Writing in the Business and Politics, Santos and Laczniak (Business and Politics 14(1) 2012) formulated a normative, ethical approach to be followed when marketers e ngage impoverished market segments. It is labeled the integrative justice model (IJM). As noted below, that approach called for authentic engagement, co-creation, and customer interest representation, among other elements, when transacting with vulnerable market segments. Basically, the IJM derived certain operational virtues, implied by moral philosophy, to be used when marketing to the poor. But (...) this well-intentioned approach raises a significant “So what?” question. Are such sentiments anything but lofty aspirations for idealists or are there steps to be taken by society and business managers of goodwill to make the adaptation of the IJM by corporations more likely and pragmatic? This paper begins to layout a roadmap that shows “how and why” the IJM might more likely be vitalized. The crux, as described below, is found in the transformational justice dimensions that are embedded in institutions (and supporting institutional arrangements); such external institutions provide a “power” impetus to assure the ethical rights claims that impoverished consumers have owed to them. In this way, the ideal exchange characteristics for bottom (or base) of the pyramid (BoP) markets argued for in the IJM can become actively transformational. The main contribution of this paper is that it begins to chart out the institutional system elements that need to exercise power in order to deliver a “fairer” marketplace for BoP consumers. (shrink)

The "justice of markets" is intricately connected to the treatment of the poor and the disadvantaged in market economies. The increased interest of multinational corporations in low-income market segments affords, on one hand, the opportunity for a more inclusive capitalism, and on the other, the threat of greater exploitation of poor and disadvantaged consumers. This article traces the contributions of Catholic Social Teaching and its basic principles toward providing insight into what constitutes "justice" in such "marketing to the impoverished" situations.

Recent work in judgment and decision-making has shown that a good’s price can have irrational effects on people’s preferences. People tend to prefer goods that cost more money and assume that such expensive goods will be more effective, even in cases where the price of the good is itself arbitrary. Although much work has documented the existence of these pricing effects, unfortunately little work has addressed where these price effects come from in the first place. Here we use a comparative (...) approach to distinguish between different accounts of this bias and to explore the origins of these effects. Specifically, we test whether brown capuchin monkeys (Cebus apella) are also susceptible to pricing effects within the context of an experimentally trained token economy. Using a capuchin population previously trained in a token market, we explored whether monkeys used price as an indicator of value across four experiments. Although monkeys demonstrated an understanding of which goods had which prices (consistently shifting preferences to cheaper goods when prices were increased), we observed no evidence that such price information affected their valuation of different kinds of goods. These results suggest that human price effects may involve more sophisticated human-unique cognitive capacities, such as an understanding of market forces and signaling. (shrink)

Writing in the Business and Politics, Santos and Laczniak 2012) formulated a normative, ethical approach to be followed when marketers e ngage impoverished market segments. It is labeled the integrative justice model. As noted below, that approach called for authentic engagement, co-creation, and customer interest representation, among other elements, when transacting with vulnerable market segments. Basically, the IJM derived certain operational virtues, implied by moral philosophy, to be used when marketing to the poor. But this well-intentioned approach raises a (...) significant “So what?” question. Are such sentiments anything but lofty aspirations for idealists or are there steps to be taken by society and business managers of goodwill to make the adaptation of the IJM by corporations more likely and pragmatic? This paper begins to layout a roadmap that shows “how and why” the IJM might more likely be vitalized. The crux, as described below, is found in the transformational justice dimensions that are embedded in institutions ; such external institutions provide a “power” impetus to assure the ethical rights claims that impoverished consumers have owed to them. In this way, the ideal exchange characteristics for bottom of the pyramid markets argued for in the IJM can become actively transformational. The main contribution of this paper is that it begins to chart out the institutional system elements that need to exercise power in order to deliver a “fairer” marketplace for BoP consumers. (shrink)

Global citizenship education (GCE) is an active entanglement in the civic priorities of the planet. In recent research, the concept has emerged as a multivalent coalescence of being, an engagement with planetary tensions and revisions of cosmopolitan ideology. In this article, I argue for a theoretical interpretation of GCE reliant on liminal-oriented practice and the potentialities of regenerative agency. Privileging Axel Honneth’s interpretation of social freedom and Boaventura de Sousa Santos’ post-abyssal thinking, I argue that interfaces with the limit (...) of our global perception reveal the regenerative qualities of our relations, allowing us to conceive ourselves as uniquely influenced by globality and possessing critical agency for otherness. Although such global perceptions can only ever be wrought within the ideological constraints of locality, a globally situated agency is more agile as a regenerative set of dispositions and inter-knowledge ‘globalities’. I further argue that regenerative liminalities hold significant implications for teaching and learning, as they signify the importance of a global consciousness over a technologically rationalized competency-based approach. (shrink)

In this article I argue that, in spite of the apparently unshakable hegemony of the historical, philosophical and sociological arguments invoked by the canonical history of Europe and the world to demonstrate the uniqueness of the West and its superiority, there is room to think of a non-Occidentalist West. By that I mean a vast array of conceptions, theories, arguments that, though produced in the West by recognized intellectual figures, were discarded, marginalized or ignored because they did not fit the (...) political objectives of capitalism and colonialism at the roots of Western modernity. In the article I tackle specifically three topics: the conceptions of antiquity, modern science and a teleology of the future. Among many others who might be selected, I resort to three eccentric figures — Lucian of Samosata, Nicholas of Cusa and Blaise Pascal — to exemplify some of the paths that might guide us in the construction of a non-capitalist, non-colonialist inter-cultural dialogue. Such paths are here designated as those of learned ignorance, ecology of knowledge, wager on another possible world and artisanship of practices. (shrink)

In this article I argue that, in spite of the apparently unshakable hegemony of the historical, philosophical and sociological arguments invoked by the canonical history of Europe and the world to demonstrate the uniqueness of the West and its superiority, there is room to think of a non-Occidentalist West. By that I mean a vast array of conceptions, theories, arguments that, though produced in the West by recognized intellectual figures, were discarded, marginalized or ignored because they did not fit the (...) political objectives of capitalism and colonialism at the roots of Western modernity. In the article I tackle specifically three topics: the conceptions of antiquity, modern science and a teleology of the future. Among many others who might be selected, I resort to three eccentric figures — Lucian of Samosata, Nicholas of Cusa and Blaise Pascal — to exemplify some of the paths that might guide us in the construction of a non-capitalist, non-colonialist inter-cultural dialogue. Such paths are here designated as those of learned ignorance, ecology of knowledge, wager on another possible world and artisanship of practices. (shrink)

Este artigo tem como objetico examinar a abordagem evolutiva do comportamento informacional e refletir acerca de algumas consequências trazidas por esta abordagem para as bases epistemológicas da biblioteconomia e ciência da informação (BCI) nos trabalhos de Amanda Spink e Armando Malheiro da Silva. Incorpora uma crítica de modelos de busca de conhecimento como o de Nicholas Belkin, por causa de seu resíduo tecnicista. Metodologia: Pesquisa bibliográfica e posterior análise das fontes recuperadas. Análise realizada através do exame argumentativo e conceitual (...) de textos considerados referenciais para cada parte do argumento. Resultados: Ressalta a distinção entre interpretações divergentes do termo “evolução”. Reconhece a exigência inevitável de uma atitude holística ou interdisciplinar para a compreensão do comportamento informacional. Destaca a valorização dos comportamentos humanos de caráter informal e lúdico em relação à informação. (shrink)

Ethical naturalism holds that ethical facts about such matters as good and bad, right and wrong, are part of a purely natural world — the world studied by the sciences. It is supported by the apparent reasonableness of many moral explanations. It has been thought to face an epistemological challenge because of the existence of an “is-ought gap”; it also faces metaphysical objections from philosophers who hold that ethical facts would have to be supernatural or “nonnatural,” sometimes on the grounds (...) that ethical thought has a practical role that no thought about purely natural facts could have. Its defenders have argued resourcefully against these challenges. (shrink)

In mainstream analytic epistemology, Reformed theology has made its presence prominently felt in Reformed epistemology, the view of religious belief according to which religious beliefs can be properly basic and warranted when formed by the proper functioning of the sensus divinitatis, an inborn capacity or faculty for belief in God that can be prompted to generate certain religious beliefs when presented with things (e.g., certain majestic aspects of creation). A major competitor to Reformed epistemology is Wittgensteinian quasi-fideism, a position drawn (...) from the epistemology of Wittgenstein’s On Certainty, according to which some foundational religious commitments are not properly basic beliefs but some kind of apodictic, unshakeable certainties that form part of the structure of one’s rationality and worldview. I argue that the Reformed tradition has contained elements of quasi-fideism at least as far back as Calvin’s account of faith from the Institutes of the Christian Religion, book 3, chapter 2. (shrink)

Can findings from psychology and cognitive neuroscience about the neural mechanisms involved in decision-making can tell us anything useful about the commonly-understood mental phenomenon of making voluntary choices? Two philosophical objections are considered. First, that the neural data is subpersonal, and so cannot enter into illuminating explanations of personal level phenomena like voluntary action. Secondly, that mental properties are multiply realized in the brain in such a way as to make them insusceptible to neuroscientific study. The paper argues that both (...) objections would be weakened by the discovery of empirical generalisations connecting subpersonal properties with the personal level. It gives three case studies that furnish evidence to that effect. It argues that the existence of such interrelations are consistent with a plausible construal of the personal-subpersonal distinction. Furthermore, there is no reason to suppose that the notion subpersonal representation relied on in cognitive neuroscience illicitly imports personal-level phenomena like consciousness or normativity, or is otherwise explanatorily problematic. (shrink)

A clearly written, authoritative introduction to Taylor's work.

Authors De Marco and colleagues have presented a new model on the concept of invasiveness, redefining both its technical definition and practical implementation.1 While the authors raise valid critiques regarding the discrepancy in definitions, I cannot help but wonder about the purpose of redefining terms for which little confusion, if any, exists? This commentary seeks to scrutinise the rationale supporting the new model in the absence of significant clinical confusion and to explore the implications for clinical practice. Initially, one may (...) notice there is no mention of clinical relevancy, confusion among patients or whether the discrepancy in terms is causing miscommunication. It seems reasonable that some clinical confusion may exist, but so too does a similar imbalance of terms when speaking technically across the specialties; take depression and its definition as a primary example. While I certainly agree with the illustration of non-invasive prenatal testing being compared with venous blood draws as a disparity in terminology, little evidence suggests confusion concerning the nosology.2 The medical community, including both physicians and patients, recognises that the terminology is specifically used within the …. (shrink)

According to the ‘One Object’ reading of Kant's transcendental idealism, the distinction between the appearance and the thing in itself is not a distinction between two objects, but between two ways of considering one and the same object. On the ‘Metaphysical’ version of the One Object reading, it is a distinction between two kinds of properties possessed by one and the same object. Consequently, the Metaphysical One Object view holds that a given appearance, an empirical object, is numerically identical to (...) the thing in itself that appears as that object. I raise various indiscernibility arguments against that view; because an appearance has different spatiotemporal and modal properties than a thing in itself, no appearance can be identical to a thing in itself. I point out that these arguments are similar to arguments against Monism, the view that material objects are numerically identical to the matter of which they are made. I outline some strategies Monists have developed to respond to these indiscernibility arguments and then develop parallel responses on behalf of the Metaphysical One Object view. However, I then raise another indiscernibility argument, to which, I argue, the Metaphysical One Object view cannot respond, even using the resources I have developed thus far. I develop a modified version of the Metaphysical One Object view that can respond to this new indiscernibility argument, but, I argue, this modified version of the One Object view is only a terminological variant of the Two Object view. When the Metaphysical One Object view is fully thought through it becomes the Two Object view. I conclude that Kantian appearances are not numerically identical to the things in themselves that appear to us. (shrink)

The question of whether it is permissible to quantify into a modal context is re-examined from an empiricist perspective. Following Wiggins, it is argued that an ontology of continuants implies essentialism, but it is also argued, against Wiggins, that the only conception of necessity that we need to start out with is that of analyticity. Essentialism, of a limited kind, can then be actually generated from this. An exceptionally fine-grained identity criterion for continuants is defended in this context. The debate (...) between Wiggins and Ayer over the legitimacy of de re modality is then examined in the light of these results, and it is argued that my position is consistent with Ayer’s minimalist assumptions. It is also argued that non-continuants will not sustain the essential/accidental distinction, thus giving some concessions to the sceptics. It is also shown that there are close connections between these issues and the more modern two-dimensionalist way of disentangling the necessary from the a posteriori, and that the latter needs to learn from the former. (shrink)

Draws on a broad range of scientific evidence to theorize an evolutionary basis for religion, considering how religion may have served as an essential component of early society survival and that the brain may be inherently inclined toward religious behavior.

: In the epistemology of the late Wittgenstein, a central place is given to the notion of the hinge: an arational commitment that provides a foundation of some sort for the rest of our beliefs. Quasi-fideism is an approach to the epistemology of religion that argues that religious belief is on an epistemic par with other sorts of belief inasmuch as religious and non-religious beliefs all rely on hinges. I consider in this paper what it takes to find the appropriate (...) hinge for a quasi-fideist approach to the epistemology of religion. (shrink)

I take pseudoscience to be a pretence at science. Pretences are innumerable, limited only by our imagination and credulity. As Stove points out, ‘numerology is actually quite as different from astrology as astrology is from astronomy’ (Stove 1991, 187). We are sure that ‘something has gone appallingly wrong’ (Stove 1991, 180) and yet ‘thoughts…can go wrong in a multiplicity of ways, none of which anyone yet understands’ (Stove 1991, 190). Often all we can do is give a careful description of (...) a way of pretending, a motivation for pretence, a source of pretension. In this chapter I attempt the latter. We will be concerned with the relation of conviction to rational belief. I shall be suggesting that the question of whether an enquiry is a pretence at science can be, in part, a question over the role of conviction in rational belief, and that the answer is to be found in the philosophical problem of the role of values in rational belief. (shrink)

We discuss the rational role of highly inattentive experiences, and argue that they can provide rational support for beliefs.

In this paper, I critically analyze the notion that self-interest distorts moral belief-formation. This belief is widely shared among modern moral epistemologists, and in this paper, I seek to undermine this near consensus. I then offer a principle which can help us to sort cases in which self-interest distorts moral belief from cases in which it does not. As it turns out, we cannot determine whether such distortion has occurred from the armchair; rather, we must inquire into mechanisms of social (...) power and advantage before declaring that some moral position is distorted by self-interest. (shrink)

David Benatar has argued both for anti-natalism and for a certain pessimism about life's meaning. In this paper, I propose that these positions are expressions of a deeply impersonal philosophical temperament. This is not a problem on its own; we all have our philosophical instincts. The problem is that this particular temperament, I argue, leads Benatar astray, since it prevents him from answering a question that any moral philosopher must answer. This is the question of rational authority, which requires the (...) moral philosopher to say why existing human agents have strong practical reasons to comply with the philosopher's dictates. A purely impersonal ethical system can never do this, and this is why Benatar has no answer to this question. (shrink)

Block’s well-known distinction between phenomenal consciousness and access consciousness has generated a large philosophical literature about putative conceptual connections between the two. The scientific literature about whether they come apart in any actual cases is rather smaller. Empirical evidence gathered to date has not settled the issue. Some put this down to a fundamental methodological obstacle to the empirical study of the relation between phenomenal consciousness and access consciousness. Block (2007) has drawn attention to the methodological puzzle and attempted to (...) answer it. While the evidence Block points to is relevant and important, this paper puts forward a more systematic framework for addressing the puzzle. To give it a label, the approach is to study phenomenal consciousness as a natural kind. The approach allows consciousness studies to move beyond the initial means of identifying instances of the kind, like verbal report, and to find its underlying nature. It is wellrecognised that facts about an underlying kind may allow identification of instances of the kind that do not match the initial means of identification (cp. non-liquid samples of water). This paper shows that the same method can be deployed to investigate phenomenal consciousness independently of access consciousness. (shrink)

If a speaker selflessly asserts that p, the speaker has good evidence that p is true, asserts that p on the basis of that evidence, but does not believe that p. Selfless assertions are widely thought to be acceptable, and therefore to pose a threat to the Knowledge Norm of Assertion. Advocates for the Knowledge Norm tend to respond to this threat by arguing that there are no such things as selfless assertions. They argue that those who appear to be (...) selfless asserters either: believe what they assert, perform a speech act other than assertion, or assert a proposition other than the one that they seem to. I argue that such counterarguments are unsuccessful. There really are selfless assertions. But I also argue that they are no threat to the Knowledge Norm. There is a good case to be made that knowledge does not require belief. And if it does not, then the fact that some selfless assertions are appropriate does not tell against the Knowledge Norm. Indeed, I argue that selfless asserters know the propositions that they assert to be true. (shrink)

In Republican Guard , Nicholas Xenos describes the Straussian network and its nature, focusing upon delineating what in Leo Strauss’ writings has influenced and can tell us about the ‘character of American power today and the rhetoric through which it is enhanced and sustained.’ In the end he argues and demonstrates that Strauss’ political theory provides the means by which an imperial project can be camouflaged under the cloak of an appeal to liberal democracy. This book will be of (...) interest to students and scholars of politics and international relations. (shrink)

Plato recognizes faction as a serious threat to any political community. The Republic’s proposed solution to faction relies on bringing citizens into a relation of ὁμόνοια. On the dominant line of interpretation, ὁμόνοια is understood along the lines of “explicit agreement” or “consensus.” Commentators have consequently thought that the καλλίπολις becomes resistant to faction when all or most of its members explicitly agree with one another about certain fundamentals of their political association—for example, they agree regarding who should govern in (...) the καλλίπολις.We argue that ὁμόνοια in Plato’s political philosophy has been under-analyzed and misunderstood. We show that, in Alcibiades I, rendering ὁμόνοια simply as agreement results in confusion about how expertise, political friendship, and civic unity are compossible in a well-ordered political community. In our view, Plato refines and adds philosophical depth to the concept of ὁμόνοια in the Republic. We claim that ὁμόνοια is a relation of psychological “like-mindedness” that obtains among members of different occupational classes in a political community. A community is rendered resistant to faction, then, when its members are, in some significant way, psychologically alike. Additionally, while Platonic ὁμόνοια can naturally be expected to result in substantive agreement among citizens, we argue that Platonic ὁμόνοια does not consist solely in agreement. (shrink)

This paper examines the justice of unconditional basic income (UBI) through the lens of the Hegel-inspired recognition-theory of justice. As explained in the first part of the paper, this theory takes everyday social roles to be the primary subject-matter of the theory of justice, and it takes justice in these roles to be a matter of the kind of freedom that is available through their performance, namely ‘social’ freedom. The paper then identifies the key criteria of social freedom. The extent (...) to which the introduction of an UBI would meet these criteria is then examined, with a focus on the social role that stands to be most affected by an UBI, namely that of the worker-earner. It is argued that while an UBI is likely to be only partially effective as an instrument of specifically social freedom, its main justification lies not here, but in securing a basis for the subjective freedom that social freedom presupposes. (shrink)

How can we think about things in the outside world? There is still no widely accepted theory of how mental representations get their meaning. In light of pioneering research, Nicholas Shea develops a naturalistic account of the nature of mental representation with a firm focus on the subpersonal representations that pervade the cognitive sciences.

I suggest that the post-Hegelian tradition presents us with three contrasting normative models of work. According to the first model, the core norms of work are those of means-ends rationality. In this model, the modern world of work is constitutively a matter of deploying the most effective means to bring about given ends. The rational kernel of modern work, the core norm that has shaped its development, is on this view instrumental reason, and this very same normative core, in the (...) shape of advanced technology and more efficient, time-saving production, can help to liberate it. The second model, by contrast, takes the core norms of work to be internal to working activity. Rather than work gaining its normativity from something external to it, from ends to which the work is a contingent means, on this second view the core norms of work are expressions of values or meanings that are immanent to working practices themselves. The expressive model of work regards the actual world of work to be constituted historically by work-specific norms, norms which working subjects themselves have invoked and mobilised around in the course of their struggles for emancipation. According to the third model, the core norms of work have to do neither with instrumental rationality nor authentic self-expression. Rather they concern norms that relate either to individual achievement or contribution through work (in the form of esteem) or to the conditions that must in place for individuals to participate in the exchange of services by which market societies reproduce themselves (in the form of mutual respect). (shrink)

While acknowledging the importance of sophisticated reformulations of some of the traditional arguments for “natural and revealed” religion, the bulk of this chapter expounds and then compares and contrasts the other two main developments over the past half century in the epistemology of religious belief: Wittgensteinian philosophy of religion, and Reformed epistemology. What unites these two movements is that both insist that religious belief does not typically have its origin in the attempt to explain things, both insist that religious belief (...) typically consists of a more or less comprehensive perspective on reality rather than consisting of beliefs about God simply added on to one’s other beliefs, and both insist that religious belief does not have to be rationally grounded in order to be acceptable. What especially differentiates the two movements is the difference of their polemical partners—Enlightenment evidentialism for the Reformed epistemologists versus logical positivism for Wittgenstein—and the fact that the Reformed epistemologists are resolutely realist concerning God whereas most of the Wittgensteinians are apparently not theistic realists. In closing, I point out important similarities between some remarks of early Heidegger and the shared positions of the Wittgensteinians and the Reformed epistemologists. (shrink)

I begin by picking up on Brandom’s suggestion that expressivism follows American pragmatism in seeking to advance the cause of the Enlightenment. This provides us with a first point of contrast with Taylor’s understanding of expressivism, since Taylor takes expressivism to be inseparably bound up with the Romantic critique of the Enlightenment and as fundamentally opposed to Enlightenment naturalism. I then distinguish two features of what we ordinarily mean by the term ‘expression’, one of which provides an intuitive basis for (...) understanding Brandom’s expressivist program, the other of which provides an interpretive key for understanding Taylor’s version of expressivism. After looking briefly at the main tenets of Taylor’s expressivism, I conclude by considering its relation to Romanticism on the one hand, and to Brandom’s expressivist renewal of the Enlightenment project on the other. (shrink)

This book explores the core categories of communism and capital in conjunction with a wealth of contemporary and historical political concepts and movements - from the lumpenproletariat and anarchism, to Italian autonomia and Antonia Negri, immaterial labour and the refusal of work. Drawing on literary figures such as Kafka and Beckett, Deleuze, Marx and Politics develops a politics that breaks with the dominant frameworks of post-Marxism and one-dimensional models of resistance toward a concern with the inventions, styles and knowledges that (...) emerge through minority engagement with social flows and networks. (shrink)

The other chapters in this volume discuss the important, but neglected, topic of systematicity in metaphysics. In this chapter I begin by taking a step back and asking: why is systematicity important in metaphysics? Assuming that metaphysics should be systematic, why is this the case? I canvas some answers that emerge naturally within contemporary philosophy and argue that none of them adequately explains why metaphysics should be systematic. I then turn to Kant’s account of systematicity for his explanation. I argue (...) that, while Kant’s explanation of the systematicity of metaphysics rests on a host of additional weighty philosophical commitments that many philosophers would rather do without (e.g., transcendental idealism), he is not alone in this. The contemporary answers I earlier found wanting can be transformed into satisfying explanations, I argue, but only at the cost of philosophical commitments at least as weighty as Kant’s. I conclude on a note of agnosticism: it is far from clear whether contemporary philosophy has done, or can do, better than Kant at explaining the role of systematicity in metaphysics. (shrink)

How should an acknowledgement of contingency affect our understanding of moral identity? The book considers various ways of thinking about this question in contemporary moral and political theory. Drawing on the work of Gadamer, Ricoeur, Taylor and others, it defends a realist but pluralist 'strong hermeneutic' view.

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

This paper raises puzzles concerning our grasp of others’ aesthetic selves. I first articulate a conception of an aesthetic self, understood as an autonomously adopted orientation to objects of aesthetic value, encompassing the embrace of aesthetic reasons and the qualitative appreciative states that follow. This articulation is motivated by the commonplace observation that people’s aesthetic identities are important to them. Given this importance, we might think it salutary to grasp other people’s aesthetic selves, under the general auspices of ‘interpersonal understanding’. (...) Given the conception of aesthetic selves, we might think that empathy is an appropriate way to do so. But, second, I argue that you can’t find out about another’s aesthetic self via empathy. We might instead think that aesthetic conversation is the way to grasp aesthetic selves. However, third, I argue that the aim of finding out about others’ aesthetic selves is at odds with the ostensible aims of aesthetic conversation, which are to do with effacing individuality and creating commonality. So aesthetic selves seem hard to grasp. I finally briefly canvass some ways of solving this problem, without settling on a firm answer, and consider how the thoughts might extend to practical identities more generally. (shrink)

A many-valued (aka multiple- or multi-valued) semantics, in the strict sense, is one which employs more than two truth values; in the loose sense it is one which countenances more than two truth statuses. So if, for example, we say that there are only two truth values—True and False—but allow that as well as possessing the value True and possessing the value False, propositions may also have a third truth status—possessing neither truth value—then we have a many-valued semantics in the (...) loose but not the strict sense. A many-valued logic is one which arises from a many-valued semantics and does not also arise from any two-valued semantics [Malinowski, 1993, 30]. By a ‘logic’ here we mean either a set of tautologies, or a consequence relation. We can best explain these ideas by considering the case of classical propositional logic. The language contains the usual basic symbols (propositional constants p, q, r, . . .; connectives ¬, ∧, ∨, →, ↔; and parentheses) and well-formed formulas are defined in the standard way. With the language thus specified—as a set of well-formed formulas—its semantics is then given in three parts. (i) A model of a logical language consists in a free assignment of semantic values to basic items of the non-logical vocabulary. Here the basic items of the non-logical vocabulary are the propositional constants. The appropriate kind of semantic value for a proposition is a truth value, and so a model of the language consists in a free assignment of truth values to basic propositions. Two truth values are countenanced: 1 (representing truth) and 0 (representing falsity). (ii) Rules are presented which determine a truth value for every proposition of the language, given a model. The most common way of presenting these rules is via truth tables (Figure 1). Another way of stating such rules—which will be useful below—is first to introduce functions on the truth values themselves: a unary function ¬ and four binary functions ∧, ∨, → and ↔ (Figure 2).. (shrink)