*Editorial note: This story is the closing chapter of The Kingfisher Story Collection (3rd Ed.) [1]. It was translated by Minh-Hoang Nguyen from the original Vietnamese version.

Hilbert’s program in the philosophy of mathematics comes in two parts. One part is a technical part. To carry out this part of the program one has to prove a certain technical result. The other part of the program is a philosophical part. It is concerned with philosophical questions that are the real aim of the program. To carry out this part one, basically, has to show why the technical part answers the philosophical questions one wanted to have answered. Hilbert (...) probably thought that he had completed the philosophical part of his program, maybe up to a few details. What was left to do was the technical part. To carry it out one, roughly, had to give a precise axiomatization of mathematics and show that it is consistent on purely finitistic grounds. This would come down to giving a relative consistency proof of mathematics in finitist mathematics, or to give a proof-theoretic reduction of mathematics on to finitist mathematics (we will look at these notions in more detail soon). It is widely believed that Gödel’s theorems showed that the technical part of Hilbert’s program could not be carried out. Gödel’s theorems show that the consistency of arithmetic can not even be proven in arithmetic, not to speak of by finitistic means alone. So, the technical part of Hilbert’s program is hopeless, and since Hilbert’s program essentially relied on both the technical and the philosophical part, Hilbert’s program as a whole is hopeless. Justified as this attitude is, it is a bit unfortunate. It is unfortunate because it takes away too much attention from the philosophical part of Hilbert’s program. And this is unfortunate for two reasons. (shrink)

In this paper, the (possible) role of model theory forstructuralism and structuralist definitions of ``reduction'' arediscussed. Whereas it is somewhat undecisive with respect tothe first point – discussing some pro's and con's ofthe model theoretic approach when compared with a syntacticand a structuralist one – it emphasizes that severalstructuralist definitions of ``reducibility'' do not providegenerally acceptable explications of ``reducibility''. This claimrests on some mathematical results proved in this paper.

The structuralist program has developed a useful metascientific resource: ontological reductive links (ORLs) between the constituents of the potential models of reduced and reducing theories. This resource was developed initially to overcome an objection to structuralist ``global'' accounts of the intertheoretic reduction relation. But it also illuminates the way that concepts at a higher level of scientific investigation (e.g., cognitive psychology) become ``structured through reduction'' to lower-level investigations (e.g., cellular/molecular neuroscience). After (briefly) explaining this structuralist background, I demonstrate (...) how this resource illuminates an actual, emerging scientific example: the link between the psychological concept of a ``consolidation switch'' from short-term to long-term memory and the cellular/molecular mechanisms of the transition from early- to late-phases of long-term potentiation (LTP) (an important type of synaptic plasticity in mammalian hippocampus and cortex). (shrink)

In view of the arguments put forward by Clifton and Monton [this volume], we reconsider the alleged conflict of dynamical reduction models with the enumeration principle. We prove that our original analysis of such a problem is correct, that the GRW model does not meet any difficulty and that the reasoning of the above authors is inappropriate since it does not take into account the correct interpretation of the dynamical reduction theories.

Relationships between current theories, and relationships between current theories and the sought theory of quantum gravity (QG), play an essential role in motivating the need for QG, aiding the search for QG, and defining what would count as QG. Correspondence is the broad class of inter-theory relationships intended to demonstrate the necessary compatibility of two theories whose domains of validity overlap, in the overlap regions. The variety of roles that correspondence plays in the search for QG are illustrated, using examples (...) from specific QG approaches. Reduction is argued to be a special case of correspondence, and to form part of the definition of QG. Finally, the appropriate account of emergence in the context of QG is presented, and compared to conceptions of emergence in the broader philosophy literature. It is argued that, while emergence is likely to hold between QG and general relativity, emergence is not part of the definition of QG, and nor can it serve usefully in the development and justification of the new theory. (shrink)

Sabina Alkire shows how Nobel Prize-winning economist Amartya Sen's capability approach can be coherently---and practically---put to work in poverty reduction activities so that the voices and values of the poor matter. This provides economists, philosophers, theologians, and development practitioners with a way forward that addresses both theoretical and practical challenges.

In this essay, we consider questions arising from cases in which people request medical assistance in dying (MAiD) in unjust social circumstances. We develop our argument by asking two questions. First, can decisions made in the context of unjust social circumstance be meaningfully autonomous? We understand ‘unjust social circumstances’ to be circumstances in which people do not have meaningful access to the range of options to which they are entitled and ‘autonomy’ as self-governance in the service of personally meaningful goals, (...) values and commitments. People in these circumstances would choose otherwise, were conditions more just. We consider and reject arguments that the autonomy of people choosing death in the context of injustice is necessarily reduced, either by restricting their options for self-determination, through their internalisation of oppressive attitudes or by undermining their hope to the point that they despair.Second, should MAiD be available to people in such circumstances, even when a sound argument can be made that the agents in question are autonomous? In response, we use a harm reduction approach, arguing that even though such decisions are tragic, MAiD should be available. Our argument engages with relational theories of autonomy as well as recent criticism raised against them and is intended to be general in application, although it emerges in response to the Canadian legal regimen around MAiD, with a focus on recent changes in Canada’s eligibility criteria to qualify for MAiD. (shrink)

Something is wrong with current discussions about theory reduction. The question of whether higher level theories are reducible to lower level theories cannot be posed in a sensible way if methodological principles that are needed to evaluate scientific theories are disregarded. If this is recognized, the problem looses much of its alleged importance.

We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them and introduce a new characteristic (...) of relations, ternarity, that measures their ‘complexity of relating’ and allows to refine reduction results. In particular, we refine Peirce’s controversial reduction thesis, and show that reducibility behaviour is dramatically different on finite and infinite domains. (shrink)

Twentieth Century philosophical thought has expressed itself for the most part through two great Movements: the phenomenological and the analytical. Each movement originated in reaction against idealistic—or at least antirealistic—views of "the world". And each has collapsed back into an idealism not different in effect from that which it initially rejected. Both movements began with an appeal to meanings or concepts, regarded as objective realities capable of entering the flow of experience without loss of their objective status or of their (...) power to reveal to us an objective world as it would be if there were no subjective apprehensions of it. Both movements ended with a surrender of the objectivity of meanings and concepts in this strong sense, coming to treat them as at most more-or-less shareable components of a somehow communalized experience, but in any case incapable of revealing how things are irrespective of actual human experience. For the old Egocentric Predicament, with its "ideas" etc., is substituted a Lingocentric or Histrocentric Predicament of "language" and its elements. Hilary Putnam speaks for the current consensus: 'Internal realism says that we don't know what we are talking about when we talk about "things in themselves"' ( The Many Faces of Realism , p. 36). (shrink)

In a recent article, Fabrice Correia explores the project of reducing the notion of grounding to that of essence. He then goes on to provide several candidate definitions and test each of them against a number of objections. His final take on the situation is, roughly, that two of the definitions can handle all of the considered objections. The aim of this paper is to re-evaluate Correia's conclusions in the light of two sources of insights: Firstly, I will argue that (...) one of the objections treated by Correia has been somewhat underestimated, and that it still constitutes a threat against definitions of grounding in terms of essence. Secondly, there are at least two further objections that should be considered by the advocate of such definitions. As I will show, one of them can be neutralized; but the other one is more serious and suggests a clear dialectical edge to an operationalist definition. (shrink)

The Reformation, it has been said, changed the course of history. Most people would agree. At the very least, agree or not, they would hold the proposition to be one worth considering. They would be unlikely to reject it out of hand as incapable of being either true or false because it had no meaning. For, of course, “everybody knows” what the Reformation was and, elaborating a little, we can make clear what we meant by changing the course of history. (...) Yet it is just statements of this sort that cause much methodological wrangling. Their controversial nature is due, in large part, to controversy over the status of such terms as “the Reformation” and, generally, group or macroscopic concepts. Since not only history, but sociology, political science, social psychology, and economics also widely use concepts referring to groups and their properties, rather than to individuals, the controversy has wide ramifications. And because there are, as it were, so many vested interests involved, the dispute also tends to acquire an ideological tone not altogether consonant with dispassionate inquiry. Bad temper and mutual recrimination in scientific discussion are generally a sign that ideological defenses are being shored up. Just possibly, a philosopher whose substantive concern in any empirical field is minimal may hope to be considered above the battle, as one who, having no private axe to grind, can be concerned only with clarifying the logical issues involved. In this hope, I wish to explore as systematically as possible the tangled web of issues woven about the status of group concepts and their relationship to those referring to individuals. Intertwined in this controversy are two different issues. One has to do with the nature of the terms or concepts of social science; the other with the nature of its laws and theories and their relationship in turn to those in other areas. The first issue is one of meaning, the second of reduction. Success in unsnarling the various strands of this web may alone help abate the fury of the controversy. (shrink)

Reductionism is a central issue in the philosophy of biology. One common objection to reduction is that molecular explanation requires reference to higher-level properties, which I refer to as the context objection. I respond to this objection by arguing that a well-articulated notion of a mechanism and what I term mechanism extension enables one to accommodate the context-dependence of biological processes within a reductive explanation. The existence of emergent features in the context could be raised as an objection to (...) the possibility of reduction via this strategy. I argue that this objection can be overcome by showing that there is no tenable argument for the existence of emergent properties that are not susceptible to a reductive explanation. (shrink)

THIS PAPER ARGUES THAT GLOBAL SUPERVENIENCE IS NOT\nEQUIVALENT TO KIM'S STRONG SUPERVENIENCE (AS HE HAS ARGUED\nIT IS) AND THAT IT DOES NOT ENTAIL THE TYPE OR TOKEN\nREDUCIBILITY OF THE SUPERVENIENT PROPERTIES TO THE\nPROPERTIES UPON WHICH THEY SUPERVENE (AS STRONG\nSUPERVENIENCE DOES). IT THEN TURNS TO AN EXAMINATION OF THE\nARGUMENT THAT GLOBAL SUPERVENIENCE IS EQUIVALENT TO\nIMPLICIT DEFINABILITY WHICH ACCORDING TO BETH'S THEOREM\nENTAILS EXPLICIT DEFINABILITY. THE AUTHOR HOPES TO SHOW\nTHAT GLOBAL SUPERVENIENCE IS A DISTINCT AND ESPECIALLY\nINTERESTING RELATION WHICH CAPTURES ASPECTS OF THE\nRELATIONSHIP BETWEEN (...) PHYSICAL PROPERTIES AND THOSE\nPROPERTIES WHICH ARE DETERMINED BY THEM THAT OTHER\nRELATIONS DO NOT DO JUSTICE TO. (shrink)

Dispositions may be identical to their categorical bases but should we say, with Quine, that all properties are categorical or, with Popper, that all properties are dispositional? Both positions make implicit claims of ontological reduction but if this consists in nothing more than identity then, identity being a symmetrical relation, neither categorical nor dispositional monism is provided. A supervenience relation may be thought decisive, but if the identities are token- token, reduction is ruled out; if the identities are (...) type- type there is no direction of supervenience hence no determination of reduction. It is concluded that both ontologies have been argued inadequately. (shrink)

The applicability of Nagel's concept of theory reduction, and related concepts of reduction, to the reduction of genetics to molecular biology is examined using the lactose operon in Escherichia coli as an example. Geneticists have produced the complete nucleotide sequence of two of the genes which compose this operon. If any example of reduction in genetics should fit Nagel's analysis, the lactose operon should. Nevertheless, Nagel's formal conditions of theory reduction are inapplicable in this case. (...) Instead, it is argued that genetics has been partially reduced to molecular biology in the sense of token-token reduction. (shrink)

Watson and Crick’s discovery of the structure of DNA led to developments that transformed many biological sciences. But what were the relevant developments and how did they transform biology? Much of the philosophical discussion concerning this question can be organized around two opposing views: theoretical reductionism and layer-cake antireductionism. Theoretical reductionist and their anti-reductionist foes hold two assumptions in common. First, both hold that biological knowledge is structured like a layer cake, with some biological sciences, such as molecular biology cast (...) at lower levels of organization, and others, such as classical genetics, cast at higher levels. Second, both assume that scientific knowledge is structured by theory and that the productivity of scientific research depends on whether the underlying theory identifies the fundamentals upon which the phenomena to be explained and investigated depend. In the first part of this paper, I challenge these assumptions. In the second part, I show how recasting the basic theory of classical genetics made it possible to retool the methodologies of genetics. It was the investigative power of these retooled methodologies, and not the explanatory power of a gene-based theory, that transformed biology. (shrink)

Harm-reduction approaches are used to reduce the burden of risky human behaviour without necessarily aiming to stop the behaviour. We discuss what an introduction of harm reduction for doping in sports would mean in parallel with a relaxation of the antidoping rule. We analyse what is ethically at stake in the following five levels: (1) What would it mean for the athlete (the self)? (2) How would it impact other athletes (the other)? (3) How would it affect the (...) phenomenon of sport as a game and its fair play basis (the play)? (4) What would be the consequences for the spectator and the role of sports in society (the display)? and (5) What would it mean for what some consider as essential to being human (humanity)? For each level, we present arguments for and against doping and then discuss what a harm-reduction approach, within a dynamic regime of a partially relaxed antidoping rule, could imply. We find that a harm-reduction approach is morally defensible and potentially provides a viable escape out of the impasse resulting from the impossibility of attaining the eradication of doping. The following question remains to be answered: Would a more relaxed position, when combined with harm-reduction measures, indeed have less negative consequences for society than today9s all-out antidoping efforts that aim for abstinence? We provide an outline of an alternative policy, allowing a cautious step-wise change to answer this question and then discuss the ethical aspects of such a policy change. (shrink)

It has often been remarked that the metatheory of strong reduction $\succ$ , the combinatory analogue of βη-reduction ${\twoheadrightarrow_{\beta\eta}}$ in λ-calculus, is rather complicated. In particular, although the confluence of $\succ$ is an easy consequence of ${\twoheadrightarrow_{\beta\eta}}$ being confluent, no direct proof of this fact is known. Curry and Hindley’s problem, dating back to 1958, asks for a self-contained proof of the confluence of $\succ$ , one which makes no detour through λ-calculus. We answer positively to this question, (...) by extending and exploiting the technique of transitivity elimination for ‘analytic’ combinatory proof systems, which has been introduced in previous papers of ours. Indeed, a very short proof of the confluence of $\succ$ immediately follows from the main result of the present paper, namely that a certain analytic proof system G e [ $\mathbb {C}$ ] , which is equivalent to the standard proof system CL ext of Combinatory Logic with extensionality, admits effective transitivity elimination. In turn, the proof of transitivity elimination—which, by the way, we are able to provide not only for G e [ $\mathbb {C}$ ] but also, in full generality, for arbitrary analytic combinatory systems with extensionality—employs purely proof-theoretical techniques, and is entirely contained within the theory of combinators. (shrink)

Cognitive dissonance has been studied for more than sixty years and many insightful findings have come from this research. However, some important theoretical and methodological issues are yet to be resolved, particularly regarding dissonance reduction. In this paper, we place dissonance theory in the larger framework of appraisal theories of emotion, emotion regulation, and coping. The basic premise of dissonance theory is that people experience negative affect (to varying degrees) following the detection of cognitive conflict. The individual will be (...) motivated to alleviate these emotional reactions and could do so by reducing dissonance in some manner. We argue that detection of dissonance will follow the same principles as when people interpret any other stimuli as emotionally significant. Thus, appraisal theory of emotion, which argues that emotions are generated via the cognitive evaluation of surrounding stimuli, should be applicable to the dissonance-detection process. In short, we argue that dissonance-reduction strategies (attitude change, trivialization, denial of responsibility, etc.) can be understood as emotion-regulation strategies. We further argue that this perspective contributes to reconciling fragmented (and sometimes contrary) viewpoints present in the literature on dissonance reduction. In addition to proposing the general model of dissonance reduction, we illustrate at the hand of empirical data how research on dissonance reduction can be performed without relying on experimental paradigms that focus on a specific reduction strategy. (shrink)

We analyse a recent paper in which an alleged devastating criticism of the so called GRW proposal to account for the objectification of the properties of macroscopic systems has been presented and we show that the author has not taken into account the precise implications of the GRW theory. This fact makes his conclusions basically wrong. We also perform a survey of measurement theory aimed to focus better on the physical and the conceptual aspects of the so-called macro-objectification problem.

This book collects twelve original articles, arranged in three sections, plus an introduction.

Arguments, claims, and discussions about the “level of description” of a theory are ubiquitous in cognitive science. Such talk is typically expressed more precisely in terms of the granularity of the theory, or in terms of Marr’s three levels. I argue that these ways of understanding levels of description are insufficient to capture the range of different types of theoretical commitments that one can have in cognitive science. When we understand these commitments as points in a multi-dimensional space, we find (...) that we must also reconsider our understanding of intertheoretic relations. In particular, we should understand cognitive theories as constraining one another, rather than reducing to one another. (shrink)

The proof-theoretic results on axiomatic theories oftruth obtained by different authors in recent years are surveyed.In particular, the theories of truth are related to subsystems ofsecond-order analysis. On the basis of these results, thesuitability of axiomatic theories of truth for ontologicalreduction is evaluated.

The article discusses some of Heinz Post's views on correspondence and whether revolutions occur in science a la Kuhn. For example Post points out that the periodic table of the chemical elements has withstood any revolutions. Specific issues examined include the Paneth-Fajans controversy, the extent to which quantum mechanics provides an explanation for the periodic table and ab initio calculations in quantum chemistry.

Non-naturalists claim that the nature of normativity precludes the possibility of normative naturalism. In particular, they think that normative reduction amounts to normative elimination. This is because it always leaves out the normative. In this paper, I examine the force that the normativity objection has against Humean reductionism. I argue that the normativity objection has no argumentative force against reductionism. When it is presented as a bare intuition, it begs the question against reduction. A more interesting reading of (...) the argument claims that the normative cannot be explained in terms of the natural because the natural is arbitrary. Yet, this version of the argument fails as well because the natural is not arbitrary in the relevant sense. The natural is contingent, so what has value is contingent. That is not an elimination of the normative though, because contingent reasons are still reasons. (shrink)

So far, the value dimension underlying affectivity disorders has remained out of focus in phenomenological psychopathology. As early as at the beginning of the 20th century, however, German phenomenologist Max Scheler examined in depth the relationship between affectivity and value dimension through the concept of valueception (Wertnehmung). In this sense, a recent noteworthy contribution has been provided by John Cutting, who has drawn attention to the importance of Scheler’s analyses for psychiatry. In this work I take into consideration only two (...) aspects of Cutting’s proposal: 1) the relationship between the impairments of valueception and the perception of certain value classes; and 2) the interpretation of Scheler’s phenomenological reduction and its juxtaposition with the modus vivendi of schizophrenia. According to Cutting, in the modus vivendi of schizophrenia the valueception impairment entails putting vital values in brackets and focusing on personal values, with a process that recalls Scheler’s phenomenological reduction. Regarding the first aspect, I share Cutting’s starting point, but then shift the focus on how important the valueception is for the intersubjective dimension. In particular, I maintain that rather than compromising the perception of vital values, valueception impairments in the modus vivendi of schizophrenia interfere with the intersubjective dimension and are interwoven with a process of disembodiment. My thesis is that the modus vivendi of schizophrenia involves a disturbance of the intersubjective dimension that arises from the level of valueception and that determines the person’s self-referential closure. With regard to the second point, by analyzing Scheler’s phenomenological reduction, I sustain that its main objective is to increase both the interaction with otherness and the openness to the world (Weltoffenheit). As a consequence, the modus vivendi of schizophrenia, in my opinion, is not comparable, as Cutting claims, with Scheler’s phenomenological reduction, but goes in a different direction. (shrink)