One of the promising approaches to the problem of consciousness has been the Higher-Order Monitoring Theory of Consciousness. According to the Higher-Order Monitoring Theory, a mental state M of a subject S is conscious iff S has another mental state, M*, such that M* is an appropriate representation of M. Recently, several philosophers have developed a Higher-Order Monitoring theory with a twist. The twist is that M and M* are construed as entertaining some kind (...) of constitutive relation, rather than being logically independent of each other. We may call this the Same-Order Monitoring Theory of Consciousness. In this paper, I discuss the nature of the Same-Order Monitoring Theory and argue for its superiority over the more traditional Higher-Order Monitoring Theory. (shrink)

Monitoring approaches to consciousness claim that a mental state is conscious when it is suitably monitored. Higher-order monitoring theory makes the monitoring state and the monitored state logically independent. Same-order monitoring theory claims a constitutive, non-contingent connection between the monitoring state and the monitored state. In this paper, I articulate different versions of the same-order monitoring theory and argue for its supremacy over the higher-order monitoring theory.

The same-order representation theory of consciousness holds that conscious mental states represent both the world and themselves. This complex representational structure is posited in part to avoid a powerful objection to the more traditional higher-order representation theory of consciousness. The objection contends that the higher-order theory fails to account for the intimate relationship that holds between conscious states and our awareness of them--the theory 'divides the phenomenal labor' in an illicit fashion. This (...) 'failure of intimacy' is exposed by the possibility of misrepresentation by higher-order states. In this paper, I argue that despite appearances, the same-order theory fails to avoid the objection, and thus also has troubles with intimacy. (shrink)

In this paper we study the idea of theories with containers, like sets, pairs, sequences. We provide a modest framework to study such theories. We prove two concrete results. First, we show that first-order theories of finite signature that have functional non-surjective ordered pairing are definitionally equivalent to extensions in the same language of the basic theory of non-surjective ordered pairing. Second, we show that a first-order theory of finite signature is sequential (is a (...) class='Hi'>theory of sequences) iff it is definitionally equivalent to an extension in the same language of a system of weak set theory called WS. (shrink)

We try to answer the question which is the “right” foundation of mathematics, second order logic or set theory. Since the former is usually thought of as a formal language and the latter as a first order theory, we have to rephrase the question. We formulate what we call the second order view and a competing set theory view, and then discuss the merits of both views. On the surface these two views seem to (...) be in manifest conflict with each other. However, our conclusion is that it is very difficult to see any real difference between the two. We analyze a phenomenon we call internal categoricity which extends the familiar categoricity results of second order logic to Henkin models and show that set theory enjoys the same kind of internal categoricity. Thus the existence of non-standard models, which is usually taken as a property of first order set theory, and categoricity, which is usually taken as a property of second order axiomatizations, can coherently coexist when put into their proper context. We also take a fresh look at complete second order axiomatizations and give a hierarchy result for second order characterizable structures. Finally we consider the problem of existence in mathematics from both points of view and find that second order logic depends on what we call large domain assumptions, which come quite close to the meaning of the axioms of set theory. (shrink)

We present well-ordering proofs for Martin-Löf's type theory with W-type and one universe. These proofs, together with an embedding of the type theory in a set theoretical system as carried out in Setzer show that the proof theoretical strength of the type theory is precisely ψΩ1Ω1 + ω, which is slightly more than the strength of Feferman's theory T0, classical set theory KPI and the subsystem of analysis + . The strength of intensional and extensional (...) version, of the version à la Tarski and à la Russell are shown to be the same. (shrink)

Goffman is credited with enriching our understanding of the details of interaction, but not with challenging our theoretical understanding of social organization. While Goffman's position is not consistent, the outlines for a theory of an interaction order sui generis may be found in his work. It is not theoretically adequate to understand Goffman as an interactionist within the dichotomy between agency and social structure. Goffman offers a way of resolving this dichotomy via the idea of an interaction (...) class='Hi'>order which is constitutive of self and at the same time places demands on social structure. This has significant implications for our understanding of social organization in general. (shrink)

Aristotle attaches particular significance to the homonymy of many central concepts in philosophy and science: that is, to the diversity of ways of being common to a single general concept. His preoccupation with homonymy influences his approach to almost every subject that he considers, and it clearly structures the philosophical methodology that he employs both when criticizing others and when advancing his own positive theories. Where there is homonymy there is multiplicity: Aristotle aims to find the order within this (...) multiplicity, and believes that doing so is crucial to scientific inquiry and philosophical progress.Christopher Shields investigates and evaluates Aristotle's approach to questions about homonymy, characterizing the metaphysical and semantic commitments necessary to establish the homonymy of a given concept. Then, in a series of case-studies, Shields examines in detail some of Aristotle's principal applications of homonymy--to the body, sameness and oneness, life, goodness, and being. Shields's aim is not only to give a fuller understanding of Aristotle's methodology and to illuminate his specific doctrines in a variety of areas, but to show that this methodology remains fruitful today. (shrink)

We explore and provide an account for a recently identified judgment anomaly, i.e., an order effect that changes the strength of intentionality ascriptions for some side effects (e.g., when a chairman's pursuit of profits has the foreseen but unintended consequence of harming the environment). Experiment 1 replicated the previously unanticipated order effect anomaly controlling for general individual differences. Experiment 2 revealed that the order effect was multiply determined and influenced by factors such as beliefs (i.e., that the (...) same actor was involved in bringing about both good and bad side effects) and philosophical training (i.e., more training was associated with smaller differences in judgment when harm followed help). Results provide more evidence that the folk's philosophically relevant intuitions are predictably fragmented and depend on the dynamic interplay between persons, process, and environments. Methodological and theoretical implications are discussed. (shrink)

Several philosophers of science construe models of scientific theories as set-theoretic structures. Some of them moreover claim that models should not be construed as structures in the sense of model theory because the latter are language-dependent. I argue that if we are ready to construe models as set-theoretic structures (strict semantic view), we could equally well construe them as model-theoretic structures of higher-order logic (liberal semantic view). I show that every family of set-theoretic structures has an associated language (...) of higher-order logic and an up to signature isomorphism unique model-theoretic counterpart, which is able to serve the same purposes. This allows to carry over every syntactic criterion of equivalence for theories in the sense of the liberal semantic view to theories in the sense of the strict semantic view. Taken together, these results suggest that the recent dispute about the semantic view and its relation to the syntactic view can be resolved. (shrink)

We generalize the Unstable Formula Theorem characterization of stable theories from Shelah [11], that a theory T is stable just in case any infinite indiscernible sequence in a model of T is an indiscernible set. We use a generalized form of indiscernibles from [11], in our notation, a sequence of parameters from an L-structure M, , indexed by an L′-structure I is L′-generalized indiscernible inM if qftpL′=qftpL′ implies tpL=tpL for all same-length, finite ¯,j from I. Let Tg be (...) the theory of linearly ordered graphs in the language with signature Lg={<,R}. Let Kg be the class of all finite models of Tg. We show that a theory T has NIP if and only if any Lg-generalized indiscernible in a model of T indexed by an Lg-structure with age equal to Kg is an indiscernible sequence. (shrink)

In this article I investigate the phenomenon of minimum and minimal models of second-order set theories, focusing on Kelley–Morse set theory KM, Gödel–Bernays set theory GB, and GB augmented with the principle of Elementary Transfinite Recursion. The main results are the following. (1) A countable model of ZFC has a minimum GBC-realization if and only if it admits a parametrically definable global well order. (2) Countable models of GBC admit minimal extensions with the same sets. (...) (3) There is no minimum transitive model of KM. (4) There is a minimum β-model of GB+ETR. The main question left unanswered by this article is whether there is a minimum transitive model of GB+ETR. (shrink)

A theory T is tight if different deductively closed extensions of T (in the same language) cannot be bi-interpretable. Many well-studied foundational theories are tight, including $\mathsf {PA}$ [39], $\mathsf {ZF}$, $\mathsf {Z}_2$, and $\mathsf {KM}$ [6]. In this article we extend Enayat’s investigations to subsystems of these latter two theories. We prove that restricting the Comprehension schema of $\mathsf {Z}_2$ and $\mathsf {KM}$ gives non-tight theories. Specifically, we show that $\mathsf {GB}$ and $\mathsf {ACA}_0$ each admit different (...) bi-interpretable extensions, and the same holds for their extensions by adding $\Sigma ^1_k$ -Comprehension, for $k \ge 1$. These results provide evidence that tightness characterizes $\mathsf {Z}_2$ and $\mathsf {KM}$ in a minimal way. (shrink)

Ian Mason [25] has shown that the meta-theory of propositional calculus is not axiomatizable. That is not to say that its meta-theory cannot be studied. There may be a sequence of theories, indexed by the ordinals, which encompass the entire meta-theory. The same goes for other forms of logic too. Herein is proposed one candidate for such a sequence, for a wide range of logics.

William Lycan has articulated “a simple argument” for higher-order representation (HOR) theories of a variety of consciousness sometimes labeled ‘awareness consciousness’ (Lycan, Analysis 61.1, January 3–4, 2001). The purpose of this article is to critically assess the influential argument-strategy of the simple argument. I argue that, as stated, the simple argument fails since it is invalid. Moreover, I argue that an obvious “quick fix” would beg the question against competing same-order representation (SOR) theories of awareness consciousness. I (...) then provide a reconstruction of the argument and argue that although the reconstructed argument deserves consideration, it is also too simple as stated. In particular, it raises several controversial questions about the nature of mental representation. These questions must be addressed before a verdict as to the cogency of the HOR argument-strategy can be reached. But since the questions are controversial, a cogent argument for HOR theories of awareness consciousness is unlikely to be simple. (shrink)

Nonnaturalist realism is the view that normative properties are unique kind of stance-independent properties. It has been argued that such views fail to explain why two actions that are exactly alike otherwise must also have the same normative properties. Mark Schroeder and Knut Olav Skarsaune have recently suggested that nonnaturalist realists can respond to this supervenience challenge by taking the primary bearers of normative properties to be action kinds. This paper develops their response in two ways. First, it provides (...) additional motivation for the previous claim about the bearers of normative properties by drawing from the work of H. A. Prichard. Second, and more importantly, it formulates a plausible metaphysical framework based on the contemporary trope theory to explain why action kinds would have their second-order properties, including their normative properties, necessarily. (shrink)

I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only (...) the cardinalities of these sets matters, and that not all pairs of infinite sets determine the same logic. I use so-called two-cardinal theorems from model theory to investigate the space of logics and consequence relations determined by pairs of infinite sets, and show how to eliminate the assumption that worlds are individuals from Williamson’s argument. (shrink)

The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω-inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. (...) Secondly, I show that in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω- inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth. (shrink)

A first order theory T of power λ is called unidimensional if any twoλ+-saturated models of T of the same cardinality are isomorphic. We prove here that such theories are superstable, solving a problem of Shelah. The proof involves an existence theorem and a definability theorem for definable groups in stable theories, and an analysis of their relation to regular types.

The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The invariance to the axiom of (...) choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying their unification. Its deformation is representable correspondingly as gravitation in the deformed pseudo-Riemannian space of general relativity and the entanglement of two or more quantum systems. The standard model studies a single quantum system and thus privileges a single reference frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the standard model. As the standard model refers to a single quantum system, it is necessarily linear and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the initial position of a privileged reference frame as the corresponding breaking of the symmetry. The standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the “Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the “Big Bang” with the observed nonlinearity of the further expansion of the universe described very well by general relativity. Quantum information links the standard model and general relativity in another way by mediation of entanglement. The linearity and absoluteness of the former and the nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same whole divided into parts entangled in general. (shrink)

One popular approach to theorizing about phenomenal consciousness has been to connect it to representations of a certain kind. Representational theories of consciousness can be further sub-divided into first-order and higher-order theories. Higher-order theories are often interpreted as invoking a special relation between the first-order state and the higher-order state. However there is another way to interpret higher-order theories that rejects this relational requirement. On this alternative view phenomenal consciousness consists in having suitable higher- (...) class='Hi'>order representations. I call this ‘HOROR’ (‘Higher-Order Representation Of a Representation’) theory to distinguish it from relational versions of higher- order theory. In this paper I make the case that HOROR theory is a plausible account of the real nature of phenomenal consciousness whatever one’s views are about whether it is physical/reducible or not. I first clarify HOROR theory and compare it to the more traditional same-order and higher-order thought theories. Afterwards I move to presenting some considerations in favor of HOROR theory. (shrink)

T.H. Green argues that rights cannot exist, save for in a society in which people recognise each other as “ ἴσοι καὶ ὅμοιοι.” Green leaves the phrase untranslated, and there is a certain ambiguity about what exactly Green meant and a lack of attention to this stipulation in the secondary literature. This essay argues that equality and sameness in Green must be understood as two categorically different criteria, both of which must be satisfied in order to make rights recognition (...) possible. Further, this essay examines a tension this distinction between equality and sameness reveals in Green’s work: Green’s commitment to patriotism in his Lectures on the Principles of Political Obligation may seem at first to be at odds with his more cosmopolitan tendencies in the Prolegomena to Ethics. However, a way of resolving this tension is suggested: re-conceiving what patriotism and “sameness” means by reading Green’s work as less dependent on the concept of “nation” than that of subsequent British idealists such as Bernard Bosanquet demonstrates that sameness and equality, though different, complement each other. (shrink)

Fiona Nicoll and Melissa Gregg met on the job at a new university having both moved from Sydney to Brisbane to take up their appointments. Here they share reflections on teaching a cultural theory course that they inherited from a prominent Australian Professor of Cultural Studies, offering the perspectives of two consecutive generations of cultural studies theorists now teaching in the field since the early 1990s. This situation gives rise to new interpretations regarding the value and uses of (...) class='Hi'>theory in the classroom. Noting the subtle differences involved in teaching the same theoretical material in different cities, the ironies of teaching radical cultural theory in a conservative institutional environment, and the specific opportunities and challenges of teaching cultural studies theory as opposed to others, the article considers some of the silences teachers must also contend with in their classroom practice, drawing on and expanding the terrain established by Thorkelson's thesis. (shrink)

We show that a coherent theory of partially ordered connectives can be developed along the same line as partially ordered quantification. We estimate the expressive power of various partially ordered connectives and use methods like Ehrenfeucht games and infinitary logic to get various undefinability results.

Ignacio Jane has argued that second-order logic presupposes some amount of set theory and hence cannot legitimately be used in axiomatizing set theory. I focus here on his claim that the second-order formulation of the Axiom of Separation presupposes the character of the power set operation, thereby preventing a thorough study of the power set of infinite sets, a central part of set theory. In reply I argue that substantive issues often cannot be separated from (...) a logic, but rather must be presupposed. I call this the logic-metalogic link. There are two facets to the logic-metalogic link. First, when a logic is entangled with a substantive issue, the same position on that issue should be taken at the meta- level as at the object level; and second, if an expression has a clear meaning in natural language, then the corresponding concept can equally well be deployed in a formal language. The determinate nature of the power set operation is one such substantive issue in set theory. Whether there is a determinate power set of an infinite set can only be presupposed in set theory, not proved, so the use of second-order logic cannot be ruled out by virtue of presupposing one answer to this question. Moreover, the legitimacy of presupposing in the background logic that the power set of an infinite set is determinate is guaranteed by the clarity and definiteness of the notions of all and of subset. This is also exactly what is required for the same presupposition to be legitimately made in an axiomatic set theory, so the use of second-order logic in set theory rather than first-order logic does not require any new metatheoretic commitments. (shrink)

Question order effects are commonly observed in self-report measures of judgment and attitude. This article develops a quantum question order model (the QQ model) to account for four types of question order effects observed in literature. First, the postulates of the QQ model are presented. Second, an a priori, parameter-free, and precise prediction, called the QQ equality, is derived from these mathematical principles, and six empirical data sets are used to test the prediction. Third, a new index (...) is derived from the model to measure similarity between questions. Fourth, we show that in contrast to the QQ model, Bayesian and Markov models do not generally satisfy the QQ equality and thus cannot account for the reported empirical data that support this equality. Finally, we describe the conditions under which order effects are predicted to occur, and we review a broader range of findings that are encompassed by these very same quantum principles. We conclude that quantum probability theory, initially invented to explain order effects on measurements in physics, appears to be a powerful natural explanation for order effects of self-report measures in social and behavioral sciences, too. (shrink)

We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the structure comprised of the light ceers. We also show the same for the structure of L-degrees in the dark, light, or complete structure. In each case, we show that there is an interpretable copy of (N, +, \times) .

As they are conventionally formulated, Boolean games assume that players make their choices in ignorance of the choices being made by other players – they are games of simultaneous moves. For many settings, this is clearly unrealistic. In this paper, we show how Boolean games can be enriched by dependency graphs which explicitly represent the informational dependencies between variables in a game. More precisely, dependency graphs play two roles. First, when we say that variable x depends on variable y, then (...) we mean that when a strategy assigns a value to variable x, it can be informed by the value that has been assigned to y. Second, and as a consequence of the first property, they capture a richer and more plausible model of concurrency than the simultaneous-action model implicit in conventional Boolean games. Dependency graphs implicitly define a partial ordering of the run-time events in a game: if x is dependent on y, then the assignment of a value to y must precede the assignment of a value to x; if x and y are independent, however, then we can say nothing about the ordering of assignments to these variables—the assignments may occur concurrently. We refer to Boolean games with dependency graphs as partial-order Boolean games. After motivating and presenting the partial-order Boolean games model, we explore its properties. We show that while some problems associated with our new games have the same complexity as in conventional Boolean games, for others the complexity blows up dramatically. We also show that the concurrency in partial-order Boolean games can be modelled using a closure-operator semantics, and conclude by considering the relationship of our model to Independence-Friendly logic. (shrink)

Second-order abstract categorial grammars (de Groote in Association for computational linguistics, 39th annual meeting and 10th conference of the European chapter, proceedings of the conference, pp. 148–155, 2001) and hyperedge replacement grammars (Bauderon and Courcelle in Math Syst Theory 20:83–127, 1987; Habel and Kreowski in STACS 87: 4th Annual symposium on theoretical aspects of computer science. Lecture notes in computer science, vol 247, Springer, Berlin, pp 207–219, 1987) are two natural ways of generalizing “context-free” grammar formalisms for string (...) and tree languages. It is known that the string generating power of both formalisms is equivalent to (non-erasing) multiple context-free grammars (Seki et al. in Theor Comput Sci 88:191–229, 1991) or linear context-free rewriting systems (Weir in Characterizing mildly context-sensitive grammar formalisms, University of Pennsylvania, 1988). In this paper, we give a simple, direct proof of the fact that second-order ACGs are simulated by hyperedge replacement grammars, which implies that the string and tree generating power of the former is included in that of the latter. The normal form for tree-generating hyperedge replacement grammars given by Engelfriet and Maneth (Graph transformation. Lecture notes in computer science, vol 1764. Springer, Berlin, pp 15–29, 2000) can then be used to show that the tree generating power of second-order ACGs is exactly the same as that of hyperedge replacement grammars. (shrink)

It is shown, assuming the linear case of Schinzel's Hypothesis, that the first-order theory of the structure $\langle \omega; +, P\rangle$ , where P is the set of primes, is undecidable and, in fact, that multiplication of natural numbers is first-order definable in this structure. In the other direction, it is shown, from the same hypothesis, that the monadic second-order theory of $\langle\omega; S, P\rangle$ is decidable, where S is the successor function. The latter (...) result is proved using a general result of A. L. Semenov on decidability of monadic theories, and a proof of Semenov's result is presented. (shrink)

For arbitrary finite group $G$ and countable Dedekind domain $R$ such that the residue field $R/P$ is finite for every maximal $R$ -ideal $P$ , we show that the localizations at every maximal ideal of two $RG$ -lattices are isomorphic if and only if the two lattices satisfy the same first order sentences. Then we investigate generalizations of the above results to arbitrary $R$ -torsion-free $RG$ -modules and we apply the previous results to show the decidability of the (...) theory of ${\vec Z}C(2)^2$ -lattices. Eventually, we show that ${\vec Z} [i] C(2)^2$ -lattices have undecidable theory. (shrink)

The history of building automated theorem provers for higher-order logic is almost as old as the field of deduction systems itself. The first successful attempts to mechanize and implement higher-order logic were those of Huet [13] and Jensen and Pietrzykowski [17]. They combine the resolution principle for higher-order logic (first studied in [1]) with higher-order unification. The unification problem in typed λ-calculi is much more complex than that for first-order terms, since it has to take (...) the theory of αβη-equality into account. As a consequence, the higher-order unification problem is undecidable and sets of solutions need not even always have most general elements that represent them. Thus the mentioned calculi for higher-order logic have take special measures to circumvent the problems posed by the theoretical complexity of higher-order unification. In this paper, we will exemplify the methods and proof- and model-theoretic tools needed for extending first-order automated theorem proving to higherorder logic. For the sake of simplicity take the tableau method as a basis (for a general introduction to first-order tableaux see part I.1) and discuss the higherorder tableau calculi HT and HTE first presented in [19]. The methods in this paper also apply to higher-order resolution calculi [1, 13, 6] or the higher-order matings method of Peter [3], which extend their first-order counterparts in much the same way. Since higher-order calculi cannot be complete for the standard semantics by Gödel’s incompleteness theorem [11], only the weaker notion of Henkin models [12] leads to a meaningful notion of completeness in higher-order logic. It turns out that the calculi in [1, 13, 3, 19] are not Henkin-complete, since they fail to capture the extensionality principles of higher-order logic. We will characterize the deductive power of our calculus HT (which is roughly equivalent to these calculi) by the semantics of functional Σ-models. To arrive at a calculus that is complete with respect to Henkin models, we build on ideas from [6] and augment HT with tableau construction rules that use the extensionality principles in a goal-oriented way.. (shrink)

relative to the actual world) of a propositional theory are defined. A theory is ‘closer to the truth’ the logically stronger its positive content and the logically weaker its negative content. This proposal delivers the same verisimilar preordering of theories that has been defined by Brink and Heidema as a ‘power ordering’. The preordering may be collapsed to a partial ordering and then embedded into a complete distributive lattice. The preordering may also be refined to a partial (...) ordering by employing the ‘convex content’ and the ‘non-convex content’ of each theory. Philosophical implications and historical relations are discussed. (shrink)

Amartya Sen argues that for the advancement of justice identification of ‘perfect’ justice is neither necessary nor sufficient. He replaces ‘perfect’ justice with comparative justice. Comparative justice limits itself to comparing social states with respect to degrees of justice. Sen’s central thesis is that identifying ‘perfect’ justice and comparing imperfect social states are ‘analytically disjoined’. This essay refutes Sen’s thesis by demonstrating that to be able to make adequate comparisons we need to identify and integrate criteria of comparison. This is (...) precisely the aim of a theory of justice (such as John Rawls’s theory): identifying, integrating and ordering relevant principles of justice. The same integrated criteria that determine ‘perfect’ justice are needed to be able to adequately compare imperfect social states. Sen’s alternative approach, which is based on social choice theory, is incapable of avoiding contrary, indeterminate or incoherent directives where plural principles of justice conflict. (shrink)

The so-called theory of karma is one of the distinguishing aspects of Hinduism and other non-Hindu south-Asian traditions. At the same time that the theory can be seen as closely connected with the freedom of will and action that we humans supposedly have, it has many times been said to be determinist and fatalist. The purpose of this paper is to analyze in some deepness the relations that are between the theory of karma on one side (...) and determinism, fatalism and free-will on the other side. In order to do that, I shall use what has been described as the best formal approach we have to indeterminism: branching time theory. More specifically, I shall introduce a branching time semantic framework in which, among other things, statements such as “state of affairs e is a karmic effect of agent a”, “a wills it to be the case that e” and “e is inevitable” could be properly represented. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A Theory of International Bioethics: Multiculturalism, Postmodernism, and the Bankruptcy of Fundamentalism 1Robert Baker (bio)AbstractThis first of two articles analyzing the justifiability of international bioethical codes and of cross-cultural moral judgments reviews “moral fundamentalism,” the theory that cross-cultural moral judgments and international bioethical codes are justified by certain “basic” or “fundamental” moral principles that are universally accepted in all cultures and eras. Initially propounded by the judges (...) at the 1947 Nuremberg Tribunal, moral fundamentalism has become the received justification of international bioethics, and of cross-temporal and cross-cultural moral judgments. Yet today we are said to live in a multicultural and postmodern world. This article assesses the challenges that multiculturalism and postmodernism pose to fundamentalism and concludes that these challenges render the position philosophically untenable, thereby undermining the received conception of the foundations of international bioethics. The second article, which follows, offers an alternative model—a model of negotiated moral order—as a viable justification for international bioethics and for transcultural and transtemporal moral judgments.Man in the Twentieth Century can not be circumscribed by the standards of any single culture.American Anthropological Association (1948) in a statement officially denouncing the 1948 United Nation’s Declaration of Human Rights.Recently... so-called “liberal” medicine has revived the old rights of a clinic understood in terms of a special contract, a tacit pact made between one man and another. This patient gaze has even been attributed the power of assuming [a role in clinical decision making].Miracles are not so easy to come by....Michel Foucault (1975, p. 5) [End Page 201]An Overview of the AnalysisInternational bioethics originated in the trauma of the Holocaust, specifically, in the 1946–1947 Nuremberg “Doctors Trial” when a tribunal of three American judges convicted Nazi medical researchers of “crimes against humanity.” In justifying their judgment, the Nuremberg Tribunal cited 10 principles for morally permissible research, which, they claimed, were based on “fundamental” principles that civilized societies “all agree” upon and accept as the foundations of their “moral, ethical, and legal” norms. Foremost among the principles was one stating that morally permissible human experiments require the informed voluntary consent of the subject. The Nuremberg judgment soon became associated with the ideal of human rights declared in the 1948 United Nations Charter. These two ideas—fundamental principles of morality and human rights—have been linked in all major formulations of international bioethics promulgated in the past 50 years, including the Council of Europe’s 1997 Convention for the Protection of Human Rights and Dignity of the Human Being with Regard to the Application of Biology and Biomedicine (Council of Europe 1997; Dommel and Alexander 1997). In this paper, I explore the received justification for international bioethics—the idea that it is grounded in fundamental principles accepted in all societies—tracing it from its initial, almost off-hand, promulgation by the Nuremberg Tribunal, through its more thoughtful development by such bioethicists as Ruth Macklin, to its more complex use by the President’s Advisory Committee on Human Radiation Experiments.After a brief review of the evolution of the received justification, I discuss the viability of this justification in the face of the critique implicit in two important intellectual movements: multiculturalism and postmodernism. In the international context, multiculturalism asserts the claim that there are no common moral principles shared by all cultures. Postmodernism asserts a similar claim against all universal standards, moral and nonmoral. In the 1990s, bioethicists have attempted to respond to these claims in various ways. These responses are documented, analyzed, and then shown to be “bankrupt,” in the sense that they undercut the most important objective of moral fundamentalism: the justification of transcultural moral judgments, such as the condemnation of the Nazi doctors.A second article, which follows the present one in the same issue of the Kennedy Institute of Ethics Journal, revisits the contractarian tradition [End Page 202] of Hobbes and Locke, as it has been reinterpreted by David Gauthier (1986), John Rawls (1971, 1993), and Robert Nozick (1974), to develop the idea of negotiated moral order as the basis of international bioethics. When conceptualized as a negotiated moral order, international bioethics can accept the genuine insights... (shrink)

This paper is an attempt to develop the many-valued first-order fuzzy logic. The set of its truth, values is supposed to be either a finite chain or the interval 0, 1 of reals. These are special cases of a residuated lattice L, , , , , 1, 0. It has been previously proved that the fuzzy propositional logic based on the same sets of truth values is semantically complete. In this paper the syntax and semantics of the first- (...) class='Hi'>order fuzzy logic is developed. Except for the basic connectives and quantifiers, its language may contain also additional n-ary connectives and quantifiers. Many propositions analogous to those in the classical logic are proved. The notion of the fuzzy theory in the first-order fuzzy logic is introduced and its canonical model is constructed. Finally, the extensions of Gödel's completeness theorems are proved which confirm that the first-order fuzzy logic is also semantically complete. (shrink)

The paper presents Property Theory with Curry Typing (PTCT) where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting fine-grained intensionality, the basic theory is essentially first-order, so that implementations using the theory can apply standard first-order theorem proving techniques. The paper sketches a system of tableau rules that implement the theory. Some extensions to the type theory are discussed, including type polymorphism, which provides (...) a useful analysis of conjunctive terms. Such terms can be given a single polymorphic type that expresses the fact that they can conjoin phrases of any one type, yielding an expression of the same type. (shrink)

The paper presents Property Theory with Curry Typing where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting fine-grained intensionality, the basic theory is essentially first-order, so that implementations using the theory can apply standard first-order theorem proving techniques. The paper sketches a system of tableau rules that implement the theory. Some extensions to the type theory are discussed, including type polymorphism, which provides a (...) useful analysis of conjunctive terms. Such terms can be given a single polymorphic type that expresses the fact that they can conjoin phrases of any one type, yielding an expression of the same type. (shrink)

Let S2S [WS2S] espectively be the storn [weak] monadic second order theory of the binary tree T in the language of two successor functions. An S2S-formula whose free variables are just individual variables defines a relation on T (rather than on the power set of T). We show that S2S and WS2S define the same relations on T, and we give a simple characterization of these relations.

This article is a comparative study between predictive processing (PP, or predictive coding) and cognitive dissonance (CD) theory. The theory of CD, one of the most influential and extensively studied theories in social psychology, is shown to be highly compatible with recent developments in PP. This is particularly evident in the notion that both theories deal with strategies to reduce perceived error signals. However, reasons exist to update the theory of CD to one of “predictive dissonance.” First, (...) the hierarchical PP framework can be helpful in understanding varying nested levels of CD. If dissonance arises from a cascade of downstream and lateral predictions and consequent prediction errors, dissonance can exist at a multitude of scales, all the way up from sensory perception to higher order cognitions. This helps understand the previously problematic dichotomy between “dissonant cognitive relations” and “dissonant psychological states,” which are part of the same perception-action process while still hierarchically distinct. Second, since PP is action-oriented, it can be read to support recent action-based models of CD. Third, PP can potentially help us understand the recently speculated evolutionary origins of CD. Here, the argument is that responses to CD can instill meta-learning which serves to prevent the overfitting of generative models to ephemeral local conditions. This can increase action-oriented ecological rationality and enhanced capabilities to interact with a rich landscape of affordances. The downside is that in today’s world where social institutions such as science a priori separate noise from signal, some reactions to predictive dissonance might propagate ecologically unsound (underfitted, confirmation-biased) mental models such as climate denialism. (shrink)

Theodor Adorno's Aesthetic Theory is a vast labyrinth that anyone interested in modern aesthetic theory must at some time enter. Because of his immense difficulty of the same order as Derrida - Adorno's reception has been slowed by the lack of a comprehensive and comprehensible account of the intentions of his aesthetics. This is the first book to put Aesthetic Theory into context and outline the main ideas and relevant debates, offering readers a valuable guide (...) through this huge, difficult, but revelatory work. Its extended argument is that, despite Adorno's assumptions of autonomism, cognitivism, and aesthetic modernism, his idea of artistic truth content offers crucial insights for contemporary philosophical aesthetics.The eleven chapters are divided into three parts: Context, Content, and Critique. The first part offers a brief biography, describes Adorno's debates with Benjamin, Brecht, and Lukács, and outlines his philosophical program. The second part is an interpretation of Adorno's aesthetics, examining how he situates art in society, production, politics, and history and uncovering the social, political, and historical dimensions of his idea of artistic truth. The third part evaluates Adorno's contribution by confronting it with the critiques of Peter Bürger, Frederic Jameson, and Albrecht Wellmer.Lambert Zuidervaart is Professor of Philosophy at Calvin College. (shrink)

Beyond different starting points, stakeholder theory and Catholic Social Thought share many compatible perspectives when analyzing the role of the firm in economic activity, especially regarding the attention of the firm to different social and economic actors. Additionally, ST bears limitations regarding its ethical and anthropological foundation, and also about the legitimation of the different stakeholders’ interests. Therefore, ST lacks clear criteria to solve possible conflicts of interest between stakeholders. This paper analyzes the potentiality of ST, widely accepted in (...) corporate management, to integrate CST principles in order to solve those conflicts. At the same time, the paper studies the possibility of finding in the principles of CST an anthropological and ethical foundation for ST. This foundation could be the source of criteria to discuss the levels of legitimation and prioritization between stakeholders´ interests, especially when those interests collide. (shrink)

Eric Voegelin's new study of Greek civilization, part of his continuing study of Order and History, contains elements of both such approaches to antiquity. In briefest compass, it is Voegelin's contention that order in history depends upon the recognition of the transcendental source of order; disorder is engendered by the "immanentization" of this source. Nevertheless, the transcendental source of order, the Christian God, is experienced within history, and civilizations are evaluated in terms of their anticipation of, (...) approach to, or withdrawal from this God. In terms of Christ's revelation, Greek thought is prejudged as a defective preliminary vision of historical and metaphysical truth. Just as Christ completes the Greek vision in "existential" terms, so Thomas Aquinas remedies the faults of Greek theory. In the process of being rejected or completed, classical thought takes on a remarkably Christian appearance. Despite his conservative or transcendental intentions, Voegelin's version of Christianity places great emphasis upon history as "open" to the future, and so the christianization of the Greeks produces anachronisms of the most extreme liberalism. At the same time, however, the Greek failure to transcend either the polis as a form of temporal order or an immanent conception of Being is severely criticized. (shrink)

The system called F is essentially a sub-theory of Frege Arithmetic without the ad infinitum assumption that there is always a next number. In a series of papers (Systems for a Foundation of Arithmetic, True” Arithmetic Can Prove Its Own Consistency and Proving Quadratic Reciprocity) it was shown that F proves a large number of basic arithmetic truths, such as the Euclidean Algorithm, Unique Prime Factorization (i.e. the Fundamental Law of Arithmetic), and Quadratic Reciprocity, indeed a sizable amount of (...) arithmetic. In particular, F proves some (but not all) of the Peano Axioms; that is, F proves the axioms of a sub-theory - call it FPA - of second-order Peano-Arithmetic. This short technical note will demonstrate that the converse also holds, in the following sense. F has the same language as second-order Peano Arithmetic except that, in addition, it has a two-place predicate symbol “Μ”. Then it is possible to provide a definition, indeed a reasonable definition, for “Μ” such that FPA proves all the axioms of F. So F and FPA effectively have the same proof-theoretic strength. In particular FPA, which lacks the Successor Axiom stating that every natural number has a successor, is able to prove the Euclidean Algorithm, Unique Prime Factorization, and Quadratic Reciprocity, indeed (again) a sizable amount of arithmetic. (shrink)