52,105 research outputs found
The hardness of the iconic must: Can Peirceâs existential graphs assist modal epistemology?
Charles Peirceâs diagrammatic logic - the Existential Graphs - is presented as a tool for illuminating how we know necessity, in answer to Benacerrafâs famous challenge that most âsemantics for mathematicsâ do not âfit an acceptable epistemologyâ. It is suggested that necessary reasoning is in essence a recognition that a certain structure has the structure that it has. This means that, contra Hume and his contemporary heirs, necessity is observable. One just needs to pay attention, not just to individual things but to how those things are related in larger structures, certain aspects of which force certain others to be a particular way
Probabilistic Consensus of the Blockchain Protocol
We introduce a temporal epistemic logic with probabilities as an extension of temporal epistemic logic. This extension enables us to reason about properties that characterize the uncertain nature of knowledge, like âagent a will with high probability know after time s same factâ. To define semantics for the logic we enrich temporal epistemic Kripke models with probability functions defined on sets of possible worlds. We use this framework to model and reason about probabilistic properties of the blockchain protocol, which is in essence probabilistic since ledgers are immutable with high probabilities. We prove the probabilistic convergence for reaching the consensus of the protocol
Modality is Not Explainable by Essence
Some metaphysicians believe that metaphysical modality is explainable by the essences of objects. In §II, I spell out the definitional view of essence, and in §III, a working notion of metaphysical explanation. Then, in §IV, I consider and reject five natural ways to explain necessity by essence: in terms of the principle that essential properties can't change, in terms of the supposed obviousness of the necessity of essential truth, in terms of the logical necessity of definitions, in terms of Fine's logic of essence, and in terms of the theory of real definitions. I will conclude that the present evidence favours rejecting the hypothesis that modality is explainable by essence
Logicism, Possibilism, and the Logic of Kantian Actualism
In this extended critical discussion of 'Kant's Modal Metaphysics' by Nicholas Stang (OUP 2016), I focus on one central issue from the first chapter of the book: Stangâs account of Kantâs doctrine that existence is not a real predicate. In §2 I outline some background. In §§3-4 I present and then elaborate on Stangâs interpretation of Kantâs view that existence is not a real predicate. For Stang, the question of whether existence is a real predicate amounts to the question: âcould there be non-actual possibilia?â (p.35). Kantâs view, according to Stang, is that there could not, and that the very notion of non-actual or âmereâ possibilia is incoherent. In §5 I take a close look at Stangâs master argument that Kantâs Leibnizian predecessors are committed to the claim that existence is a real predicate, and thus to mere possibilia. I argue that it involves substantial logical commitments that the Leibnizian could reject. I also suggest that it is danger of proving too much. In §6 I explore two closely related logical commitments that Stangâs reading implicitly imposes on Kant, namely a negative universal free logic and a quantified modal logic that invalidates the Converse Barcan Formula. I suggest that each can seem to involve Kant himself in commitment to mere possibilia
The intuitionistic fragment of computability logic at the propositional level
This paper presents a soundness and completeness proof for propositional
intuitionistic calculus with respect to the semantics of computability logic.
The latter interprets formulas as interactive computational problems,
formalized as games between a machine and its environment. Intuitionistic
implication is understood as algorithmic reduction in the weakest possible --
and hence most natural -- sense, disjunction and conjunction as
deterministic-choice combinations of problems (disjunction = machine's choice,
conjunction = environment's choice), and "absurd" as a computational problem of
universal strength. See http://www.cis.upenn.edu/~giorgi/cl.html for a
comprehensive online source on computability logic
Computer Science and Metaphysics: A Cross-Fertilization
Computational philosophy is the use of mechanized computational techniques to
unearth philosophical insights that are either difficult or impossible to find
using traditional philosophical methods. Computational metaphysics is
computational philosophy with a focus on metaphysics. In this paper, we (a)
develop results in modal metaphysics whose discovery was computer assisted, and
(b) conclude that these results work not only to the obvious benefit of
philosophy but also, less obviously, to the benefit of computer science, since
the new computational techniques that led to these results may be more broadly
applicable within computer science. The paper includes a description of our
background methodology and how it evolved, and a discussion of our new results.Comment: 39 pages, 3 figure
The logic of interactive Turing reduction
The paper gives a soundness and completeness proof for the implicative
fragment of intuitionistic calculus with respect to the semantics of
computability logic, which understands intuitionistic implication as
interactive algorithmic reduction. This concept -- more precisely, the
associated concept of reducibility -- is a generalization of Turing
reducibility from the traditional, input/output sorts of problems to
computational tasks of arbitrary degrees of interactivity. See
http://www.cis.upenn.edu/~giorgi/cl.html for a comprehensive online source on
computability logic
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