Some axiomatic theories of truth and related subsystems of second-order arithmetic are surveyed and shown to be conservative over their respective base theory. In particular, it is shown by purely finitistically means that the theory PA ÷ "there is a satisfaction class" and the theory FS of [2] are conservative over PA.

It is noteworthy that much of recent liberal scholarship aimed at empowering aboriginal peoples, and supporting their land rights, has often unwittingly embraced the conservative Lockean‐Nozickian tradition rather than the tradition of left‐leaning thinkers. Many of the supporters of aboriginal land rights tend to view property rights as contingently determined historical entitlements which are established independently of the state’s authority, thereby creating structures which morally bind the authority of the state. This, in fact, also represents the view of the (...) conservative supporters of untrammelled capitalism. Secondly, there is often little discussion of the bundle of rights which are derived from these acts of original acquisition. This may lead one to the assumption that these supporters of aboriginal land rights agree with the conservative view that all the recognised components of modern liberal ownership, from the right to use, to the right to income, are acquired in the initial events associated with historical entitlement. It is my argument in this paper that basing aboriginal land claims solely on customary historical entitlement results in too close an alignment with a conservative ideology which has been used to support unrestrained capitalism. (shrink)

Conservation problems can reveal unsuspected complexities in the ontological make-up of modern and contemporary artworks. Using a problem in the conservation of one of Sol LeWitt’s Wall Drawings as my starting point, I argue that Goodman’s well-known and often criticized distinction between autographic and allographic art can be fruitfully used to articulate the different options in conservation dilemmas, but only if used in a non-disjunctive way and in the context of a biographical approach to the works under consideration.

In response to calls for greater interdisciplinary involvement from the social sciences and humanities in the development, governance, and study of artificial intelligence systems, this paper presents one sociologist’s view on the problem of algorithmic bias and the reproduction of societal bias. Discussions of bias in AI cover much of the same conceptual terrain that sociologists studying inequality have long understood using more specific terms and theories. Concerns over reproducing societal bias should be informed by an understanding of the ways (...) that inequality is continually reproduced in society—processes that AI systems are either complicit in, or can be designed to disrupt and counter. The contrast presented here is between conservative and radical approaches to AI, with conservatism referring to dominant tendencies that reproduce and strengthen the status quo, while radical approaches work to disrupt systemic forms of inequality. The limitations of a conservative approach to racial bias are discussed through the specific example of biased criminal risk assessments and Indigenous overrepresentation in Canada’s criminal justice system. This illustrates the dangers of treating racial bias as a generalizable problem and equality as a generalizable solution, emphasizing the importance of considering inequality in context. Societal issues can no longer be out of scope for AI and machine learning, given the impact of these systems on human lives. This requires engagement with a growing body of critical AI scholarship that goes beyond biased data to analyze structured ways of perpetuating inequality, opening up the possibility for interdisciplinary engagement and radical alternatives. (shrink)

Drones deployed to monitor endangered species often crash. These crashes teach us that using drones for conservation is a contingent practice ensnaring humans, technologies, and animals. This article advances a crash theory in which pilots, conservation drones, and endangered megafauna are relata, or related actants, that intra-act, cocreating each other and a mutually constituted phenomena. These phenomena are entangled, with either reciprocal dependencies or erosive entrapments. The crashing of conservation drones and endangered species requires an ethics of care, repair, (...) or reworlding. Diffractions, disruptions that expose difference, result from crashes and reveal the precarious manner by which technologies, laws, and discourses bring nature and culture together. To support crash theory, this article presents three ethnographic cases. A drone crash in the United Kingdom near white rhinoceroses while building machine learning training data exhibits the involvement of the electromagnetic spectrum; the threat of crashes in the Pacific Northwest near Puget Sound orcas discloses the impacts of drone laws; and drone crashes in Sri Lanka among Asian elephants presents the problems of technoliberal ideals around programming natural worlds. Throughout the article, a methodology is developed, parallelism, which attends to the material similarities in lateral phenomena. (shrink)

An algebraic block-diagonalization of the Dirac Hamiltonian in a time-independent external field reveals a charge-index conservation law which forbids the physical phenomena of the Klein paradox type and guarantees a single-particle nature of the Dirac equation in strong external fields. Simultaneously, the method defines simpler quantum-mechanical objects—paulions and antipaulions, whose 2-component wave functions determine the Dirac electron states through exact operator relations. Based on algebraic symmetry, the presented theory leads to a new understanding of the Dirac equation physics, including (...) new insight into the Dirac measurements and a consistent scheme of relativistic quantum mechanics of electron in the paulion representation. Along with analysis of the mathematical anatomy of the Klein paradox falsity, a complete set of paradox-free eigenfunctions for the Klein problem is obtained and investigated via stationary solutions of the Pauli-like equations with respective paulion Hamiltonians. It is shown that the physically correct Dirac states in the Klein zone are characterized by the total particle reflection from the potential step and satisfy the fundamental charge-index conservation law. (shrink)

I defend the conserved quantity theory of causation against two objections: firstly, that to tie the notion of “cause” to conservation laws is impossible, circular or metaphysically counterintuitive; and secondly, that the conserved quantity theory entails an undesired notion of identity through time. My defence makes use of an important meta-philosophical distinction between empirical analysis and conceptual analysis. My claim is that the conserved quantity theory of causation must be understood primarily as an empirical, not a conceptual, (...) analysis of causation. (shrink)

Constructive set theory a' la Myhill-Aczel has been extended in (Cantini and Crosilla 2008, Cantini and Crosilla 2010) to incorporate a notion of (partial, non--extensional) operation. Constructive operational set theory is a constructive and predicative analogue of Beeson's Inuitionistic set theory with rules and of Feferman's Operational set theory (Beeson 1988, Feferman 2006, Jaeger 2007, Jaeger 2009, Jaeger 1009b). This paper is concerned with an extension of constructive operational set theory (Cantini and Crosilla 2010) by (...) a uniform operation of Transitive Closure, \tau. Given a set a, \tau produces its transitive closure \tau a. We show that the theory ESTE of (Cantini and Crosilla 2010) augmented by \tau is still conservative over Peano Arithmetic. (shrink)

In Ruling Passions, Simon Blackburn contends that we should reject sensibility theory because it serves to support a conservative complacency. Blackburn's strategy is attractive in that it seeks to win this metaethical dispute – which ultimately stems from a deep disagreement over antireductionism – on the basis of an uncontroversial normative consideration. Therefore, Blackburn seems to offer an easy solution to an apparently intractable debate. We will show, however, that Blackburn's argument against sensibility theory does not succeed; (...) it is no more supportive of conservative complacency than Blackburn's noncognitivism. A victory for noncognitivism cannot be so easily won. (shrink)

The concept of practice is thematically central to modern conservative thought, as evident in Edmund Burke’s writings on the aesthetic and his diatribe against the French Revolution. It is also the main organizing thread in the framework in the human sciences known as practice theory, which extends back at least to Karl Marx’s ‘Theses on Feuerbach’. This article historicizes ‘practice’ in conservative thought and practice theory, accounts for the family resemblance between the two, and takes apart (...) that family resemblance to reveal differences. The ingredients of practice theory (historical inheritance, embodiment, cognitive limits, loose coupling between conscious thought and action) are in many cases also distinctive traits of conservative thought. But the similarity is deceptive. Practice theory and conservative thought constitute two distinct interpretations of practice, two disparate endeavours for connecting human science with political strategy, and two different formulas for opposing theory and practice. The present study will argue that this is primarily a political opposition for conservative thought, while it is a human-scientific opposition for practice theory. Conservative thought is initially political and then human-scientific; practice theory is initially human-scientific and then political. This article advocates for practice theory against conservative thought as differently amended versions of a politics that recognizes human finitude. (shrink)

In this paper I offer an 'integrating account' of singular causation, where the term 'integrating' refers to the following program for analysing causation. There are two intuitions about causation, both of which face serious counterexamples when used as the basis for an analysis of causation. The 'process' intuition, which says that causes and effects are linked by concrete processes, runs into trouble with cases of 'misconnections', where an event which serves to prevent another fails to do so on a particular (...) occasion and yet the two events are linked by causal processes. The chance raising intuition, according to which causes raise the chance of their effects, easily accounts for misconnections but faces the problem of chance lowering causes, a problem easily accounted for by the process approach. The integrating program attempts to provide an analysis of singular causation by synthesising the two insights, so as to solve both problems. In this paper I show that extant versions of the integrating program due to Eells, Lewis, and Menzies fail to account for the chance-lowering counterexample. I offer a new diagnosis of the chance lowering case, and use that as a basis for an integrating account of causation which does solve both cases. In doing so, I accept various assumptions of the integrating program, in particular that there are no other problems with these two approaches. As an example of the process account, I focus on the recent CQ theory of Wesley Salmon (1997). (shrink)

An application of diagrams for separating modes of theory development.

Advocates of the conserved quantity (CQ) theory of causation have their own peculiar problem with conservation laws. Since they analyze causal process and interaction in terms of conserved quantities that are in turn defined as physical quantities governed by conservation laws, they must formulate conservation laws in a way that does not invoke causation, or else circularity threatens. In this paper I will propose an adequate formulation of a conservation law that serves CQ theorists' purpose.

I defend the conserved quantity theory of causation against two objections: firstly, that to tie the notion of "cause"to conservation laws is impossible, circular or metaphysically counterintuitive ; and secondly, that the conser quantity theory entails an undesired notion of identity through time. My defence makes use of an important meta-philosophical distinction between empirical analysis and conceptual analysis. My claim is that the conserved quantity theory of causation must be understood primarily as an empirical, not a conceptual, (...) analysis of causation. (shrink)

This paper examines Wesley Salmon's "process" theory of causality, arguing in particular that there are four areas of inadequacy. These are that the theory is circular, that it is too vague at a crucial point, that statistical forks do not serve their intended purpose, and that Salmon has not adequately demonstrated that the theory avoids Hume's strictures about "hidden powers". A new theory is suggested, based on "conserved quantities", which fulfills Salmon's broad objectives, and which avoids (...) the problems discussed. (shrink)

This work contrasts conservative or minimally mutilating revisions of empirical theories as they are identified in the presently dominant AGM model of formal belief revision and the structuralist program for the reconstruction of empirical theories. The aim is to make understandable why both approaches only partly succeed in substantially informing and formally restraining the issue. With respect to the rationality of minimal change, the overall result is negative. Readers with an interest in formal epistemology are provided with application cases (...) (mercury anomaly, revision of early thermo-dynamics, introduction of the neutrino), the historically inclined reader is offered a systematic perspective. The discussion can largely be followed without a background in formal logic. (shrink)

Hartry Field argues that conservative rather than true mathematical sentences facilitate deductions in nominalist (i.e., abstracta-free) science without prejudging its empirical outcomes. In this paper, I identify one branch of mathematics as nonconservative, for its indispensable role in enabling nominalist language about a fundamental scientific property, in a fictional scientific community. The fundamental property is electromagnetic reflectance, and the mathematics is Fourier analysis, which renders reflectance ascribable, and nominalist reflectance claims utterable, by this community. Using a recent characterization of (...) conservativeness by Kenneth Boyce, I argue that infinitudes can be rendered inherently mathematical and non-nominalizable in the fictional community, and that rendering infinitudes inherently mathematical for all real communities would yield a convincing counterexample to Fieldian conservativeness. (shrink)

Fundamental aspects of human use of the environment can be explained by game theory. Game theory explains aggregate behaviour of the human species driven by perceived costs and benefits. In the 'game' of global environmental protection and conservation, the stakes are the living conditions of all species including the human race, and the playing field is our planet. The question is can we control humanity's hitherto endless appetite for resources before we irreparably harm the global ecosystem and cause (...) extinction of even more species? The central problem is that some proportion of the individuals or groups will behave selfishly. The inducement for using more than a fair share, or 'cheating', increases as that resource becomes rarer, thus the benefits of cheating increase. In addition, the total number of people is increasing, so the proportion of cheaters must decrease to even keep total resource use constant. Cost benefit analysis of the effect of regulation and incentives on potential cheaters may provide a rational approach to controlling environmental problems. While it is debatable that environmental values are constant across cultures, communal use of resources seems to follow global rules. Cooperative use and punishment of those who use more than their share appear to be ubiquitous in human societies. Schemes for controlling human impact on the global environment must take into consideration basic behaviours including development of social norms and the positive feedback created because resources become more valuable with increasing rarity leading to more incentive for consumption. (shrink)

It is plausible that Newcomb problems in which causal maximizers and evidential maximizers would do different things would not be possible for ideal maximizers who are attentive to metatickles. An objection to Eells’s first argument for this makes welcome a second. Against it I argue that even ideal evidential and causal maximizers would do different things in some non-dominance Newcomb problems; and that they would hope for different things in some third-person and non-action problems, which is relevant if a good (...) theory of rational choices of acts should fit smoothly into a good theory of rational desires for facts. (shrink)

The theory of the conservation of energy and the Second Law of Thermodynamics have been described as the two most firmly established “findings” of modern science. Scientists frequently refer to them, not as theories or assumptions, but as facts. During the last two decades of the nineteenth century, however, Edmund Montgomery—an unsung Texas philosopher—repeatedly challenged, not only the notions that energy is convertible and is indestructible, but the very idea that there is such a thing as energy which can (...) be imposed ab extra upon matter. For his trouble he received censure and ridicule on every hand; friends usually apologized for this eccentricity of his. Montgomery, of course, has not been entirely alone in criticizing the theory of the conservation of energy, though he was the first to make a persistent attack on the merits of the theory as a principle of scientific explanation. Busse, for one, contended that if, as he thought likely, the theory were incompatible with psychophysical interactionism, it should be discarded on the grounds that the evidence in its behalf is far from compelling. Emergent evolutionists remind us occasionally that it is still within the province of reason to question this great dogma notwithstanding the fact that it is a god at whose feet many scientists worship with blind and jealous devotion. Of all these critics Montgomery attacked the theory where its greatest weaknesses lie. (shrink)

We show that for various set theories T including ZF, T + AC is conservative over T for sentences of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall x \exists! y}$$\end{document}A(x, y) where A(x, y) is a Δ0 formula.

The conserved quantity theory of causation aims to analyze causal processes and interactions in terms of conserved quantities. In order to be successful, the theory must correctly distinguish between causal processes and interactions, on the one hand, and pseudoprocesses and mere intersections on the other.Moreover, it must do this while satisfying two further criteria: it must avoid circularity; and the appeal to conserved quantities must not be redundant. I argue that the theory is not successful in meeting (...) these criteria. (shrink)

We formulate a general theory of conservation laws and other invariants for a physical system through equivalence relations. The conservation laws are classified according to the type of equivalence relation, with group equivalence, homotopical equivalence, and other types of equivalence relations giving respective kinds of conservation laws. The stability properties in the topological (and differentiable) sense are discussed using continuous deformations with respect to control parameters. The conservation laws due to the Abelian symmetries are shown to be stable through (...) application of well-known theorems. (shrink)

For all i ≥ 1, Ti+11 is not ∀Σb2-conservative over Ti1.

In this paper, we develop the system LZF of set theory with the unrestricted comprehension in full linear logic and show that LZF is a conservative extension of ZF– i.e., the Zermelo-Fraenkel set theory without the axiom of regularity. We formulate LZF as a sequent calculus with abstraction terms and prove the partial cut-elimination theorem for it. The cut-elimination result ensures the subterm property for those formulas which contain only terms corresponding to sets in ZF–. This implies (...) that LZF is a conservative extension of ZF– and therefore the former is consistent relative to the latter. (shrink)

Phil Dowe has argued persuasively for a reductivist theory of causality. Drawing on Wesley Salmon's mark transmission theory and David Fair's transferencetheory, Dowe proposes to reduce causality to the exchange of conserved quantities. Dowe's account has the virtue of being simple and offering a definite "visible" idea of causation. According to Dowe and Salmon, it is also virtuous in being localist. That a theory of causation is localist means that it does not need the aid of counterfactuals (...) and/or laws to work. Moreover, it can become the means by which we explain counterfactuals and laws. In this paper, I will argue that the theory is not localist (and hence, that it is less simple than it seems). As far as I can see, the theory needs the aid of laws. (shrink)

Phil Dowe has argued persuasively for a reductivist theory of causality. Drawing on Wesley Salmon's mark transmission theory and David Fair's transferencetheory, Dowe proposes to reduce causality to the exchange of conserved quantities. Dowe's account has the virtue of being simple and offering a definite "visible" idea of causation. According to Dowe and Salmon, it is also virtuous in being localist. That a theory of causation is localist means that it does not need the aid of counterfactuals (...) and/or laws to work. Moreover, it can become the means by which we explain counterfactuals and laws. In this paper, I will argue that the theory is not localist (and hence, that it is less simple than it seems). As far as I can see, the theory needs the aid of laws. (shrink)

It is shown that any hidden variable model that reproduces quantum mechanics for a single particle must either be nonlocal or violate conservation of momentum. This is established by deriving an inequality which must hold in any local, momentum-conserving hidden variable model for a modified form of the double-slit experiment. It is then shown that any hidden variable model that reproduces quantum mechanics must violate the inequality. The inconsistency between the classical and quantum views of the world is therefore demonstrated (...) in a new way. (shrink)

The paper aims to provide precise proof theoretic characterizations of Myhill–Friedman-style “weak” constructive extensional set theories and Aczel–Rathjen analogous constructive set theories both enriched by Mostowski-style collapsing axioms and/or related anti-foundation axioms. The main results include full intuitionistic conservations over the corresponding purely arithmetical formalisms that are well known in the reverse mathematics – which strengthens analogous results obtained by the author in the 80s. The present research was inspired by the more recent Sato-style “weak weak” classical extensional set theories (...) whose proof theoretic strengths are shown to strongly exceed the ones of the intuitionistic counterparts in the presence of the collapsing axioms. (shrink)

Deflationists argue that ‘true’ is merely a logico-linguistic device for expressing blind ascriptions and infinite generalisations. For this reason, some authors have argued that deflationary truth must be conservative, i.e. that a deflationary theory of truth for a theory S must not entail sentences in S’s language that are not already entailed by S. However, it has been forcefully argued that any adequate theory of truth for S must be non-conservative and that, for this reason, (...) truth cannot be deflationary :493–521, 1998; Ketland in Mind 108:69–94, 1999). We consider two defences of conservative deflationism, respectively proposed by Waxman :429–463, 2017) and Tennant :551–582, 2002), and argue that they are both unsuccessful. In Waxman’s hands, deflationists are committed either to a non-purely expressive notion of truth, or to a conception of mathematics that does not allow them to justifiably exclude non-conservative theories of truth. Tennant’s conservative deflationism fares no better: if deflationist truth must be conservative over arithmetic, it can be shown to collapse into a non-conservative variety of deflationism. (shrink)

In classical electrodynamics, it can be challenging to demonstrate the balance between minus of power of radiating particles and retarded radiation energy flux for radiation in the free-space because of the field’s singularity. In an alternative radiation theory of Wheeler–Feynman absorber theory, which is based on a first principle of time-symmetric interaction between radiating particles surrounded by the absorber at large distance, the singularity is eliminated but the balance cannot be preserved due to advanced effects. This is quantitatively (...) demonstrated with an argument of consequent non-classical light radiated by classical current. (shrink)

This paper attempts to get some critical distance on the increasingly fashionable issue of realism in political theory. Realism has an ambiguous status: it is sometimes presented as a radical challenge to the _status quo_; but it also often appears as a conservative force, aimed at clipping the wings of more ‘idealistic’ political theorists. I suggest that what we might call ‘actually existing realism’ is indeed a conservative presence in political philosophy, and that its ambiguous status plays (...) a part in making it so. But I also argue that there is no necessary connection between realism and conservatism. This paper describes the three contingent and suspiciously quick steps which lead from an initial commitment to being attentive to the real world, via a particular kind of pessimism about political possibilities, to an unnecessarily conservative destination. In the process, I try to show how the ubiquitous trinity of realism, pessimism and conservatism might be pulled apart, thus removing the artificial tension between ‘being realistic’ and the demand for far-reaching social change. (shrink)