Ng :255–285, 1995. https://doi.org/10.1007/bf00852469) models the evolutionary dynamics underlying the existence of suffering and enjoyment and concludes that there is likely to be more suffering than enjoyment in nature. In this paper, we find an error in Ng’s model that, when fixed, negates the original conclusion. Instead, the model offers only ambiguity as to whether suffering or enjoyment predominates in nature. We illustrate the dynamics around suffering and enjoyment with the most plausible parameters. In our illustration, we find surprising results: (...) the rate of failure to reproduce can improve or worsen average welfare depending on other characteristics of a species. Our illustration suggests that for organisms with more intense conscious experiences, the balance of enjoyment and suffering may lean more toward suffering. We offer some suggestions for empirical study of wild animal welfare. We conclude by noting that recent writings on wild animal welfare should be revised based on this correction to have a somewhat less pessimistic view of nature. (shrink)

This paper develops a (nontrivial) theory of cardinal numbers from a naive set comprehension principle, in a suitable paraconsistent logic. To underwrite cardinal arithmetic, the axiom of choice is proved. A new proof of Cantor’s theorem is provided, as well as a method for demonstrating the existence of large cardinals by way of a reflection theorem.

The need to find an intrinsic characterization of what makes a relation between events causal arises not only in local theories of causation like Salmon's process theory but also in global approaches like Lewis' counterfactual theory. According to the localist intuition, whether a process connecting two events is causal should depend only on what goes on between the events, not on conditions that hold elsewhere in the world. If such intrinsic characterizations could be found, an identification of the causal relation (...) in the actual world (though not in other possible worlds) with physical processes may be feasible (the a posteriori identification). I consider recent proposals made for intrinsic characterizations of causality and conclude that none of them is able to deliver the intended result. (shrink)

Kim’s model of ‘functional reduction’ of properties is shown to fail in a class of cases from physics involving properties at different spatial levels. The diagnosis of this failure leads to a non-reductive account of the relation of micro and macro properties.

We examine some assumptions about the nature of 'levels of reality' in the light of examples drawn from physics. Three central assumptions of the standard view of such levels (for instance, Oppenheim and Putnam 1958) are (i) that levels are populated by entities of varying complexity, (ii) that there is a unique hierarchy of levels, ranging from the very small to the very large, and (iii) that the inhabitants of adjacent levels are related by the parthood relation. Using examples from (...) physics, we argue that it is more natural to view the inhabitants of levels as the behaviors of entities, rather than entities themselves. This suggests an account of reduction between levels, according to which one behavior reduces to another if the two are related by an appropriate limit relation. By considering cases where such inter-level reduction fails, we show that the hierarchy of behaviors differs in several respects from the standard hierarchy of entities. In particular, while on the standard view, lower-level entities are 'micro' parts of higher-level entities, on our view, a system's macro-level behavior can be seen as a ('non-spatial') part of its micro-level behavior. We argue that this second hierarchy is not really in conflict with the standard view and that it better suits examples of explanation in science. (shrink)

In contrast to rationalist views about beauty as a sort of perfection, Kant argues that judgements of taste about beauty are ‘entirely independent from the concept of perfection’ (5: 226).1 In the...

The paper argues that renormalization in quantum field theory was not a radically new - and possibly ad hoc - technique to save a badly flawed theory, but rather the culmination of a methodological strategy that physicists had been applying for a long time. The strategy was to obtain reliable results from unreliable theories by making the derivation of the results independent of possible future modifications of the theory. Examples of this practice include Bohr's use of the Correspondence Principle and (...) Heisenberg's S-matrix theory. (shrink)

I discuss the prospects of perspectival realism for resolving the problem of incompatible models or theories in scientific practice. My diagnosis is that the perspectivist can secure the ‘realism’ in her position only by employing suitable relations between the models. It is such relations that do the work, not the general philosophical claim about the perspectival nature of knowledge claims. But appeal to such relations has also been the preferred strategy of scientific realist approaches to the problem. With respect to (...) the problem of incompatible models, then, it is not clear that perspectivism has a clear advantage—even though the issue was among the motivating problems for proposing this view. I suggest, however, that the required inter-model relations embody a narrower notion of perspective, a notion that is explicitly part of the models themselves and that is essential in maintaining a realist view. (shrink)

A world is trivial if it makes every proposition true all at once. Such a world is impossible, an absurdity. Our world, we hope, is not an absurdity. It is important, nevertheless, for semantic and metaphysical theories that we be able to reason cogently about absurdities—if only to see that they are absurd. In this note we describe methods for ‘observing’ absurd objects like the trivial world without falling in to incoherence, using some basic techniques from modal logic. The goal (...) is to begin to locate the trivial world’s relative position in modal space; the outcome is that the less we assume about relative possibility, the more detail we can discern at the edge of reason. (shrink)

First-order Gödel logics are a family of finite- or infinite-valued logics where the sets of truth values V are closed subsets of [0,1] containing both 0 and 1. Different such sets V in general determine different Gödel logics GV (sets of those formulas which evaluate to 1 in every interpretation into V). It is shown that GV is axiomatizable iff V is finite, V is uncountable with 0 isolated in V, or every neighborhood of 0 in V is uncountable. Complete (...) axiomatizations for each of these cases are given. The r.e. prenex, negation-free, and existential fragments of all first-order Gödel logics are also characterized. (shrink)

Given that scientific realism is based on the assumption that there is a connection between a model's predictive success and its truth, and given the success of multiple incompatible models in scientific practice, the realist has a problem. When the different models can be shown to arise as different approximations to a unified theory, however, one might think the realist to be able to accommodate such cases. I discuss a special class of models and argue that a realist interpretation has (...) to understand these models of a system as ‘ perspectival ’, in close analogy to different spatial perspectives onto the same object. For this sort of case, I also respond to Morrison's recent claim that in the process of unifying models into an overarching theory, explanatory and descriptive power are lost, leaving the unified theory with less of a claim to a realist interpretation than the models themselves. Introduction Perspectival models from singular perturbation problems Unification of perspectives without losses of explanatory power Perspectives as different levels of a system Perspectival models, idealizations and pluralism. (shrink)

This paper explicates two notions of emergencewhich are based on two ways of distinguishinglevels of properties for dynamical systems.Once the levels are defined, the strategies ofcharacterizing the relation of higher level to lower levelproperties as diachronic and synchronic emergenceare the same. In each case, the higher level properties aresaid to be emergent if they are novel or irreducible with respect to the lower level properties. Novelty andirreducibility are given precise meanings in terms of the effectsthat the change of a bifurcation (...) or perturbation parameterin the system has. (The same strategy can be applied to otherways of separating levels of properties, like themicro/macro distinction.)The notions of emergence developed here are notions of emergencein a weak sense: the higher level emergent properties wecapture are always structural properties (or are realized insuch properties), that is, they are defined in terms of the lowerlevel properties and their relations. Diachronic and synchronicemergent properties are distinctions within thecategory of structural properties. (shrink)

ABSTRACTDo truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears in the foreground. Rather than (...) any one logic being privileged, then, on this count partisans across the logical spectrum are in relatively similar dialectical positions. (shrink)

In a recent article, Emil Badici contends that the inclosure schema substantially fails as an analysis of the paradoxes of self-reference because it is question-begging. The main purpose of this note is to show that Badici's critique highlights a necessity condition for the success of dialectic about paradoxes. The inclosure argument respects this condition and remains solvent.

Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber (...) directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary. (shrink)

The Curry-Howard isomorphism is a proof-theoretic result that establishes a connection between derivations in natural deduction and terms in typed lambda calculus. It is an important proof-theoretic result, but also underlies the development of type systems for programming languages. This fact suggests a potential importance of the result for a philosophy of code.

I argue that the free play of the faculties in Kant's theory of beauty should be interpreted as an activity that involves, over and above cognition, the aesthetic presentation of rational ideas. Two consequences of this proposal are then discussed: (1) Beauty in nature is not systematically prior to, or more basic than, artificial beauty; (2) genius and taste are connected more closely in the notion of the free play than Kant admits in the final version of his theory; this (...) more intimate association can be traced in the reflections on aesthetics from the 1770s. (shrink)

Closure is the idea that what is true about a theory of truth should be true in it. Commitment to closure under truth motivates non-classical logic; commitment to closure under validity leads to substructural logic. These moves can be thought of as responses to revenge problems. With a focus on truth in mathematics, I will consider whether a noncontractive approach faces a similar revenge problem with respect to closure under provability, and argue that if a noncontractive theory is to be (...) genuinely closed, then it must be free of all contraction, even in the metatheory. (shrink)

I try to identify the characteristic and distinguishing features of a theory of natural beauty (as opposed to the sublime) that can be found in Kant's Critique of Judgement. Lest this may seem superfluous, I argue first that, contrary to a common view, Kant's theory does not take the experience of beauty in nature as theoretically basic and that he does not deal with beauty in art only as a derivative case of aesthetic experience. I then try to understand what (...) it means to require, as Kant famously does, that beautiful nature has to look as if it were art. Does this commit him to a projectionist view, according to which we appreciate nature aesthetically only for what it really is not (namely art) rather than for what it is? Pursuing this question we find that for Kant nature can be the object of pure judgements of taste only insofar as nature can be explained scientifically, which in Kant's framework means purely mechanically. This ‘blind mechanism’ of nature plays an important role in Kant's explication of the moral significance the experience of beautiful nature has for us. (shrink)

Non-reductive physicalists have made a number of attempts to provide the relation of supervenience between levels of properties with enough bite to analyze interesting cases without at the same time losing the relation's acceptability for the physicalist. I criticize some of these proposals and suggest an alternative supplementation of the supervenience relation by imposing a requirement of robustness which is motivated by the notion of structural stability familiar from dynamical systems theory. Robust supervenience, I argue, captures what the non-reductive physicalist (...) wants from supervenience; most importantly, it provides a natural background for reconstructing the notion of (diachronic) property emergence in a way acceptable to physicalists. (shrink)

This paper begins an axiomatic development of naive set theoryin a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead (...) to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis. (shrink)

Philosophers like Duhem and Cartwright have argued that there is a tension between laws' abilities to explain and to represent. Abstract laws exemplify the first quality, phenomenological laws the second. This view has both metaphysical and methodological aspects: the world is too complex to be represented by simple theories; supplementing simple theories to make them represent reality blocks their confirmation. We argue that both aspects are incompatible with recent developments in nonlinear dynamics. Confirmation procedures and modelling strategies in nonlinear dynamics (...) show that there are simple, abstract theories that can be confirmed without encountering the problems pointed to by Cartwright. (shrink)

After a brief flirtation with logicism around 1917, David Hilbertproposed his own program in the foundations of mathematics in 1920 and developed it, in concert with collaborators such as Paul Bernays andWilhelm Ackermann, throughout the 1920s. The two technical pillars of the project were the development of axiomatic systems for everstronger and more comprehensive areas of mathematics, and finitisticproofs of consistency of these systems. Early advances in these areaswere made by Hilbert (and Bernays) in a series of lecture courses atthe (...) University of Göttingen between 1917 and 1923, and notably in Ackermann's dissertation of 1924. The main innovation was theinvention of the -calculus, on which Hilbert's axiom systemswere based, and the development of the -substitution methodas a basis for consistency proofs. The paper traces the developmentof the ``simultaneous development of logic and mathematics'' throughthe -notation and provides an analysis of Ackermann'sconsistency proofs for primitive recursive arithmetic and for thefirst comprehensive mathematical system, the latter using thesubstitution method. It is striking that these proofs use transfiniteinduction not dissimilar to that used in Gentzen's later consistencyproof as well as non-primitive recursive definitions, and that thesemethods were accepted as finitistic at the time. (shrink)

This paper considers a generalisation of the sorites paradox, in which only topological notions are employed. We argue that by increasing the level of abstraction in this way, we see the sorites paradox in a new, more revealing light—a light that forces attention on cut-off points of vague predicates. The generalised sorites paradox presented here also gives rise to a new, more tractable definition of vagueness.

Agent-based models (ABMs) are one of the main sources of evidence for decisions regarding mitigation and suppression measures against the spread of SARS-CoV-2. These models have not been previously included in the hierarchy of evidence put forth by the evidence-based medicine movement, which prioritizes those research methods that deliver results less susceptible to the risk of confounding. We point out the need to assess the quality of evidence delivered by ABMs and ask the question of what is the risk that (...) assumptions entertained in ABMs do not include all the key factors and make model predictions susceptible to the problem of confounding. (shrink)

Initially, you judge that p. You then learn that most experts disagree. All things considered, you believe that the experts are probably right. Still, p continues to seem right to you, in some sense. You don’t yet see what, if anything, is wrong with your original reasoning. In such a case, we’ll say that you are ‘inclined’ toward p. This paper explores various roles that this state of inclination can play, both within epistemology and more broadly. Specifically, it will be (...) argued that: (i) inclinations can promote the accuracy of inquiring groups; (ii) they can support rational participation within philosophy despite pervasive disagreement; (iii) they allow us to make sense of an important way in which two people can continue to disagree even after they ‘conciliate’; (iv) inclinations carry information about individuals’ independent judgments and for this reason must be accounted for when updating on the opinions of others; (v) inclinations are connected to understanding in a way that belief is not; (vi) and awareness of the inclination-belief distinction enables us to respond to a provocative challenge purporting to show that critical thinking, or ‘thinking for oneself’, typically reduces expected accuracy and hence should be discouraged. (shrink)

The naive set theory problem is to begin with a full comprehension axiom, and to find a logic strong enough to prove theorems, but weak enough not to prove everything. This paper considers the sub-problem of expressing extensional identity and the subset relation in paraconsistent, relevant solutions, in light of a recent proposal from Beall, Brady, Hazen, Priest and Restall [4]. The main result is that the proposal, in the context of an independently motivated formalization of naive set theory, leads (...) to triviality. (shrink)

Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected . In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of (...) empty parts, in delivering a balanced and bounded metaphysics of naive space. (shrink)

There are many approaches to paraconsistency, ranging from the very moderate to the more radical. In this paper I explore and extend the more radical end of the spectrum, where there are truth-value gluts. In particular I will look at paraconsistent metatheory – the machinery of truth, validity, and proof  as developed in a glut-friendly paraconsistent setting. The aim is to evaluate the philosophical and technical tenability of such an approach. I will show that there are very significant technical (...) challenges to face on this sort of radical approach, but that there is good philosophical support for facing these challenges. (shrink)

Prevailing opinion—defended by Jason Brennan and others—is that voting to change the outcome is irrational, since although the payoffs of tipping an election can be quite large, the probability of doing so is extraordinarily small. This paper argues that prevailing opinion is incorrect. Voting is shown to be rational so long as two conditions are satisfied: First, the average social benefit of electing the better candidate must be at least twice as great as the individual cost of voting, and second, (...) the chance of casting the decisive vote must be at least 1/N, where N stands for the number of citizens. It is argued that both of these conditions are often true in the real world. (shrink)

Beauty, or at least natural beauty, is famously a symbol of the morally good in Kant's theory of taste. Natural beauty is also, we argue, a symbol of the systematicity of nature. This symbolic connection of beauty and systematicity in nature sheds light on the relation between the principles underlying the use of reflecting judgement. The connection also motivates a more general interpretive proposal: the fact that the imagination can symbolize ideas plays a crucial role in the theory of taste; (...) it is the mechanism that underlies pure judgements of taste, the operation by which the imagination ‘schematizes without a concept’. (shrink)

Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...) primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged. (shrink)

ABSTRACTIn ‘Theism and Dialetheism’, Cotnoir explores the idea that dialetheism can help with some puzzles about omnipotence in theology. In this note, I delineate another asp...

I exploit parallel considerations in the philosophy of mind and metaethics to argue that the reasoning employed in an important argument for panpsychism overgeneralizes to support an analogous position in metaethics: panmoralism. Next, I raise a number of problems for panmoralism and thereby build a case for taking the metaethical parallel to be a reductio ad absurdum of the argument for panpsychism. Finally, I contrast panmoralism with a position recently defended by Einar Duenger Bohn and argue that the two suffer (...) from similar problems. I conclude by drawing some general lessons for panpsychism. (shrink)

This article suggests a novel way to advance a current debate in the philosophy of mathematics. The debate concerns the role of diagrams and visual reasoning in proofs—which I take to concern the criteria of legitimate representation of mathematical thought. Drawing on the so-called ‘maverick’ approach to philosophy of mathematics, I turn to mathematical practice itself to adjudicate in this debate, and in particular to category theory, because there (a) diagrams obviously play a major role, and (b) category theory itself (...) addresses questions of representation and information preservation over mappings. We obtain a mathematical answer to a philosophical question: a good mathematical representation can be characterized as a category theoretic natural transformation. (shrink)

This essay examines the anti-producing human body in its limit case of public self-induced starvation, as figured in Franz Kafka's short story ‘A Hunger Artist’ and Steve McQueen's film Hunger. Both works represent the fasting body as hollowed out, a resistance to capitalist-spectator capture that spatialises itself as a smoothing, a relative reconfiguration of parts to whole through the evacuation of flows. In both works the human body becomes a local body without organs, paradoxically disarticulated from the more complex assemblages (...) that constitute it while recording potential circuits of disturbance or resonance predicated upon the porousness of bodily boundaries. (shrink)

The god term of journalism—the be-all and end-all, the term without which the entire enterprise fails to make sense—is the public.As a doctrine and a movement, public journalism has suffered through theoretical critiques, practical difficulties, fiscal exigencies, professional resistances, and the explosion of new media technologies. Though public journalism has not supported a single definition, Jay Rosen, the movements' most vocal intellectual representative, suggests that public journalists "are not merely chroniclers of the political scene, but players in the game who (...) can (and should) try to shape the outcome" (1992, 8).1 Hundreds of newspapers and television outlets have taken part in experiments in becoming .. (shrink)

The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and accessible presentations of its theory on the other. One significant early result for the original axiomatic proof system for the epsilon-calculus is the first epsilon theorem, for which a proof is sketched. The system itself is discussed, also relative to possible semantic interpretations. The problems facing (...) the development of proof-theoretically well-behaved systems are outlined. (shrink)

Were there interactions between the development of Kant's aesthetics and the development of his moral philosophy? How did Kant view pleasure and displeasure and what role did they play in the formation of his system of the faculties? In this book, Alexander Rueger situates Kant's account of pleasure and displeasure in its eighteenth-century context, with special attention to Leibniz, Wolff, Crusius, and Mendelssohn. He traces the development of Kant's views on pleasure from the 1770s to his Critique of Aesthetic (...) Judgment in 1790, and shows that throughout, Kant understood pleasure as the satisfaction of faculty interests. The significance of this theory for the completion of Kant's critical system in the third Critique is discussed in detail. Rueger's study illuminates both the role of pleasure and displeasure in Kant's thought, and their important connections to the power of judgment. (shrink)