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Profile: Zach Weber (University of Otago)
Profile: Zach Weber
  1.  51
    Zach Weber (2010). Transfinite Numbers in Paraconsistent Set Theory. 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.  16
    Zach Weber (2014). Naive Validity. Philosophical Quarterly 64 (254):99-114.
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  3.  73
    Zach Weber, David Ripley, Graham Priest, Dominic Hyde & Mark Colyvan (2014). Tolerating Gluts. Mind 123 (491):813-828.
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  4.  26
    Zach Weber (2012). Transfinite Cardinals in Paraconsistent Set Theory. 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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  5.  10
    Zach Weber (2016). Intrinsic Value and the Last Last Man. Ratio 29 (2):n/a-n/a.
    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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  6.  54
    Zach Weber (2010). Extensionality and Restriction in Naive Set Theory. 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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  7.  18
    Zach Weber, Guillermo Badia & Patrick Girard (forthcoming). What Is an Inconsistent Truth Table? Australasian Journal of Philosophy:1-16.
    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.  46
    Maarten McKubre-Jordens & Zach Weber (2012). Real Analysis in Paraconsistent Logic. 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.  10
    Colin R. Caret & Zach Weber (2015). A Note on Contraction-Free Logic for Validity. 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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  10.  30
    Zach Weber & Mark Colyvan (2010). A Topological Sorites. Journal of Philosophy 107 (6):311-325.
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  11.  15
    Patrick Girard & Zach Weber (2015). Bad Worlds. 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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  12. Eric Dietrich & Zach Weber (eds.) (2011). Philosophy’s Future.
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  13.  21
    Zach Weber & A. J. Cotnoir (2015). Inconsistent Boundaries. 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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  14.  3
    Zach Weber (2010). Extensionality and Restriction in Naive Set Theory. Studia Logica 94 (1):87-104.
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  15.  37
    Zach Weber (2011). Reply to Bjørdal. Review of Symbolic Logic 4 (1):109-113.
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  16.  20
    Zach Weber (2013). Lloyd Humberstone , The Connectives . Reviewed By. Philosophy in Review 33 (4):305-307.
  17.  38
    Zach Weber (2011). Wittgenstein's Notes on Logic. By Michael Potter. [REVIEW] Metaphilosophy 42 (1-2):166-170.
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  18. Zach Weber, Figures, Formulae, and Functors.
    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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  19.  21
    Zach Weber (2012). Review of C. Mortensen, Inconsistent Geometry. [REVIEW] 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.  26
    Zach Weber (2010). Explanation And Solution In The Inclosure Argument. 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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  21.  5
    Zach Weber (2013). Notes on Inconsistent Set Theory. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer 315--328.
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  22.  5
    Zach Weber (2012). Piotr Łukowski , Paradoxes , Tr. Marek Gensler. Reviewed By. Philosophy in Review 32 (4):307-309.
  23.  13
    Zach Weber (2009). Review of Peter Schotch, Bryson Brown, Raymond Jennings (Eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. [REVIEW] Notre Dame Philosophical Reviews 2009 (9).
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  24.  5
    Zach Weber (2013). An Introduction to the Philosophy of Mathematics, by Colyvan Mark. Australasian Journal of Philosophy 91 (4):828-828.
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  25.  2
    Zach Weber (2011). Issue Introduction. Essays in Philosophy 12 (2):1.
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  26.  3
    Zach Weber (2013). An Introduction to the Philosophy of Mathematics, by Colyvan Mark: Cambridge: Cambridge University Press, 2012, Pp. X+ 188, AU $46.95 (Paperback). [REVIEW] Australasian Journal of Philosophy 91 (4):828-828.
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  27. Zach Weber (2010). Jc Beall: Spandrels of Thruth. Bulletin of Symbolic Logic 16 (2).
     
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  28. Zach Weber (2010). Spandrels of Truth. [REVIEW] Bulletin of Symbolic Logic 16 (2):284-285.
     
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