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)

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)

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)

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.

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)

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.

In the present commentary, I argue that Foster has attacked an uncharitable reconstruction of Etchemendy's argument against Tarski's account of the logical properties. I provide an alternative, more charitable reconstruction of that argument that withstands Foster's objections.

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)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 43.1 (2005) 83-105 [Access article in PDF] Does Malebranche Need Efficacious Ideas? The Cognitive Faculties, the Ontological Status of Ideas, and Human Attention Susan Peppers-Bates But whatever effort of mind I make, I cannot find an idea of force, efficacy, of power, save in the will of the infinitely perfect Being. Malebranche, Elucidation 15 One of the signatures of 17th century rationalists (...) is their replacement of the Scholastics's dependence on the deliverances of the senses with a dependence on the deliverances of the intellect as the key to gaining knowledge.1 Correct use of the intellect leading to freedom from the passions and to certain knowledge figures prominently in the works of Spinoza and Leibniz. Descartes's Meditations uses skeptical doubt to withdraw the mind from the senses, and his reliance on the meditative genre not only reveals to his readers the intellect as a distinct source of knowledge, but also trains them to use properly their will or faculty of judgment. Commentators have argued persuasively that overthrowing the sense-based epistemology and metaphysics of the Aristotelians depended on "discovering" the primacy of one's intellect over the senses, and using the deliverances of the mind to establish solid foundations for a new metaphysics and epistemology.2 Indeed, [End Page 83] outlining the proper use of the mind's faculties arguably lay at the basis of the Cartesian program in particular. This importance can be seen in Arnauld and Nicole's influential Port-Royal Logic, which aimed at training its readers in the proper use of the intellect.3Few would question Nicolas Malebranche's inclusion in the rationalist tradition.4 For while Malebranche famously takes ideas out of the Cartesian mind and transports them to God's—thus privileging the divine over the natural light—he shares Descartes's belief that our intellect, not our senses, holds the key to metaphysical truths such as the essence of matter, the mind-body distinction, and the existence of God.5 Yet, recently, Nicholas Jolley has contended that Malebranche's later commitment to "efficacious ideas" undermines his earlier belief in the power of the cognitive faculties: he believes that Malebranche abandons his view that the mind makes "real use" of the intellect to know intelligible objects.6 Jolley's position builds upon Alquié and Robinet's claims that around 1694-95 Malebranche moved from a vision "in" God to a vision "by" God. Now God's ideas act on and modify the soul with both sensations and intellectual concepts, rather than the human intellect contemplating ideas in the Divine Reason.7Alquié and Robinet argue that Malebranche, pushed by the battles with Arnauld and Régis over the status of ideas, introduced the language of "efficacious" ideas to explain how the union of the human and the divine mind is supposed to work.8 Robinet in particular suggests that in cashing out the metaphor of God enlightening human minds, Malebranche moved from a static "ontologist" view of idea-objects in God to an active "illuminationist" view whereby divine ideas cause(intellectual [End Page 84] and sensory) perception by modifying the soul.9 Once one accepts this view of the place and function of efficacious ideas in Malebranche's metaphysics, it seems natural to accept Jolley's declaration that the only way for the mind to apprehend ideas in God is if those ideas "act directly on the mind; [if] they thereby cause cognitive states to arise in a substance which is devoid of all genuine cognitive capacities of its own."10 Indeed, Jolley suggests that Malebranche ultimately made the soul passive in all its states, including its volitional ones.11In this paper, I argue that a strong interpretation of efficacious ideas, whereby they appear to become true causal agents, must be rejected precisely because it pushes us into an incorrect reading of Malebranche's theory of the divine and human faculties. Making ideas true causal agents within God privileges divine reason at the... (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)

Purpose Underlying much recent development in data science and artificial intelligence (AI) is a dependence on the labour of precarious crowdworkers via platforms such as Amazon Mechanical Turk. These platforms have been widely critiqued for their exploitative labour relations, and over recent years, there have been various efforts by academic researchers to develop interventions aimed at improving labour conditions. The aim of this paper is to explore US-based crowdworkers’ views on two proposed interventions: a browser plugin that detects automated quality (...) control “Gold Question” (GQ) checks and a proposal for a crowdworker co-operative. Design/methodology/approach The authors interviewed 20 US-based crowdworkers and undertook a thematic analysis of collected data. Findings The findings indicate that US-based crowdworkers tend to have negative and mixed feelings about the GQ detector, but were more enthusiastic about the crowdworker co-operative. Originality/value Drawing on theories of precarious labour, this study suggests an explanation for the findings based on US-based workers’ objective and subjective experiences of precarity. The authors argue that for US-based crowdworkers “constructive” interventions such as a crowdworker co-operative have more potential to improve labour conditions. (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)

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)

This article consists of two important parts. The first is a specific defense of some of the central claims made by stanley cavell in "must we mean what we say" against the criticisms of fodor and katz in "the availability of what we say." the major issue concerns the question of whether evidence of some sort is needed to support a claim by a native speaker about what we mean when we say something. Further speculations on this topic occupy the (...) other part of the paper. (shrink)

The swamping problem is the problem of explaining why reliabilist knowledge (reliable true belief) has greater value than mere true belief. Swamping problem advocates see the lack of a solution to the swamping problem (i.e., the lack of a value-difference between reliabilist knowledge and mere true belief) as grounds for rejecting reliabilism. My aims here are (i) to specify clear requirements for a solution to the swamping problem that are as congenial to reliabilism's critics as possible, (ii) to clear away (...) various existing reliabilist solutions on the basis of these requirements, and (iii) to present a reliabilist solution that succeeds in meeting all of them. To meet all the requirements, my solution develops a more nuanced understanding of the epistemic end than is currently discussed, and with it a novel way of individuating beliefs. I close with a brief discussion of the question whether reliabilism's critics might impose further demands which reliabilism cannot possibly meet. (shrink)

A comprehensive account of the role of the imagination in Hegel's philosophy.

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)

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 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)

In the 1920s, Ackermann and von Neumann, in pursuit of Hilbert's programme, were working on consistency proofs for arithmetical systems. One proposed method of giving such proofs is Hilbert's epsilon-substitution method. There was, however, a second approach which was not reflected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert's first epsilon theorem and a certain "general consistency result" due to Bernays. An analysis of the form of this so-called "failed proof" (...) sheds further light on an interpretation of Hilbert's programme as an instrumentalist enterprise with the aim of showing that whenever a "real" proposition can be proved by ?ideal? means, it can also be proved by "real", finitary means. (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.

Paraconsistent logic makes it possible to study inconsistent theories in a coherent way. From its modern start in the mid-20th century, paraconsistency was intended for use in mathematics, providing a rigorous framework for describing abstract objects and structures where some contradictions are allowed, without collapse into incoherence. Over the past decades, this initiative has evolved into an area of non-classical mathematics known as inconsistent or paraconsistent mathematics. This Element provides a selective introductory survey of this research program, distinguishing between `moderate' (...) and `radical' approaches. The emphasis is on philosophical issues and future challenges. (shrink)

On the basis of psychological research, a group of philosophers known as 'situationists' argue that the evidence belies the existence of broad and stable (or 'global') character traits. They argue that this condemns as psychologically unrealistic those traditions in moral theory in which global virtues are upheld as ideals. After a survey of the debate to date, this article argues that the thesis of situationism is ill-supported by the available evidence. Situationists overlook the explanatory potential of a large class of (...) global character traits, namely, vices that do not involve other-directed malevolence, such as laziness, cowardice, and selfishness. A detailed discussion of the relevant empirical studies bearing on moral psychology shows that the behavioral patterns observed in these studies are consistent with the widespread possession of such non-malicious vices. This means, contrary to the situationist thesis, that the empirical record is fully compatible with the common existence of global character traits. (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)

Six people are in trouble. We can save five of them or just the sixth. What should we do? John Taurek (1977) defends a radical view: We are not required to save the greater number. Taurek's paper has persuaded some. But even the unpersuaded agree that Taurek poses a deep and important challenge: From where does the priority of the many derive? It seems difficult, or even impossible, to convince someone who denies the importance of the numbers... to care about (...) the numbers. That’s what this paper aims to do. It will argue that the priority of the many follows, with minimal other assumptions, from something all should accept: the modest premise that if we can improve one person's chance of survival—without affecting anyone else—we should. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 61.4 (2000) 577-593 [Access article in PDF] Machina Ex Deo: William Harvey and the Meaning of Instrument Don Bates Introduction Since our clocks do consistently disclose each hour of the day and night--do they not seem to partake of another body (beyond the elements), and that more divine? But if, under the dominion and management of [our human] Art, such splendid things (...) are daily achieved beyond the powers of the objects themselves,... And if, in serving men they carry out such things as are to be marvelled at, what I ask, may we expect from them when they be instruments in the hand of God? These words come near the end of William Harvey's De generatione animalium. 1 As he does often in this work, he is arguing that it is possible for a material object to behave supra vires elementorum, i.e., in a manner that exceeds what can be explained merely from the qualities of the elements from which it is made. In fact, just before this, he argues that human craftsmanship enables the elements of air and water to make ships sail in opposite directions, fire to do one sort of thing in the kitchen, another in the shops of metal-workers, including the production of iron, which in its turn peacefully tills the soil or besieges the town in war. So if even human Art is capable of making something as wonderful as a clock out of the elements, how much more might God be able to do with them? [End Page 577]Not only is it entirely conceivable that the (divinely) artful manipulation of these same elements can account for the wonders of God's nature--such as the generation of a chick out of an egg--there is also no need to infer the existence of additional entities such as faculties, qualities, agents, and the like. All that is needed is the concept of "instrument." Today such things as his appeal to a clock, his reference to "art," and the word "instrument" itself, are liable to arouse in our minds a fairly mechanical sort of image. Therefore, we need to put this idea in its intellectual context, by looking at where Harvey's notion of instrument is coming from.First, our much more mechanical world view was just coming into being as Harvey (1578-1657) wrote these words. Although the philosophy of his younger contemporary, René Descartes (1596-1650) was not yet in full bloom (he died a year before Harvey's book appeared), Cartesianism was certainly on the explanatory horizon, 2 as was the work of another contemporary and contributor to the "new philosophy," Pierre Gassendi (1592-1655). 3 And, of course, Harvey had certainly known Francis Bacon (1561-1626). 4 Nevertheless, Harvey was a devout Aristotelian who was adamantly opposed to the efforts of these contemporaries to replace Aristotle. 5 Moreover, it was from the Aristotelian tradition, not from the new mechanics, that Harvey had derived the concept of instrument.If, broadly speaking, the "new philosophy" was about a universe that was built like a clock, then the "old" natural philosophies, whether dominated by Platonism, Aristotelianism, Christian theology, or some combination, were about a universe that was socially constructed. 6 Not only was man at the center, to a large extent the workings of the universe were envisioned in terms of social experience. The regularity, predictability, harmony, and wonder of natural phenomena seemed best explained in the language of reason, moral values, motives, responsibilities, hierarchies, laws (in the social sense), and the like, explanatory resources that, in the late ancient and medieval intellectual cultures of Europe, far outweighed either those that appealed to the passively material and the mechanical, or to the random and the chance.But very central to that social model of nature was the concept of instrument, which gave to it something of a mechanical twist. To see how this was so, we need to go back temporarily to the works of Aristotle, the influence of... (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)

What should a person do when, through no fault of her own, she ends up believing a false moral theory? Some suggest that she should act against what the false theory recommends; others argue that she should follow her rationally held moral beliefs. While the former view better accords with intuitions about cases, the latter one seems to enjoy a critical advantage: It seems better able to render moral requirements ‘followable’ or ‘action-guiding.’ But this tempting thought proves difficult to justify. (...) Indeed, whether it can be justified turns out to depend importantly on the rational status of epistemic akrasia. Furthermore, it can be argued, from premises all parties to the moral ignorance debate should accept, that rational epistemic akrasia is possible. If the argument proves successful, it follows that a person should sometimes act against her rationally held moral convictions. (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)

This thesis divides naturally into two parts, each concerned with the extent to which the theory of $L$ can be changed by forcing.The first part focuses primarily on applying generic-absoluteness principles to how that definable sets of reals enjoy regularity properties. The work in Part I is joint with Itay Neeman and is adapted from our paper Happy and mad families in $L$, JSL, 2018. The project was motivated by questions about mad families, maximal families of infinite subsets of $\omega (...) $ of which any two have only finitely many members in common. We begin, in the spirit of Mathias, by establishing a strong Ramsey property for sets of reals in the Solovay model, giving a new proof of Törnquist’s theorem that there are no infinite mad families in the Solovay model.In Chapter 3 we stray from the main line of inquiry to briefly study a game-theoretic characterization of filters with the Baire Property.Neeman and Zapletal showed, assuming roughly the existence of a proper class of Woodin cardinals, that the boldface theory of $L$ cannot be changed by proper forcing. They call their result the Embedding Theorem, because they conclude that in fact there is an elementary embedding from the $L$ of the ground model to that of the proper forcing extension. With a view toward analyzing mad families under $\mathsf {AD}^+$ and in $L$ under large-cardinal hypotheses, in Chapter 4 we establish triangular versions of the Embedding Theorem. These are enough for us to use Mathias’s methods to show that there are no infinite mad families in $L$ under large cardinals and that $\mathsf {AD}^+$ implies that there are no infinite mad families. These are again corollaries of theorems about strong Ramsey properties under large-cardinal assumptions and $\mathsf {AD}^+$, respectively. Our first theorem improves the large-cardinal assumption under which Todorcevic established the nonexistence of infinite mad families in $L$. Part I concludes with Chapter 5, a short list of open questions.In the second part of the thesis, we undertake a finer analysis of the Embedding Theorem and its consistency strength. Schindler found that the the Embedding Theorem is consistent relative to much weaker assumptions than the existence of Woodin cardinals. He defined remarkable cardinals, which can exist even in L, and showed that the Embedding Theorem is equiconsistent with the existence of a remarkable cardinal. His theorem resembles a theorem of Harrington–Shelah and Kunen from the 1980s: the absoluteness of the theory of $L$ to ccc forcing extensions is equiconsistent with a weakly compact cardinal. Joint with Itay Neeman, we improve Schindler’s theorem by showing that absoluteness for $\sigma $ -closed $\ast $ ccc posets—instead of the larger class of proper posets—implies the remarkability of $\aleph _1^V$ in L. This requires a fundamental change in the proof, since Schindler’s lower-bound argument uses Jensen’s reshaping forcing, which, though proper, need not be $\sigma $ -closed $\ast $ ccc in that context. Our proof bears more resemblance to that of Harrington–Shelah than to Schindler’s.The proof of Theorem 6.2 splits naturally into two arguments. In Chapter 7 we extend the Harrington–Shelah method of coding reals into a specializing function to allow for trees with uncountable levels that may not belong to L. This culminates in Theorem 7.4, which asserts that if there are $X\subseteq \omega _1$ and a tree $T\subseteq \omega _1$ of height $\omega _1$ such that X is codable along T, then $L$ -absoluteness for ccc posets must fail.We complete the argument in Chapter 8, where we show that if in any $\sigma $ -closed extension of V there is no $X\subseteq \omega _1$ codable along a tree T, then $\aleph _1^V$ must be remarkable in L.In Chapter 9 we review Schindler’s proof of generic absoluteness from a remarkable cardinal to show that the argument gives a level-by-level upper bound: a strongly $\lambda ^+$ -remarkable cardinal is enough to get $L$ -absoluteness for $\lambda $ -linked proper posets.Chapter 10 is devoted to partially reversing the level-by-level upper bound of Chapter 9. Adapting the methods of Neeman, Hierarchies of forcing axioms II, we are able to show that $L$ -absoluteness for $\left |\mathbf {R}\right |\cdot \left |\lambda \right |$ -linked posets implies that the interval $[\aleph _1^V,\lambda ]$ is $\Sigma ^2_1$ -remarkable in L.prepared by Zach Norwood.E-mail: [email protected]. (shrink)

Despite a predominantly digital, 21st century music production landscape, analogue hardware professional audio technologies persist. In the discoursal throes of the leading online audio technology message forum Gearslutz, such technologies are routinely objectified, sexualized, fetishized and socialized into gear. Situated in a contemporary critical, interdisciplinary framework of fetish, masculinity and sexuality studies, this research interrogates how audio technologies manufactured and intended for music production contexts become sexy. Applying a mixed-mode methodology, including an intensive discourse, image and material-semiotic analysis of an (...) ‘epic’ sexy gear thread, we collated extensive data about technological fetishization. Sexy gear discourse articulates themes of voyeurism, acquisition, control and animation – linking the fetish value of technological objects and their connoisseurship with the erotic potential of sexualized objects. Such discourses ultimately serve to maintain social order, and become sites for performing the maintenance work of hegemonic masculine formations. This research provides new insights into how hegemonic masculinities depend upon the organization of online and offline sociability around fetishized material objects. Furthermore, our findings align with those of current scholarship focused on representational politics of technoculture. (shrink)

Trinucleotide repeat expansions are now a well‐established mutational mechanism in human genetic disease. An unstable CAG repeat is known to be responsible for three neurodegenerative disorders: Huntington's disease, spinal and bulbar musclar atrophy and spinocerebellar ataxia type 1. Similarities in the genetics of these diseases, the size of the repeat expansions and the position of the unstable repeat within the gene (when known) suggest a common basis to the observed phenotypes. The cloning of two regions at which chromosome breakage can (...) be induced (FRAXA and FRAXE) has in each case uncovered an unstable CG‐rich triplet repeat which becomes methylated when fully expanded. In addition to these two classes of mutation, the presence of an expanded CTG repeat in the 3′ untranslated region of a protein kinase causes myotonic dystrophy. The size of the respective expansions, repeat stability, mutational origins and possible mechanisms of action are discussed. (shrink)

The inclosure schema has been proposed by Priest as the structure of many paradoxes. The inclosure analysis has many virtues, especially as a step toward a uniform solution to the paradoxes. Inclosure suggests that paradoxes arise at the limits of thought because the limits can be surpassed, and also not; and so dialetheism is true. I explore the consequences of accepting Priest’s proposal. From a thoroughly dialetheic perspective, then, I find that the import of inclosure changes: some limit phenomena cannot (...) be contradictory, on pain of absurdity, and true contradictions are better thought of as local, not “limit” phenomena. Dialetheism leads back from the edge of thought, to the inconsistent in the every day. (shrink)