This paper introduces the logic _Q__L__E__T_ _F_, a quantified extension of the logic of evidence and truth _L__E__T_ _F_, together with a corresponding sound and complete first-order non-deterministic valuation semantics. _L__E__T_ _F_ is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (_FDE_) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘_A_ entails that _A_ behaves classically, ∙_A_ follows from _A_’s violating some classically valid inferences. The semantics of _Q__L__E__T_ (...) _F_ combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin’s method. By providing sound and complete semantics for first-order extensions of _FDE_, _K3_, and _LP_, we show how these tools, which we call here the method of _anti-extensions + valuations_, can be naturally applied to a number of non-classical logics. (shrink)

This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

We give a valuation theoretic characterization for a real closed field to be recursively saturated. This builds on work in [9], where the authors gave such a characterization forκ-saturation, for a cardinal$\kappa \ge \aleph _0 $. Our result extends the characterization of Harnik and Ressayre [7] for a divisible ordered abelian group to be recursively saturated.

A central question for psychologists, economists, and philosophers is how human lives should be valued. Whereas egalitarian considerations give rise to models emphasizing that every life should be valued equally, empirical research has demonstrated that valuations of lives depend on a variety of factors that often do not conform to specific normative expectations. Such factors include emotional reactions to the victims and cognitive considerations leading to biased perceptions of lives at risk (e.g., attention, mental imagery, pseudo-inefficacy, and scope neglect). (...) They can lead to a valuation function with decreasing marginal value and sometimes even decreasing absolute value as the number of victims increases. As a result, people spend more money to save an individual while at the same time being insensitive and apathetic to large losses of life, despite endorsing egalitarian norms. In this conceptual paper, we propose a descriptive model highlighting the role of different motivations and the conditions under which cognitions and emotions result in deviations from egalitarian normative valuations of human lives. (shrink)

Is there anything irrational, or self-undermining, about having "inconsistent" attitudes of caring or valuing? In this paper, I argue that, contra suggestions of Harry Frankfurt and Charles Taylor, the answer is "No." Here I focus on "valuations," which are endorsed desires or attitudes. The proper characterization of what I call "valuational inconsistency" I claim, involves not logical form (valuing A and not-A), but rather the co-possibility of what is valued; valuations are inconsistent when there is no possible world (...) in which what is valued can co-exist. Essentially conflicting valuations, I show, are no worse for an agent than contingently conflicting ones, which are common and no threat to rationality or well-being. Partly based on reflections about a conflicted mother, who values staying at home and also having a career, I argue that valuational inconsistency does not render a person unable to act, does not make a person's actions ineffective because of vacillation, does not undermine a person's autonomy, and need not make a person dissatisfied with himself. I defend my characterization of inconsistency as an apt one; I offer some reasons to value inconsistency itself; and I draw out some implications for coherence thinking in moral philosophy. (shrink)

Valuation consists in a positive or negative response by a subject S to an entity X. Any positive or negative response has a structure that involves a cognitive and a non-cognitive component, as well as a reason relationship between these. This structure is shown to be present in the explicit value judgement 'Hans is a kraut', and then also pointed out in the reflex-like feeding behaviour of a frog, where S treats X as providing an affordance. The conclusion is that (...) valuation need not involve mental states. The article ends with a discussion of the elusive question: what makes a response positive or negative? (shrink)

Valuation is portrayed here as a dynamic and interactive process, not a static notion linked to willingness to pay. Valuation through economic measures can be built upon by creating trusting and legitimising procedures of stakeholder negotiation and mediation. This is a familiar practice in the US, but it is only beginning to be recognised as an environmental management tool in the UK. The introduction of strategic environmental and landuse appraisal plans for shorelines, estuaries, river catchments and rural landscapes, combined with (...) the mobilisation of protest around landuse proposals that are not seemingly justified on the basis of 'need' suggest that a more legitimate participatory form of democracy is required to reveal valuation through consensual negotiation. (shrink)

In this paper, we present valuation semantics for the Propositional Intuitionistic Calculus (also called Heyting Calculus) and three important subcalculi: the Implicative, the Positive and the Minimal Calculus (also known as Kolmogoroff or Johansson Calculus). Algorithms based in our definitions yields decision methods for these calculi. DOI:10.5007/1808-1711.2010v14n1p125.

This paper investigates how people conceive and evaluate nature through language, in a climate change context. With material consisting of 1,200 answers to open-ended questions in nationally representative surveys in Norway, we explore what semantic roles and values the respondents attribute to nature as well as to how they interact with the public debate about climate change. We observe that different conceptions and valuations of nature are tied to different perspectives on the climate change issue: some address the responsibilities (...) of causing climate change, others its consequences, and others yet its potential solutions. The study provides knowledge about the variety of conceptions of nature that can be mobilised by individuals and suggests that policy measures and public communication could benefit by taking this diversity into account. (shrink)

Economics takes an individualistic approach to human behaviour. This is reflected in the use of 'contingent valuation' surveys to conduct cost benefit analysis for economic policy evaluation. An individual's valuation of a policy is assumed to be unaffected by the burdens it places on others. We report a survey experiment to test this supposition in the context of climate change policy. Willingness to pay for climate change mitigation was higher when richer individuals were to bear higher costs than when, as (...) is usual, no explicit information was provided about cost distribution. This result is inconsistent with the usual interpretation of contingent valuation data. It also suggests that the data may be biased indicators of policy acceptance. Additional survey questions suggest that a collective mode of reasoning is common. (shrink)

Values, Valuations, and Axiological Norms in Richard Rorty's Neopragmatism sympathetically discusses Richard Rorty's neopragmatist philosophy. This book brings together a range of interpretations and possibilities on a variety of humanistic topics, including philosophy, literature, culture, film, economics, social issues, politics, and more. Skowroński involves the work of philosophers such as Kant, Dewey, Santayana, and Kołakowski as he delves into various philosophical problems using the lens of Rorty’s neopragmatist thought.

We study the algebraic implications of the non-independence property and variants thereof on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a henselian valuation. Our results mainly focus on Hahn fields and build up on Will Johnson’s “The canonical topology on dp-minimal fields” :1850007, 2018).

We define and study abstract valuation semantics for logics, an algebraically well-behaved version of valuation semantics. Then, in the context of the behavioral approach to the algebraization of logics, we show, by means of meaningful bridge theorems and application examples, that abstract valuations are suited to play a role similar to the one played by logical matrices in the traditional approach to algebraization.

Valuations are ubiquitous. We may be for or against genetically modified food; we find some politicians irresponsible; we prefer Beethoven to rock ‘n’ roll or vice versa; some enjoy bird-watching while others find it boring; and we may think that we have to tighten up on green-house gas emissions. Valuing is pervasive and often we are not even aware that we are valuing. However, many of our valuations are ill grounded and rationally defective. They are frequently based on (...) misinformation, sloppy thinking, prejudice, and are biased in many ways as psychological research shows. For this reason there is widespread agreement among phi-losophers that we need an account of substantive valuational rationality, both for the theory of practical reasoning and for ethics as well. My main object in this paper is to outline such an account and to present a principle that allows a non-technical rational criticism of valuations. (shrink)

In this paper, the author revisits “the emotive theory of value” and argues that values are not entities but nothing other than “linguistic fictions”. Accordingly, valuations—i.e., valuing actions—can be defined as approving or disapproving attitudes of a subject to some object. In this perspective, values cannot be true or false: What we can do is just compare them with regard to strength. As a consequence, value judgments are to be understood as sentences which are used either to say that (...) a subject s values an object o positively or negatively, or to express (evince) a valuation. The author then shows some relations between normative and evaluative discourses. First, he claims that norms as well as valuations are not true or false. Second, he argues that both may be explained or justified, even if the former are usually justified teleologically whereas the latter are explained referring back to the subject's background and life‐style. Third, he notes that a legal order originates from the fact that valuations “crystallize” into norms. Finally, the author examines some further questions related to his analysis. In particular, he argues that the different realms of values, e.g., morals, aesthetics, politics, etc., do not correspond to different evaluative attitudes, but to different phenomena and diverse spheres of human life. (shrink)

The origins of both economic and philosophical value theory are examined and shown to be closely related. The status of neo-classical value theory is that it is internally flawed in any attempt to describe the real world. Cost-benefit analysis as it applies to the valuation of environmental agents relies upon the claim that this neo-classical theory has a particular status in optimal welfare maximisation and, therefore, suffers the same problems of internal consistency. Economic valuation of the environment is not a (...) scientific process derived from external law but a social process relying upon social agreement. Alternatives to economic valuation are considered and may possess a more plausible social base. However, all environmental valuation is at odds with beliefs based upon the existence of objective and intrinsic values. (shrink)

If a certain semantic relation (which we call 'local consequence') is allowed to guide expectations about which rules are derivable from other rules, these expectations will not always be fulfilled, as we illustrate. An alternative semantic criterion (based on a relation we call 'global consequence'), suggested by work of J.W. Garson, turns out to provide a much better - indeed a perfectly accurate - guide to derivability.

I explore three points about the relationship between C.I. Lewis’s conceptual pragmatism and W.V. Quine’s naturalized epistemology inspired by Robert Sinclair’s Quine, Conceptual Pragmatism, and the Analytic-Synthetic Distinction. First, I highlight Lewis’s long-standing commitment to Platonism about meaning and its connection to his reflective philosophical method and rejection of a linguistic account of analyticity. Second, I consider Sinclair’s claim that “Lewis’s epistemology provides no indication concerning how, despite different sensory experiences, we still come to agree on what we are talking (...) about and what counts as evidence” (2022, 113). I find more hints, especially in Lewis’s account of how we verify that two people share meaning in common. However, some of the pragmatic and broadly empirical factors Lewis appeals to are not part of Quine’s naturalized epistemology. Finally, I relate these points to Quine’s (1953/1980) claim to advance a more “thorough pragmatism” than Lewis. Quine does not say much about action, value, and ethics, but these are central parts of Lewis’s conceptual pragmatism and a source of his reluctance to abandon those parts of his epistemology that Sinclair argues Quine found dispensable. (shrink)

This paper reports a Contingent Valuation application to estimate the non-market costs and benefits of hydro scheme developments in an Icelandic wilderness area. A deliberative group -based approach, called Market Stall, is compared to a control group consisting of conventional in-person interviews, in order to investigate flaws of Contingent Valuation, such as poor validity and protest responses. Perceived property rights suggested the use of willingness-to-accept in compensation for wilderness loss and willingness-to-pay for hydro scheme benefits. The study is novel as (...) it applies participant behaviour observation to gain insights into the shortcomings of conventional data collection modes. Main drawbacks with in-person interviews were found to be low motivation, standardised information and time pressure which hindered individuals from carefully considering their preferences. Market Stall performed better in the study: welfare estimates were more easily explained by socio-economic variables, the non-response rate was lower, and respondents were more engaged. Our research findings also suggest that participant behaviour can be used to supplement conventional validity tests. (shrink)

This paper reports a Contingent Valuation application to estimate the non-market costs and benefits of hydro scheme developments in an Icelandic wilderness area. A deliberative group-based approach, called Market Stall, is compared to a control group consisting of conventional in-person interviews, in order to investigate flaws of Contingent Valuation, such as poor validity and protest responses. Perceived property rights suggested the use of willingness-to-accept in compensation for wilderness loss and willingness-to-pay for hydro scheme benefits. The study is novel as it (...) applies participant behaviour observation to gain insights into the shortcomings of conventional data collection modes. Main drawbacks with in-person interviews were found to be low motivation, standardised information and time pressure which hindered individuals from carefully considering their preferences. Market Stall performed better in the study: welfare estimates were more easily explained by socio-economic variables, the non-response rate was lower, and respondents were more engaged. Our research findings also suggest that participant behaviour can be used to supplement conventional validity tests. (shrink)

In the philosophy of perception, olfaction is the perennial problem child, presenting a range of difficulties to those seeking to define its proper referents, and its phenomenological content. Here, we argue that many of these difficulties can be resolved by recognizing the object-like representation of odors in the brain, and by postulating that the basic objects of olfaction are best defined by their biological value to the organism, rather than physico-chemical dimensions of stimuli. Building on this organism-centered account, we speculate (...) that the phenomenological space of olfaction is organized into a number of coarse affective dimensions that apply categorically. This organization may be especially useful for coupling sensation to decision-making and instrumental action in a sensory modality where the stimulus space is especially complex and high-dimensional. (shrink)

This paper introduces valuation structures associated with preferential models. Based on KLM valuation structures, we present a canonical approach to obtain injective preferential models for any preferential relation satisfying the property INJ, and give uniform proofs of representation theorems for injective preferential relations appeared in the literature. In particular, we show that, in any propositional language (finite or infinite), a preferential inference relation satisfies INJ if and only if it can be represented by a standard preferential model. This conclusion generalizes (...) the result obtained by Freund. In addition, we prove that, when the language is finite, our framework is sufficient to establish a representation theorem for any injective relation. (shrink)

The final portion of the thesis surveys proposals for the introduction of hidden variables into quantum mechanics, proofs of the impossibility of such hidden-variable proposals, and criticisms of these impossibility proofs. And arguments in favour of the partial-Boolean algebra, rather than the orthomodular lattice, formalization of the quantum propositional structures are reviewed. ;As for , each quantum state-induced expectation-function on a P truth-functionally assigns 1 and 0 values to the elements in a ultrafilter and dual ultraideal of P, where in (...) general the union of an ultrafilter and its dual ultraideal is smaller than the entire structure. Thus it is argued that each expectation-function is the quantum analog of a classical semantic mapping, even though the domain where each expectation-function is bivalent and truth-functional is usually a non-Boolean substructure of P. ;In classical propositional logic, propositions form a Boolean algebra, and each semantic mapping assigns the value 1 to the members of a certain subset of the algebra, namely, an ultrafilter, and assigns 0 to the members of the dual ultraideal, where the union of these two subsets is the entire algebra. The propositional structures of classical mechanics are likewise Boolean algebras, so one can straightforwardly provide a classical semantics, which also satisfies . However, quantum propositional structures are non-Boolean, so it is an open question whether a semantics satisfying , and can be provided. ;Von Neumann first proposed that the algebraic structures of the subspaces of Hilbert space be regarded as the propositional structures P of quantum mechanics. These structures have been formalized in two ways: as orthomodular lattices which have the binary operations "and", "or", defined among all elements, compatible and incompatible ; and as partial-Boolean algebras which have the binary operations defined among only compatible elements. In the thesis, two basic senses in which these structures are non-Boolean are discriminated. And two notions of truth-functionality are distinguished: truth-functionality ,) applicable to the Plattices; and truth-functionality ) applicable to both the Plattices and partial-Boolean algebras. Then it is shown how the lattice definitions of "and", "or", among incompatibles rule out a bivalent, truth-functional ,) semantics for any PQM lattice containing incompatible elements. In contrast, the Gleason and Kochen-Specker proofs of the impossibility of hidden-variables for quantum mechanics show the impossibility of a bivalent, truth-functional ) semantics for three-or-higher dimensional Hilbert space PQM structures; and the presence of incompatible elements is necessary but is not sufficient to rule out such a semantics. ;The thesis investigates the possibility of a classical semantics for quantum propositional structures. A classical semantics is defined as a set of mappings each of which is bivalent, i.e., the value 1 or 0 is assigned to each proposition, and truth-functional, i.e., the logical operations are preserved. In addition, this set must be "full", i.e., any pair of distinct propositions is assigned different values by some mapping in the set. When the propositions make assertions about the properties of classical or of quantum systems, the mappings should also be "state-induced", i.e., values assigned by the semantics should accord with values assigned by classical or by quantum mechanics. (shrink)

This article shows that forms of analysis and calculation specific to finance are spreading, and changing valuation processes in various social settings. This perspective is used to contribute to the study of the recent transformations of capitalism, as financialisation is usually seen as marking the past three decades. After defining what is meant by “financialised valuation,” different examples are discussed. Recent developments concerning the valuation of assets in accounting standards and credit risk in banking regulations are used to suggest that (...) colonisation of financial activities by financialised valuations is taking place. Other changes, concerning the valuation of social or cultural activities and environmental issues are also highlighted in order to support the hypothesis of a parallel colonisation of non-financial activities by financialised valuations. Specifically, the language of finance appears to gradually being incorporated into public policies, especially in Europe—and this trend seems to have gathered pace since the 2000s. Some interpretations are proposed to understand why public policies are seemingly increasingly reliant on financialised valuations. (shrink)

For paediatric medicine to advance, research must be conducted specifically with children. Concern about poor recruitment has led to debate about payments to child research participants. Although concerns about undue influence by such ‘compensation’ have been expressed, it is useful to determine whether children can relate the time and inconvenience associated with participation to the value of payment offered. This study explores children's ability to determine fair remuneration for research participation, and reviews payments to children participating in research. Forty children (...) were interviewed before outpatient visits at two London Hospitals: Great Ormond Street Children's Hospital and the Whittington Hospital District General Hospital. Children were asked to value their involvement in two hypothetical research scenarios – the first an ‘additional blood sample’, the second also involving daily oral oil capsules taken for a fortnight before further venesection. Background knowledge about familiarity with money, and experience with hospitalisation was assessed. The mean valuation of involvement in the second scenario (£13.18) was higher than in the first (£2.84) (p<0.001). This higher valuation persisted when children were categorised into groups ‘aged 12+’ and ‘below 12’. Those undergoing a blood test on the day placed a higher valuation on participation in the second scenario (£10.43, £21.67, p=0.044). These children aged 8–16 demonstrated the capacity to discern a fair valuation for participation in medical research. The monetary sums are influenced by the time and inconvenience involved in the research, and by the extent of recent experience with hospital procedures. The authors review current ethical thinking regarding payments to child research participants and suggest that a fair wage model might be an ethically acceptable way to increase participation of children in research. (shrink)

Market-like devices that enact quantification and monetization processes (QM) underpin a growing number of valuation practices, but the widespread take-up of QM has given rise to the ‘cooptation charge’: for all the good intentions and results produced by those who deploy QM, they are complicit in reinforcing problematic neoliberal tendencies. A political discourse-theoretical perspective, combined with a pragmatist scholarship that has made significant advances in our understanding of QM, suggests that the cooptation charge relies on an overly simplified picture of (...) both QM and neoliberalism. However, while we acknowledge this as an important advance, we argue that the normative, political, and ideological significance of QM remains surprisingly underspecified. We still lack a convincing theoretical framework that provides a more rounded multi-dimensional critical perspective within which to navigate the evaluative dilemmas produced by these increasingly widespread techniques, including cooptation worries. Drawing on the logics approach of the Essex school of political discourse theory, we develop a framework that brings together the strategic, normative, and ideological dimensions that otherwise tend to be treated separately in the literature, allowing a fuller assessment of such technologies. (shrink)

Surprisal and Valuation in the Predictive Brain.

One of the initial obstacles to the study of the theory of value is the fact that practically every author whom the student consults on the subject characterizes value and valuation differently, and seems to trace them ultimately to a different source. For example, one writer will formulate a theory of value in terms of pain and pleasure ; another, in terms of feeling ; another, in terms of desires or wants ; still others, in terms of “requiredness”, of interest, (...) of striving ; and so on. (shrink)

This paper uses the notion of Galois-connection to examine the relation between valuation-spaces and logics. Every valuation-space gives rise to a logic, and every logic gives rise to a valuation space, where the resulting pair of functions form a Galois-connection, and the composite functions are closure-operators. A valuation-space (resp., logic) is said to be complete precisely if it is Galois-closed. Two theorems are proven. A logic is complete if and only if it is reflexive and transitive. A valuation-space is complete (...) if and only if it is closed under formation of super-valuations. (shrink)

Society Semantics, introduced by W. Carnielli and M. Lima-Marques, is a method for obtaining new logics from the combination of agents of a given logic. The goal of this paper is to present several generalizations of this method, as well as to show some applications to many-valued logics. After a reformulation of Society Semantics in a wider setting, we develop in detail two examples of application of the new formalism, characterizing a hierarchy of paraconsistent logics called Pn and a hierarchy (...) of paracomplete logics In. We also propose three further generalizations, obtaining Society Semantics for several many-valued logics, including a hierarchy of logics called In Pk which are both paraconsistent and paracomplete. (shrink)

Despite receiving a great deal of research attention, the effect of corporate philanthropy on shareholder value remains inconclusive. To address this issue, the present paper examines emotionality as an important factor based on which investors infer about the firm’s motive as well as the beneficiary’s worthiness and react accordingly. Consistent with attribution theory, our event study shows that announcements with more emotional expressions are associated with higher cumulative abnormal stock returns and the effect is stronger when investor attention is greater. (...) We further find that the positive interaction effect between emotionality and investor attention is more pronounced for scandal-free firms than for firms with corporate social irresponsibility (CSI). The empirical evidence remains consistent under various robustness tests. The paper concludes with implications for future research and managerial practices. (shrink)

The paper examines Nietzsche's claim that valuations born out of a psychological condition he calls "ressentiment" are objectionable. It argues for a philosophically sound construal of this type of criticism, according to which the criticism is directed at the agent who holds values out of ressentiment, rather than at those values themselves. After presenting an analysis of ressentiment, the paper examines its impact on valuation and concludes with an inquiry into Nietzsche's reasons for claiming that ressentiment valuation is "corrupt." (...) Specifically, the paper proposes that ressentiment valuation involves a form of self-deception, that such self-deception is objectionable because it undermines the integrity of the self, and that the lack of such integrity ensnares the agent in a peculiar kind of practical inconsistency. The paper ends with a brief review of the problems and prospects of this interpretation. (shrink)

This paper argues the case that tests of how investors value corporate social performance (CSP) based upon realised stock market returns are liable to be weak tests if markets are efficient and firms change CSP policies infrequently. We provide a theoretical explanation of why this will be the case using examples to illustrate. Subsequently, we set out an alternative theoretical framework for the purposes of investigating whether markets place a positive, or a negative, valuation on CSP, and show why this (...) is superior to tests based upon Tobin’s Q. Using US KLD data, we demonstrate that, as theorised, markets place a positive value on CSP that is not detected by conventional returns-based tests. Our conclusion is that researchers who are interested in the question of whether engagement with a corporate social responsibility agenda is a value-enhancing activity for a company (as argued by some stakeholder theorists) or value destructive (as argued by Friedman, The social responsibility of business is to increase its profits, The New York Times Magazine, 1970), need to look beyond returns-based tests to answer the research question posed. (shrink)

Scholars have critiqued mainstream economic approaches to environmental valuation for decades. These critiques have intensified with the increased prominence of environmental valuation in decision-making. This paper has three goals. First, we summarise prominent critiques of monetary valuation, drawing mostly on the work of Clive Spash, who worked extensively on cost–benefit analysis early in his career and then became one of monetary valuation's most thorough and ardent critics. Second, we, as a group of scholars who study relational values, describe how relational (...) values research engages with and addresses many of the critiques of monetary valuation. Third, we offer suggestions for relational values research that continues and deepens its ability to respond to critiques of monetary valuation and contributes to transformative change towards sustainability. (shrink)

Arguing against the long-standing belief that Thuc. 3.82.4 refers to words changing their meanings, this article shows that, according to the passage, the way in which people value actions and apply value-words to actions in peace differs from how they value and apply value-words to the same types of actions in stasis. But the meaning of the value-words themselves remains the same in both circumstances. The passage is about neither meaning nor the propagandistic manipulation of language but about the distorting (...) effect of stasis on the moral assessment of actions. (shrink)

We give a definition, in the ring language, of Zp inside Qp and of Fp[[t]] inside Fp), which works uniformly for all p and all finite field extensions of these fields, and in many other Henselian valued fields as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modification of the language of Macintyre. Furthermore, we show the negative result that in the language of rings there does not exist a uniform definition (...) by an existential formula and neither by a universal formula for the valuation rings of all the finite extensions of a given Henselian valued field. We also show that there is no existential formula of the ring language defining Zp inside Qp uniformly for all p. For any fixed finite extension of Qp, we give an existential formula and a universal formula in the ring language which define the valuation ring. (shrink)