This paper analyzes the logical form of valuing. I argue that valuing a concept or property is a universal statement qua logical form, that valuing an object is an existential statement qua logical form, and, furthermore, that a correct analysis of the logical form of valuing contains doxastic operators. I show that these ingredients give rise to an interesting interplay between uniform and ununiform quantification, on the one hand, and de dicto and de re beliefs, on the other. I apply (...) this analysis to the value of political freedom. The received view is that the value of freedom lies in the value of the specific things one is free to do. But Ian Carter has recently shown that freedom has irreducible, "non-specific" value, too. I show that underlying the debate between the proponents of the received view and their critics is a disagreement about logical form: ununiform de dicto beliefs about freedom as a concept, for the received view, and uniform half-de dicto-half-de re beliefs about freedom as an object, for its critics. (shrink)

Formal axiology, as does every scientific system, stems from the unfolding of its axiom or axioms. The axiom of formal axiology is the following: Value is the degree in which a thing fulfills the attributes contained in the intension of its concept. "Fulfillment" means the possession by a thing of a set of properties corresponding to the set of attributes in the intension of its concept. A thing is good if it possesses all the properties in question. The development (...) of this axiom constitutes an axiological system, which establishes the dimensions of value, a hierarchy of value, a language of value and a logic of value. (shrink)

This paper represents an attempt to indicate the idea of a logic slightly more general than sentential calculus, which is applicable to many philosophical issues. In particular, I shall use this generalized calculus to discuss a variation of the logic of imperatives. In part I, certain general considerations about indicative calculi provide the basis, as well as indicate the need, for the more formal construction of part II. Part III illustrates the analytical power of the tool constructed, and (...) tries to show its relevance for philosophy. (shrink)

Beginnings and the hyperthematic structures of game and narrative -- Hyperthematic structures of dance and music -- Hyperthematic expansion of light and color -- The hyperthematic structure of visual arts -- Hyperthematization of the corporation -- Expansive reconstruction of H5 to H15 -- Expansive reconstruction of the hyperthemes of light and color -- Expansive reconstruction of the hyperthemes of the visual arts.

This article argues that Nietzsche's transvaluation project refers not to a mere inversion or negation of a set of values but, instead, to a different conception of what a value is and how it functions. Traditional values function within a standard logical framework and claim legitimacy and bindingness based on exogenous authority with absolute extension. Nietzsche regards this framework as unnecessarily reductive in its attempted exclusion of contradiction and real opposition among competing values and proposes a nonstandard, dialetheic model (...) of valuation. (shrink)

This article argues that Nietzsche’s transvaluation project refers not to a mere inversion or negation of a set of nihilism-prone, Judeo-Christian values but, instead, to a different conception of what a value is and how it functions. Traditional values function within a standard logical framework and claim legitimacy and “bindingness” based on exogenous authority with absolute extension. Nietzsche regards this framework as unnecessarily reductive in its attempted exclusion of contradiction and real opposition among competing values. I propose a nonstandard, (...) dialetheic model of valuation that requires a value to be both true and false as well as neither true nor false.In our Europe, life is no longer quite so uncertain, contingent, nonsensical. [...] The power man has achieved now allows a reduction of those means of discipline of which the moral interpretation was the strongest.— KSA 12:5[71]The logic of our conscious thinking is only a crude and facilitated form of the thinking needed by our organism [...] A simultaneity-thinking [ein Zugleichdenken], for example, is needed of which we have hardly an inkling. [...] We are still growing continually, our sense of time and place, etc., is still developing.— KSA 11:34[124]. (shrink)

A system of values plays an important intermediary role in the human conceptual system. An individual associates a value – an abstract valence and quantity – with a past, present, or contemplated object or action in the environment, and uses values to help determine what actions to take. Value can be categorized into a number of different types, the most important of which for the purposes of the present article are affective value, normative value, and esteem. (...) Normative value in turn divides into several subdomains such as moral value, legality, etiquette, and religious value. In addition, values can be divided along the orthogonal dimension of objective versus subjective. Each type of value plays its own characteristic role in affecting choice of action in interaction with the others.Given an explicit formulation of systems of value, it then becomes possible to work out more precise accounts of value-laden systems of concepts. Two are explored here: fairness and freely chosen reciprocity, the latter including retaliation, restitution, honoring, shaming, and apologizing.The overall hypothesis that emerges from the investigation is that the basic categories of value and the inference rules built on them are human universals. Cultures' value systems differ primarily in what actions and objects are assigned what values and the relative weighting of different sources of value in cases where they interact. (shrink)

After putting forward a formal account of value disagreement via imprecise measures, I develop a logic of value attribution and of agreement based on truthmaker semantics.

David Benatar, in Better Never to Have Been , sets out two arguments in support of the view that coming into existence is always a net harm. Remarkably, the first argument seems to imply that coming into existence would be a net harm even if the only bad we experienced in our lives were a ‘single pin-prick’. This argument hinges on a purported asymmetry: that whereas the absence of pains in non-existence is good, the absence of pleasures in non-existence is (...) not bad (rather than bad ). It also hinges on the non-badness at issue here being relative (no worse than the presence of pleasures in existence) rather than intrinsic (value neutral). To establish the crucial claim that the non-badness of absent pleasures in non-existence is relative rather than intrinsic, Benatar constructs an analogy involving two people, Sick and Healthy. In this paper, I show the inaptness of the analogy and also provide positive reason to doubt the soundness of the argument as it stands. What emerges from this critical analysis of the analogy is a plausible theory of value at odds with Benatar’s argument as a whole. (shrink)

This paper sheds light on the relationship between the logic of generalized truth values and the logic of bilattices. It suggests a definite solution to the problem of axiomatizing the truth and falsity consequence relations, \ and \ , considered in a language without implication and determined via the truth and falsity orderings on the trilattice SIXTEEN 3 . The solution is based on the fact that a certain algebra isomorphic to SIXTEEN 3 generates the variety of commutative (...) and distributive bilattices with conflation. (shrink)

This is the first critical study of The Logic of Sense, Gilles Deleuze's most important work on language and ethics, as well as the main source of his vital philosophy of the event.James Williams explains the originality of Deleuze's work with careful definitions of all his innovative terms and a detailed description of the complex structure he constructs. This reading makes connections to his ground-breaking work on literature, to his critical but also progressive relation to the sciences, and to (...) his controversial denial of the priority of standard logics, human values and 'meaning' in thinking.This book will open new debates and develop current ones around Deleuze's work in philosophy, politics, literature, linguistics, cultural studies and sociology. (shrink)

Some writers have noted that valuation is often focused on foreseen changes. They say that we often don't value situations in terms of what we would have in them only but also in terms of the gains or losses that they offer us — that we then focus on departures from our status quo. They argue that such thinking conflicts with basic economic analysis, and also that it violates logic: they say that it is irrational. I agree that (...) it seems to be common. But is such a way of setting one's values a challenge to economics? And does it conflict with being rational? (shrink)

The main aim of this paper is to introduce the logics of evidence and truth $$LET_{K}^+$$ and $$LET_{F}^+$$ together with sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics $$LET_{K}$$ and $$LET_{F}^-$$ with rules of propagation of classicality, which are inferences that express how the classicality operator $${\circ }$$ is transmitted from less complex to more complex sentences, and vice-versa. The six-valued semantics here proposed extends the 4 values of Belnap-Dunn logic with 2 more (...) values that intend to represent (positive and negative) reliable information. A six-valued non-deterministic semantics for $$LET_{K}$$ is obtained by means of Nmatrices based on swap structures, and the six-valued semantics for $$LET_{K}^+$$ is then obtained by imposing restrictions on the semantics of $$LET_{K}$$. These restrictions correspond exactly to the rules of propagation of classicality that extend $$LET_{K}$$. The logic $$LET_{F}^+$$ is obtained as the implication-free fragment of $$LET_{K}^+$$. We also show that the 6 values of $$LET_{K}^+$$ and $$LET_{F}^+$$ define a lattice structure that extends the lattice L4 defined by the Belnap-Dunn four-valued logic with the 2 additional values mentioned above, intuitively interpreted as positive and negative reliable information. Finally, we also show that $$LET_{K}^+$$ is Blok-Pigozzi algebraizable and that its implication-free fragment $$LET_{F}^+$$ coincides with the degree-preserving logic of the involutive Stone algebras. (shrink)

This study concentrates on exploring the ‘logic’ of modern universities in China-a working concept that promotes a more in-depth discourse on the implicit illustrations of the ‘logic’ of universiti...

Classical logic of formal provability includes Löb’s theorem, but not reflection. In contrast, intuitions about the inferential behavior of informal provability (in informal mathematics) seem to invalidate Löb’s theorem and validate reflection (after all, the intuition is, whatever mathematicians prove holds!). We employ a non-deterministic many-valued semantics and develop a modal logic T-BAT of an informal provability operator, which indeed does validate reflection and invalidates Löb’s theorem. We study its properties and its relation to known provability-related paradoxical arguments. (...) We also argue that T-BAT is a fairly sensible candidate for a formal logic of informal provability. (shrink)

The four-valued semantics of Belnap–Dunn logic, consisting of the truth values True, False, Neither, and Both, gives rise to several nonclassical logics depending on which feature of propositions we wish to preserve: truth, nonfalsity, or exact truth. Interpreting equality of truth values in this semantics as material equivalence of propositions, we can moreover see the equational consequence relation of this four-element algebra as a logic of material equivalence. In this paper, we axiomatize all combinations of these four-valued logics, (...) for example, the logic of truth and exact truth or the logic of truth and material equivalence. These combined systems are consequence relations which allow us to express implications involving more than one of these features of propositions. (shrink)

Political liberalism has increasingly come under fire from both the right and the left, in politics as well as in philosophy. In this new study, G.B. Madison offers a systematic rebuttal to these contemporary critics, attempting to demonstrate that the basic principles of classical liberal philosophy are not only internally valid and coherent but also directly relevant to the problems faced by society in the post-industrial age. Building on the theory of Frank H. Knight and other liberal tinkers, Madison outlines (...) the postmodern theory of reason that is presupposed within classical liberal theory and makes the case that as a political philosophy liberalism can be justified entirely within its own terms, without reference to arbitrary or absolute values. (shrink)

How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions (Section 1), we argue that a stronger account of conditional can be obtained in two steps: firstly, by reminding its historical roots inside modal logic and set-theory (Section 2); secondly, by revising the meaning of logical values, thereby getting rid of the paradoxes of material implication whilst showing the bivalent roots of conditional as a speech-act based on (...) affirmations and rejections (Section 3). Finally, the two main inference rules for conditional, viz. Modus Ponens and Modus Tollens, are reassessed through a broader definition of logical consequence that encompasses both a normal relation of truth propagation and a weaker relation of falsity non-propagation from premises to conclusion (Section 3). (shrink)

In the monograph [1] of Chang and Keisler, a considerable extent of model theory of the first order continuous logic is ingeniously developed without using any notion of provability.In this paper we shall define the notion of provability in continuous logic as well as the notion of matrix, which is a natural extension of one in finite-valued logic in [2], and develop the syntax and semantics of it mostly along the line in the preceding paper [2]. Fundamental (...) theorems of model theory in continuous logic, which have been proved with purely model-theoretic proofs in [1], will be proved with proofs which are natural extensions of those in two-valued logic. (shrink)

The essay introduces a non-Diodorean, non-Kantian temporal modal semantics based on part-whole, rather than class, theory. Formalizing Edmund Husserl’s theory of inner time consciousness, §3 uses his protention and retention concepts to define a relation of self-awareness on intentional events. §4 introduces a syntax and two-valued semantics for modal first-order predicate object-languages, defines semantic assignments for variables and predicates, and truth for formulae in terms of the axiomatic version of Edmund Husserl’s dependence ontology (viz. the Calculus [CU] of Urelements) introduced (...) by The Ontology of Intentionality I & II. It then uses the §3 results to define the modalities of truth, and §5 extends the semantics to identity claims. §6 defines and contrasts synthetic a priori truths to analytic a priori truths, and §7 compares Brentano School noetic semantic and Leibnizian possible-world semantic perspectives on modality. The essay argues that the modal logics it defines semantically are two-valued, first-order versions of the type of language which Husserl viewed as the language of any ontology of experience (i.e. of any science), and conceived as the logic of intentionality. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first (...) order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

The writings of Nishida Kitar , whose name has become almost synonymous with Japanese philosophy, continue to attract attention around the world. Yet studies of his thought in Western languages have tended to overlook two key areas: first, the influence of the generation of Japanese philosophers who preceded Nishida; and second, the logic of basho (place), the cornerstone of Nishida's mature philosophical system. The Logic of Nothingness addresses both of these topics. Robert Wargo argues that the overriding concern (...) of Nishida's mature philosophy, the attempt to give a reasonable account of reality that includes the reasonableness of that account itself--or what Wargo calls the problem of completeness--has its origins in Inoue Enryo's (1858-1919) and Inoue Tetsujiro's (1855-1944) preoccupation with the problem of standpoints. A translation of one of Nishida's most demanding texts, included here as an appendix, demonstrates the value of Wargo's insightful analysis of the logic of basho as an aid to deciphering the philosopher's early work. (shrink)

Fine and Saad-Filho are wrong to insist that an abstract category of production should be the starting point of Marxist value-theory in logical, temporal and causal terms. Marx, in Capital, begins with a repertoire of simpler categories and slowly constructs the complex category of capitalist production. It is vital that exploitation should be seen as one phase of a process of capital-in-motion, and due weight given to money, competition and realisation.

The paper turns attention to some very general questions that concern the nature of logic – it deals with the problem of the identity of logic. It suggests that we can view the notion of value as one through which we can approach the elusive issues which surround the question of the nature of logic. The first part of the paper addresses the question of the value of logic as a discipline. In other words (...) – it aims at answering the question what is (or could/should be) the benefit of exercising logic. The second part focuses on the question of what role values play (or could/should play) ‘inside’ of logic. It suggests that the elusive and general term “value” can perhaps turn out quite useful in the project of delineation of the realm of logic. The conclusion can be formulated in the provocative slogan: logic can be seen as a kind of general formal theory of values. (shrink)

Belnap–Dunn’s relevance logic, \(\textsf{BD}\), was designed seeking a suitable logical device for dealing with multiple information sources which sometimes may provide inconsistent and/or incomplete pieces of information. \(\textsf{BD}\) is a four-valued logic which is both paraconsistent and paracomplete. On the other hand, De and Omori, while investigating what classical negation amounts to in a paracomplete and paraconsistent four-valued setting, proposed the expansion \(\textsf{BD2}\) of the four valued Belnap–Dunn logic by a classical negation. In this paper, we introduce (...) a four-valued expansion of BD called \({\textsf{BD}^\copyright }\), obtained by adding an unary connective \({\copyright }\,\ \) which is a consistency operator (in the sense of the Logics of Formal Inconsistency, _LFI_s). In addition, this operator is the unique one with the following features: it extends to \(\textsf{BD}\) the consistency operator of LFI1, a well-known three-valued _LFI_, still satisfying axiom _ciw_ (which states that any sentence is either consistent or contradictory), and allowing to define an undeterminedness operator (in the sense of Logic of Formal Undeterminedness, _LFU_s). Moreover, \({\textsf{BD}^\copyright }\) is maximal w.r.t. LFI1, and it is proved to be equivalent to BD2, up to signature. After presenting a natural Hilbert-style characterization of \({\textsf{BD}^\copyright }\) obtained by means of twist-structures semantics, we propose a first-order version of \({\textsf{BD}^\copyright }\) called \({\textsf{QBD}^\copyright }\), with semantics based on an appropriate notion of four-valued Tarskian-like structures called \(\textbf{4}\) -structures. We show that in \({\textsf{QBD}^\copyright }\), the existential and universal quantifiers are interdefinable in terms of the paracomplete and paraconsistent negation, and not by means of the classical negation. Finally, a Hilbert-style calculus for \({\textsf{QBD}^\copyright }\) is presented, proving the corresponding soundness and completeness theorems. (shrink)