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Zach Weber [21]Z. Weber [2]Zack Weber [1]
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Profile: Zach Weber (University of Otago)
Profile: Zach Weber
  1. 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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  2. Zach Weber (2014). Naive Validity. Philosophical Quarterly 64 (254):99-114.
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  3. Zach Weber, David Ripley, Graham Priest, Dominic Hyde & Mark Colyvan (2014). Tolerating Gluts. Mind 123 (491):813-828.
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  4. 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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  5. 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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  6. Zach Weber (2013). Lloyd Humberstone , The Connectives . Reviewed By. Philosophy in Review 33 (4):305-307.
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  7. 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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  8. 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. 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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  10. Zach Weber (2012). Piotr Łukowski , Paradoxes , Tr. Marek Gensler. Reviewed By. Philosophy in Review 32 (4):307-309.
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  11. 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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  12. Jc Beall, Graham Priest & Zack Weber (2011). Can U Do That? Analysis 71 (2):280-285.
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  13. Eric Dietrich & Zach Weber (eds.) (2011). Philosophy’s Future.
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  14. Z. Weber (2011). A Paraconsistent Model of Vagueness. Mind 119 (476):1025-1045.
    Vague predicates, on a paraconsistent account, admit overdetermined borderline cases. I take up a new line on the paraconsistent approach, to show that there is a close structural relationship between the breakdown of soritical progressions, and contradiction. Accordingly, a formal picture drawn from an appropriate logic shows that any cut-off point of a vague predicate is unidentifiable, in a precise sense. A paraconsistent approach predicts and explains many of the most counterintuitive aspects of vagueness, in terms of a more fundamental (...)
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  15. Zach Weber (2011). Issue Introduction. Essays in Philosophy 12 (2):1.
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  16. Zach Weber (2011). Reply to Bjørdal. Review of Symbolic Logic 4 (1):109-113.
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  17. 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 (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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  19. 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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  20. Zach Weber (2010). Jc Beall: Spandrels of Thruth. Bulletin of Symbolic Logic 16 (2).
     
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  21. 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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  22. Zach Weber & Mark Colyvan (2010). A Topological Sorites. Journal of Philosophy 107 (6):311-325.
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  23. 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. Z. Weber (2007). On Paraconsistent Ethics. 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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