Results for 'Zach Thornton'

146 found
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  1.  47
    The Identity of Necessary Indiscernibles.Zach Thornton - forthcoming - Philosophers' Imprint.
    I propose a novel metaphysical explanation of identity and distinctness facts called the Modal Proposal. According to the Modal Proposal, for each identity fact – that is, each fact of the form a=b – that fact is metaphysically explained by the fact that it is necessary that the entities involved are indiscernible, and for each distinctness fact –that is, each fact of the form a≠b – that fact is metaphysically explained by the fact that it is possible for the entities (...)
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  2. Hilbert's program then and now.Richard Zach - 2006 - In Dale Jacquette (ed.), Philosophy of Logic. North Holland. pp. 411–447.
    Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...)
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  3.  34
    Logic in mathematics and computer science.Richard Zach - forthcoming - In Filippo Ferrari, Elke Brendel, Massimiliano Carrara, Ole Hjortland, Gil Sagi, Gila Sher & Florian Steinberger (eds.), Oxford Handbook of Philosophy of Logic. Oxford, UK: Oxford University Press.
    Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...)
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  4. Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...)
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  5. Place-based philosophical education: Reconstructing ‘place’, reconstructing ethics.Simone Thornton, Mary Graham & Gilbert Burgh - 2021 - Childhood and Philosophy 17:1-29.
    Education as identity formation in Western-style liberal-democracies relies, in part, on neutrality as a justification for the reproduction of collective individual identity, including societal, cultural, institutional and political identities, many aspects of which are problematic in terms of the reproduction of environmentally harmful attitudes, beliefs and actions. Taking a position on an issue necessitates letting go of certain forms of neutrality, as does effectively teaching environmental education. We contend that to claim a stance of neutrality is to claim a position (...)
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  6. Incompleteness and Computability: An Open Introduction to Gödel's Theorems.Richard Zach - 2019 - Open Logic Project.
    Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.
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  7. Why You Should Vote to Change the Outcome.Zach Barnett - 2020 - Philosophy and Public Affairs 48 (4):422-446.
    Prevailing opinion—defended by Jason Brennan and others—is that voting to change the outcome is irrational, since although the payoffs of tipping an election can be quite large, the probability of doing so is extraordinarily small. This paper argues that prevailing opinion is incorrect. Voting is shown to be rational so long as two conditions are satisfied: First, the average social benefit of electing the better candidate must be at least twice as great as the individual cost of voting, and second, (...)
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  8. Natural Deduction for the Sheffer Stroke and Peirce’s Arrow (and any Other Truth-Functional Connective).Richard Zach - 2015 - Journal of Philosophical Logic 45 (2):183-197.
    Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...)
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  9. Rational Moral Ignorance.Zach Barnett - 2021 - Philosophy and Phenomenological Research 102 (3):645-664.
    What should a person do when, through no fault of her own, she ends up believing a false moral theory? Some suggest that she should act against what the false theory recommends; others argue that she should follow her rationally held moral beliefs. While the former view better accords with intuitions about cases, the latter one seems to enjoy a critical advantage: It seems better able to render moral requirements ‘followable’ or ‘action-guiding.’ But this tempting thought proves difficult to justify. (...)
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  10. No free lunch: The significance of tiny contributions.Zach Barnett - 2018 - Analysis 78 (1):3-13.
    There is a well-known moral quandary concerning how to account for the rightness or wrongness of acts that clearly contribute to some morally significant outcome – but which each seem too small, individually, to make any meaningful difference. One consequentialist-friendly response to this problem is to deny that there could ever be a case of this type. This paper pursues this general strategy, but in an unusual way. Existing arguments for the consequentialist-friendly position are sorites-style arguments. Such arguments imagine varying (...)
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  11. Belief dependence: How do the numbers count?Zach Barnett - 2019 - Philosophical Studies 176 (2):297-319.
    This paper is about how to aggregate outside opinion. If two experts are on one side of an issue, while three experts are on the other side, what should a non-expert believe? Certainly, the non-expert should take into account more than just the numbers. But which other factors are relevant, and why? According to the view developed here, one important factor is whether the experts should have been expected, in advance, to reach the same conclusion. When the agreement of two (...)
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  12. Conciliationism and merely possible disagreement.Zach Barnett & Han Li - 2016 - Synthese 193 (9):1-13.
    Conciliationism faces a challenge that has not been satisfactorily addressed. There are clear cases of epistemically significant merely possible disagreement, but there are also clear cases where merely possible disagreement is epistemically irrelevant. Conciliationists have not yet accounted for this asymmetry. In this paper, we propose that the asymmetry can be explained by positing a selection constraint on all cases of peer disagreement—whether actual or merely possible. If a peer’s opinion was not selected in accordance with the proposed constraint, then (...)
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  13. Carthage: Aristotle’s Best (non-Greek) Constitution.Thornton C. Lockwood - 2024 - In Luca Gili, Benoît Castelnérac & Laetitia Monteils-Laeng (eds.), Actes du colloque Influences étrangères. pp. 182-205.
    Aristotle’s discussions of natural slavery, ‘barbarian kingship’, and the natural characteristics of barbarians or non-Greeks are usually read as calling into question the intellectual, ethical, and political accomplishments of non-Greeks. Such accounts of non-Greek inferiority or inability to self-govern also appear to presuppose a climatic or environmental account that on the whole would imply severe limitations on the possibility of political flourishing for peoples living outside the Greek Mediterranean basin. In light of such accounts, it is somewhat astounding to find (...)
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  14.  40
    Non-human animals in the Nicomachean and Eudemian Ethics.Thornton C. Lockwood - forthcoming - In Peter Adamson & Miira Tuominen (eds.), Animals in Greek, Arabic, and Latin Philosophy.
    At first glance, it looks like Aristotle can’t make up his mind about the ethical or moral status of non-human animals in his ethical treatises. Somewhat infamously, the Nicomachean Ethics claims that “there is neither friendship nor justice towards soulless things, nor is there towards an ox or a horse” (EN 8.11.1161b1–2). Since Aristotle thinks that friendship and justice are co-extensive (EN 8.9.1159b25–32), scholars have often read this passage to entail that humans have no ethical obligations to non-human animals. By (...)
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  15. Competing ways of life and ring-composition in NE x 6-8.Thornton Lockwood - 2014 - In Ronald Polansky (ed.), The Cambridge Companion to Aristotle's Nicomachean Ethics. Cambridge, UK: pp. 350-369.
    The closing chapters of Aristotle’s Nicomachean Ethics x are regularly described as “puzzling,” “extremely abrupt,” “awkward,” or “surprising” to readers. Whereas the previous nine books described—sometimes in lavish detail—the multifold ethical virtues of an embodied person situated within communities of family, friends, and fellow-citizens, NE x 6-8 extol the rarified, god-like and solitary existence of a sophos or sage (1179a32). The ethical virtues that take up approximately the first half of the Ethics describe moral exempla who experience fear fighting for (...)
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  16. Aristote et l’autre non-Grec.Thornton Lockwood - 2020 - In Pierre Pellegrin & Fracois Graziani (eds.), L'héritage d'Aristote aujourd’hui : Nature et société. pp. 249-261.
    Il est communément admis, aussi bien par les spécialistes que les non-spécialistes de la Grèce antique, qu'Aristote considère le barbaros ou l'autre Non-Grec comme radicalement distinct des Grecs (peut-être même racialement) et intrinsèquement inférieur à eux. Cette idée puise sa source dans ses remarques sur l'esclavage, sur les institutions politiques non grecques, sur les caractères naturels ou ethniques. Mais l’idée la plus répandue manque de nuance, et est souvent affirmée à tort en faisant l’économie d’un examen attentif des bases textuelles. (...)
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  17. Philosophy Without Belief.Zach Barnett - 2019 - Mind 128 (509):109-138.
    Should we believe our controversial philosophical views? Recently, several authors have argued from broadly conciliationist premises that we should not. If they are right, we philosophers face a dilemma: If we believe our views, we are irrational. If we do not, we are not sincere in holding them. This paper offers a way out, proposing an attitude we can rationally take toward our views that can support sincerity of the appropriate sort. We should arrive at our views via a certain (...)
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  18. Topical Bibliography to Aristotle's Nicomachean Ethics.Thornton Lockwood - 2014 - In Ronald Polansky (ed.), The Cambridge Companion to Aristotle's Nicomachean Ethics. New York, NY, USA: pp. 428-464.
    Topical bibliography of Aristotle's Nicomachean Ethics, organized by books/subjects within the Ethics. Includes editions and lexica for the study of Aristotle's Eudemian Ethics and Magna Moralia.
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  19. Tolerance and the distributed sorites.Zach Barnett - 2019 - Synthese 196 (3):1071-1077.
    On some accounts of vagueness, predicates like “is a heap” are tolerant. That is, their correct application tolerates sufficiently small changes in the objects to which they are applied. Of course, such views face the sorites paradox, and various solutions have been proposed. One proposed solution involves banning repeated appeals to tolerance, while affirming tolerance in any individual case. In effect, this solution rejects the reasoning of the sorites argument. This paper discusses a thorny problem afflicting this approach to vagueness. (...)
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  20. Aristotle on the (alleged) inferiority of poetry to history.Thornton C. Lockwood - 2017 - In William Wians & Ron Polansky (eds.), Reading Aristotle: Argument and Exposition. Boston: Brill. pp. 315-333.
    Aristotle’s claim that poetry is ‘a more philosophic and better thing’ than history (Poet 9.1451b5-6) and his description of the ‘poetic universal’ have been the source of much scholarly discussion. Although many scholars have mined Poetics 9 as a source for Aristotle’s views towards history, in my contribution I caution against doing so. Critics of Aristotle’s remarks have often failed to appreciate the expository principle which governs Poetics 6-12, which begins with a definition of tragedy and then elucidates the terms (...)
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  21. Vagueness, Logic and Use: Four Experimental Studies on Vagueness.Phil Serchuk, Ian Hargreaves & Richard Zach - 2011 - Mind and Language 26 (5):540-573.
    Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is Bonini et al. (1999), who report empirical results on the use of vague predicates by Italian speakers, and take the results to count in favor of epistemicism. Yet several methodological difficulties mar their experiments; we outline these problems and devise revised experiments that do not show the same results. We then (...)
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  22. Politics in Socrates’ Cave: Comments on Adriel M. Trott.Thornton Lockwood - 2021 - In Gary Gurtler & Daniel Maher (eds.), Proceedings of the Boston Area Colloquium on Ancient Philosophy, vol. 36. pp. 57-62.
    In her “Saving the Appearances in Plato’s Cave,” Dr. Adriel M. Trott argues that “the philosopher’s claim to true knowledge always operates within the realm of the cave.” In order to probe her claim, I challenge her to make sense of “politics in the cave,” namely the status and practices of two categories of people in the cave: “woke” cave dwellers (namely, those who recognize shadows as shadows but have not left the cave) and “woke” puppeteers (namely, philosophers ruling within (...)
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  23. The Epsilon Calculus and Herbrand Complexity.Georg Moser & Richard Zach - 2006 - Studia Logica 82 (1):133-155.
    Hilbert's ε-calculus is based on an extension of the language of predicate logic by a term-forming operator εx. Two fundamental results about the ε-calculus, the first and second epsilon theorem, play a rôle similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential (...)
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  24. The Genealogy of ‘∨’.Landon D. C. Elkind & Richard Zach - 2023 - Review of Symbolic Logic 16 (3):862-899.
    The use of the symbol ∨for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and (...)
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  25. Completeness before Post: Bernays, Hilbert, and the development of propositional logic.Richard Zach - 1999 - Bulletin of Symbolic Logic 5 (3):331-366.
    Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...)
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  26. Epimorphism between Fine and Ferguson’s Matrices for Angell’s AC.Richard Zach - 2023 - Logic and Logical Philosophy 32 (2):161-179.
    Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.
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  27. Philosophy goes to school in Australia: A history 1982-2016.Gilbert Burgh & Simone Thornton - 2016 - Journal of Philosophy in Schools 3 (1):59-83.
    This paper is an attempt to highlight significant developments in the history of philosophy in schools in Australia. We commence by looking at the early years when Laurance Splitter visited the Institute for the Advancement for Philosophy for Children (IAPC). Then we offer an account of the events that led to the formation of what is now the Federation of Australasian Philosophy in Schools Associations (FAPSA), the development and production of a diverse range of curriculum and supporting materials for philosophy (...)
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  28. The development of mathematical logic from Russell to Tarski, 1900-1935.Paolo Mancosu, Richard Zach & Calixto Badesa - 2011 - In Leila Haaparanta (ed.), The development of modern logic. New York: Oxford University Press.
    The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...)
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  29. Rumfitt on truth-grounds, negation, and vagueness.Richard Zach - 2018 - Philosophical Studies 175 (8):2079-2089.
    In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.
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  30. Fool me once: Can indifference vindicate induction?Zach Barnett & Han Li - 2018 - Episteme 15 (2):202-208.
    Roger White (2015) sketches an ingenious new solution to the problem of induction. He argues from the principle of indifference for the conclusion that the world is more likely to be induction- friendly than induction-unfriendly. But there is reason to be skeptical about the proposed indifference-based vindication of induction. It can be shown that, in the crucial test cases White concentrates on, the assumption of indifference renders induction no more accurate than random guessing. After discussing this result, the paper explains (...)
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  31. Numbers and functions in Hilbert's finitism.Richard Zach - 1998 - Taiwanese Journal for History and Philosophy of Science 10:33-60.
    David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...)
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  32. 양상논리 맛보기 (Tasting Modal Logic).Robert Trueman, Richard Zach & Chanwoo Lee - manuscript - Translated by Chanwoo Lee.
    This booklet is a Korean adaptation and translation of Part VIII of forall x: Calgary (Fall 2021 edition), which is intended to be introductory material for modal logic. The original text is based on Robert Trueman's A Modal Logic Primer, which is revised and expanded by Richard Zach and Aaron Thomas-Bolduc in forall x: Calgary. (forall x: Calgary is based on forall x: Cambridge by Tim Button, which is in turn based on forall x by P. D. Magnus, and (...)
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  33. Epsilon theorems in intermediate logics.Matthias Baaz & Richard Zach - 2022 - Journal of Symbolic Logic 87 (2):682-720.
    Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ - (...)
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  34. Evaluation of a student-oriented logic course.Aaron Thomas-Bolduc & Richard Zach - 2018 - ISSOTL 2018 Annual Meeting.
    In Winter 2017, the first author piloted a course in formal logic in which we aimed to (a) improve student engagement and mastery of the content, and (b) reduce maths anxiety and its negative effects on student outcomes, by adopting student oriented teaching including peer instruction and classroom flipping techniques. The course implemented a partially flipped approach, and incorporated group-work and peer learning elements, while retaining some of the traditional lecture format. By doing this, a wide variety of student learning (...)
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  35. “Sparta in Greek political thought: Xenophon, Plato, Aristotle, Plutarch,”.Thornton C. Lockwood - unknown - In Carol Atack (ed.), Oxford Handbook on Ancient Greek Political Thought. Oxford University Press.
    In his account of the Persian Wars, the 5th century historian Herodotus reports an exchange between the Persian monarch Xerxes and a deposed Spartan king, Demaratus, who became what Lattimore later classified as a “tragic warner” to Xerxes. On the eve of the battle of Thermopylae, Xerxes asks how a small number of free Spartiates can stand up against the massive ranks of soldiers that Xerxes has assembled. Herodotus has Demaratus reply: So is it with the Lacedaemonians; fighting singly they (...)
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  36. Hilbert’s Finitism: Historical, Philosophical, and Metamathematical Perspectives.Richard Zach - 2001 - Dissertation, University of California, Berkeley
    In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...)
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  37. Non-Analytic Tableaux for Chellas's Conditional Logic CK and Lewis's Logic of Counterfactuals VC.Richard Zach - 2018 - Australasian Journal of Logic 15 (3):609-628.
    Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.
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  38. Kurt Gödel, paper on the incompleteness theorems (1931).Richard Zach - 2004 - In Ivor Grattan-Guinness (ed.), Landmark Writings in Mathematics. North-Holland. pp. 917-925.
    This chapter describes Kurt Gödel's paper on the incompleteness theorems. Gödel's incompleteness results are two of the most fundamental and important contributions to logic and the foundations of mathematics. It had been assumed that first-order number theory is complete in the sense that any sentence in the language of number theory would be either provable from the axioms or refutable. Gödel's first incompleteness theorem showed that this assumption was false: it states that there are sentences of number theory that are (...)
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  39. Kurt Gödel and Computability Theory.Richard Zach - 2006 - In Beckmann Arnold, Berger Ulrich, Löwe Benedikt & Tucker John V. (eds.), Logical Approaches to Computational Barriers. Second Conference on Computability in Europe, CiE 2006, Swansea. Proceedings. Springer. pp. 575--583.
    Although Kurt Gödel does not figure prominently in the history of computabilty theory, he exerted a significant influence on some of the founders of the field, both through his published work and through personal interaction. In particular, Gödel’s 1931 paper on incompleteness and the methods developed therein were important for the early development of recursive function theory and the lambda calculus at the hands of Church, Kleene, and Rosser. Church and his students studied Gödel 1931, and Gödel taught a seminar (...)
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  40. Artemisia of Halicarnassus: Herodotus’ excellent counsel.Thornton C. Lockwood - 2023 - Classical World: A Quarterly Journal on Antiquity 116:147–172.
    Numerous ancient sources attest that Artemisia of Halicarnassus, a fifth-century BCE tyrant whose polis came under Persian rule in 524 BCE, figures prominently in Xerxes’ naval campaign against Greece. At least since Pompeius Trogus’ first-century BCE Philippic History, interpretations of Artemisia have juxtaposed her “virile courage” (uirilem audaciam) with Xerxes’ “womanish fear” (muliebrem timorem) primarily as a means of belittling the effeminate non-Greeks. My paper argues that although Herodotus is aware of such interpretations of Artemisia, he depicts her primarily as (...)
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  41. Philosophy for children in Australia: Then, now, and where to from here?Gilbert Burgh & Simone Thornton - 2016 - Re-Engaging with Politics: Re-Imagining the University, 45th Annual Conference of the Philosophy of Education Society of Australasia, ACU, Melbourne, 5-8 Dec 2015.
    In the late 1960s Matthew Lipman and his colleagues at IAPC developed an educational philosophy he called Philosophy for Children. At the heart of Philosophy for Children is the community of Inquiry, with its emphasis on classroom dialogue, in the form of collaborative philosophical inquiry. In this paper we explore the development of educational practice that has grown out of Philosophy for Children in the context of Australia. -/- Australia adapted Lipman’s ideas on the educational value of practicing philosophy with (...)
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  42. Is Natural Slavery Beneficial?Thornton Lockwood - 2007 - Journal of the History of Philosophy 45 (2):207-221.
    Aristotle's account of natural slavery appears to be internally inconsistent concerning whether slavery is advantageous to the natural slave. Whereas the Politics asserts that slavery is beneficial to the slave, the ethical treatises deny such a claim. Examination of Aristotle's arguments suggests a distinction which resolves the apparent contradiction. Aristotle distinguishes between the common benefit between two people who join together in an association And the same benefit which exists between a whole and its parts. Master and slave share no (...)
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  43. Boxes and Diamonds: An Open Introduction to Modal Logic.Richard Zach - 2019 - Open Logic Project.
    A textbook for modal and other intensional logics based on the Open Logic Project. It covers normal modal logics, relational semantics, axiomatic and tableaux proof systems, intuitionistic logic, and counterfactual conditionals.
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  44. Sets, Logic, Computation: An Open Introduction to Metalogic.Richard Zach - 2021 - Open Logic Project.
    An introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic.
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  45. Politics II: Political Critique, Political Theorizing, Political Innovation.Thornton Lockwood - 2015 - In Thornton C. Lockwood & Than Samaras (eds.), Aristotle’s Politics: A Critical Guide. Cambridge, UK: pp. 64-83.
    The second book of Aristotle’s Politics is generally taken to examine politeiai or constitutions that either exist in cities that are said to be well governed or were proposed by theoreticians and are thought to be well organized (II.1, 1260b30–32; II.12, 1274b26–28). Prominent are Aristotle’s examinations of Plato’s Republic and the constitution of Sparta; but Aristotle also devotes chapters to the examination of Plato’s Laws, the proposed constitutions of Phaleas of Chalcedon and Hippodamos of Miletus, and the existing constitutions of (...)
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  46. Engagement as dialogue: Camus, pragmatism and constructivist pedagogy.Gilbert Burgh & Simone Thornton - 2015 - Education as Philosophies of Engagement, 44th Annual Conference of the Philosophy of Education Society of Australasia, Kingsgate Hotel, Hamilton, New Zealand, 22–25 November 2014.
    In this paper we will explore how Albert Camus has much to offer philosophers of education. Although a number of educationalists have attempted to explicate the educational implications of Camus’ literary works (Denton, 1964; Oliver, 1965; Götz, 1987; Curzon-Hobson, 2003; Marshall, 2007, 2008; Weddington, 2007; Roberts, 2008, 2013; Gibbons, 2013; Heraud, 2013; Roberts, Gibbons & Heraud, 2013) these analyses have not attempted to extrapolate pedagogical guidelines to develop an educational framework for children’s philosophical practice in the way Matthew Lipman did (...)
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  47. Justice in Aristotle’s Household and City.Thornton C. Lockwood - 2003 - Polis 20 (1-2):1-21.
    In Nicomachean Ethics V.6 Aristotle contrasts political justice with household justice, paternal justice, and despotic justice. My paper expands upon Aristotle’s sometimes enigmatic remarks about political justice through an examination of his account of justice within the oikia or ‘household’. Understanding political justice requires explicating the concepts of freedom and equality, but for Aristotle, the children and wife within the household are free people even if not citizens, and there exists proportionate equality between a husband and wife. Additionally, Aristotle’s articulation (...)
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  48. ‘Do not block the way of inquiry’: cultivating collective doubt through sustained deep reflective thinking.Gilbert Burgh, Simone Thornton & Liz Fynes-Clinton - 2018 - In Ellen Duthie, Félix García Moriyón & Rafael Robles Loro (eds.), Parecidos de familia. Propuestas actuales en Filosofía para Niños / Family Resemblances: Current trends in philosophy for children. Madrid, Spain: pp. 47-61.
    We provide a Camusian/Peircean notion of inquiry that emphasises an attitude of fallibilism and sustained epistemic dissonance as a conceptual framework for a theory of classroom practice founded on Deep Reflective Thinking (DTR), in which the cultivation of collective doubt, reflective evaluation and how these relate to the phenomenological aspects of inquiry are central to communities of inquiry. In a study by Fynes-Clinton, preliminary evidence demonstrates that if students engage in DRT, they more frequently experience cognitive dissonance and as a (...)
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  49. Cicero's Philosophy of Just War.Thornton Lockwood - manuscript
    Cicero’s ethical and political writings present a detailed and sophisticated philosophy of just war, namely an account of when armed conflict is morally right or wrong. Several of the philosophical moves or arguments that he makes, such as a critique of “Roman realism” or his incorporation of the ius fetiale—a form of archaic international law—are remarkable similar to those of the contemporary just war philosopher Michael Walzer, even if Walzer is describing inter-state war and Cicero is describing imperial war. But (...)
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  50. Ethical Justice and Political Justice.Thornton Lockwood - 2006 - Phronesis 51 (1):29-48.
    The purpose of Aristotle's discussion of political justice (τό πολιὸν[unrepresentable symbol]δν δί[unrepresentable symbol]αιον) in "EN" V.6-7 has been a matter of dispute. Although the notion of political justice which Aristotle seeks to elucidate is relatively clear, namely the notion of justice which obtains between free and equal citizens living within a community aiming at self-sufficiency under the rule of law, confusion arises when one asks how political justice relates to the other kinds of justice examined in "EN" V. Is political (...)
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