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Hilbert proposed the epsilonsubstitution method as a basis for consistency proofs. Hilbert's Ansatz for finding a solvingsubstitution for any given finite set of transfinite axioms is, starting with the nullsubstitution 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 thread we formulate the epsilonsubstitution method for the theory ID1 of non-iterated inductive definitions for disjunctions of simply universal and existential operators, and give a termination proof of the H-process based on Ackermann 162). The termination proof is based on transfinite induction up to the Howard ordinal. (shrink)

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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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We apply Mints’ technique for proving the termination of the epsilonsubstitution method via cut-elimination to the system of Peano Arithmetic with Transfinite Induction given by Arai.

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Sensorysubstitution 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 sensorysubstitution. We will show how sensorysubstitution devices work by (...) exploiting the cross-modal plasticity of sensory cortex: the ability of sensory cortex to pick up some types of information about the external environment irrespective of the nature of the sensory inputs it is processing. We explore the implications of cross-modal plasticity for theories of the senses that attempt to make distinctions between the senses on the basis of neurobiology. (shrink)

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Many philosophers use findings about sensorysubstitution devices in the grand debate about how we should individuate the senses. The big question is this: Is “vision” assisted by (tactile) sensorysubstitution really vision? Or is it tactile perception? Or some sui generis novel form of perception? My claim is that sensorysubstitution 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 is a special form of mental imagery that is triggered by corresponding sensory stimulation in a different sense modality, which I call “multimodal mental imagery.”. (shrink)

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Sensorysubstitution 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 of a SSD is best described in terms of spatial phenomenology, only. (shrink)

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Substituted judgement is often used in the absence of advanced directives to guide decision-making when patients lack decisional capacity. We present a remarkable case of family members exercising substituted misjudgement for a 42-year-old man hospitalized with multiorgan failure on life support. Feeling that their loved one would rather die than face severe disability, they elected to withdraw life support. Although this was done, the patient remained alive and recovered enough to clearly indicate his preference for life, even with severe disability. (...) This case suggests that in instances of unusual quality-of-life judgements where the patient's wishes cannot be known with reasonable certainty, families and physicians should be very wary using substituted judgement to refuse life support. Unless there are strong considerations based on the patient's prior statements, actions and values to decline life support, it would seem ethically appropriate to continue treatment, even with substantial disability the likely outcome. (shrink)

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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 (...)substitution on a proposition (property, etc.) and, among other things, uses this idea to elucidate a number of theoretically important distinctions. A class of structures are identified which can be used to model a wide range of positions about the granularity of reality; certain of these structures are seen to receive a natural treatment in the category of M-sets. (shrink)

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In this commentary I argue that Byrne & Hilbert commit a number of philosophical solecisms: They beg the question of “realism,” they take the phenomenon and the theoretical model to be the same thing, and they surreptitiously substitute data sets for the life-world.

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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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Sensorysubstitution 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 visual perception might be subsequently employed in response to auditory perception, using an SSD as a mediator. They infer from the existence of such BT that the learned skill is amodally represented. After a brief overview I identify ways to more fully test for BT within this experimental paradigm and argue that their conclusion about amodal representation is premature. Additionally, I argue that their preferred SSD (Eyemusic) is of limited value for the project. While my remarks are critical, my intention is to be constructive, particularly in light of the fact that Levy-Tzedek et al. (2012), is, I believe, the first output from Amedi's lab concerning this line of research. (shrink)

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One of the many important tasks of semantics is to provide an account of thesubstitution 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 (...) theories as regards substitutivity in belief reports. This is why it is important to articulate an acceptable principle ofsubstitution. A traditional statement of the principle ofsubstitution holds that codesignative singular terms should be intersubtitutable salva veritate. In the past I have argued that such a principle is not connected properly to some pretheoretical data about the function of referring terms. In this chapter I argue that such a principle does not gain support either from other, more fundamental, laws. I end by defending the adequacy of a different principle ofsubstitution. (shrink)

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This essay discusses rules and semantic clauses relating toSubstitution—Leibniz’s law in the conjunctive-implicational form s=t ∧ A(s) → A(t)—as these are put forward in Priest’s books "In Contradiction" and "An Introduction to Non-Classical Logic: From If to Is." The stated rules and clauses are shown to be too weak in some cases and too strong in others. New ones are presented and shown to be correct. Justification for the various rules are probed and it is argued that (...) class='Hi'>Substitution ought to fail. (shrink)

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On a traditional interpretation of the substituted judgement standard a person who makes treatment decisions on behalf of a non-competent patient ought to decide as the patient would have decided had she been competent. I propose an alternative interpretation of SJS in which the surrogate is required to infer what the patient actually thought about these end-of-life decisions. In clarifying SJS it is also important to differentiate the patient's consent and preference. If SJS is part of an autonomy ideal of (...) the sort found in Kantian ethics, consent seems more important than preference. From a utilitarian perspective a preference-based reading of SJS seems natural. I argue that the justification of SJS within a utilitarian framework will boil down to the question whether a non-competent patient can be said to have any surviving preferences. If we give a virtue-ethical justification of SJS the relative importance of consent and preferences depends on which virtue one stresses-respect or care. I argue that SJS might be an independent normative method for extending the patient's autonomy, both from a Kantian and a virtue ethical perspective. (shrink)

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We formulate epsilonsubstitution method for elementary analysisEA (second order arithmetic with comprehension for arithmetical formulas with predicate parameters). Two proofs of its termination are presented. One uses embedding into ramified system of level one and cutelimination for this system. The second proof uses non-effective continuity argument.

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When a user integrates a sensorysubstitution 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 sensorysubstitution devices. I then use these findings to answer a philosophical question. Much of the philosophical debate surrounding sensory (...) class='Hi'>substitution devices concerns what happens after perceptual learning occurs. In particular, should the resultant perceptual experience be classified in the substituted modality (as vision), in the substituting modality (as auditory or tactile), or in a new sense modality? I propose a novel empirical test to help resolve this philosophical debate. (shrink)

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It is hoped that modern sensorysubstitution 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 sensorysubstitution 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 the usefulness of these devices, to outline the different sorts of experience that might be created, and what the evidence tells us about these experiences. While there are some reasons to be hopeful about the powers of sensorysubstitution devices, there are also reasons to wonder whether they will ever really have the practical applications that we hope they might have. The second aim is to look to see whether the study of modern sensorysubstitution and augmentation devices can shed light on the nature of our senses and perception in general. Much of the philosophical, psychological, and neuroscientific work that takes place concerning sensorysubstitution and augmentation is keenly aware of the possibility that it might help our understanding and it seeks to comprehend many different aspects of perception. (shrink)

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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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Substituted judgment has increasingly become the accepted standard for rendering decisions for incapacitated adults in the USA. A broad exception exists with regard to patients with diminished capacity secondary to depressive disorders, as such patients’ previous wishes are generally not honoured when seeking to turn down life-preserving care or pursue aid-in-dying. The result is that physicians often force involuntary treatment on patients with poor medical prognoses and/or low quality of life as a result of their depressive symptoms when similarly situated (...) incapacitated patients without such depressive symptoms would have their previous wishes honoured via substituted judgment. This commentary argues for reconsidering this approach and for using a substituted judgment standard for a subset of EMP/LQL patients seeking death. (shrink)

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We investigate thesubstitution 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 of finite depth and width, and typical examples of logics of finite width and infinite depth. In most cases, we actually show an equivalence with the usual system for classical logic with respect to a naturally defined translation.On the other hand, we establish exponential speed-up of over for all modal and si logics of infinite branching, extending recent lower bounds by P. Hrubeš. We develop a model-theoretical characterization of maximal logics of infinite branching to prove this result. (shrink)

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Substituted judgment is widely used at the bedside, but the moral value that underpins its use needs examination. I argue that this value is the value of leading an authentic life. I then argue that an authentic life has multiple axes and that patients (like all human beings) vary widely in how they score on these axes. This entails that the moral weight of the value of authenticity in bedside decision-making also varies widely. And that means that, at the bedside, (...) substituted judgment should not be seen as a moral trump. Put differently, when a surrogate must make a bedside decision, the answer to the “What would the patient choose?” question should not be morally decisive for that decision. The answer to that question should be a part, but only a part, of a more complex decision-making process. (shrink)

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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 thesubstitution 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 syllogism so that more complex quantification inferences can be captured. I conclude that thesubstitution of thinking elements is the basic characteristics of human thinking, and the substitutions can be further applied not only to all research fields of abstract and image thinking but also to practical fields of action methodology. (shrink)

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The set, the closure of F, is the closure with respect tosubstitution and concatenation recursion on notation of a set of basic functions comprehending the set F. By improving earlier work, we show that is thesubstitution closure of a simple function set and characterize well‐known function complexity classes as thesubstitution closure of finite sets of simple functions.

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The Reference Principle states that co-referring expressions are everywhere intersubstitutable salva congruitate. On first glance, looks like a truism, but a truism with some bite: transforms difficult philosophical questions about co-reference into easy grammatical questions about substitutability. This has led a number of philosophers to think that we can use to make short work of certain longstanding metaphysical debates. For example, it has been suggested that all we need to do to show that the predicate ‘ is a horse’ does (...) not refer to a property is point out that ‘ is a horse’ and ‘the property of being a horse’ are not everywhere intersubstitutable salva congruitate. However, when we understand ‘substitution’ in the simplest and most straightforward way, is no truism; in fact, natural languages are full of counterexamples to the principle. In this paper, I introduce a new notion ofsubstitution, and then develop and argue for a version of that is immune to these counterexamples. Along the way I touch on the following topics: the relation between argument forms and their natural language instances; the reification of sense; the difference between terms and predicates; and the relation between reference and disquotation. I end by arguing that my new version of cannot be used to settle metaphysical debates quite as easily as some philosophers would like. (shrink)

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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 (...) practice has been largely forgotten. Premodern understandings of human diversity based in climate, temperament, and politics collapsed with the Galenic medical tradition with which they harmonized. Yet temperament continued to be a feature of moral philosophies and philosophical anthropologies even into the twentieth century, and arguably has had a symbiotic relationship with the egalitarian aspirations of modern moral and political thought. This essay surveys the development and practical consequences of the theory of the temperaments developed by one of the greatest prophets of modern values, Immanuel Kant.Temperament was a feature in Kant's course in anthropology from the 1760s until the end of his life. Kant's teachings on temperament are by turns creative and conservative, and bespeak a deep understanding of the logic and rationale of humoral characterology in ethics. But as Kant moves from an ethics based in feeling to an ethics based on the possibility of autonomy, his theory of temperament also changes. In 1764's Observations on the Feeling of the Beautiful and the Sublime, Kant eloquently celebrates the melancholy as the temperament capable of "genuine virtue" (Obs2:217-18/60); by the time of Anthropology from a Pragmatic Point of View (1798), he is commending instead "phlegma as strength" (a variant of a temperament he had earlier dismissed), which can serve as a "substitute for wisdom" (Ant7:290/155). 1 Both of these [End Page 259] positions are distinctive, especially for an eighteenth-century thinker. As we will see, however, they are not without precedent in the tradition of temperament theory. Whether Kant knew he was developing countertraditions of temperament or not, his arguments in each case creatively exploit tensions in the humoral system which go back to its origins in ancient Greece.The mature Kant defended the classic foursome at a time when it had come under fire from many quarters. The early nineteenth century historian of temperament theories Harro Wilhelm Dircksen thought Kant played a decisive role in saving the classical theory from oblivion. 2 Why did Kant think it worth retrieving? One would expect him to reject a category which eighteenth-century German Popularphilosophie understood as a proto-psychological category bridging the gap between body and mind, nature and freedom. Yet, as I shall argue, the very things which might seem to render a theory of temperament incompatible with his mature ethics of autonomy make it important to [End Page 260] Kant. An understanding of human embodiment and diversity like that of the tradition of the temperaments forms part of the background to Kant's practical thought, and ethical formalism makes more rather than less sense if difference is taken seriously. For the same reason, it is important to have the right account of diversity. The complicated view of temperament in the Anthropology furnishes a microcosm of Kant's understanding of the fraught role of empirical considerations in recognizing and promoting freedom in rational agents embodied in human form(s).In this essay I will (1) provide a brief survey of the tradition of temperament theorizing before Kant, and expound Kant's (2) early and (3) mature views of temperament in the context of this tradition, as well as in the context of his emerging practical philosophy. 3 Some well-known parts of Kant's ethics make a new kind of sense when read in the light of the fact that their author thought humanity subdivided into temperaments. 1. The Tradition of the Temperaments 1.1. The history of moralizing about and through the temperaments is complex and—once one moves beyond the melancholy—largely uncharted. Here I will... (shrink)

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The aim of this article is to provide a plausible conceptual model of a specific use of images described assubstitution in recent art-historical literature. I bring to light the largely implicit shared commitments of the art historians’ discussion ofsubstitution, each working as they do in a different idiom, and I draw consequences from these commitments for the concept ofsubstitution by image—the major being the distinction between nonportrayingsubstitution andsubstitution by portrayal. I (...) then develop an argument thatsubstitution by image in the desired, nonportraying sense needs to be thought of in terms of a figurative representation of an image’s subject as a generic object, what I will call its figurative instantiation. (shrink)

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I present an analysis according to which the current state of the definition ofsubstitution 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-lesssubstitution which blocks the contradiction in a non-ad hoc way. I elaborate on (...) the consequences of the amended definition, namely the invalidity of the Church-Rosser theorem. I present a counterexample to the validity of the theorem in TIL with an amended definition ofsubstitution. (shrink)

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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, asubstitution 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 instances are satisfied by all variable assignments. Logical consequence is defined analogously. Satisfaction is taken to be a primitive notion and axiomatized.For every set‐theoretic model in the sense of model theory there exists a corresponding substitutional interpretation in a sense to be specified. Conversely, however, there are substitutional interpretations – in particular the ‘intended’ interpretation – that lack a model‐theoretic counterpart. The substitutional definition of logical validity overcomes the weaknesses of more restrictive accounts of substitutional validity; unlike model‐theoretic logical consequence, the substitutional notion is trivially and provably truth preserving. In Kreisel's squeezing argument the formal notion of substitutional validity naturally slots into the place of intuitive validity. (shrink)

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The doctrine of the atonement is a subject of perpetual curiosity for a number of contemporary theologians. The penalsubstitution 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 PenalSubstitution theory, namely, that Christ’s work does not (...) accomplish anything for those whom it appears he undertakes his atoning work, but merely makes provision for salvation. (shrink)

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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 (...) judgment standard. Ethicists and judges have carefully outlined how substituted judgments ought to be made and evaluated. Although differences arise, especially at the state court level, regarding the scope of the substituted judgment standard and its relation to other standards of surrogate decision making, agreement is fairly widespread on the priority of substituted judgment and on the necessity of sufficient evidence being available in order to support a particular substituted judgment. (shrink)

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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 of Indiscernibility of (...) Identicals and Leibniz's Law of Substitutivity; the assumption that all sentences that exhibit failures of substitutivity have in common a certain structure, that they include explicit or implicit intensional operators, which cause failures of substitutivity; the presumption that the extensionalist principles of substitutivity follow from a thesis of compositionality of meaning,according to which the meaning of a complex expression is determined by the meanings of its components and the mode of composition. Second, the intuitive foundations of a theory about the contributions of terms to the assertions expressed by uses of sentences are explored. I claim that this theory provides strong reasons to reject the extensionalist approach to substitutivity. (shrink)

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The capital approach is frequently used to model sustainability. A development is deemed to be sustainable when capital is not reduced. There are different definitions of sustainability, based on whether or not they allow that different forms of capital may be substituted for each other. A development that allows for thesubstitution of different forms of capital is called weakly sustainable. This article shows that in a risky world and a risk-averse society even under the assumptions of weak sustainability (...) the circumstances under which different forms of capital may be substituted are limited. This is due to the risk-reducing effect of diversification. Using Modern Portfolio Theory this article shows under which conditionssubstitution of different forms of capital increases risk for future generations. (shrink)

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One of the central limitations of sensorysubstitution 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 some importance. We offer a novel solution. Researchers can produce hedonic and aesthetic responses by eliciting these feelings artificially, pairing distal objects that should be pleasurable to pleasurable stimulus outputs from the SSD. We outline two strategies for accomplishing this: first, by means of a prefixed, hardwired, association of pleasant distal objects to pleasant stimulus outputs from the SSD; second, by means of a flexible, feedback-based association which creates associations based on a subject-directed matching of distal objects to patterns of stimuli from the SSD which the subject takes to have the corresponding hedonic properties. We evaluate some problems with both strategies, and we argue that the feedback-based strategy is more promising. Researchers can use this strategy to help the blind, allowing them to take pleasure in the objects they perceive using SSDs. (shrink)

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Alex Oliver has offered a variety of counterexamples to Crispin Wright's Reference Principle. I suggest that these counterexamples rely on too simple a notion ofsubstitution to be compelling. However, this is not a satisfactory place to leave the discussion: we need some alternative account ofsubstitution in English. In his recent paper, Dolby has attempted to give just such an account. I argue that Dolby's account is viciously circular. I then draw some morals from the discussion.

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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 (...) process of substitute decision-making. The personal experiences of providing direct support to seven men and women with ID living in residential care, however, showed that substitute decision-making took two forms, depending on the type of decision to be made. The first process, ‘strategic substitute decision-making’, paralleled the MCA’s legal and ethical framework, whilst the second process, ‘relational substitute decision-making’, was markedly different from these statutory procedures. In this setting, ‘relational substitute decision-making’ underpinned everyday personal and social interventions connected with residents’ daily living, and was situated within a framework of interpersonal and interdependent care relationships. The implications of these findings for residential services and the implementation of the MCA are discussed. (shrink)

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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 ofsubstitution in Russell’s logic. If he was aware of the substitutional (_p_0_a_0) paradox in 1906, why did he advertise “Insolubilia” (...) as a solution to the Epimenides? If he was dissatisfied with the solution, as his correspondence suggests, why did he go on to publish it? Why didsubstitution reappear with orders in “Mathematical Logic as Based on the Theory of Types” if he had rejected a hierarchy of orders as intolerable? I offer the following as possible explanations: he construed the “logical Epimenides” as a version of the _p_0_a_0 paradox; his dissatisfaction with the “Insolubilia” solution was philosophical, not technical; andsubstitution re-emerged because he hoped for a new philosophical gloss on orders. Whether or not my explanations are correct, these issues must be addressed in accounting for Russell’s reasons for ramification. (shrink)

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The task of this paper is to clarify the status and implications of Levinas's insistence on the necessity of subjectivity to the ethical relation. Focusing in particular on the discussion ofsubstitution in Otherwise than Being, it is argued that the description of subjectivity assubstitution enables Levinas to articulate the necessity of the subject to the approach of the other in a manner which avoids the transcendental character which such claims to necessity usually embody. This argument proceeds (...) from an initial characterization ofsubstitution within the constellation of themes pursued by Levinas in Otherwise than Being to a detailed examination of the first four sections of theSubstitution chapter. The essay concludes by noting the unity of the ethical exceeding of the transcendental character of subjectivity with the project which animates Levinas's work from its beginnings: the exceeding of the ontological by the ethical. (shrink)

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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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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 (...) certain choice nodes, i.e., indifference between a and b is not stable. Using this result, I answer a question posed by Rabinowicz (1997) concerning admissibility in sequential decisions when indifferent options are substituted at choice nodes. (shrink)

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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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The λσ-calculus adds explicit substitutions to the λ-calculus so as to provide a theoretical framework within which the implementation of functional programming languages can be studied. This paper generalises the λσ-calculus to provide a linear calculus of explicit substitutions, called xDILL, which analogously describes the implementation of linear functional programming languages.Our main observation is that there are non-trivial interactions between linearity and explicit substitutions and that xDILL is therefore best understood as a synthesis of its underlying logical structure and the (...) technology of explicit substitutions. This is in contrast to the λσ-calculus where the explicit substitutions are independent of the underlying logical structure. (shrink)

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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 (...) universalsubstitution and that the more restrictive structure of thesubstitution group of Quantum Logic prevents us from defining truth in a classical fashion. These observations lead to a more profound understanding of the Logic of Quantum Mechanics and of the role that symmetry principles play in that theory. (shrink)

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We show that it is impossible to define asubstitution 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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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 (...) view” seems to be an oversimplification. Assuming an “interaction-centered approach”, this article identifies three essential ways in which cognitive artifacts carry out their function: complementing, constituting and substituting our cognitive processes, and builds a taxonomy of these objects that is grounded on these relations. In so doing, it also addresses the chaotic set of different micro-functions carried out by cognitive artifacts, which have not thus far been dealt with, sorting these functions into three corresponding categories. The second part of the article analyzes in greater detail how cognitive artifacts work in our cognitive life, identifying a new kind of functions, called semi-proper functions, and providing a new definition of cognitive artifact based on the previous analysis of these objects. (shrink)

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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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This report highlights and explores five questions that arose from the workshop on sensorysubstitution and augmentation at the British Academy, March 26th through 28th, 2013.

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This is an excerpt from a report on the SensorySubstitution and Augmentation Conference at the British Academy in March of 2013. This portion of the report explores the question: Does sensorysubstitution generate perceptual or cognitive states?

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This is an excerpt from a report on the SensorySubstitution and Augmentation Conference at the British Academy in March of 2013. This portion of the report explores the question: How does sensorysubstitution interact with the brain’s architecture?

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