regular conditional logic CR. Extensions of this system are of interest because it is among the strongest well-known systems of conditional logic that can be augmented with connexive theses without inconsistency resulting. These connexive extensions are characterized axiomatically and their relations to one another are examined proof-theoretically. Subsequently, algebraic semantics are given and soundness, completeness, and decidability are proved for each system. The semantics is (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  4.  54
    Basic Intuitionistic Conditional Logic.Yale Weiss - 2019 - Journal of Philosophical Logic 48 (3):447-469.
    Conditional logics have traditionally been intended to formalize various intuitively correct modes of reasoning involving conditional expressions in natural language. Although conditional logics have by now been thoroughly studied in a classical context, they have yet to be systematically examined in an intuitionistic context, despite compelling philosophical and technical reasons to do so. This paper addresses this gap by thoroughly examining the basic intuitionistic conditional logic ICK, the intuitionistic counterpart of Chellas’ important classical system CK. I give ICK both worlds (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  5. Frontiers of Conditional Logic.Yale Weiss - 2019 - Dissertation, The Graduate Center, City University of New York
    Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional (...)
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  6.  64
    Did Aristotle Endorse Aristotle’s Thesis? A Case Study in Aristotle’s Metalogic.Yale Weiss - 2022 - Notre Dame Journal of Formal Logic 63 (4):551-579.
    Since McCall (1966), the heterodox principle of propositional logic that it is impossible for a proposition to be entailed by its own negation—in symbols, ¬(¬φ→φ)—has gone by the name of Aristotle’s thesis, since Aristotle apparently endorses it in Prior Analytics 2.4, 57b3–14. Scholars have contested whether Aristotle did endorse his eponymous thesis, whether he could do so consistently, and for what purpose he endorsed it if he did. In this article, I reconstruct Aristotle’s argument from this passage and show that (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  7.  76
    Semantics for Counterpossibles.Yale Weiss - 2017 - Australasian Journal of Logic 14 (4):383-407.
    The object of this paper is to examine two approaches to giving non-vacuous truth conditions for counterpossibles, counterfactuals with impossible antecedents. I first develop modifications of a Lewis-style sphere semantics with impossible worlds. I argue that this approach sanctions intuitively invalid inferences and is supported by philosophically problematic foundations. I then develop modifications of certain ceteris paribus conditional logics with impossible worlds. Tableaux are given for each of these in an appendix and soundness and completeness results are proved. While certain (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  8.  66
    Sextus Empiricus' Fourth Conditional and Containment Logic.Yale Weiss - 2019 - History and Philosophy of Logic 40 (4):307-322.
    In his Outlines of Pyrrhonism 2.110–113, Sextus Empiricus presents four different accounts of the conditional, presumably all from the Hellenistic period, in increasing logical strength. While the interpretation and provenance of the first three accounts is relatively secure, the fourth account has perplexed and frustrated interpreters for decades or longer. Most interpreters have ultimately taken a dismissive attitude towards the fourth account and discounted it as being of both little historical and logical interest. We argue that this attitude is unwarranted (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  9.  60
    Augustine and the KK Principle.Yale Weiss - 2024 - History of Philosophy & Logical Analysis 27 (1):79-92.
    In On the Trinity 15.12.21, Augustine appears to endorse the KK principle (that if one knows that φ, then one knows that one knows that φ) in the course of giving an argument – the Multiplicity Argument – against the Academic skeptics. Gareth Matthews has disputed Augustine’s endorsement of the KK principle and presented a different reading of the Multiplicity Argument. In this note, I show that Matthews’s construal of the Multiplicity Argument is both interpretively and technically defective and defend (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  10. A Fourth Alternative in Interpreting Parmenides.John E. Sisko & Yale Weiss - 2015 - Phronesis 60 (1):40-59.
    According to current interpretations of Parmenides, he either embraces a token-monism of things, or a type-monism of the nature of each kind of thing, or a generous monism, accepting a token-monism of things of a specific type, necessary being. These interpretations share a common flaw: they fail to secure commensurability between Parmenides’ alētheia and doxa. We effect this by arguing that Parmenides champions a metaphysically refined form of material monism, a type-monism of things; that light and night are allomorphs of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  11.  30
    A Characteristic Frame for Positive Intuitionistic and Relevance Logic.Yale Weiss - 2020 - Studia Logica 109 (4):687-699.
    I show that the lattice of the positive integers ordered by division is characteristic for Urquhart’s positive semilattice relevance logic; that is, a formula is valid in positive semilattice relevance logic if and only if it is valid in all models over the positive integers ordered by division. I show that the same frame is characteristic for positive intuitionistic logic, where the class of models over it is restricted to those satisfying a heredity condition. The results of this article highlight (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  12.  43
    A Conservative Negation Extension of Positive Semilattice Logic Without the Finite Model Property.Yale Weiss - 2020 - Studia Logica 109 (1):125-136.
    In this article, I present a semantically natural conservative extension of Urquhart’s positive semilattice logic with a sort of constructive negation. A subscripted sequent calculus is given for this logic and proofs of its soundness and completeness are sketched. It is shown that the logic lacks the finite model property. I discuss certain questions Urquhart has raised concerning the decision problem for the positive semilattice logic in the context of this logic and pose some problems for further research.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  13.  90
    Are Contradictions Believable?Yale Weiss - 2019 - Thought: A Journal of Philosophy 8 (1):42-49.
    A number of philosophers deny that contradictions can be believed. Are they correct? In this note, I show that even in quite weak logics, on pain of inconsistency, if there are false beliefs, either there are propositions which are true but unbelievable or contradictions are believable. Since the antecedent clearly holds, I offer some considerations in favor of the latter disjunct. Objections and variants of the main argument are considered.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  14.  61
    The relevance logic of Boolean groups.Yale Weiss - 2023 - Logic Journal of the IGPL 31 (1):96-114.
    In this article, I consider the positive logic of Boolean groups (i.e. Abelian groups where every non-identity element has order 2), where these are taken as frames for an operational semantics à la Urquhart. I call this logic BG. It is shown that the logic over the smallest nontrivial Boolean group, taken as a frame, is identical to the positive fragment of a quasi-relevance logic that was developed by Robles and Méndez (an extension of this result where negation is included (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  15. Revisiting Constructive Mingle: Algebraic and Operational Semantics.Yale Weiss - 2022 - In Katalin Bimbo (ed.), Essays in Honor of J. Michael Dunn. College Publications. pp. 435-455.
    Among Dunn’s many important contributions to relevance logic was his work on the system RM (R-mingle). Although RM is an interesting system in its own right, it is widely considered to be too strong. In this chapter, I revisit a closely related system, RM0 (sometimes known as ‘constructive mingle’), which includes the mingle axiom while not degenerating in the way that RM itself does. My main interest will be in examining this logic from two related semantical perspectives. First, I give (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  16.  66
    A Reinterpretation of the Semilattice Semantics with Applications.Yale Weiss - 2021 - Logica Universalis 15 (2):171-191.
    In the early 1970s, Alasdair Urquhart proposed a semilattice semantics for relevance logic which he provided with an influential informational interpretation. In this article, I propose a BHK-inspired reinterpretation of the semantics which is related to Kit Fine’s truthmaker semantics. I discuss and compare Urquhart’s and Fine’s semantics and show how simple modifications of Urquhart’s semantics can be used to characterize both full propositional intuitionistic logic and Jankov’s logic. I then present (quasi-)relevant companions for both of these systems. Finally, I (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  17.  30
    Cut and gamma I: Propositional and constant domain R.Yale Weiss - 2020 - Review of Symbolic Logic 13 (4):887-909.
    The main object of this article is to give two novel proofs of the admissibility of Ackermann’s rule (γ) for the propositional relevant logic R. The results are established as corollaries of cut elimination for systems of tableaux for R. Cut elimination, in turn, is established both nonconstructively (as a corollary of completeness) and constructively (using Gentzen-like methods). The extensibility of the techniques is demonstrated by showing that (γ) is admissible for RQ* (R with constant domain quantifiers). The status of (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  18.  34
    Colloquium 1 Commentary on Cherubin.Yale Weiss - 2018 - Proceedings of the Boston Area Colloquium of Ancient Philosophy 33 (1):22-26.
    This commentary examines the interpretation of Parmenides developed by Rose Cherubin in her paper, “Parmenides, Liars, and Mortal Incompleteness.” First, I discuss the tensions Cherubin identifies between the definitions and presuppositions of justice, necessity, fate, and the other requisites of inquiry. Second, I critically assess Cherubin’s attribution of a sort of liar paradox to Parmenides. Finally, I argue that Cherubin’s handling of the Doxa, the section of Parmenides’ poem that deals with mortal opinion and cosmology, is unsatisfactory. I suggest that (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  19. The Myth of Hippasus and One Mathematical Paradigm Shift.Yale Weiss - 2016 - Dialogue 55 (2):89-94.
    No categories
     
    Export citation  
     
    Bookmark  
  20.  45
    Review: Hugh H. Benson. Clitophon's Challenge: Dialectic in Plato's Meno, Phaedo, and Republic. Oxford: Oxford University Press, 2015. 328 pages; $65.00/hardcover. [REVIEW]Yale Weiss - 2016 - Philosophical Forum 47 (1):25-29.