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Zach Weber
University of Otago
  1. Transfinite Numbers in Paraconsistent Set Theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.
    This paper begins an axiomatic development of naive set theoryin a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead (...)
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  2. Dialetheism.Francesco Berto, Graham Priest & Zach Weber - 2008 - Stanford Encyclopedia of Philosophy 2018 (2018).
    A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.
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  3.  89
    Transfinite Cardinals in Paraconsistent Set Theory.Zach Weber - 2012 - Review of Symbolic Logic 5 (2):269-293.
    This paper develops a (nontrivial) theory of cardinal numbers from a naive set comprehension principle, in a suitable paraconsistent logic. To underwrite cardinal arithmetic, the axiom of choice is proved. A new proof of Cantor’s theorem is provided, as well as a method for demonstrating the existence of large cardinals by way of a reflection theorem.
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  4. A Topological Sorites.Zach Weber & Mark Colyvan - 2010 - Journal of Philosophy 107 (6):311-325.
    This paper considers a generalisation of the sorites paradox, in which only topological notions are employed. We argue that by increasing the level of abstraction in this way, we see the sorites paradox in a new, more revealing light—a light that forces attention on cut-off points of vague predicates. The generalised sorites paradox presented here also gives rise to a new, more tractable definition of vagueness.
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  5.  84
    Extensionality and Restriction in Naive Set Theory.Zach Weber - 2010 - Studia Logica 94 (1):87-104.
    The naive set theory problem is to begin with a full comprehension axiom, and to find a logic strong enough to prove theorems, but weak enough not to prove everything. This paper considers the sub-problem of expressing extensional identity and the subset relation in paraconsistent, relevant solutions, in light of a recent proposal from Beall, Brady, Hazen, Priest and Restall [4]. The main result is that the proposal, in the context of an independently motivated formalization of naive set theory, leads (...)
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  6.  77
    Inconsistent Boundaries.Zach Weber & A. J. Cotnoir - 2015 - Synthese 192 (5):1267-1294.
    Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected . In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of (...)
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  7.  66
    What Is an Inconsistent Truth Table?Zach Weber, Guillermo Badia & Patrick Girard - 2016 - Australasian Journal of Philosophy 94 (3):533-548.
    ABSTRACTDo truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears in the foreground. Rather than (...)
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  8.  72
    Real Analysis in Paraconsistent Logic.Maarten McKubre-Jordens & Zach Weber - 2012 - Journal of Philosophical Logic 41 (5):901-922.
    This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open.
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  9.  57
    Naive Validity.Zach Weber - 2014 - Philosophical Quarterly 64 (254):99-114.
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  10. Tolerating Gluts.Zach Weber, David Ripley, Graham Priest, Dominic Hyde & Mark Colyvan - 2014 - Mind 123 (491):813-828.
  11.  42
    Computation in Non-Classical Foundations?Toby Meadows & Zach Weber - 2016 - Philosophers' Imprint 16.
    The Church-Turing Thesis is widely regarded as true, because of evidence that there is only one genuine notion of computation. By contrast, there are nowadays many different formal logics, and different corresponding foundational frameworks. Which ones can deliver a theory of computability? This question sets up a difficult challenge: the meanings of basic mathematical terms are not stable across frameworks. While it is easy to compare what different frameworks say, it is not so easy to compare what they mean. We (...)
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  12.  49
    A Note on Contraction-Free Logic for Validity.Colin R. Caret & Zach Weber - 2015 - Topoi 34 (1):63-74.
    This note motivates a logic for a theory that can express its own notion of logical consequence—a ‘syntactically closed’ theory of naive validity. The main issue for such a logic is Curry’s paradox, which is averted by the failure of contraction. The logic features two related, but different, implication connectives. A Hilbert system is proposed that is complete and non-trivial.
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  13.  38
    Atheism and Dialetheism; or, ‘Why I Am Not a (Paraconsistent) Christian’.Zach Weber - 2019 - Australasian Journal of Philosophy 97 (2):401-407.
    ABSTRACTIn ‘Theism and Dialetheism’, Cotnoir explores the idea that dialetheism can help with some puzzles about omnipotence in theology. In this note, I delineate another asp...
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  14.  24
    Modal Logic Without Contraction in a Metatheory Without Contraction.Patrick Girard & Zach Weber - 2019 - Review of Symbolic Logic 12 (4):685-701.
    Standard reasoning about Kripke semantics for modal logic is almost always based on a background framework of classical logic. Can proofs for familiar definability theorems be carried out using a nonclassical substructural logic as the metatheory? This article presents a semantics for positive substructural modal logic and studies the connection between frame conditions and formulas, via definability theorems. The novelty is that all the proofs are carried out with a noncontractive logic in the background. This sheds light on which modal (...)
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  15.  51
    Intrinsic Value and the Last Last Man.Zach Weber - 2016 - Ratio 29 (4).
    Even if you were the last person on Earth, you should not cut down all the trees—or so goes the Last Man thought experiment, which has been taken to show that nature has intrinsic value. But ‘Last Man’ is caught on a dilemma. If Last Man is too far inside the anthropocentric circle, so to speak, his actions cannot be indicative of intrinsic value. If Last Man is cast too far outside the anthropocentric circle, though, then value terms lose their (...)
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  16.  18
    Notes on Inconsistent Set Theory.Zach Weber - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 315--328.
  17.  28
    Observations on the Trivial World.Zach Weber & Hitoshi Omori - 2019 - Erkenntnis 84 (5):975-994.
    A world is trivial if it makes every proposition true all at once. Such a world is impossible, an absurdity. Our world, we hope, is not an absurdity. It is important, nevertheless, for semantic and metaphysical theories that we be able to reason cogently about absurdities—if only to see that they are absurd. In this note we describe methods for ‘observing’ absurd objects like the trivial world without falling in to incoherence, using some basic techniques from modal logic. The goal (...)
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  18.  14
    Intrinsic Value and the Last Last Man.Zach Weber - 2017 - Ratio 30 (2):165-180.
    Even if you were the last person on Earth, you should not cut down all the trees—or so goes the Last Man thought experiment, which has been taken to show that nature has intrinsic value. But ‘Last Man’ is caught on a dilemma. If Last Man is too far inside the anthropocentric circle, so to speak, his actions cannot be indicative of intrinsic value. If Last Man is cast too far outside the anthropocentric circle, though, then value terms lose their (...)
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  19.  55
    Review of 'Inconsistent Geometry', by Chris Mortensen. [REVIEW]Zach Weber - 2012 - Australasian Journal of Philosophy 90 (3):611-614.
    Australasian Journal of Philosophy, Volume 90, Issue 3, Page 611-614, September 2012.
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  20.  66
    Bad Worlds.Patrick Girard & Zach Weber - 2015 - Thought: A Journal of Philosophy 4 (2):93-101.
    The idea of relevant logic—that irrelevant inferences are invalid—is appealing. But the standard semantics for relevant logics involve baroque metaphysics: a three-place accessibility relation, a star operator, and ‘bad’ worlds. In this article we propose that these oddities express a mismatch between non-classical object theory and classical metatheory. A uniformly relevant semantics for relevant logic is a better fit.
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  21.  39
    Explanation And Solution In The Inclosure Argument.Zach Weber - 2010 - Australasian Journal of Philosophy 88 (2):353-357.
    In a recent article, Emil Badici contends that the inclosure schema substantially fails as an analysis of the paradoxes of self-reference because it is question-begging. The main purpose of this note is to show that Badici's critique highlights a necessity condition for the success of dialectic about paradoxes. The inclosure argument respects this condition and remains solvent.
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  22. Figures, Formulae, and Functors.Zach Weber - 2013 - In Sun-Joo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams. Springer. pp. 153--170.
    This article suggests a novel way to advance a current debate in the philosophy of mathematics. The debate concerns the role of diagrams and visual reasoning in proofs—which I take to concern the criteria of legitimate representation of mathematical thought. Drawing on the so-called ‘maverick’ approach to philosophy of mathematics, I turn to mathematical practice itself to adjudicate in this debate, and in particular to category theory, because there (a) diagrams obviously play a major role, and (b) category theory itself (...)
     
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  23.  47
    A Guide to Logical Pluralism for Non-Logicians.Zach Weber - 2017 - Think 16 (47):93-114.
  24. Philosophy’s Future.Eric Dietrich & Zach Weber - 2011
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  25.  21
    An Introduction to the Philosophy of Mathematics, by Colyvan Mark: Cambridge: Cambridge University Press, 2012, Pp. X + 188, AU$46.95. [REVIEW]Zach Weber - 2013 - Australasian Journal of Philosophy 91 (4):828-828.
  26.  26
    On Paraconsistent Ethics.Zach Weber - 2007 - South African Journal of Philosophy 26 (2):239-244.
    No. South African Journal of Philosophy Vol.26 (2) 2007:239-244.
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  27.  41
    On Closure and Truth in Substructural Theories of Truth.Zach Weber - forthcoming - Synthese:1-15.
    Closure is the idea that what is true about a theory of truth should be true in it. Commitment to closure under truth motivates non-classical logic; commitment to closure under validity leads to substructural logic. These moves can be thought of as responses to revenge problems. With a focus on truth in mathematics, I will consider whether a noncontractive approach faces a similar revenge problem with respect to closure under provability, and argue that if a noncontractive theory is to be (...)
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  28.  68
    Lloyd Humberstone , The Connectives . Reviewed By.Zach Weber - 2013 - Philosophy in Review 33 (4):305-307.
  29.  62
    Reply to Bjørdal.Zach Weber - 2011 - Review of Symbolic Logic 4 (1):109-113.
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  30.  55
    Wittgenstein's Notes on Logic. By Michael Potter. [REVIEW]Zach Weber - 2011 - Metaphilosophy 42 (1-2):166-170.
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  31.  12
    Paraconsistent Measurement of the Circle.Zach Weber & Maarten McKubre-Jordens - 2017 - Australasian Journal of Logic 14 (1).
    A theorem from Archimedes on the area of a circle is proved in a setting where some inconsistency is permissible, by using paraconsistent reasoning. The new proof emphasizes that the famous method of exhaustion gives approximations of areas closer than any consistent quantity. This is equivalent to the classical theorem in a classical context, but not in a context where it is possible that there are inconsistent innitesimals. The area of the circle is taken 'up to inconsistency'. The fact that (...)
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  32.  16
    Issue Introduction.Zach Weber - 2011 - Essays in Philosophy 12 (2):1.
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  33.  5
    Front Matter.Zach Weber, Maarten McKubre-Jordens & Patrick Girard - 2017 - Australasian Journal of Logic 14 (1).
    Editors' Introduction and List of Contributors.
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  34.  16
    Review of Peter Schotch, Bryson Brown, Raymond Jennings (Eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic[REVIEW]Zach Weber - 2009 - Notre Dame Philosophical Reviews 2009 (9).
  35.  6
    Reply to Bj??Rdal: Reply to Bj??Rdal.Zach Weber - 2011 - Review of Symbolic Logic 4 (1):109-113.
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  36.  9
    Piotr Łukowski , Paradoxes , Tr. Marek Gensler. Reviewed By.Zach Weber - 2012 - Philosophy in Review 32 (4):307-309.
  37.  1
    Jc Beall. Spandrels of Truth. Oxford University Press, Oxford, 2009, Xiv + 154 Pp. [REVIEW]Zach Weber - 2010 - Bulletin of Symbolic Logic 16 (2):284-286.
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  38. At the Limits of Thought.Zach Weber - 2019 - In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Springer Verlag. pp. 555-574.
    The inclosure schema has been proposed by Priest as the structure of many paradoxes. The inclosure analysis has many virtues, especially as a step toward a uniform solution to the paradoxes. Inclosure suggests that paradoxes arise at the limits of thought because the limits can be surpassed, and also not; and so dialetheism is true. I explore the consequences of accepting Priest’s proposal. From a thoroughly dialetheic perspective, then, I find that the import of inclosure changes: some limit phenomena cannot (...)
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  39. Jc Beall: Spandrels of Thruth.Zach Weber - 2010 - Bulletin of Symbolic Logic 16 (2).
  40. Spandrels of Truth. [REVIEW]Zach Weber - 2010 - Bulletin of Symbolic Logic 16 (2):284-285.