Many philosophers believe that a deflationist theory of truth must conservatively extend any base theory to which it is added. But when applied to arithmetic, it's argued, the imposition of a conservativeness requirement leads to a serious objection to deflationism: for the Gödel sentence for Peano Arithmetic is not a theorem of PA, but becomes one when PA is extended by adding plausible principles governing truth. This paper argues that no such objection succeeds. The issue turns on how we (...) understand the notion of logical consequence implicit in any conservativeness requirement, and whether we possess a categorical conception of the natural numbers. I offer a disjunctive response: if we possess a categorical conception of arithmetic, then deflationists have principled reason to accept a rich notion of logical consequence according to which the Gödel sentence follows from PA. But if we do not, then the reasons for requiring the derivation of the Gödel sentence lapse, and deflationists are free to accept a conservativeness requirement stated proof-theoretically. Either way, deflationism is in the clear. (shrink)

Truth is often considered to be a logico-linguistic tool for expressing indirect endorsements and infinite conjunctions. In this article, I will point out another logico-linguistic function of truth: to enable and validate what I call a blind argument, namely, an argument that involves indirectly endorsed statements. Admitting this function among the logico-linguistic functions of truth has some interesting consequences. In particular, it yields a new type of so-called conservativeness argument, which poses a new type of threat to deflationism about (...) truth. (shrink)

We formulate a Π1 sentence τ which is a version of the Tableau consistency of GlΔ0. The sentence τ is true and is provable in GlΔ0 + exp. We construct a model M of GlΔ0+Ω1+τ+BGs1 which has no proper end-extension to a model of GlΔ0+Ω1+τ. Also we prove that GlΔ0+Ω1+τ is not Π1 conservative over GlΔ0+τ.

My contribution to the symposium on Goedel’s philosophy of mathematics at the spring 2006 Association for Symbolic Logic meeting in Montreal. Provisional version: references remain to be added. To appear in an ASL volume of proceedings of the Goedel sessions at that meeting.

Parents can benefit their offspring by conserving resources that the offspring stand to inherit. Thus, inheritance of resources should promote the evolution of propensities to conserve. But inheritance also has another, less obvious effect: it can reduce the fertility of the conserver’s grandchildren, thus reducing the expected number of great-grandchildren. Consequently, inheritance of resources promotes the evolution of conservation less than might be supposed.

This introduction to biological conservation assesses the value judgments at the heart of conservation. The author elaborates on such questions as: how much habitat does an endangered species require?; does this particular species deserve to be saved?; who will pay for its upkeep?; and much more.

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)

Conservation biology emerged as an organized academic discipline in the United States in the 1980s though much of its theoretical framework was originally developed in Australia. Significant differences of approach in the two traditions were resolved in the late 1990s through the formulation of a consensus framework for the design and adaptive management of conservation area networks. This entry presents an outline of that framework along with a critical analysis of conceptual issues concerning the four theoretical problems that emerge from (...) it: (i) place prioritization for conservation action; (ii) the selection of surrogates for biodiversity in conservation planning; (iii) the assessment of vulnerability of conservation areas; and (iv) the synchronization of incommensurable criteria including socio-economic constraints on conservation planning. (shrink)

This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, but the (...) other does not.). (shrink)

Religious conservatives in the U.S. have frequently opposed public-health measures designed to combat STDs among minors, such as sex education, condom distribution, and HPV vaccination. Using Rawls’s method of conjecture, I will clear up what I take to be a misunderstanding on the part of religious conservatives: even if we grant their premises regarding the nature and source of sexual norms, the wide-ranging authority of parents to enforce these norms against their minor children, and the potential sexual-disinhibition effects of the (...) above public-health measures, their opposition to at least one of these measures, HPV vaccination, cannot be justified. In fact, their comprehensive doctrines, when properly interpreted, should lead them to back this measure and thereby draw closer to a policy consensus with other citizens regarding teenage sexual health. (shrink)

Scientists in anthropology, geography, and other fields within social sciences and humanities have long suggested that the environments in which people live deeply influence their cultural value systems and practices. Shota Shibasaki, Ryosuke Nakadai, and Yo Nakawake have built on this idea, demonstrating that local ecological characteristics shape the appearance of trickster animals in folklore. Based on their finding and the SM3D (Serendipity-Mindsponge-3D) knowledge management framework, we discuss how the individuals’ or groups’ ability to create cultural products depends on the (...) availability and accessibility of information from the surrounding environment. Due to biodiversity loss and climate change, such valuable resources for cultural creativity have been diminished. Thus, it is crucial to adopt biodiversity preservation and climate action as fundamental values of a progressive and humane culture. Only then can we continue to preserve and enhance the creative cultural capacity of society. (shrink)

A conservation law in physics can be either a constraint on the kinds of interaction there could be or a coincidence of the kinds of interactions there actually are. This is an important, unjustly neglected distinction. Only if a conservation law constrains the possible kinds of interaction can a derivation from it constitute a scientific explanation despite failing to describe the causal/mechanical details behind the result derived. This conception of the relation between “bottom-up” scientific explanations and one kind of “top-down” (...) scientific explanation is motivated by several examples from classical and modern physics. (shrink)

Effective altruism is a growing humanitarian movement with a track record of success in evaluating the effectiveness of charitable spending across a wide range of projects. We suggest ways in which the foundations of this movement can be applied to the complex world of conservation.

Native peoples have often been portrayed as natural conservationists, living a “balanced” existence with nature. It is argued that this perspective is a result of an imprecise operational definition of conservation. Conservation is defined here in contrast to the predictions of foraging theory, which assumes that foragers will behave to maximize their short-term harvesting rate. A behavior is deemed conservation when a short-term cost is paid by the resource harvester in exchange for long-term benefits in the form of sustainable harvests. (...) An example of the usefulness of such an operational definition is presented using data on patch and prey choice decisions of a group of subsistence hunters, the Piro of Amazonian Peru. Results indicate that the area around the Piro village is depleted of prey, and that hunters allocate more time to patches where return rates are highest. This response is consistent with both a conservation strategy and foraging theory. Contrary to the expectation of the conservation strategy, however, hunters do not restrain from pursing opportunistically encountered prey in the depleted areas. The implications for conservation policy are briefly discussed. (shrink)

We develop a conceptual framework that connects biological heredity and organization. We refer to heredity as the cross-generation conservation of functional elements, defined as constraints subject to organizational closure. While hereditary objects are functional constituents of biological systems, any other entity that is stable across generations—and possibly involved in the recurrence of phenotypes—belongs to their environment. The central outcome of the organizational perspective consists in extending the scope of heredity beyond the genetic domain without merging it with the broad category (...) of cross-generation stability. After discussing some implications, we conclude with a reflection on the relationship between stability and variation. 1Introduction2From Extended Heredity to Cross-generation Stability 2.1Extending the scope of heredity: A brief state of the art2.2Rethinking heredity: Conceptual challenges3Biological Heredity in Light of Organization 3.1Biological organization within organisms and beyond3.2Extending organization in time3.3What is biological heredity?4Implications and Objections 4.1Heredity as a specific kind of cross-generation stability4.2Heredity at various levels of description4.3Non-functional and dysfunctional objects5Conclusions: From Conservation to Variation. (shrink)

A conservation principles tell us that some quantity, quality, or aspect remains constant through change. Such principles appear already in ancient and medieval natural philosophy. In one important strand of Greek cosmology, the rotatory motion of the celestial orbs is eternal and immutable. In optics, from at least the time of Euclid, the angle of reflection is equal to the angle of incidence when a ray of light is reflected. According to some versions of the medieval impetus theory of motion, (...) impetus remains in a projected body (and the associated motion persists) permanently unless the body is subject to outside interference. These examples could be multiplied. But it was in the seventeenth century that conservation principles began to play an absolutely central role in scientific theories. Each of Galileo Galilei, René Descartes, Christiaan Huygens, Gottfried Leibniz, and Isaac Newton founded his approach to physics upon the principle of inertia—that unless interfered with a body will undergo uniform rectilinear motion. A multitude of other conservation principles gained currency during the seventeenth century—some still with us, some long ago left behind. Descartes provides an interesting example of an author who attempted to derive all of his physical principles from conservation laws (Principles of Philosophy, see especially articles 36 to 42 of Part II). Descartes believed that the principles of his physics could be derived from the immutability of God, supplemented only by very weak assumptions about the existence of change in the world. He claims, in fact, that we ought to postulate the strongest conservation laws consistent with such change. These include. (shrink)

Conservation scholarship and policies are concerned with the viability of idealized ecological communities constructed using human metrics. We argue that the discipline of conservation assumes an epistemology and ethics of human sovereignty/dominion over animals that leads to violent actions against animals. We substantiate our argument by deconstructing a case study. In the context of recent bushfires in Australia, we examine recent legislation passed by the parliament of New South Wales, policy documents, and academic articles by conservationists that support breaking communities (...) of horses and/or killing 4,000 horses in Kosciuszko National Park, NSW. Theoretically framing our deconstruction against human sovereignty over animals and anthropocentrism, we affirm an intersectional, ecofeminist approach that values animals as relational and vulnerable agents. We uncover first the epistemic violence of categorizing horses as “pests,” and the anthropocentric nature of recently passed legislation in NSW. We analyze next the deficient ethics of NSW's government, and the argument that killing animals is justifiable when they suffer from starvation and dehydration. We close with a realistic proposal that does not involve breaking horses’ communities and/or killing horses, and a plea to the government of NSW and conservationists not to harm any horses in KNP. (shrink)

Misconceptions about energy conservation abound due to the gap between physics and secondary school chemistry. This paper surveys this difference and its relevance to the 1690s–2010s Leibnizian argument that mind-body interaction is impossible due to conservation laws. Justifications for energy conservation are partly empirical, such as Joule’s paddle wheel experiment, and partly theoretical, such as Lagrange’s statement in 1811 that energy is conserved if the potential energy does not depend on time. In 1918 Noether generalized results like Lagrange’s and proved (...) a converse: symmetries imply conservation laws and vice versa. Conservation holds if and only if nature is uniform. The rise of field physics during the 1860s–1920s implied that energy is located in particular places and conservation is primordially local: energy cannot disappear in Cambridge and reappear in Lincoln instantaneously or later; neither can it simply disappear in Cambridge or simply appear in Lincoln. A global conservation law can be inferred in some circumstances. Einstein’s General Relativity, which stimulated Noether’s work, is another source of difficulty for conservation laws. As is too rarely realized, the theory admits conserved quantities due to symmetries of the Lagrangian, like other theories. Indeed General Relativity has more symmetries and hence more conserved energies. An argument akin to Leibniz’s finally gets some force. While the mathematics is too advanced for secondary school, the ideas that conservation is tied to uniformities of nature and that energy is in particular places, are accessible. Improved science teaching would serve the truth and enhance the social credibility of science. (shrink)

Tracing the historical roots of modern conservation thought & practice, this book explores current perspectives from evolutionary & community ecology, conservation biology, anthropology, political ecology, economics, and policy.

In this paper, I argue that an utterance can function to conserve or maintain the truth of its asserted content, what I call conservative speech. Conservative utterances can work to preserve the truth of their asserted content in two ways. In the first, directive conservatives, the utterance serves as an indirect directive for interlocutors to act in ways that serve to maintain the asserted content. In the second, constitutive conservatives, serve to partly constitute the truth conditions of the asserted content (...) directly. Constitutive conservatives, I argue, are particularly important because they are a central tool for how social groups enforce and thereby maintain facts about group norms and values in the face of deviation. They thus have a central role to play in understanding the role of language in the abilities of social groups to create and maintain their norms and values. (shrink)

: "Conservative" bioethics is informed by a rich view of human personhood, a decent respect for the well-considered views of people across the political spectrum, and a philosophy of the state carefully calibrated to ensure that imperfect people can live together in community. The deepest disagreements between conservatives and liberals are rooted in different ways of understanding the moral ideal of equality.

Since Leibniz's time, Cartesian mental causation has been criticized for violating the conservation of energy and momentum. Many dualist responses clearly fail. But conservation laws have important neglected features generally undermining the objection. Conservation is _local_, holding first not for the universe, but for everywhere separately. The energy in any volume changes only due to what flows through the boundaries. Constant total energy holds if the global summing-up of local conservation laws converges; it probably doesn't in reality. Energy conservation holds (...) if there is symmetry, the sameness of the laws over time. Thus, if there are time-places where symmetries fail due to nonphysical influence, conservation laws fail there and then, while holding elsewhere, such as refrigerators and stars. Noether's converse first theorem shows that conservation laws imply symmetries. Thus conservation trivially nearly entails the causal closure of the physical. But expecting conservation to hold in the brain simply assumes the falsehood of Cartesianism. Hence Leibniz's objection begs the question. Empirical neuroscience is another matter. So is Einstein's General Relativity: far from providing a loophole, General Relativity makes mental causation _harder_. (shrink)

In recent decades conservation biology has achieved a high position among the sciences. This is certainly true of South Africa, a small country, but the third most biodiverse in the world. This article traces some aspects of the transformation of South African wildlife management during the 1930s to the 1960s from game reserves based on custodianship and the "balance of nature" into scientifically managed national parks with a philosophy of "command and control" or "management by intervention." In 1910 the four (...) British colonies had formed the Union of South Africa, and by the 1920s there was wide acceptance of national parks, a development influenced by their success in the United States. It was not, however, until after the Second World War, that management of the expanding conservation estate altered from a rather unsystematic laissez faire variety, into more scientifically informed management practices with an efficient bureaucracy in charge. This was achieved by modifications in organizational structures and institutional cultures initiated by a change of government in 1948 which, this article argues, impacted in turn on wildlife management and shaped and professionalized many aspects of that field science. "Management by intervention" was the hallmark of South African wildlife and conservation biology from the 1960s until recently, when there have been shifts towards "adaptive resource management" in a period of further change in the country's politics. (shrink)

In this article, I present a semantically natural conservative extension of Urquhart’s positive semilattice logic with a sort of constructive negation. A subscripted sequent calculus is given for this logic and proofs of its soundness and completeness are sketched. It is shown that the logic lacks the finite model property. I discuss certain questions Urquhart has raised concerning the decision problem for the positive semilattice logic in the context of this logic and pose some problems for further research.

The Exclusion Argument for physicalism maintains that since (1) every physical effect has a sufficient physical cause, and (2) cases of causal overdetermination are rare, it follows that if (3) mental events cause physical events as frequently as they seem to, then (4) mental events must be physical in nature. In defence of (1), it is sometimes said that (1) is supported if not entailed by conservation laws. Against this, I argue that conservation laws do not lend sufficient support to (...) (1) to render its denial ‘unscientific’, and that those who accept (3) and deny (4) may consequently respond to the Exclusion Argument by denying (1) without thereby setting themselves at odds with current science. I also argue that conservation laws are compatible with (3) and the negation of (4), and that one can therefore accept conservation laws and (3) while denying both (1) and (4). (shrink)

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.

We discuss two desirable properties of deflationary truth theories: conservativeness and maximality. Joining them together, we obtain a notion of a maximal conservative truth theory - a theory which is conservative over its base, but can't be enlarged any further without losing its conservative character. There are indeed such theories; we show however that none of them is axiomatizable, and moreover, that there will be in fact continuum many theories of this sort. It turns out in effect that the (...) deflationist still needs some additional principles, which would permit him to construct his preferred theory of truth. (shrink)

As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the energy-momentum tensor associated with non-interacting matter is covariantly divergence-free, in connection with such theorems. I argue that the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories. I conclude (...) by discussing what it means to posit a certain spacetime geometry and the relationship between that geometry and the dynamical properties of matter. (shrink)

Philosophers have paid little attention to the distinction between conservation and preservation, apparently because they have accepted John Passmore’s suggestion that conservationism is an expression of anthropocentric motives and that “true” preservationism is an expression of nonanthropocentric motives. Philosophers have therefore concentrated their efforts on this distinction in motives. This reduction,however, is insensitive to important nuances of environmentalist objectives: there are a wide variety of human reasons for preserving natural ecosystems and wild species. Preservationist policies represent a concem to protect (...) biological diversity from the simplifying effects of human management and are motivated by the full range of values (consumptive, aesthetic, scientific, and moral) attached to a diverse biota.Conservationists and preservationists differ mainly in their emphasis on resilience measures versus predictability measures of stability, respectively. The distinction between anthropocentric and nonanthropocentric motives loses importance as emphasis is placed on the longest term values humans place on the proteetion of biological diversity. (shrink)

On estime souvent que les Grecs avaient des phénomènes économiques une approche triviale et non scientifique. Ce point de vue est en partie motivé par ce que l’économiste et historien de la pensée économique J.A. Schumpeter et l’historien de la Grèce antique M.I. Finley considèrent être l’excessive préoccupation des penseurs grecs pour les « vaines » considérations domestiques de nature matérielle, au détriment de l’analyse scientifique des phénomènes économiques. Contre une telle interprétation, l’hypothèse présentée ici est que cette préoccupation répond (...) au souci de la conservation des biens qui, avec leur acquisition et leur bon usage, est l’une des trois activités principales de l’art économique ou oikonomique. L’examen détaillé des deux opérations de conservation que sont le rangement et la gestion, en lien avec les divers aspects du Bien économique qui leur sont associés, permet de le montrer. (shrink)

Conservativeness has been proposed as an important requirement for deflationary truth theories. This in turn gave rise to the so-called ‘conservativeness argument’ against deflationism: a theory of truth which is conservative over its base theory S cannot be adequate, because it cannot prove that all theorems of S are true. In this paper we show that the problems confronting the deflationist are in fact more basic: even the observation that logic is true is beyond his reach. This seems (...) to conflict with the deflationary characterization of the role of the truth predicate in proving generalizations. However, in the final section we propose a way out for the deflationist — a solution that permits him to accept a strong theory, having important truth-theoretical generalizations as its theorems. (shrink)

Conservatives commonly claim that systems of formal education are biased against conservative ideology. I argue that this claim is incorrect, but not because there is no bias against conservatives in formal education. A wide swath of psychological evidence linking personality and ideology indicates that conservatives and liberals differ in their learning orientations, that is, in the values, motivations, and beliefs they bring to learning tasks. These differences in operative epistemologies explain many demographic phenomena relating educational achievement and political ideology. Systems (...) of formal education thus disadvantage conservatives, especially in the later stages of formal education. Conservatives are therefore ‘selected against’ in the process of formal education, not due to their values or ideology but because their learning orientations are not especially conducive to academic success beyond a certain point. However, because the bias against conservatives in not ideological in origin, a case cannot be made that conservatives are victims of institutional injustice. This bias against conservatives in formal education could be mitigated were the purposes of formal education radically modified (the education of the military class in Plato’s Republic serves as a model). But such a model of formal education would ill serve the needs of modern, industrialized, information-driven societies. (shrink)

Are laws of nature necessary, and if so, are all laws of nature necessary in the same way? This question has played an important role in recent discussion of laws of nature. I argue that not all laws of nature are necessary in the same way: conservation laws are perhaps to be regarded as metaphysically necessary. This sheds light on both the modal character of conservation laws and the relationship between different varieties of necessity.

One of the main problems plaguing neo-logicism is the Bad Company challenge: the need for a well-motivated account of which abstraction principles provide legitimate definitions of mathematical concepts. In this article a solution to the Bad Company challenge is provided, based on the idea that definitions ought to be conservative. Although the standard formulation of conservativeness is not sufficient for acceptability, since there are conservative but pairwise incompatible abstraction principles, a stronger conservativeness condition is sufficient: that the class (...) of acceptable abstraction principles be strictly logically symmetrically class conservative . The article concludes with an examination of which classes of abstraction principles meet this criteria. (shrink)

_Conservative Reductionism_ sets out a new theory of the relationship between physics and the special sciences within the framework of functionalism. It argues that it is wrong-headed to conceive an opposition between functional and physical properties and to build an anti-reductionist argument on multiple realization. By contrast, all properties that there are in the world, including the physical ones, are functional properties in the sense of being causal properties, and all true descriptions that the special sciences propose can in principle (...) be reduced to physical descriptions by means of functional reduction, despite multiple realization. The book develops arguments for from the metaphysics of properties and the philosophy of physics. These arguments lead to a conservative ontological reductionism. It then develops functional reduction into a fully-fledged, conservative theory reduction by means of introducing functional sub-types that are coextensive with physical types, illustrating that conservative reductionism by means of case studies from biology. (shrink)

It is widely believed that there must be a conflict between food production and conservation, and that development must be related to economics. Both these beliefs are questioned. It is suggested that ecological agriculture, which includes ethologically and ecologically sound animal management can reduce conflicts between conservation and food production. African elephants are taken as an example illustrating different attitudes to conservation. It is proposed that, rather than developing further the present common conservation attitude of ' wildlife apartheid', the future (...) of elephants in many parts of Africa may rest on bringing them closer to the voters where the welfare of neither the human nor elephant is compromised. Here, they can act as both as workers, and as ' wildlife ambassadors'. This approach needs further research and development, but preliminary results show significant possibilities for reducing these apparently conflicting land use interests in some geographical areas. (shrink)

The genomes of vertebrates, flies, and nematodes contain highly conserved noncoding elements (CNEs). CNEs cluster around genes that regulate development, and where tested, they can act as transcriptional enhancers. Within an animal group CNEs are the most conserved sequences but between groups they are normally diverged beyond recognition. Alternative CNEs are, however, associated with an overlapping set of genes that control development in all animals. Here, we discuss the evidence that CNEs are part of the core gene regulatory networks (GRNs) (...) that specify alternative animal body plans. The major animal groups arose >550 million years ago. We propose that the cis‐regulatory inputs identified by CNEs arose during the “re‐wiring” of regulatory interactions that occurred during early animal evolution. Consequently, different animal groups, with different core GRNs, contain alternative sets of CNEs. Due to the subsequent stability of animal body plans, these core regulatory sequences have been evolving in parallel under strong purifying selection in different animal groups. (shrink)

According to inferential role semantics, for any given expression to possess a particular meaning one must be disposed to make or, alternatively, acknowledge as correct certain inferential transitions involving it. As Williamson points out, pejoratives such as ‘Boche’ seem to provide a counter-example to IRS. Many speakers are neither disposed to use such expressions nor consider it proper to do so. But it does not follow, as IRS appears to entail, that such speakers do not understand pejoratives or that they (...) lack meaning. In this paper, I examine recent responses to this problem by Boghossian and Brandom and argue that their proposed construal of the kind of inferential rules governing a pejorative such as ‘Boche’ is to be ruled out on the grounds that it is non-conservative. I defend the appeal to conservatism in this instance against criticism and, in doing so, propose an alternative approach to pejoratives on behalf of IRS that resolves the problem Williamson poses. (shrink)

The conservative, mainly Anglo-Saxon, critique of “social engineering” in Enlightenment thinking, which goes back to Edmund Burke and David Hume, among others, has recently resurfaced in the works of Michael Oakeshott, Roger Scruton, and Friedrich Hayek. This article focuses on their conservative critiques and more specifically on two common issues: the unintended negative consequences of political planning, and the institutions in civil society that act as a positive counterpart to this form of engineering.

The practice of conservation assumes that current persons have some obligations to future generations, but these obligations are complicated by a number of philosophical problems, chief among which is what Derek Parfit calls the Non-Identity Problem. Because our actions now will affect the identities of persons to be born in the distant future, we cannot say that those actions either benefit or harm those persons. Thus, a causal link between our acts and their consequences for particular persons is severed, and (...) the justification for conservation duties toward future generations undermined. I argue for an alternative justification for conservation in the capacity of foresight, which requires us to act not only upon duties that we have now, but also upon those that we will predictably have in the future. In this way, the future generations problem, at least as applied to conservation issues, is overcome. (shrink)

We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf {PA}$ and intuitionistic arithmetic $\mathsf {HA}$. Using a generalized negative translation, we first provide a structured proof of the fact that $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over $\mathsf {HA} + {\Sigma _k}\text {-}\mathrm {LEM}$ where ${\Sigma _k}\text {-}\mathrm {LEM}$ is the axiom scheme of the law-of-excluded-middle restricted to formulas in $\Sigma _k$. In addition, we show that this conservation theorem is optimal in the (...) sense that for any semi-classical arithmetic T, if $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over T, then ${T}$ proves ${\Sigma _k}\text {-}\mathrm {LEM}$. In the same manner, we also characterize conservation theorems for other well-studied classes of formulas by fragments of classical axioms or rules. This reveals the entire structure of conservation theorems with respect to the arithmetical hierarchy of classical principles. (shrink)