According to David Chalmers and Frank Jackson, conceptual competence puts one in a position to have a priori knowledge of conditional claims of the form ‘If my environment is thus and so, then water = H2O’. The rationale for this position, I argue, rests on controversial semantic assumptions about the individuation of meanings or concepts. I sketch a new model of conceptual competence, which undermines the apriority of such conditionals.

I discuss Steinhart’s argument against Benacerraf’s famous multiple-reductions argument to the effect that numbers cannot be sets. Steinhart offers a mathematical argument according to which there is only one series of sets to which the natural numbers can be reduced, and thus attacks Benacerraf’s assumption that there are multiple reductions of numbers to sets. I will argue that Steinhart’s argument is problematic and should not be accepted.

CHAPTER I INTRODUCTION Rene" Descartes started modern Western philosophy on its search for an absolutely certain foundation for knowledge. ...

What would be sufficient to show of some apparently higher-level property that it is 'nothing over and above' some complex configuration of more basic properties? This paper defends a new method for justifying reductions by demonstrating its comparative advantages over two methods recently defended in the literature. Unlike its rivals, what I'll call "the semantic method" makes a reduction's truth epistemically transparent without relying on conceptual analyses.

While all phenomenologists aim to grasp the “things themselves,” they disagree about the best method for doing this and about what the “things themselves” are. Many metaphysicians, especially Catholic realists, reject phenomenology altogether. I show that many phenomenological methods are useful for reaching the goals of both phenomenology and realist metaphysics. First, I present a history of phenomenological methods, including those used by Scheler, Husserl, Merleau-Ponty, Heidegger, Marion, Kearney, Rocha, and others. Next, I consider two sets of challenges raised to (...) some of these methods. Finally, I outline how to join these methods with each other and with the methods of realist metaphysics, ultimately arriving at an aesthetic method, inspired by the work of von Balthasar, for considering fundamental phenomena. (shrink)

Many epistemic anomalies of the neoclassical research programme originate from its ontologically reductionist meta-axioms, which predicate how economic macro-systems are constituted from their micr...

We define and study a new notion called k-immunity that lies between immunity and hyperimmunity in strength. Our interest in k-immunity is justified by the result that θ does not k-tt reduce to a k-immune set, which improves a previous result by Kobzev [7]. We apply the result to show that Φ′ does not btt-reduce to MIN, the set of minimal programs. Other applications include the set of Kolmogorov random strings, and retraceable and regressive sets. We also give a new (...) characterization of effectively simple sets and show that simple sets are not btt-cuppable. (shrink)

We investigate the index sets associated with the degree structures of computable sets under the parameterized reducibilities introduced by the authors. We solve a question of Peter Cholakand the first author by proving the fundamental index sets associated with a computable set A, {e : W e ≤ q u A} for q∈ {m, T} are Σ4 0 complete. We also show hat FPT(≤ q n ), that is {e : W e computable and ≡ q n ?}, is Σ4 (...) 0 complete. We also look at computable presentability of these classes. (shrink)

Climate change presents a fundamental challenge to the current global energy regime. Under the Framework Convention on Climate Change, the international community is developing the architecture of a policy response. Three serious flaws are examined: (a) the potential sacrifice of small island states, (b) the use of market-based policy measures to commodify the atmospheric commons, and (c) the substitution of carbon sequestration for meaningful reductions in energy use. The authors’ analysis of the politics of climate change, based on these (...) issues, suggests a new understanding of ecology is emerging—what they term postmodern ecology—in which a global environmental crisis is risked to secure the future of the world energy regime. An alternative, based on principles of sustainability and equity, is proposed that would require abandoning the global energy status quo. (shrink)

In 1839 the working hours of the computers employed on the lunar and planetary reductions of the Royal Observatory, Greenwich were reduced from eleven hours to eight hours. Previous historians have explained this decrease by reference to the generally benevolent nature of the manager of the reductions, George Biddell Airy. By contrast, this article uses the letters and notes exchanged between Airy and the computers to demonstrate that the change in the working hours originated from the computers as (...) a reaction to their poor working conditions. Through the exploration of these archival materials, the article shifts the focus of the analysis to the working experience of the computers, rather than to the administrative history of the project that inevitably tends to highlight Airy's actions. By doing so, the article shows how the computers were treated as a disposable low-skilled workforce, as opposed to aspiring astronomers with considerable mathematical talent. Through this reframing, the article takes a step towards a working history of the observatory. (shrink)

Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank strictly increases in complexity with the rank. Subsequently, Thomas proved that the complexities of the classification problems for p-local torsion-free abelian groups of fixed rank n are pairwise incomparable as p varies. We prove that if 3≤m (...) torsion-free abelian groups of rank n. (shrink)

Derek Parfit has argued that egalitarianism is exposed to a levelling down objection because it implies, implausibly, that a change, which consists only in the better-off sinking to the level of the worse-off, is in one respect better, though it is better for nobody. He claims that, in contrast, the prioritarian view that benefits to the worse-off have greater moral weight escapes this objection. This article contends, first, that prioritarianism is equally affected by the levelling down objection as is egalitarianism, (...) but that this objection lacks force. Secondly, prioritarianism is less plausible than egalitarianism because it implies that lowering the level of equality by diffusing a quantity of welfare equally over as many recipients as possible is for the better all things considered, and that the outcome of such welfare diffusion would still be better in one respect, even if the quantity of welfare was radically reduced. (shrink)

This paper makes the counterintuitive argument that apologetic offenders in both criminal and noncriminal contexts deserve reductions in punishment even according to retributive theories of justice. I argue here that accounting for post-offense apologetic meanings can make retributivism more fair and consistent much in the same way that considering pre-offense behavior such as culpable mental states like premeditation provide a more holistic and accurate view of the badness of the offense at issue. On my view, retributivists should endorse the (...) general principle that categorically apologetic offenders deserve less punishment because certain kinds of contrition can revise the very nature of the offense and thereby make it less bad and deserving of less punishment. This claim is symmetrical with the popular view that unapologetic or remorseless offenders deserve more punishment. (shrink)

Opposition against greenhouse gas emissions reductions is strong among some conservative Christian groups, especially in the United States. In this paper, we identify five scripture-based arguments against greenhouse gas mitigation put forward by a core group of Christian conservatives (‘the Cornwallists'): the anti-paganism argument, the enrichment argument, the omnipotence argument, the lack of moral relevance argument and the cost-benefit argument. We evaluate to what extent the arguments express positions that can be characterised as climate science denialist and to what (...) degree they are consistent with support for climate adaptation. Using Stefan Rahmstorf's (2004) taxonomy of climate science denial, we conclude that the Cornwallists could be labelled climate change deniers. However, their opposition is not only based on denial of climate science but often rests on premises that render the science irrelevant, a position we term ‘relevance denialism’. (shrink)

We are currently facing global healthcare crisis that has placed unprecedented stress on healthcare workers as a result of the coronavirus disease 2019. It is imperative that we develop novel tools to assist healthcare workers in dealing with the significant additional stress and trauma that has arisen as a result of the pandemic. Based in research on the effects of immersive environments on mood, a neuroscience research laboratory was rapidly repurposed using commercially available technologies and materials to create a nature-inspired (...) relaxation space. Frontline healthcare workers were invited to book 15-min experiences in the Recharge Room before, during or after their shifts, where they were exposed to the immersive, multisensory experience 496 Recharge Room users completed a short survey about their experience during an unselected, consecutive 14-day period. Average self-reported stress levels prior to entering the Recharge Room were 4.58/6. After a single 15-min experience in the Recharge Room, the average user-reported stress level was significantly reduced 1.85/6. Net Promoter Score for the experience was 99.3%. Recharge Rooms such as those described here produce significant short-term reductions in perceived stress, and users find them highly enjoyable. These rooms may be of general utility in high-stress healthcare environments. (shrink)

There is a simple technique, due to Dragalin, for proving strong cut-elimination for intuitionistic sequent calculus, but the technique is constrained to certain choices of reduction rules, preventing equally natural alternatives. We consider such a natural, alternative set of reduction rules and show that the classical technique is inapplicable. Instead we develop another approach combining two of our favorite tools—Klop’s ι-translation and perpetual reductions. These tools are of independent interest and have proved useful in a variety of settings; it (...) is therefore natural to investigate, as we do here, what they have to offer the field of sequent calculus. (shrink)

I argue that there are good reasons to assume that Quine’s theory of reference and ontology is incompatible with reductive statements – such as ‘Heat is molecular motion’ or ‘Rabbits are conglomerations of cells’. Apparently, reductive statements imply certain intertheoretical identities, yet Quine’s theory of reference and ontology seems incompatible with intertheoretical identities. I argued that treating, for the sake of reconciliation, reductive statements along the lines of Quine’s theory of an ontological reduction (which does not imply intertheoretical identity) fails. (...) Then I discussed two alternative strategies on behalf of Quine to handle reductive statements: the Holistic Strategy (which appeals to Quine’s notion of an all-encompassing background theory) and the Individuative Strategy (which draws on Quine’s notion of an apparatus of individuation). I argue that the Individuative Strategy promises to succeed. However, the Individuative Strategy obliges to revising Quine’s theory of an ontological reduction – a revision that, as I argue, can and should be implemented. (shrink)

ABSTRACT Edmund Husserl strongly emphasized the importance of reduction to his phenomenology. For his followers, however, it has proved a formidable task to specify exactly how this intricate accomplishment that opens up the possibility for phenomenological research is to be performed. In this article, we study different approaches to gaining access to reduction and conclude by suggesting that we should read Husserliana itself as a set of accomplished reductions. In other words, our task is to pinpoint chapters where the (...) movement of reduction takes place. As an example of such a reading, I will point out events that come about in Husserl???s Idea of Phenomenology. R??SUM?? Husserl a fortement insist?? sur l???importance de la r??duction dans sa ph??nom??nologie. Pour ses disciples, cependant, s???est av??r????tre redoutable la t??che de pr??ciser comment doit??tre ex??cut??e cette r??alisation complexe qui ouvre la possibilit?? pour la recherche ph??nom??nologique. Dans cet article, nous??tudions les diff??rentes approches de la r??duction et nous concluons en sugg??rant que l???ouvrage Husserliana lui-m??me doit se lire comme un ensemble de r??ductions accomplies. Notre t??che consistera donc?? identifier les chapitres o?? a lieu ce mouvement de r??duction.?? titre d???exemple d???une telle lecture, j?????voquerai quelques-uns des??v??nements de L???id??e de la ph??nom??nologie de Husserl. (shrink)

In this paper we present a method to reduce the decision problem of several infinite-valued propositional logics to their finite-valued counterparts. We apply our method to Łukasiewicz, Gödel and Product logics and to some of their combinations. As a byproduct we define sequent calculi for all these infinite-valued logics and we give an alternative proof that their tautology problems are in co-NP.

The Erdős–Moser ([Formula: see text]) theorem says that every infinite tournament admits an infinite transitive subtournament. We study the computational behavior of the [Formula: see text] theorem with respect to the arithmetic hierarchy, and prove that [Formula: see text] instances of [Formula: see text] admit low[Formula: see text] solutions for every [Formula: see text], and that if a set [Formula: see text] is not arithmetical, then every instance of [Formula: see text] admits a solution relative to which [Formula: see text] (...) is still not arithmetical. We also provide a level-wise refinement of this theorem. These results are part of a larger program of computational study of combinatorial theorems in Reverse Mathematics. (shrink)

It is generally assumed that compatibility with special relativity is guaranteed by the invariance of the fundamental equations of quantum physics under Lorentz transformations and the impossibility of transferring energy or information faster than the speed of light. Despite this, various contradictions persist, which make us suspect the solidity of that compatibility. This paper focuses on collapse theories—although they are not the only way of interpreting quantum theory—in order to examine what seems to be insurmountable difficulties we encounter when trying (...) to construct a space–time picture of such typically quantum processes as state vector reduction or the non-separability of entangled systems. The inescapable nature of such difficulties suggests the need to go further in the search for new formulations that surpass our current conceptions of matter and space–time. (shrink)

We determine the exact bounds for the length of an arbitrary reduction sequence of a term in the typed λ-calculus with β-, ξ- and η-conversion. There will be two essentially different classifications, one depending on the height and the degree of the term and the other depending on the length and the degree of the term.

The infinite pigeonhole principle for 2-partitions asserts the existence, for every set A, of an infinite subset of A or of its complement. In this paper, we study the infinite pigeonhole pr...

The present paper surveys the three most prominent accounts in contemporary debates over how sound reduction should be executed. The classical Nagelian model of reduction derives the laws of the target-theory from the laws of the base theory plus some auxiliary premises (so-called bridge laws) connecting the entities of the target and the base theory. The functional model of reduction emphasizes the causal definitions of the target entities referring to their causal relations to base entities. The new-wave model of reduction (...) deduces not the original target theory but an analogous image of it, which remains inside the vocabulary of the base theory. One of the fundamental motivations of both the functional and the new-wave model is to show that bridge laws can be evaded. The present paper argues that bridge laws—in the original Nagelian sense—are inevitable, i.e. that none of these models can evade them. On the one hand, the functional model of reduction needs bridge laws, since its fundamental concept, functionalization, is an inter-theoretical process dealing with entities of two different theories. Theoretical entities of different theories (in a general heterogeneous case) do not have common causal relations, so the functionalization of an entity—without bridge laws—can only be executed in the framework of its own theory. On the other hand, the so-called images of the new-wave account cannot be constructed without the use of bridge laws. These connecting principles are needed to guide the process of deduction within the base theory; without them one would not be able to recognize if the deduced structure was an image of the target theory. (shrink)