Results for 'deductions'

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  1. Apodeictic Syllogisms: Deductions and Decision Procedures.Fred Johnson - 1995 - History and Philosophy of Logic 16 (1):1-18.
    One semantic and two syntactic decision procedures are given for determining the validity of Aristotelian assertoric and apodeictic syllogisms. Results are obtained by using the Aristotelian deductions that necessarily have an even number of premises.
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  2. Kant’s Deductions of Morality and Freedom.Owen Ware - 2017 - Canadian Journal of Philosophy 47 (1):116-147.
    It is commonly held that Kant ventured to derive morality from freedom in Groundwork III. It is also believed that he reversed this strategy in the second Critique, attempting to derive freedom from morality instead. In this paper, I set out to challenge these familiar assumptions: Kant’s argument in Groundwork III rests on a moral conception of the intelligible world, one that plays a similar role as the ‘fact of reason’ in the second Critique. Accordingly, I argue, there is no (...)
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  3. A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
    In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...)
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  4. Boole's Criteria for Validity and Invalidity.John Corcoran & Susan Wood - 1980 - Notre Dame Journal of Formal Logic 21 (4):609-638.
    It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...)
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  5. The Contemporary Relevance of Ancient Logical Theory.John Corcoran - 1982 - Philosophical Quarterly 32 (126):76.
    This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and his understanding (...)
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  6. Aristotle's Many-Sorted Logic.J. Corcoran - 2008 - Bulletin of Symbolic Logic 14 (1):155-156.
    As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved using my 1972 (...)
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  7. When Transmission Fails.Chris Tucker - 2010 - Philosophical Review 119 (4):497-529.
    The Neo-Moorean Deduction (I have a hand, so I am not a brain-in-a-vat) and the Zebra Deduction (the creature is a zebra, so isn’t a cleverly disguised mule) are notorious. Crispin Wright, Martin Davies, Fred Dretske, and Brian McLaughlin, among others, argue that these deductions are instances of transmission failure. That is, they argue that these deductions cannot transmit justification to their conclusions. I contend, however, that the notoriety of these deductions is undeserved. My strategy is to (...)
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  8. The Principles of Mathematics.Bertrand Russell - 1903 - Allen & Unwin.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a (...)
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  9. Impossible Worlds and Logical Omniscience: An Impossibility Result.Jens Christian Bjerring - 2013 - Synthese 190 (13):2505-2524.
    In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that (...)
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  10.  26
    The Problem with Reason.Kaius Ikejezie - manuscript
    Reason is the tool of our knowledge but in philosophy this tool encounters difficulties, especially, when it is faced with the big questions - the source of philosophy's deep disagreements. Another difficulty arises from the fact that philosophy and religion cross each other's path: the first draws deductions from rational principles in its approach to religion while the second does not remain firm on its terrain - it keeps looking for rational answers. In essence, this is what this article (...)
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  11. The Founding of Logic.John Corcoran - 1994 - Ancient Philosophy 14 (S1):9-24.
    Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...)
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  12.  93
    A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation.Nils Kürbis - 2019 - Bulletin of the Section of Logic 48 (2):81-97.
    This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.
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  13. Aristotle's Demonstrative Logic.John Corcoran - 2009 - History and Philosophy of Logic 30 (1):1-20.
    Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...)
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  14. In Defence of Single-Premise Closure.Weng Tang - 2018 - Philosophical Studies 175 (8):1887-1900.
    It’s often thought that the phenomenon of risk aggregation poses a problem for multi-premise closure but not for single-premise closure. But recently, Lasonen-Aarnio and Schechter have challenged this thought. Lasonen-Aarnio argues that, insofar as risk aggregation poses a problem for multi-premise closure, it poses a similar problem for single-premise closure. For she thinks that, there being such a thing as deductive risk, risk may aggregate over a single premise and the deduction itself. Schechter argues that single-premise closure succumbs to risk (...)
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  15. Polynomial Ring Calculus for Modal Logics: A New Semantics and Proof Method for Modalities: Polynomial Ring Calculus for Modal Logics.Juan C. Agudelo - 2011 - Review of Symbolic Logic 4 (1):150-170.
    A new proof style adequate for modal logics is defined from the polynomial ring calculus. The new semantics not only expresses truth conditions of modal formulas by means of polynomials, but also permits to perform deductions through polynomial handling. This paper also investigates relationships among the PRC here defined, the algebraic semantics for modal logics, equational logics, the Dijkstra???Scholten equational-proof style, and rewriting systems. The method proposed is throughly exemplified for S 5, and can be easily extended to other (...)
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  16. Le principe de rationalité et l'unité des sciences sociales.Philippe Mongin - 2002 - Revue Economique 53 (2):301-323.
    The paper revisits the rationality principle from the particular perspective of the unity of social sciences. It has been argued that the principle was the unique law of the social sciences and that accordingly there are no deep differences between them (Popper). It has also been argued that the rationality principle was specific to economics as opposed to the other social sciences, especially sociology (Pareto). The paper rejects these opposite views on the grounds that the rationality principle is strictly metaphysical (...)
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  17. Variable Binding Term Operators.John Corcoran, William Hatcher & John Herring - 1972 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (12):177-182.
    Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic Analysis of (...)
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  18. Notes on a Semantic Analysis of Variable Binding Term Operators.J. Corcoran & John Herring - 1971 - Logique Et Analyse 55:644-657.
    -/- A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. -/- Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give a correct (...)
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  19.  88
    Bilateralism: Negations, Implications and Some Observations and Problems About Hypotheses.Nils Kürbis - 2017 - In Thomas Piecha & Jean Fichot (eds.), Beyond Logic. Proceedings of the Conference held in Cerisy-la-Salle, 22-27 May 2017. Tübingen, Germany:
    This short paper has two loosely connected parts. In the first part, I discuss the difference between classical and intuitionist logic in relation to different the role of hypotheses play in each logic. Harmony is normally understood as a relation between two ways of manipulating formulas in systems of natural deduction: their introduction and elimination. I argue, however, that there is at least a third way of manipulating formulas, namely the discharge of assumption, and that the difference between classical and (...)
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  20. REVIEW OF 1988. Saccheri, G. Euclides Vindicatus (1733), Edited and Translated by G. B. Halsted, 2nd Ed. (1986), in Mathematical Reviews MR0862448. 88j:01013.John Corcoran - 1988 - MATHEMATICAL REVIEWS 88 (J):88j:01013.
    Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...)
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  21. ARISTOTELIAN LOGIC AND EUCLIDEAN GEOMETRY.John Corcoran - 2014 - Bulletin of Symbolic Logic 20 (1):131-2.
    John Corcoran and George Boger. Aristotelian logic and Euclidean geometry. Bulletin of Symbolic Logic. 20 (2014) 131. -/- By an Aristotelian logic we mean any system of direct and indirect deductions, chains of reasoning linking conclusions to premises—complete syllogisms, to use Aristotle’s phrase—1) intended to show that their conclusions follow logically from their respective premises and 2) resembling those in Aristotle’s Prior Analytics. Such systems presuppose existence of cases where it is not obvious that the conclusion follows from the (...)
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  22. Counterfactuals: The Epistemic Analysis.John-Michael Kuczynski - 2005 - Philosophia Scientiae 9 (1):83-126.
    Ordinarily counterfactuals are seen as making statements about states of affairs, albeit ones that hold in merely possible or alternative worlds. Thus analyzed, nearly all counterfactuals turn out to be incoherent. Any counterfactual, thus analyzed, requires that there be a metaphysically (not just epistemically) possible world w where the laws are the same as here, and where almost all of the facts are the same as here. (The factual differences relate to the antecedent and consequent of the counter-factual.) But, as (...)
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  23. Book Review: Chris Cuomo. The Philosopher Queen: Feminist Essays on War, Love, and Knowledge. Lanham, Md.: Rowman and Littlefield Publishers, Inc., 2003. [REVIEW]Alison Bailey - 2005 - Hypatia 20 (3):218-221.
    The Philosopher Queen: Feminist Essays on War, Love, and Knowledge. By Chris Cuomo. Lanham, Md.: Rowman and Littlefield Publishers, Inc., 2003. The Philosopher Queen is a powerful illustration of what Cherríe Moraga calls a "theory in the flesh." That is, theorizing from a place where "physical realities of our lives—our skin color, the land or concrete we grow up on, our sexual longings—all fuse to create a politic [and, I would add, an ethics, spirituality, and epistemology] born out of necessity" (...)
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  24. “Truth-Preserving and Consequence-Preserving Deduction Rules”,.John Corcoran - 2014 - Bulletin of Symbolic Logic 20 (1):130-1.
    A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...)
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  25. Discourse Grammars and the Structure of Mathematical Reasoning III: Two Theories of Proof,.John Corcoran - 1971 - Journal of Structural Learning 3 (3):1-24.
    ABSTRACT This part of the series has a dual purpose. In the first place we will discuss two kinds of theories of proof. The first kind will be called a theory of linear proof. The second has been called a theory of suppositional proof. The term "natural deduction" has often and correctly been used to refer to the second kind of theory, but I shall not do so here because many of the theories so-called are not of the second kind--they (...)
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  26. Letter From a Gentleman in Dunedin to a Lady in the Countryside.Charles Pigden - 2010 - In Hume on Is and Ought.
    I argue 1) That in his celebrated Is/Ought passage, Hume employs ‘deduction’ in the strict sense, according to which if a conclusion B is justly or evidently deduced from a set of premises A, A cannot be true and B false, or B false and the premises A true. 2) That Hume was following the common custom of his times which sometimes employed ‘deduction’ in a strict sense to denote inferences in which, in the words of Dr Watts’ Logick, ‘the (...)
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  27.  51
    Traditional Catholic Philosophy: Baby and Bathwater.James Franklin - 2006 - In Michael Whelan (ed.), Issues for Church and Society in Australia. Sydney, Australia: St Pauls. pp. 15-32.
    The teaching of the Aquinas Academy in its first thirty years was based on the scholastic philosophy of Thomas Aquinas, then regarded as the official philosophy of the Catholic Church. That philosophy has not been so much heard of in the last thirty years, but it has a strong presence below the surface. Its natural law theory of ethics, especially, still informs Vatican pronouncements on moral topics such as contraception and euthanasia. It has also been important in Australia in the (...)
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  28.  99
    Identity Logics.John Corcoran & Stanley Ziewacz - 1979 - Notre Dame Journal of Formal Logic 20 (4):777-784.
    In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its (...) include both the direct and the indirect deductions constructed with the three traditional rules. IL3 is a hybrid of IL1 and IL2: its deductions are all direct as in IL1 but it deals with identities and inidentities as in IL2. IL1 and IL2 have a high degree of naturalness. Although the hybrid system IL3 was constructed as an artifact useful in the mathematical study of IL1 and IL2, it nevertheless has some intrinsically interesting aspects. The main motivation for describing and studying such simple systems is pedagogical. In teaching beginning logic one would like to present a system of logic which has the following properties. First, it exemplifies the main ideas of logic: implication, deduction, non-implication, counterargument(or countermodel), logical truth, self-contradiction, consistency,satisfiability, etc. Second, it exemplifies the usual general metaprinciples of logic: contraposition and transitivity of implication, cut laws, completeness,soundness, etc. Third, it is simple enough to be thoroughly grasped by beginners. Fourth, it is obvious enough so that its rules do not appear to be arbitrary or purely conventional. Fifth, it does not invite confusions which must be unlearned later. Sixth, it involves a minimum of presuppositions which are no longer accepted in mainstream contemporary logic. (shrink)
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  29.  55
    Deducción/Deducibilidad.John Corcoran - 2011 - In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta. pp. 168--169.
    Following Quine [] and others we take deductions to produce knowledge of implications: a person gains knowledge that a given premise-set implies a given conclusion by deducing—producing a deduction of—the conclusion from those premises. How does this happen? How does a person recognize their desire for that knowledge of a certain implication, or that they lack it? How do they produce a suitable deduction? And most importantly, how does their production of that deduction provide them with knowledge of the (...)
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  30.  74
    Eliminating Undecidability and Incompleteness in Formal Systems.Pete Olcott - manuscript
    To eliminate incompleteness, undecidability and inconsistency from formal systems we only need to convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive inference model. -/- Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusion) thus unlike the formal proofs of symbolic logic provability cannot diverge from truth.
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  31.  12
    Heuristics of String Theory.Nicolae Sfetcu - manuscript
    Since string theory has not been able to explain phenomena to date, it may seem that this confirms Feyerabend's view that there is no "method" of science. And yet, string theory is still the most active research program for quantum gravity. But, compared to other non-falsifiable theories, this has something extra, especially mathematical language, with a clear logic of deductions. Up to a point it can reproduce classical gauge theories and general relativity. And there is hope that in the (...)
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  32. Logical Consequence in Modal Logic II: Some Semantic Systems for S4.George Weaver - 1974 - Notre Dame Journal of Formal Logic 15:370.
    ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be equivalent; (...)
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  33. Mobile Phones and the Breakdown of Face-to-Face Communication: Kierkegaard's Call to Friluftsliv.Bjørn Ralf Kristensen - manuscript
    In this paper, I address the negative side effects on face-to-face communication and well-being resulting from our continual use of mobile-mediated technology. I consider these consequences by drawing on Søren Kierkegaard's deductions on deficient communication, and discuss one remedy he suggests: a closer relationship with nature. However, technology is so ubiquitous in the modern age that the prospect of escaping it, is nearly futile. In response, I offer a solution from the ideology of friluftsliv, which views a regular relationship (...)
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