Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic properties of the action. In classical logic there is a strong dichotomy: while over finitely many propositional variables everything is trivial, the study of the continuous transformations of the Cantor space is the subject of an extensive literature, and is far from (...) being a completed task. In many-valued logic this dichotomy disappears: already in the finite-variable case many interesting phenomena occur, and the present paper aims at displaying some of these. (shrink)

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.

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.

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 (...) 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)

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)

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

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 (...) 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)

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 (...) 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)

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 (...) substitution inferences. It is attempted to show that this picture is incompatible with, but preferable to, Knobe’s theory. In closing, some further observations and suggestions are given with respect to further research into the apparent effect of moral valence. (shrink)

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 (...) 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)

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.

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.

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 (...) 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 sensory substitution 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 sensory substitution 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 sensory substitution 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)

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.

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)

This paper explores the relation between the philosophical idea that logic is a science studying logical forms, and a mathematical feature of logical systems called the principle of uniform substitution, which is often regarded as a technical counterpart of the philosophical idea. We argue that at least in one interesting sense the principle of uniform substitution does not capture adequately the requirement that logic is a matter of form and that logical truths are formal truths. We show that some specific (...) logical expressions can produce propositions of different kinds and the resulting diversity of informational types can lead to a justified failure of uniform substitution without undermining the view that logic is a purely formal discipline. (shrink)

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 (...) 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)

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)

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 (...) syllogism so that more complex quantification inferences can be captured. I conclude that the substitution 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)

Life expectancy and health differ greatly between emerging and developed countries and within countries. Global dependence on fossil fuels contributes to health inequalities through air pollution, the geopolitics of scarce resources and probable climate change arising from global warming. Substituting for fossil fuels (C), hydrogen (H2), as vector and store of energy produced from low-carbon and/or renewable sources could reduce health inequalities by improving the environment. It is unlikely that the global market would initiate such a change. Nation-states would not (...) act alone and would need to cooperate in leading it. Global recession might be the incentive that is needed to restructure a C-economy into an H2-economy. Yet, the transition would carry high costs, which would have to be borne by the developed countries in order to achieve a new treaty that included emerging countries. H2 for C is thus not only a technical fix, but also a global-ethical choice. (shrink)

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 (...) substitution 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)

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)

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)

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

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 (...) 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)

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 (...) rejected too broadly for “never‐capacitated” patients. It then lays out a three‐condition test for using substituted judgment in these cases. For a subset of “never‐capacitated” patients who belong to distinctive religious or cultural communities with clear medical values and have an appropriate surrogate, these values may prove helpful in vindicating the interests of the never‐capacitated and should not be blanketly dismissed. (shrink)

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

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.

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)

It is commonly thought that when a patient is unable to make a treatment decision for herself, patient autonomy should be respected by consulting the views of a patient surrogate, normally either the next-of-kin or a person previously designated by the patient. On one view, the task of this surrogate is to make the treatment decision that the patient would have made if competent. But this so-called ‘substituted judgment standard’ (SJS) has come in for has come in for a good (...) deal of criticism recently. For instance, some question whether surrogates are able to reliably predict what the patient would have chosen. Others wonder how respecting a patient's counter-factual, rather than actual, choices is supposed to respect her autonomy. Such concerns have lead some to reject the SJS and argue for alternative characterisations of the role of surrogate decision-makers. (shrink)

We formulate epsilon substitution 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.

There are two main ways of understanding the function of surrogate decision making in a legal context: the Best Interests Standard and the Substituted Judgment Standard. First, we will argue that the Best Interests Standard is difficult to apply to unconscious patients. Application is difficult regardless of whether they have ever been conscious. Second, we will argue that if we accept the least problematic explanation of how unconscious patients can have interests, we are also obliged to accept that the Substituted (...) Judgment Standard can be coherently applied to patients who have never been conscious at the same extent as the Best Interests Standard. We then argue that acknowledging this result is important in order to show patients respect. (shrink)

Kripke’s substitutional interpretation of quantifiers is usually said to be unsatisfactory for independence-friendly (IF) languages. The purpose of this paper is to question this claim. Two accounts of substitutional semantics for IF sentences will be written down, and the objection of the so-called ‘dummy variables’ will be ruled out. Moreover, it will be argued, against the traditional view, that Game-Theoretical Semantics (GTS) should be conceived of as substitutional. The paper ends with some remarks concerning the reasons why substitution is especially (...) suitable for dynamic semantics. (shrink)

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

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

This paper uses duality to elaborate Slutzky equations of risks in quasi-linear decision models extended by independent background risks. Wealth, substitution and total effects are characterized in terms of mean-variance preferences. It is shown that both Pratt and Zeckhauser’s proper risk aversion and Kimball’s standard risk aversion are sufficient for negative substitution effects.

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.

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 (...) coincidence of these innovations in Jevons, through ‘substitution’, captures the way the modern world was set on its current trajectory, progressing towards a ‘substitution society’. The article concludes that as the key values of human life cannot be substituted, substitution as a general principle applied to human existence is absurd; economic theory, however, as shown in the ideas of Jevons, is founded on the exclusion of such genuine and meaningful concerns. (shrink)

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.

A primary goal of clinical practice is to respect patient autonomy. To promote this goal for patients who have lost the ability to make their own decisions, commentators recommend that surrogates make their treatment decisions based on the substituted judgment standard. This standard is commonly interpreted as directing surrogates to make the decision the patient would have made in the circumstances, if the patient were competent. However, recent commentators have argued that this approach—attempting to make the decision the patient would (...) have made if competent—is theoretically problematic, practically infeasible, and ignores the interests of the patient9s family and loved ones. These commentators conclude that the substituted judgment standard should be revised significantly, or abandoned altogether. While this response would avoid the cited problems, it also would require substantial changes to clinical practice and would raise significant problems of its own. The present paper thus considers the possibility that the criticisms do not point to problems with the substituted judgment standard itself; instead, they point to problems with the way it is most commonly interpreted. This analysis suggests that the substituted judgment standard need not be dramatically revised or abandoned. Instead, it should be interpreted in a way that effectively promotes respect for the autonomy of incompetent patients. The ‘endorsed life’ interpretation described here helps clinicians and surrogates to achieve this important goal. To clarify this approach, we explain how it differs from three other recently proposed alternatives to the standard interpretation of the substituted judgment standard. (shrink)

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 (...) thread we formulate the epsilon substitution 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)

Sensory substitution and augmentation devices are used to replace or enhance one sense by using another. Fiona Macpherson brings together neuroscientists, psychologists and philosophers to focus on the nature of the perceptual experiences, the sensory interactions, and the changes that occur in the mind and brain while using these technologies.

ZusammenfassungEin Großteil der medizinisch und ethisch schwierigen Therapieentscheidungen betrifft kritisch kranke, einwilligungsunfähige Patienten und wird auf Basis des mutmaßlichen Patientenwillens getroffen. Das Gesetz kann hierzu nur allgemeine Vorgaben geben. Es ist für die behandelnden Ärzte essentiell, sich ein konkretes Vorgehen zu erarbeiten. Wie in der Praxis vorgegangen wird, ist bisher kaum untersucht. Ziel dieser Studie ist es, die Vielfalt der Herangehensweisen und Erfahrungen von Klinikern zum mutmaßlichen Patientenwillen zu erforschen. Wir führten semistrukturierte Interviews mit 18 Ärzten und elf Pflegekräften von (...) intensiv- und palliativmedizinischen Abteilungen eines Universitätsklinikums durch. Die Abschriften der Tonaufnahmen wurden mithilfe der Qualitativen Datenanalyse ausgewertet. Auf einer numerischen Ratingskala wurde erhoben, wie hilfreich die Kliniker das Konzept des mutmaßlichen Willens fanden. Die meisten Studienteilnehmer hielten das Konzept des mutmaßlichen Willens für sehr hilfreich. Zu ihrem Vorgehen berichteten sie, dass sie zumeist die nächsten Angehörigen befragen, zuweilen auch Professionelle und falls möglich die Patienten selbst. Gefragt werde nach früheren Äußerungen der Patienten, nach ihrer Lebenspraxis und -einstellung sowie ihrem aktuellen Verhalten. Benannt wurden auch zahlreiche Unsicherheiten und Schwierigkeiten psychologischer, sozialer, praktischer und konzeptioneller Natur. Der mutmaßliche Patientenwille wird, so unser Ergebnis, in der von uns untersuchten klinischen Praxis entsprechend den gesetzlichen Vorgaben ermittelt. Da jedoch zahlreiche Probleme berichtet werden, stellen wir konkrete Empfehlungen zur Ermittlung des mutmaßlichen Willens vor. (shrink)

This essay discusses rules and semantic clauses relating to Substitution—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 Substitution ought (...) to fail. (shrink)

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 (...) theories as regards substitutivity in belief reports. This is why it is important to articulate an acceptable principle of substitution. A traditional statement of the principle of substitution 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 of substitution. (shrink)

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 (...) 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)

The 'substitution argument' purports to demonstrate the falsity of Russellian accounts of belief-ascription by observing that, e.g., these two sentences: (LC) Lois believes that Clark can fly. (LS) Lois believes that Superman can fly. could have different truth-values. But what is the basis for that claim? It seems widely to be supposed, especially by Russellians, that it is simply an 'intuition', one that could then be 'explained away'. And this supposition plays an especially important role in Jennifer Saul's defense of (...) Russellianism, based upon the existence of an allegedly similar contrast between these two sentences: (PC) Superman is more popular than Clark. (PS) Superman is more popular than Superman. The latter contrast looks pragmatic. But then, Saul asks, why shouldn't we then say the same about the former? The answer to this question is that the two cases simply are not similar. In the case of (PC) and (PS), we have only the facts that these strike us differently, and that people will sometimes say things like (PC), whereas they will never say things like (PS). By contrast, there is an argument to be given that (LS) can be true even if (LC) is false, and this argument does not appeal to anyone's 'intuitions'. The main goal of the paper is to present such a version of the substitution argument, building upon the treatment of the Fregan argument against Russellian accounts of belief itself in "Solving Frege's Puzzle". A subsidiary goal is to contribute to the growing literature arguing that 'intuitions' simply do not play the sort of role in philosophical inquiry that so-called 'experimental philosophers' have supposed they do. (shrink)

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 . (...) Here NNIL is the class of propositional formulas with no nestings of implications to the left . The identical embedding of IPC -derivability into a consequence relation has in many cases a left adjoint. The main tool of the present paper will be an algorithm to compute this left adjoint in the case of NNIL -preservativity. In the last section, we employ the methods developed in the paper to give a characterization the closed fragment of the provability logic of HA. (shrink)