Seven lectures graced the second in the annual series at the Irish college devoted to the 13th-century saint and theologian. The topics include friendship and love, the desire for happiness as a way to God, the separated soul's natural knowledge, and truth as a good. Appended is a guide to consultat.

In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual(s) of fusion.

The notion of an object file figures prominently in recent work in philosophy and cognitive science. Object files play a role in theories of singular reference, object individuation, perceptual memory, and the development of cognitive capacities. However, the philosophical literature lacks a detailed, empirically informed theory of object files. In this paper, we articulate and defend the multiple-slots view, which specifies both the format and architecture of object files. We argue that object files represent in a non-iconic, propositional format that (...) incorporates discrete symbols for separate features. Moreover, we argue that features of separate categories are stored in separate memory slots within an object file. We supplement this view with a computational framework that characterizes how information about objects is stored and retrieved. (shrink)

One recurring criticism of the best interests standard concerns its vagueness, and thus the inadequate guidance it offers to care providers. The lack of an agreed definition of ‘best interests’, together with the fact that several suggested considerations adopted in legislation or professional guidelines for doctors do not obviously apply across different groups of persons, result in decisions being made in murky waters. In response, bioethicists have attempted to specify the best interests standard, to reduce the indeterminacy surrounding medical decisions. (...) In this paper, we discuss the bioethicists’ response in relation to the state's possible role in clarifying the best interests standard. We identify and characterise two clarificatory strategies employed by bioethicists —elaborative and enumerative—and argue that the state should adopt the latter. Beyond the practical difficulties of the former strategy, a state adoption of it would inevitably be prejudicial in a pluralistic society. Given the gravity of best interests decisions, and the delicate task of respecting citizens with different understandings of best interests, only the enumerative strategy is viable. We argue that this does not commit the state to silence in providing guidance to and supporting healthcare providers, nor does it facilitate the abuse of the vulnerable. Finally, we address two methodological worries about adopting this approach at the state level. The adoption of the enumerative strategy is not defeatist in attitude, nor does it eventually collapse into (a form of) the elaborative strategy. (shrink)

This paper explores allowing truth value assignments to be undetermined or "partial" and overdetermined or "inconsistent", thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I (...) investigate twelve natural extensions containing nested implications, all of which can be viewed as coming from natural variations on Kripke's semantics for intuitionistic logic. Many of these logics exist antecedently in the literature, in particular Nelson 's "constructible falsity". (shrink)

We present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutatively and associatively are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding a coimplication operator, (...) similar to Curry's subtraction operator, which is resituated with Linear Logic's contensor product. And we can add contraction to get nondistributive Relevance Logic. The model rests heavily on Urquhart's representation of nondistributive lattices and also on Dunn's Gaggle Theory. Indeed, the paper may be viewed as an investigation into nondistributive Gaggle Theory restricted to binary operations. The valuations on the Kripke model are three valued: true, false, and indifferent. The lattice representation theorem of Urquhart has the nice feature of yielding Priestley's representation theorem for distributive lattices if the original lattice happens to be distributive. Hence the representation is consistent with Stone's representation of distributive and Boolean lattices, and our semantics is consistent with the Lemmon-Scott representation of modal algebras and the Routley-Meyer semantics for Relevance Logic. (shrink)

This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects.

in Cambridge Handbook of Consciousness edited by Zelazo P., Moscovitch M. and Thompson E. (2007).

Theoretical explication of a growing body of empirical data on consciousness-related anomalous phenomena is unlikely to be achieved in terms of known physical processes. Rather, it will first be necessary to formulate the basic role of consciousness in the definition of reality before such anomalous experience can adequately be represented. This paper takes the position that reality is constituted only in the interaction of consciousness with its environment, and therefore that any scheme of conceptual organization developed to represent that reality (...) must reflect the processes of consciousness as well as those of its environment. In this spirit, the concepts and formalisms of elementary quantum mechanics, as originally proposed to explain anomalous atomic-scale physical phenomena, are appropriated via metaphor to represent the general characteristics of consciousness interacting with any environment. More specifically, if consciousness is represented by a quantum mechanical wave function, and its environment by an appropriate potential profile, Schrödinger wave mechanics defines eigenfunctions and eigenvalues that can be associated with the cognitive and emotional experiences of that consciousness in that environment. To articulate this metaphor it is necessary to associate certain aspects of the formalism, such as the coordinate system, the quantum numbers, and even the metric itself, with various impressionistic descriptors of consciousness, such as its intensity, perspective, approach/avoidance attitude, balance between cognitive and emotional activity, and receptive/assertive disposition. With these established, a number of the generic features of quantum mechanics, such as the wave/particle duality, and the uncertainty, indistinguishability, and exclusion principles, display metaphoric relevance to familiar individual and collective experiences. Similarly, such traditional quantum theoretic exercises as the central force field and atomic structure, covalent molecular bonds, barrier penetration, and quantum statistical collective behavior become useful analogies for representation of a variety of consciousness experiences, both normal and anomalous, and for the design of experiments to study these systematically. (shrink)

The aim of this review is to show the fruitfulness of using images of facial expressions as experimental stimuli in order to study how neural systems support biologically relevant learning as it relates to social interactions. Here we consider facial expressions as naturally conditioned stimuli which, when presented in experimental paradigms, evoke activation in amygdala–prefrontal neural circuits that serve to decipher the predictive meaning of the expressions. Facial expressions offer a relatively innocuous strategy with which to investigate these normal variations (...) in affective information processing, as well as the promise of elucidating what role the aberrance of such processing might play in emotional disorders. (shrink)

Prominent philosophers have argued that contradictions contain either too much or too little information to be useful. We dispute this with what we call the “Paradox of the Two Firefighters.” Suppose you are awakened in your hotel room by a fire alarm. You open the door. You see three possible ways out: left, right, straight ahead. You see two firefighters. One says there is exactly one safe route and it is to your left. The other says there is exactly one (...) safe route and it is to your right. While the two firemen are giving you contradictory information, they are also both giving you the perhaps useful information that there is a safe way out and it is not straight ahead. We give two analyses. The first uses the “Opinion Tetrahedron,” introduced by Dunn as a generalization of Audun Jøsang’s “Opinion Triangle.” The Opinion Tetrahedron in effect embeds the values of the “Belnap-Dunn 4-valued Logic” into a context of subjective probability generalized to allow for degrees of belief, disbelief, and two kinds of uncertainty—that in which the reasoner has too little information and that in which the reasoner has too much information. Jøsang had only a single value for uncertainty. We also present an alternative solution, again based on subjective probability but of a more standard type. This solution builds upon “linear opinion pooling.” Kiefer had already developed apparatus for assessing risk using expert opinion, and this influences the second solution. Finally, we discuss how these solutions might apply to “Big Data” and the World Wide Web. (shrink)

Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. _Generalized Galois Logics_ develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.

We study an application of gaggle theory to unary negative modal operators. First we treat negation as impossibility and get a minimal logic system Ki that has a perp semantics. Dunn 's kite of different negations can be dealt with in the extensions of this basic logic Ki. Next we treat negation as “unnecessity” and use a characteristic semantics for different negations in a kite which is dual to Dunn 's original one. Ku is the minimal logic that (...) has a characteristic semantics. We also show that Shramko's falsification logic FL can be incorporated into some extension of this basic logic Ku. Finally, we unite the two basic logics Ki and Ku together to get a negative modal logic K-, which is dual to the positive modal logic K+ in [7]. Shramko has suggested an extension of Dunn 's kite and also a dual version in [12]. He also suggested combining them into a “united” kite. We give a united semantics for this united kite of negations. (shrink)

This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects.

The Fort Worth basin is one of the most fully developed shale gas fields in North America. Although there are hundreds of drilled wells in the basin, almost none of them reach the Precambrian basement. Imaged by perhaps 100 3D seismic surveys, the focus on the relatively shallow, flat-lying Barnett Shale objective has resulted in little published work on the basement structures underlying the Lower Paleozoic strata. Subtle folds and systems of large joints are present in almost all 3D seismic (...) surveys in the FWB. At the Cambro-Ordovician Ellenburger level, these joints are often diagenetically altered and exhibit collapse features at their intersections. We discovered how the basement structures relate to overlying Paleozoic reservoirs in the Barnett Shale and Ellenburger Group. In support of our investigation, the Marathon Oil Company provided a high-quality, wide-azimuth, 3D seismic data near the southeast fringe of the FWB. In addition to the seismic volume, we integrated the seismic results with gravity, magnetic, well log, and geospatial data to understand the basement and subbasement structures in the southeast FWB. Major tectonic features including the Ouachita frontal thrust belt, Lampasas arch, Llano uplift, and Bend arch surround the southeast FWB. Euler deconvolution and integrated forward gravity modeling helped us extend our interpretation beyond the 3D seismic survey into a regional context. (shrink)

We give a set of postulates for the minimal normal modal logicK + without negation or any kind of implication. The connectives are simply , , , . The postulates (and theorems) are all deducibility statements . The only postulates that might not be obvious are.

Both I and Belnap, motivated the "Belnap-Dunn 4-valued Logic" by talk of the reasoner being simply "told true" (T) and simply "told false" (F), which leaves the options of being neither "told true" nor "told false" (N), and being both "told true" and "told false" (B). Belnap motivated these notions by consideration of unstructured databases that allow for negative information as well as positive information (even when they conflict). We now experience this on a daily basis with the Web. (...) But the 4-valued logic is deductive in nature, and its matrix is discrete: there are just four values. In this paper I investigate embedding the 4-valued logic into a context of probability. Jøsang's Subjective Logic introduced uncertainty to allow for degrees of belief, disbelief, and uncertainty. We extend this so as to allow for two kinds of uncertainty— that in which the reasoner has too little information (ignorance) and that in which the reasoner has too much information (conflicted). Jøsang's "Opinion Triangle" becomes an "Opinion Tetrahedron" and the 4-values can be seen as its vertices. I make/prove various observations concerning the relation of non-classical "probability" to non-classical logic. (shrink)

The scientific, personal, and social implications of this revolutionary work are staggering. MARGINS OF REALITY is nothing less than a fundamental reevaluation of how the world really works.