Results for 'substitutivity'

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  1. Organ donation and transplantation.Human Organs & Substituted Judgement Doctrine - 1984 - Bioethics Reporter 1 (1).
     
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  2.  36
    Sensory substitution and multimodal mental imagery.Bence Nanay - 2017 - Perception 46:1014-1026.
    Many philosophers use findings about sensory substitution devices in the grand debate about how we should individuate the senses. The big question is this: Is “vision” assisted by (tactile) sensory substitution really vision? Or is it tactile perception? Or some sui generis novel form of perception? My claim is that sensory substitution assisted “vision” is neither vision nor tactile perception, because it is not perception at all. It is mental imagery: visual mental imagery triggered by tactile sensory stimulation. But it (...)
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  3.  72
    Substitute Decision-Making for Adults with Intellectual Disabilities Living in Residential Care: Learning Through Experience.Michael C. Dunn, Isabel C. H. Clare & Anthony J. Holland - 2008 - Health Care Analysis 16 (1):52-64.
    In the UK, current policies and services for people with mental disorders, including those with intellectual disabilities (ID), presume that these men and women can, do, and should, make decisions for themselves. The new Mental Capacity Act (England and Wales) 2005 (MCA) sets this presumption into statute, and codifies how decisions relating to health and welfare should be made for those adults judged unable to make one or more such decisions autonomously. The MCA uses a procedural checklist to guide this (...)
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  4.  4
    Substitution: On the Animating Spirit of Economic Rationality.Arpad Szakolczai - forthcoming - Theory, Culture and Society.
    The term ‘substitution’, given minimal attention in thinking, became important in modern logic, but its treatment is highly technical. After a short review of its conceptual-historical background, the article discusses two important contemporary social and cultural theorists of substitution, Roberto Calasso and Michel Serres. It then turns to William Stanley Jevons, who first took up Boole’s logic, formulated the principle ‘substitution of similars’, the presumed heart of reasoning itself, constructed the first computer, and was a founder of neoclassical economics. The (...)
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  5.  92
    Epsilon substitution for transfinite induction.Henry Towsner - 2005 - Archive for Mathematical Logic 44 (4):397-412.
    We apply Mints’ technique for proving the termination of the epsilon substitution method via cut-elimination to the system of Peano Arithmetic with Transfinite Induction given by Arai.
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  6.  56
    Substitution, Identity, and the Subject-Predicate Structure.Genoveva Martı - 2005 - In Michael O'Rourke & Corey Washington (eds.), Situating Semantics: Essays on the Philosophy of John Perry. MIT Press. pp. 93.
    One of the many important tasks of semantics is to provide an account of the substitution patterns of a language—that is, to furnish an explanation of the conditions under which semantic values of complexes are preserved when components are replaced. The importance of this issue is plain: we only have to recall the debates regarding substitutivity between proponents of direct reference theories and advocates of some version of Fregeanism, as well as the disagreements among different proponents of direct reference (...)
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  7.  42
    Substitution Frege and extended Frege proof systems in non-classical logics.Emil Jeřábek - 2009 - Annals of Pure and Applied Logic 159 (1-2):1-48.
    We investigate the substitution Frege () proof system and its relationship to extended Frege () in the context of modal and superintuitionistic propositional logics. We show that is p-equivalent to tree-like , and we develop a “normal form” for -proofs. We establish connections between for a logic L, and for certain bimodal expansions of L.We then turn attention to specific families of modal and si logics. We prove p-equivalence of and for all extensions of , all tabular logics, all logics (...)
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  8.  28
    Substituted judgment for the never‐capacitated: Crossing Storar's bridge too far.Jacob M. Appel - 2021 - Bioethics 36 (2):225-231.
    Since several landmark legal decisions in the 1970s and 1980s, substituted judgment has become widely accepted as an approach to decision‐making for incapacitated patients that incorporates their autonomy and interests. Two notable exceptions have been cases involving minors and those involving cognitively or psychiatrically impaired individuals who never previously possessed the ability to contemplate the medical decisions involved in their care. While a best interest standard may have universal merit in pediatric cases, this paper argues that substituted judgement has been (...)
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  9.  7
    Substitute: going to school with a thousand kids.Nicholson Baker - 2016 - New York: Blue Rider Press.
    Describes how the author became an on-call substitute teacher in pursuit of the realities of American public education, describing his complex difficulties with helping educate today's students in spite of flawed curriculums and interpersonal challenges.
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  10. Substitution Structures.Andrew Bacon - 2019 - Journal of Philosophical Logic 48 (6):1017-1075.
    An increasing amount of twenty-first century metaphysics is couched in explicitly hyperintensional terms. A prerequisite of hyperintensional metaphysics is that reality itself be hyperintensional: at the metaphysical level, propositions, properties, operators, and other elements of the type hierarchy, must be more fine-grained than functions from possible worlds to extensions. In this paper I develop, in the setting of type theory, a general framework for reasoning about the granularity of propositions and properties. The theory takes as primitive the notion of a (...)
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  11.  76
    The Substitutional Quantifier.James B. Scoggin - 1978 - The Monist 61 (3):408-425.
    If the substitutional interpretation of quantification is tenable, it provides a basis for reinterpreting any formal language-system as nominalist: each substituend for the variables of quantification either designates a concrete object or it is empty.
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  12. Substituting the senses.Julian Kiverstein, Mirko Farina & Andy Clark - 2015 - In Mohan Matthen (ed.), The Oxford Handbook of the Philosophy of Perception. New York, NY: Oxford University Press UK.
    Sensory substitution devices are a type of sensory prosthesis that (typically) convert visual stimuli transduced by a camera into tactile or auditory stimulation. They are designed to be used by people with impaired vision so that they can recover some of the functions normally subserved by vision. In this chapter we will consider what philosophers might learn about the nature of the senses from the neuroscience of sensory substitution. We will show how sensory substitution devices work by exploiting the cross-modal (...)
     
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  13.  41
    Reparative Substitution and the ‘Efficacy Objection’: Toward a Modified Satisfaction Theory of Atonement.Joshua R. Farris & S. Mark Hamilton - 2017 - Perichoresis 15 (3):97-110.
    The doctrine of the atonement is a subject of perpetual curiosity for a number of contemporary theologians. The penal substitution theory of atonement in particular has precipitated a great deal of recent interest, being held up by many Protestants as ‘the’ doctrine of atonement. In this essay, we make a defense against the objection to the Anselmian theory of atonement that is often leveled against it by exponents of the Penal Substitution theory, namely, that Christ’s work does not accomplish anything (...)
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  14.  13
    Secular substitutes for religion in the modern world.John Rex - 2007 - The Politics and Religion Journal 1 (1):3-10.
    This article seeks to consider the ways in which substitutes for religion have been found both through a discussion of the treatment of religion in the classical sociological theories of Weber; Durkheim and Marx and then the way in which in modern societies alternative sets of belief and practices which fulfi l the same function as religion have been developed in the Communist and the postCommunist and Western worlds.
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  15. Substitutivity, Obstinacy, and the Case of Giorgione.Stefano Predelli - 2010 - Journal of Philosophical Logic 39 (1):5-21.
    In this essay, I propose an analysis of Quine’s example ’Giorgione was so-called because of his size’, grounded on the idea of an obstinate demonstrative. In the first sections, I discuss the advantages and drawbacks of the demonstrative and logophoric treatments of ‘so called’, I highlight certain parallelisms with Davidson’s paratactic view of quotation, and I introduce independent considerations in favor of the idea of an obstinate demonstrative. In the second half of my essay, I apply this notion to Quine’s (...)
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  16. Sensory Substitution and Perceptual Learning.Kevin Connolly - 2018 - In Fiona Macpherson (ed.), Sensory Substitution and Augmentation. Oxford: Proceedings of the British Academy, Oxford University Press.
    When a user integrates a sensory substitution device into her life, the process involves perceptual learning, that is, ‘relatively long-lasting changes to an organism’s perceptual system that improve its ability to respond to its environment’ (Goldstone 1998: 585). In this paper, I explore ways in which the extensive literature on perceptual learning can be applied to help improve sensory substitution devices. I then use these findings to answer a philosophical question. Much of the philosophical debate surrounding sensory substitution devices concerns (...)
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  17. Substitution by Image: The Very Idea.Jakub Stejskal - 2019 - Journal of Aesthetics and Art Criticism 77 (1):55-66.
    The aim of this article is to provide a plausible conceptual model of a specific use of images described as substitution in recent art-historical literature. I bring to light the largely implicit shared commitments of the art historians’ discussion of substitution, each working as they do in a different idiom, and I draw consequences from these commitments for the concept of substitution by image—the major being the distinction between nonportraying substitution and substitution by portrayal. I then develop an argument that (...)
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  18.  41
    Substitution contradiction, its resolution and the Church-Rosser Theorem in TIL.Miloš Kosterec - 2020 - Journal of Philosophical Logic 49 (1):121-133.
    I present an analysis according to which the current state of the definition of substitution leads to a contradiction in the system of Transparent Intensional Logic. I entail the contradiction using only the basic definitions of TIL and standard results. I then analyse the roots of the contradiction and motivate the path I take in resolving the contradiction. I provide a new amended definition of collision-less substitution which blocks the contradiction in a non-ad hoc way. I elaborate on the consequences (...)
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  19. Sensory Substitution is Substitution.Jean-Rémy Martin & François Le Corre - 2015 - Mind and Language 30 (2):209-233.
    Sensory substitution devices make use of one substituting modality to get access to environmental information normally accessed through another modality . Based on behavioural and neuroimaging data, some authors have claimed that using a vision-substituting device results in visual perception. Reviewing these data, we contend that this claim is untenable. We argue that the kind of information processed by a SSD is metamodal, so that it can be accessed through any sensory modality and that the phenomenology associated with the use (...)
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  20. Can Substitution Inferences Explain the Knobe Effect?Corey McGrath - 2011 - Review of Philosophy and Psychology 2 (4):667-679.
    The Knobe effect is the phenomenon demonstrated in the course of repeated studies showing that moral valence affects the way in which we apply concepts. Knobe explains the effect by appealing to the nature of the concepts themselves: whether they actually apply in some situation depends upon the moral valence of some element of that situation. In this paper, a different picture of the effect is presented and given motivation. It is suggested that subjects apply concepts on the basis of (...)
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  21.  19
    Sensory substitution devices and behavioural transference: a commentary on recent work from the lab of Amir Amedi.Derek H. Brown - 2018 - In Fiona Macpherson (ed.), Sensory Substitution and Augmentation. Oxford: Proceedings of the British Academy, Oxford University Press. pp. 122-129.
    Sensory substitution devices (SSDs) are most familiar from their use with subjects who are deficient in a target modality (e.g. congenitally blind subjects), but there is no doubt that the use and potential value of SSDs extend to persons without such deficits. Recent work by Amedi and his team (in particular Levy-Tzedek et al. 2012) has begun to explore this. Their idea is that SSDs may facilitate behavioural transference (BT) across sense modalities. In this case, a motor skill learned through (...)
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  22.  6
    Moral substitution reimagined.William Cooke, Drew Craddock & Sandra Visser - 2024 - International Journal for Philosophy of Religion 96 (3):191-197.
    In this paper, we suggest that those asking contemporary moral questions involving the punishment of groups, such as the justice of requiring corporations to make recompense for past wrongs or whether one race ought to make reparation payments to another, would find it fruitful to consider an older response to the question of moral substitution. We argue that Anselm of Canterbury’s theory of substitutionary atonement offers some surprising insights into the conditions under which one moral agent making recompense for another’s (...)
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  23.  18
    Substitution Logic: An Extension of Syllogism.Lei Ma - 2019 - Philosophical Forum 50 (2):191-223.
    I examine the theoretical difficulties of Aristotle’s syllogism and the traditional syllogism. I propose a more unified ordinary thinking logic different from the syllogism. I show that the new logic based on the substitution of thinking elements can be used to describe the reasoning process of human minds more properly, bypassing rigid figures, moods and cumbersome rules of the syllogism. I also show that the new logic combines the categorical inference with relation and modal inferences, expanding the scope of the (...)
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  24.  69
    Substituted Judgment in Medical Practice: Evidentiary Standards on a Sliding Scale.Mark R. Tonelli - 1997 - Journal of Law, Medicine and Ethics 25 (1):22-29.
    Consensus is growing among ethicists and lawyers that medical decision making for incompetent patients who were previously competent should be made in accordance with that person's prior wishes and desires. Moreover, this legal and ethical preference for the substituted judgment standard has found its way into the daily practice of medicine. However, what appears on the surface to be an agreement between jurists, bioethicists, and clinicians obscures the very real differences between disciplines regarding the actual implementation of the sub stituted (...)
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  25. Sensory Substitution and Augmentation: An Introduction.Fiona Macpherson - 2018 - In Sensory Substitution and Augmentation. Oxford: Proceedings of the British Academy, Oxford University Press.
    It is hoped that modern sensory substitution and augmentation devices will be able to replace or expand our senses. But to what extent has this been achieved to date? To what extent are the experiences created by sensory substitution devices like the sensory experiences that we are trying to replace? To what extent can we augment people’s senses providing them with new information and new experiences? The first aim of this introduction is to delve deeply into this question to discover (...)
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  26. The Substitutional Analysis of Logical Consequence.Volker Halbach - 2019 - Noûs 54 (2):431-450.
    A substitutional account of logical validity for formal first‐order languages is developed and defended against competing accounts such as the model‐theoretic definition of validity. Roughly, a substitution instance of a sentence is defined as the result of uniformly substituting nonlogical expressions in the sentence with expressions of the same grammatical category and possibly relativizing quantifiers. In particular, predicate symbols can be replaced with formulae possibly containing additional free variables. A sentence is defined to be logically true iff all its substitution (...)
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  27. Substitutivity.Genoveva Marti - 1989 - Dissertation, Stanford University
    This dissertation examines critically the assumptions of extensionalism and the traditional doctrine of substitutivity, according to which codesignativeness or coextensionality of terms should be a sufficient condition to guarantee intersubstitution of expression salva veritate. First, the discussion focuses on the traditional justifications of the extensionalist principles of substitutivity. The following alleged sources of support for extensionalism are examined: the claim that the extensionalist approach to substitutivity relies on fundamental principles outside the domain of semantics, like the Law (...)
     
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  28. Propositions and the Substitution Anomaly.Steven E. Boër - 2009 - Journal of Philosophical Logic 38 (5):549-586.
    The Substitution Anomaly is the failure of intuitively coreferential expressions of the corresponding forms “that S” and “the proposition that S” to be intersubstitutable salva veritate under certain ‘selective’ attitudinal verbs that grammatically accept both sorts of terms as complements. The Substitution Anomaly poses a direct threat to the basic assumptions of Millianism, which predict the interchangeability of “that S” and “the proposition that S”. Jeffrey King has argued persuasively that the most plausible Millian solution is to treat the selective (...)
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  29.  75
    Substitutions of Σ10-sentences: explorations between intuitionistic propositional logic and intuitionistic arithmetic.Albert Visser - 2002 - Annals of Pure and Applied Logic 114 (1-3):227-271.
    This paper is concerned with notions of consequence. On the one hand, we study admissible consequence, specifically for substitutions of Σ 1 0 -sentences over Heyting arithmetic . On the other hand, we study preservativity relations. The notion of preservativity of sentences over a given theory is a dual of the notion of conservativity of formulas over a given theory. We show that admissible consequence for Σ 1 0 -substitutions over HA coincides with NNIL -preservativity over intuitionistic propositional logic . (...)
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  30. Why Substitutional Quantification Does Not Express Existence.Philip Hugly & Charles Sayward - 1987 - Theory and Decision 50:67-75.
    Fundamental to Quine’s philosophy of logic is the thesis that substitutional quantification does not express existence. This paper considers the content of this claim and the reasons for thinking it is true.
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  31.  17
    Substitutability in time allocation.Howard Rachlin, John H. Kagel & Raymond C. Battalio - 1980 - Psychological Review 87 (4):355-374.
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  32.  99
    Substitution and truth in quantum logic.Itamar Pitowsky - 1982 - Philosophy of Science 49 (3):380-401.
    If p(x 1 ,...,x n ) and q(x 1 ,...,x n ) are two logically equivalent propositions then p(π (x 1 ),...,π (x n )) and q(π (x 1 ),...,π (x n )) are also logically equivalent where π is an arbitrary permutation of the elementary constituents x 1 ,...,x n . In Quantum Logic the invariance of logical equivalences breaks down. It is proved that the distribution rules of classical logic are in fact equivalent to the meta-linguistic rule of (...)
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  33.  6
    Substitutional Quantification in Truth-Theories for Modal Languages.Yannis Stephanou - forthcoming - Studia Logica:1-43.
    If we wish to formulate an axiomatic truth-theory interpreting a modal language and treat the symbol of necessity as a sentential operator and not as a quantifier over possible worlds, there arise various problems. These are due partly to the fact that words could have meant something other than what they actually mean and partly to certain principles of modal metaphysics. One of those principles is existentialism about propositions: a proposition that is expressed in a sentence containing a non-empty name (...)
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  34.  37
    A note on substitutions in representable cylindric algebras.Tarek Sayed Ahmed - 2009 - Mathematical Logic Quarterly 55 (3):280-287.
    We show that it is impossible to define a substitution operator for arbitrary representable cylindric algebras that agrees in its basic properties with the notion of substitutions introduced for dimension complemented algebras.
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  35. Sensory Substitution and the Challenge from Acclimatisation.Paul Noordhof - 2018 - In Fiona Macpherson (ed.), Sensory Substitution and Augmentation. Oxford: Proceedings of the British Academy, Oxford University Press. pp. 73-93.
    A refined characterisation of sensory substitution has, as a consequence, that the substituting sense plus sensory substitution device is not always appropriately classified as the substituted sense. As a result, I argue, acclimatisation to a sensory substitution device is plausibly thought of as providing presentations of properties. Externalist accounts of experience together with objectivist characterisations of such properties have the upshot that properties putatively proprietary to a sense modality can be presented in another modality in cases of substitution. I consider (...)
     
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  36. Sensory Substitution and Non-Sensory Feelings.David Suarez, Diana Acosta Navas, Umut Baysan & Kevin Connolly - 2018 - In Fiona Macpherson (ed.), Sensory Substitution and Augmentation. Oxford: Proceedings of the British Academy, Oxford University Press.
    One of the central limitations of sensory substitution devices (SSDs) is their inability to reproduce the non-sensory feelings that are normally associated with visual experiences, especially hedonic and aesthetic responses. This limitation is sometimes reported to cause SSD users frustration. To make matters worse, it is unclear that improvements in acuity, bandwidth, or training will resolve the issue. Yet, if SSDs are to actually reproduce visual experience in its fullness, it seems that the reproduction of non-sensory feelings will be of (...)
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  37.  69
    Substitution of indifferent options at choice nodes and admissibility: a reply to Rabinowicz.Teddy Seidenfeld - 2000 - Theory and Decision 48 (4):305-310.
    Tiebreak rules are necessary for revealing indifference in non- sequential decisions. I focus on a preference relation that satisfies Ordering and fails Independence in the following way. Lotteries a and b are indifferent but the compound lottery f, 0.5b> is strictly preferred to the compound lottery f, 0.5a>. Using tiebreak rules the following is shown here: In sequential decisions when backward induction is applied, a preference like the one just described must alter the preference relation between a and b at (...)
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  38. Simple sentences, substitution, and intuitions.Jennifer Mather Saul - 2007 - New York: Oxford University Press.
    Substitution and simple sentences -- Simple sentences and semantics -- Simple sentences and implicatures -- The enlightenment problem and a common assumption -- Abandoning (EOI) -- Beyond matching propositions -- App. A : extending the account -- App. B : belief reporting.
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  39. A propositional semantics for substitutional quantification.Geoff Georgi - 2015 - Philosophical Studies 172 (5):1183-1200.
    The standard truth-conditional semantics for substitutional quantification, due to Saul Kripke, does not specify what proposition is expressed by sentences containing the particular substitutional quantifier. In this paper, I propose an alternative semantics for substitutional quantification that does. The key to this semantics is identifying an appropriate propositional function to serve as the content of a bound occurrence of a formula containing a free substitutional variable. I apply this semantics to traditional philosophical reasons for interest in substitutional quantification, namely, theories (...)
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  40.  38
    The Substitutional Paradox in Russell's 1907 Letter to Hawtrey [see corrected reprint in next issue].Bernard Linsky - 2002 - Russell: The Journal of Bertrand Russell Studies 22 (1):47-55.
    This note presents a transcription of Russell's letter to Hawtrey of 22 January 1907 accompanied by some proposed emendations. In that letter Russell describes the paradox that he says "pilled" the "substitutional theory" developed just before he turned to the theory of types. A close paraphrase of the derivation of the paradox in a contemporary Lemmon-style natural deduction system shows which axioms the theory must assume to govern its characteristic notion of substituting individuals and propositions for each other in other (...)
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  41.  79
    Substitutes for Wisdom: Kant's Practical Thought and the Tradition of the Temperaments.Mark Joseph Larrimore - 2001 - Journal of the History of Philosophy 39 (2):259-288.
    In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.2 (2001) 259-288 [Access article in PDF] Substitutes for Wisdom:Kant's Practical Thought and the Tradition of the Temperaments Mark Larrimore [Appendix]For much of Western history, the theory of the four temperaments played a vital part in medicine, anthropology, and moral reflection. The Hippocratic foursome of sanguine, choleric, melancholy, and phlegmatic survives on the margins of modernity, but its role in moral theory and (...)
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  42.  69
    (2 other versions)Epsilon substitution method for ID1.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 121 (2):163-208.
    Hilbert proposed the epsilon substitution method as a basis for consistency proofs. Hilbert's Ansatz for finding a solving substitution for any given finite set of transfinite axioms is, starting with the null substitution S0, to correct false values step by step and thereby generate the process S0,S1,… . The problem is to show that the approximating process terminates. After Gentzen's innovation, Ackermann 162) succeeded to prove termination of the process for first order arithmetic. Inspired by G. Mints as an Ariadne's (...)
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  43. Information dynamics and uniform substitution.Wesley H. Holliday, Tomohiro Hoshi & Thomas F. Icard Iii - 2013 - Synthese 190 (1):31-55.
    The picture of information acquisition as the elimination of possibilities has proven fruitful in many domains, serving as a foundation for formal models in philosophy, linguistics, computer science, and economics. While the picture appears simple, its formalization in dynamic epistemic logic reveals subtleties: given a valid principle of information dynamics in the language of dynamic epistemic logic, substituting complex epistemic sentences for its atomic sentences may result in an invalid principle. In this article, we explore such failures of uniform substitution. (...)
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  44.  27
    Epsilon substitution for $$\textit{ID}_1$$ ID 1 via cut-elimination.Henry Towsner - 2018 - Archive for Mathematical Logic 57 (5-6):497-531.
    The \-substitution method is a technique for giving consistency proofs for theories of arithmetic. We use this technique to give a proof of the consistency of the impredicative theory \ using a variant of the cut-elimination formalism introduced by Mints.
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  45.  26
    Substitution’s Unsolved “Insolubilia”.Jolen Galaugher - 2013 - Russell: The Journal of Bertrand Russell Studies 33 (1):5-30.
    Russell’s substitutional theory conferred philosophical advantages over the simple type theory it was to emulate. However, it faced propositional paradoxes, and in a 1906 paper “On ‘Insolubilia’ and Their Solution by Symbolic Logic”, he modified the theory to block these paradoxes while preserving Cantor’s results. My aim is to draw out several quandaries for the interpretation of the role of substitution in Russell’s logic. If he was aware of the substitutional (_p_0_a_0) paradox in 1906, why did he advertise “Insolubilia” as (...)
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  46.  37
    The Substitutional Paradox in Russell's 1907 Letter to Hawtrey [corrected reprint].Bernard Linsky - 2002 - Russell: The Journal of Bertrand Russell Studies 22 (2).
    This note presents a transcription of Russell's letter to Hawtrey of 22 January 1907 accompanied by some proposed emendations. In that letter Russell describes the paradox that he says "pilled" the "substitutional theory" developed just before he turned to the theory of types. A close paraphrase of the derivation of the paradox in a contemporary Lemmon-style natural deduction system shows which axioms the theory must assume to govern its characteristic notion of substituting individuals and propositions for each other in other (...)
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  47. Substitutional Validity for Modal Logic.Marco Grossi - 2023 - Notre Dame Journal of Formal Logic 64 (3):291-316.
    In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.
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  48.  95
    Substitutive, Complementary and Constitutive Cognitive Artifacts: Developing an Interaction-Centered Approach.Marco Fasoli - 2018 - Review of Philosophy and Psychology 9 (3):671-687.
    AbtractTechnologies both new and old provide us with a wide range of cognitive artifacts that change the structure of our cognitive tasks. After a brief analysis of past classifications of these artifacts, I shall elaborate a new way of classifying them developed by focusing on an aspect that has been previously overlooked, namely the possible relationships between these objects and the cognitive processes they involve. Cognitive artifacts are often considered as objects that simply complement our cognitive capabilities, but this “complementary (...)
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  49.  44
    Epsilon substitution method for theories of jump hierarchies.Toshiyasu Arai - 2002 - Archive for Mathematical Logic 41 (2):123-153.
    We formulate epsilon substitution method for theories (H)α0 of absolute jump hierarchies, and give two termination proofs of the H-process: The first proof is an adaption of Mints M, Mints-Tupailo-Buchholz MTB, i.e., based on a cut-elimination of a specially devised infinitary calculus. The second one is an adaption of Ackermann Ack. Each termination proof is based on transfinite induction up to an ordinal θ(α0+ ω)0, which is best possible.
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  50. Epsilon-substitution method for the ramified language and Δ 1 1 -comprehension rule.Grigori Mints & S. Tupailo - 1999 - In Grigori Mints & S. Tupailo (eds.), ¸ Itecantini1999. Springer.
     
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