Formal series are associated with ascriptions of numbers. They are ordered by formal operations that, unlike negation and disjunction, are not truth-operations. In spite of this, they are required to build propositions involving generic reference to numbers, and are essential to the Tractarian version of the logicist project.

In this paper I am concerned with the semantic analysis of sentences of the form 'It is true that p'. I will compare different proposals that have been made to analyse such sentences and will defend a view that treats this sentences as a mere sytactic variation of sentences of the form 'That p is true'.

The syntax of Frege's scientific language is commonly taken to be characterized by two oddities: the representation of the intended illocutionary role of sentences by a special sign, the judgement-stroke, and the treatment of sentences as a species of singular terms. In this paper, an alternative view is defended. The main theses are: the syntax of Frege's scientific language aims at an explication of the logical form of judgements; the judgement-stroke is, therefore, a truth-operator, not a pragmatic (...) class='Hi'>operator; in Frege's first system, '⊦ Δ' expresses that the circumstance Δ is a fact, and in his second system that the truth-value - Δ is the True; in both systems, the judgement-stroke is construed as a sign sui generis, not as a genuine predicate; its counterpart in natural language is the syntactic "form of assertoric sentences", not the truth-predicate; neither in Frege's first nor in his second system sentences are treated as singular terms. (shrink)

The Embracing Revenge account of semantic paradox avoids the expressive limitations of previous approaches based on the Kripkean fixed point construction by replacing a single language with an indefinitely extensible sequence of languages, each of which contains the resources to fully characterize the semantics of the previous languages. In this paper we extend the account developed in Cook, Cook, Schlenker, and Tourville and Cook via the addition of intensional operators such as ``is paradoxical''. In this extended framework we are able (...) to characterize the difference between sentences, such as the Liar and the Truth-teller, that receive the same semantic value in minimal fixed points yet seem to involve distinct semantic phenomena. (shrink)

The logic with independent truth and falsehood operators TFL is proposed. In TFL(→) standard truth-conditions for the implication are adopted. Nevertheless the laws of classical logic are not valid. In this language more then 107 different binary connectives can be defined. So this logic can be treated as universal logic relatively to the class of sentential logics.

The main question of our article is: What is the logical form of statements containing expressions such as “… is true” and “it is true that …”? We claim that these expressions are generally not used in order to assign a certain property to sentences. We indicate that a predicative interpretation of these expressions was rejected by Frege and adherents to the prosentential conception of truth. We treat these expressions as operators. The main advantage of our operational reading is (...) the fact that it adequately represents how the words, “true” and “truth,” function in everyday speech. Our approach confirms the intuition that so-called T-equivalences are not contingent truths, and explains why they seem to be—in some sense—necessary sentences. Moreover, our operational readingof truth expressions dissolves problems arising from the belief that there is some specific property—truth. The fact that we reject that truth is a certain property does not mean that we deny that the concept of truth plays a very important role in our language, and hence in our life. We indicate that the concept of truth is inseparable from the concept of sentence and vice versa—it is impossible to explicate one of these concepts without appeal to the other. (shrink)

Just about everything today comes with an operating manual--from your computer to your car, from your cell phone to your iPad. Is it possible that Life comes with an operating manual, as well? That's the simple, but powerful premise of Tom Shadyac's inspiring and provocative first book. Written as a series of essays and dialogues, we are invited into a conversation that is both challenging and empowering. The question now is, can we discern what is written inside of this operating (...) manual and garner the courage to live in accordance with its precepts. (shrink)

Formalization of reasoning which accepts rules of inference leading to conclusions whose logical values are not smaller than the logical value of the “weakest” premise leads to the concept of consequence operation preserving degrees of truth. Several examples of such consequence operation have already been considered . In the present paper we give a general notion of the consequence operation preserving degrees of truth and its characterization in terms of projective generation and selfextensionality.

The Operator Argument against eternalism holds that having non-vacuous tense operators in the language is incompatible with the claim that every proposition has its truth-value eternally. Assuming that (1) there are non-vacuous tense operators, (2) tense operators operate on propositions and (3) tense operators which operate on eternal entities are vacuous, it may be argued that eternalism is false. In this paper, I examine the Operator Argument. The goal is threefold. First, I want to present some aspects (...) of the debate in a more elaborate way, especially those concerning formal matters. Secondly, I will argue that eternalism can escape the Operator Argument. There are two main strategies for handling the Operator Argument. The first one is based on replacing temporal operators with object-language quantifiers. The second rejects the identification of compositional semantic value with assertoric content. My third goal is to show that none of them is as good as the strategy that adopts Timestamp Semantics (Fritz in Philosl Stud 176:2933–2959, 2019). I am going to argue that the quantificational treatment of tenses is compatible with temporalism and that the arguments for rejecting the identification of compositional semantic value with assertoric content provide, in fact, a motivation for the temporalist position. At the end, I will develop Timestamp Semantics by providing a novel formalization of it, and defend it against three potential counter-arguments. (shrink)

The choice of connectives for many valued propositional logics suitable for theoretical and applicational interests in most cases is an open problem up to now. We will not offer a general solution here, but support the point of view of some recent developments in fuzzy set theory that the triangular norms – t-norms for short – of Schweizer/Sklar [3] and the ϕ-operators of Pedrycz [2] represent quite general classes of connectives at least for many valued logics with truth value (...) set the real interval [0,1] . Special classes of t-norms and general properties of them have been discussed in some papers just recently, e.g. by Dombi [1], Weber [4], Yager [5] to mention only a few of them. (shrink)

This note presents some new results from [1] about the Suszko operator and truth‐equational logics, following the works of Czelakowski [11] and Raftery [17]. It is proved that the Suszko operator relative to a truth‐equational logic preserves suprema and commutes with endomorphisms. Together with injectivity, proved by Raftery in [17], the Suszko operator relative to a truth‐equational logic is a structural representation, as defined in [15]. Furthermore, if is a quasivariety, then the Suszko (...) class='Hi'>operator relative to a truth‐equational logic is continuous. Finally, it is proved that truth is equationally definable in the class if and only if is a ‐algebraic semantics for and the Suszko operator preserves suprema and commutes with substitutions. (shrink)

(No abstract is available for this citation).

It is advisable to treat some sorts of discourse about fiction with the aid of an intensional operator "in such-And-Such fiction...." the operator may appear either explicitly or tacitly. It may be analyzed in terms of similarity of worlds, As follows: "in the fiction f, A" means that a is true in those of the worlds where f is told as known fact rather than fiction that differ least from our world, Or from the belief worlds of the (...) community in which the fiction originated. (shrink)

Łukasiewicz presented two different analyses of modal notions by means of many-valued logics: the linearly ordered systems Ł3,..., Open image in new window,..., \; the 4-valued logic Ł he defined in the last years of his career. Unfortunately, all these systems contain “Łukasiewicz type paradoxes”. On the other hand, Brady’s 4-valued logic BN4 is the basic 4-valued bilattice logic. The aim of this paper is to show that BN4 can be strengthened with modal operators following Łukasiewicz’s strategy for defining (...) class='Hi'>truth-functional modal logics. The systems we define lack “Łukasiewicz type paradoxes”. Following Brady, we endow them with Belnap–Dunn type bivalent semantics. (shrink)

It is widely asserted that we are now living in a post-truth society. What that means, this book argues, is that the contemporary global world is thoroughly infested not only with trickster figures but an entire and operational trickster logic; or, that we now live in a Trickster Land - an argument advanced by the claim that in modernity liminality has become permanent; or that modern life is patently absurd. The first part of the book presents a series of (...) 'guides' to this condition, in the form of key thinkers and writers who can help us understand and navigate our Trickster Land. Such guides include Hermann Broch, Lewis Hyde, Roberto Calasso, Michel Serres, Sándor Márai, Colin Thubron, and Albert Camus. The second part goes on to discuss five main regions of Trickster Land: art, thought, the economy, politics, and society. This last, central chapter of the book contrasts trickster logic with the basic, foundational logic of social life, presented as gift-giving by Marcel Mauss and as sociability by Georg Simmel, and which is expressed here, combining Heraclitus and Plato with the Gospel of John, by three basic terms of ancient Greek culture, as arkhé charis logos: meaningful social life originally and in its essence is animated by the power of kind benevolence. This volume will appeal to scholars of social theory, anthropology and sociology with interests in political thought and contemporary culture. (shrink)

Some alethic pluralists maintain that there are two kinds of truths operant in our alethic discourse: a realist kind and an anti-realist kind. In this paper, we argue that such a binary conception cannot accommodate certain social truths, specifically truths about race. Most alethic pluralists surprisingly overlook the status of racial truths. Douglas Edwards is, however, an exception. In his version of alethic pluralism—Determination Pluralism—racial truths are superassertible (anti-realist) true rather than correspondence (realist) true. We argue that racial truths exhibit (...) features of both superassertibility (anti-realism) and correspondence (realism). This suggests a fuzzy boundary between realist and anti-realist kinds of truth. There may be a continuum rather than a dichotomy of truths. We conclude by sketching one way for alethic pluralists to accommodate such a notion. (shrink)

Certain passages in Kaplan’s ‘Demonstratives’ are often taken to show that non-vacuous sentential operators associated with a certain parameter of sentential truth require a corresponding relativism concerning assertoric contents: namely, their truth values also must vary with that parameter. Thus, for example, the non-vacuity of a temporal sentential operator ‘always’ would require some of its operands to have contents that have different truth values at different times. While making no claims about Kaplan’s intentions, we provide several (...) reconstructions of how such an argument might go, focusing on the case of time and temporal operators as an illustration. What we regard as the most plausible reconstruction of the argument establishes a conclusion similar enough to that attributed to Kaplan. However, the argument overgenerates, leading to absurd consequences. We conclude that we must distinguish assertoric contents from compositional semantic values, and argue that once they are distinguished, the argument fails to establish any substantial conclusions. We also briefly discuss a related argument commonly attributed to Lewis, and a recent variant due to Weber. (shrink)

The aim of this paper is to provide an overview of various forms of alethic pluralism. Along the way we will draw a number of distinctions that, hopefully, will be useful in mapping the pluralist landscape. Finally, we will argue that a commitment to alethic disjunctivism, a certain brand of pluralism, might be difficult to avoid for adherents of the other pluralist views to be discussed. We will proceed as follows: Section 1 introduces alethic monism and alethic pluralism. Section 2 (...) presents a distinction between strong and moderate versions of monism and pluralism, understood as theses about the existence of truth properties. Section 3 introduces four pluralist positions: strong alethic pluralism, alethic disjunctivism, second-order functionalism and manifestation functionalism. These positions are classified using the basic framework from Section 2, and a further distinction between pure and mixed versions of pluralism is drawn. Interestingly, alethic disjunctivism and the two kinds of functionalism—i.e. three out of four positions— have a mixed character. They incorporate a monist thesis. The only pure form of pluralism is strong alethic pluralism. Section 4 adds another distinction to the stock: one-level and two-level views. Each of the mixed positions operates with two levels, locating certain “alethically potent”—or grounding—properties at a lower level and others at a higher level. We briefly discuss the nature of grounding. In Section 5, we answer a question about mixed, two-level views, viz. whether they are as much monist as pluralist in nature, or more. They are not. Section 6 is devoted to the task of arguing that the strong pluralist, the second-order functionalist, and the manifestation functionalist will find it hard to deny a commitment to alethic disjunctivism. (shrink)

This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.

Transient Truths: An Essay in the Metaphysics of Propositions provides the first book-length exposition and defense of semantic temporalism, the view that propositions are contents or semantic values that can change their truth-values across time.

Truth-talk exhibits certain features that render it philosophically suspect and motivate a deflationary account. I offer a new formulation of deflationism that explains truth-talk in terms of semantic pretense. This amounts to a fictionalist account of truth-talk but avoids an error-theoretic interpretation and its resulting incoherence. The pretense analysis fits especially well with deflationism’s central commitment, and it handles truth-talk’s unusual features effectively. In particular, this approach suggests an interesting strategy for dealing with the Liar paradox. (...) This version of deflationism has advantages over the formulations currently available in the literature, mainly because it offers a more satisfying account of the generalizing role deflationary views take as truth-talk’s central function. Explaining the notion of truth in terms of pretense generates some special concerns, but none we cannot address through careful consideration of how pretense operates in truth-talk and of the attitudes instances of pretending involve. (shrink)

After twenty years of almost unbroken wars of choice, the deficiencies in the ethical and operational conduct of war by Western armed forces, has largely been ignored by scholarly critique. This volume addresses these deficiencies and demonstrates that they in fact represent the culmination of decades of erosion of military professionalism. Contributions in this edited collection are written by some of the UK's leading soldiers, veterans and scholars working in the fields of military ethics and contemporary conflict.

Thomas Hofweber takes the semantic paradoxes to motivate a radical reconceptualization of logical validity, rejecting the idea that an inference rule is valid just in case every instance thereof is necessarily truth-preserving. Rather than this “strict validity”, we should identify validity with “generic validity”, where a rule is generically valid just in case its instances are truth preserving, and where this last sentence is a generic, like “Bears are dangerous”. While sympathetic to Hofweber’s view that strict validity should (...) be replaced by something allowing for exceptions, I argue that this should instead be truth-conduciveness, a matter of a large majority of instances being truth-preserving. The fact that inference rules have uncountably many instances, I argue, can be handled by defining truth-conduciveness as relative to finite sets of instances. Moreover, I argue that Hofweber’s position, while seemingly radical, may be less so under closer scrutiny. For the mere claim that classical rules and unrestricted truth rules are generically valid (or truth-conducive) is not in itself controversial. Also, if there is an answer to the question of which of these are also strictly valid, then the claim that generic validity is the central notion in logic is at most an interest-relative matter, since there is then also a fact of the matter as to which inference rules are (not) strictly valid. If no solution operating with strict validity to the paradoxes can be had, however, then the claim that validity should be identified with a weaker notion is better motivated. I argue that it is reasonable, in view of past failures, to conjecture that no ordinary solution will score high enough relative to standard (uncontroversial) desiderata to merit justified belief. Hence, it is unknowable which solution is correct. I further argue that this is best explained by its being metaphysically indeterminate which solution is correct. If this conjecture is true, then we ought instead to think of validity as allowing exceptions, and then take the “true logic” to be one that takes both the classical rules and the truth rules to be valid, i.e., truth-conducive. This logic scores very high on the desiderata on logics, and is therefore preferable to any logic operating with strict validity. (shrink)

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: (...) to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense. (shrink)

According to operator theories, "if" denotes a two-place operator. According to restrictor theories, "if" doesn't contribute an operator of its own but instead merely restricts the domain of some co-occurring quantifier. The standard arguments (Lewis 1975, Kratzer 1986) for restrictor theories have it that operator theories (but not restrictor theories) struggle to predict the truth conditions of quantified conditionals like -/- (1) a. If John didn't work at home, he usually worked in his office. b. (...) If John didn't work at home, he must have worked in his office. -/- Gillies (2010) offers a context-shifty conditional operator theory that predicts the right truth conditions for epistemically modalized conditionals like (1b), thus undercutting one standard argument for restrictor theories. I explore how we might generalize Gillies' theory to adverbially quantified conditionals like (1a) and deontic conditionals, and argue that a natural generalization of Gillies' theory -- following his strategy for handling epistemically modalized conditionals -- won't work for these other conditionals because a crucial assumption that epistemic modal bases are closed (used to neutralize the epistemic quantification contributed by "if") doesn't have plausible analogs in these other domains. (shrink)

In this paper, we investigate the problem of truth approximation via belief merging, i.e., we ask whether, and under what conditions, a group of inquirers merging together their beliefs makes progress toward the truth about the underlying domain. We answer this question by proving some formal results on how belief merging operators perform with respect to the task of truth approximation, construed as increasing verisimilitude or truthlikeness. Our results shed new light on the issue of how rational (...) (dis)agreement affects the inquirers’ quest for truth. In particular, they vindicate the intuition that scientific inquiry, and rational discussion in general, benefits from some heterogeneity in opinion and interaction among different viewpoints. The links between our approach and related analyses of truth tracking, judgment aggregation, and opinion dynamics, are also highlighted. (shrink)

The well-known argument of Frederick Fitch, purporting to show that verificationism (= Truth implies knowability) entails the absurd conclusion that all the truths are known, has been disarmed by Dorothy Edgington''s suggestion that the proper formulation of verificationism presupposes that we make use of anactuality operator along with the standardly invoked epistemic and modal operators. According to her interpretation of verificationism, the actual truth of a proposition implies that it could be known in some possible situation that (...) the proposition holds in theactual situation. Thus, suppose that our object language contains the operatorA — it is actually the case that ... — with the following truth condition: vA iff w0, wherew 0 stands for the designated world of the model — the actual world. Then we can formalize the verificationist claim as follows. (shrink)

Benjamin Schnieder has argued that several traditional definitions of truth-functionality fail to capture a central intuition informal characterizations of the notion often capture. The intuition is that the truth-value of a sentence that employs a truth-functional operator depends upon the truth-values of the sentences upon which the operator operates. Schnieder proposes an alternative definition of truth-functionality that is designed to accommodate this intuition. We argue that one traditional definition of ‘truth-functionality’ is immune (...) from the counterexamples that Schnieder proposes and is preferable to Schnieder’s alternative. (shrink)

Let us sum up. The paradox of the Knower poses a direct and formal challenge to the coherence of common notions of knowledge and truth. We've considered a number of ways one might try to meet that challenge: propositional views of truth and knowledge, redundancy or operator views, and appeal to hierarchy of various sorts. Mere appeal to propositions or operators, however, seems to be inadequate to the task of the Knower, at least if unsupplemented by an (...) auxiliary recourse to hierarchy. But the cost of hierarchy appears to be an abandonment of any notion of all truth or of omniscience. What the contradictions of the Knower seem to demand, then, is at least an abandonment of these. As noted in the introduction, the argument is complicated enough that one must be wary of dogmatic and precipitate conclusions. One may legitimately wonder whether some new response, or some variation on an old one, will yet offer a way out.Far too often, however, it is asked what has gone wrong with paradox rather than what paradox may have to teach us. What the Knower may have to teach us, I think, is that there really can be no coherent notion of all truth and really can be no coherent notion of omniscience. In its own way that conclusion is perhaps as humbling as is any traditional notion of God. (shrink)

We consider an extension of Gödel logic by a unary operator that enables the addition of non-negative reals to truth-values. Although its propositional fragment has a simple proof system, first-order validity is Π2-hard. We explain the close connection to Scarpellini’s result on Π2-hardness of Łukasiewicz’s logic.

In Truthfulness and Tragedy Stanley Hauerwas provides an account of moral existence and ethical rationality that shows how Christian convictions operate, or should operate, to form and direct lives. In attempting to conceptualize the basis of Christian ethics in a manner that will render Christian convictions morally intelligible, the author casts fresh light on traditional theoretical issues and articulates the distinctive Christian response to contemporary concerns such as suicide, medical ethics, and child care. The first section of the book deals (...) with methodological issues: the meaning and nature of practical reason, obligation claims, natural law, and self deception, and the affinity of story and ethics. It focuses on the relation of truthfulness and tragedy and the need for a story--a set of religious convictions or "grammar of theology"--that does justice to the tragic character of human existence. The second section addresses substantive issues: suicide, euthanasia, and the value of survival; the moral limits of population growth; the definition of "person" for medical reasons; and social involvement and Christian ethics. The overall theme is the need for a community in which truthfulness is a way of life. In the final section, devoted to the problem of how to care for retarded children, the implications of the author's ethical position are given concrete expression. He discusses the assumptions underlying the willingness to have children, criteria for humanness, medical ethics, and how truthful communities deal with suffering. In Truthfulness and Tragedy Stanley Hauerwas extends and clarifies the ethical position set forth in his earlier books Character and the Christian Life and Vision and Virtue. He is associate professor of theology at the University of Notre Dame. He was a senior fellow in Christian medical ethics at the Joseph and Rose Kennedy Institute for the Study of Reproduction and Bioethics, and taught medical ethics at the University of Texas medical branch in Galveston. (shrink)

In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a classical (...) recapture result based on the two logics. In the second part of the paper, we compare the approach in terms of normality operators with an established approach to classical recapture, namely minimal inconsistency. Finally, we discuss technical issues connecting LPe and Ke3 to the tradition of Logics of Formal Inconsistency and Underterminedness. (shrink)

Semantic externalism in the style of McDowell and Evans faces a puzzle formulated by Pryor: to explain that a sentence such as 'Jack exists' is only a posteriori knowable, despite being logically entailed by the seemingly logical truth 'Jack is self-identical', and hence being itself a logical truth and therefore a priori knowable. Free logics can dissolve the puzzle. Moreover, Pryor has argued that the existentially hedged 'If Jack exists, then Jack is self-identical', when properly formalised, is a (...) logical truth in a system of neutral free logic and therefore a priori knowable, while it does not entail that Jack exists. The latter holds also for negative free logic. In response, Yeakel has argued that on any system of neutral free logic existence hedges will either entail some unwanted existence claims or they will not entail some wanted existence claims. The dilemma also holds for any non-positive free logic. It will be shown that the extension of one of the systems of neutral free logic with a truth operator escapes Yeakel's dilemma, whereas no other non-positive free logic when extended with the truth operator does the same (or it breaks quantifier exchangeability). (shrink)

In On Truth and the Representation of Reality, Dan Nesher develops a new theory of truth in the framework of pragmatist theory of representation. Using the pragmatist theory of perception for the basis of his epistemological explanation of our confrontation with external Reality and how it's represented, Nesher shows that in our perceptual operations we quasi-prove the truth of our perceptual judgments.

A Moderate Anti-realist approach to truth and meaning, built around the concept of knowability, will be introduced and argued for in this essay. Our starting point will be the two fundamental anti-realists principles that claim that neither truth nor meaning can outstrip knowability and our focus will be on the challenge of adequately formalizing these principles and incorporating them into a formal theory. Accordingly, the author will introduce a MAR truth operator that is built on a (...) distinction between being true and being factual. He will show then that this approach partitions propositions into eight classes, on the basis of their knowability. We will then ask the following question: Given the anti-realist principles, what kind of theory of propositional meaning can properly explain the meaninglessness of fully unknowable propositions? This question will lead us to the claim that the meaning/content of propositions should be identified not with the set of possible worlds in which the propositions are true/factual, but rather in which they are known. This modified approach will then be used to analyze both the Liar Paradox and the Strengthened Liar. To anticipate the conclusion of this essay, it will be shown that a MAR framework can render definite truth and factuality values to the Liar sentence and it will also confirm our intuition that such paradoxical sentences are devoid of proper meaning. (shrink)

Yablo’s Paradox, an infinite-sentence version of the Liar Paradox, aims to show that semantic paradox can emerge even without circularity. I will argue that the lack of meaning/content of the sentences involved is the source of the paradoxical outcome.I will introduce and argue for a Moderate Antirealist approach to truth and meaning, built around the twin principles that neither truth nor meaning can outstrip knowability. Accordingly, I will introduce a MAR truth operator that both forges an (...) explicit connection between truth and knowability and distinguishes between truth and factuality. I will also argue that the meaning/content of propositions should be identified not with the set of possible worlds in which the propositions are true/factual, but rather in which they are known.I will show that our MAR framework dissolves Yablo’s Paradox and also confirms our intuition that these sentences are all devoid of content/meaning. (shrink)

Building on conceptual insights from the history and sociology of numbers, media and surveillance studies, and theories of governance and risk, this article analyzes the forms of transparency produced by the use of numbers in social life. It examines what it is about numbers that often makes their ‘truth claims’ so powerful, investigates the role that numerical operations play in the production of retrospective, real-time and anticipatory forms of transparency in contemporary politics and economic transactions, and discusses some of (...) the implications resulting from the increasingly abstract and machine-driven use of numbers. It argues that the forms of transparency generated by machine-driven numerical operations open up for individual and collective practices in ways that are intimately linked to precautionary and pre-emptive aspirations and interventions characteristic of contemporary governance. As such, these numerical operations raise important political and ethical questions that deserve further conceptual and empirical scrutiny. (shrink)

In this paper, we use a ‘normality operator’ in order to generate logics of formal inconsistency and logics of formal undeterminedness from any subclassical many-valued logic that enjoys a truth-functional semantics. Normality operators express, in any many-valued logic, that a given formula has a classical truth value. In the first part of the paper we provide some setup and focus on many-valued logics that satisfy some of the three properties, namely subclassicality and two properties that we call (...) fixed-point negation property and conservativeness. In the second part of the paper, we introduce normality operators and explore their formal behaviour. In the third and final part of the paper, we establish a number of classical recapture results for systems of formal inconsistency and formal undeterminedness that satisfy some or all the properties above. These are the main formal results of the paper. Also, we illustrate concrete cases of recapture by discussing the logics $\mathsf{K}^{\circledast }_{3}$, $\mathsf{LP}^{\circledast }$, $\mathsf{K}^{w\circledast }_{3}$, $\mathsf{PWK}^{\circledast }$ and $\mathsf{E_{fde}}^{\circledast }$, that are in turn extensions of $\mathsf{{K}_{3}}$, $\mathsf{LP}$, $\mathsf{K}^{w}_{3}$, $\mathsf{PWK}$ and $\mathsf{E_{fde}}$, respectively. (shrink)

In this paper, we extend the expressive power of the logics K3, LP and FDE with anormality operator, which is able to express whether a for-mula is assigned a classical truth value or not. We then establish classical recapture theorems for the resulting logics. Finally, we compare the approach via normality operator with the classical collapse approach devisedby Jc Beall.

Alethic pluralism, on one version of the view , is the idea that truth is to be identified with different properties in different domains of discourse. 1 Whilst we operate with a univocal concept of truth, and a uniform truth predicate, the thought is that the truth property changes from one domain to the next. So the truth property for talk about the nature and state of the material world may be different from the (...) class='Hi'>truth property for moral discourse .Tappolet challenged alethic pluralism by asking how it can account for the truth of mixed compounds, such as a mixed conjunction like ‘this cat is wet and funny’, where each of the conjuncts are from different domains of discourse, and thus assessable in terms of different truth properties. She argues that the alethic pluralist is left in a dilemma: either admit of a ‘generic’ truth property, which can be possessed by propositions from all domains, thus rendering the plural ways of being true obsolete, or deny the truth of mixed conjunctions.In Edwards 2008, I argued that there is route out of Tappolet's dilemma. Briefly, I suggested that we acknowledge that the truth of a mixed conjunction is dependent on the truth of its conjuncts, and we should explain the truth of the conjunction by saying that it is true just in case each of its conjuncts is true. This, I argued, gives us an account of the truth of the conjunction without needing to appeal to a troublesome ‘generic’ truth property.Aaron Cotnoir criticizes my solution to Tappolet's problem. Cotnoir argues that my solution to the problem admits of an unacceptable ‘proliferation’ of truth properties, and smuggles in a generic truth property. I …. (shrink)