During the months before and after he saw Julius Caesar assassinated on the Ides of March, 44 BC, Cicero wrote two philosophical dialogues about religion and theology: On the Nature of the Gods and On Divination. This book brings to life his portraits of Stoic and Epicurean theology, as well as the scepticism of the new Academy, his own school. We meet the Epicurean gods who live a life of pleasure and care nothing for us, the determinism and beauty of (...) the Stoic universe, itself our benevolent creator, and the reply to both that traditional religion is better served by a lack of dogma. Cicero hoped that these reflections would renew the traditional religion at Rome, with its prayers and sacrifices, temples and statues, myths and poets, and all forms of divination. This volume is the first to fully investigate Cicero's dialogues as the work of a careful philosophical author. (shrink)

Three experiments explore the role of working memory in motor skill acquisition and performance. Traditional theories postulate that skill acquisition proceeds through stages of knowing, which are initially declarative but later procedural. The reported experiments challenge that view and support an independent, parallel processing model, which predicts that procedural and declarative knowledge can be acquired separately and that the former does not depend on the availability of working memory, whereas, the latter does. The behaviour of these two processes was manipulated (...) by providing or withholding visual (and auditory) appraisal of outcome feedback. Withholding feedback was predicted to inhibit the use of working memory to appraise success and, thus, prevent the formation of declarative knowledge without affecting the accumulation of procedural knowledge. While the first experiment failed to support these predictions, the second and third experiments demonstrated that procedural and declarative knowledge can be acquired independently. It is suggested that the availability of working memory is crucial to motor performance only when the learner has come to rely on its use. (shrink)

We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffie algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cut-free proofs in (...) CyLL + MIX. This can be viewed as a fully faithful representation of a free *-autonomous category, canonically enriched over vector spaces. This paper is a natural extension of the authors' previous work, "Linear Lauchli Semantics", where a similar theorem is obtained for the commutative logic MLL + MIX. In that paper, we interpret proofs as dinaturals which are invariant under certain actions of the additive group of integers. Here we also present a simplification of that work by showing that the invariance criterion is actually a consequence of dinaturality. The passage from groups to Hopf algebras in this paper corresponds to the passage from commutative to noncommutative logic. However, in our noncommutative setting, one must still keep the invariance condition on dinaturals. (shrink)

Three experiments explore the role of working memory in motor skill acquisition and performance. Traditional theories postulate that skill acquisition proceeds through stages of knowing, which are initially declarative but later procedural. The reported experiments challenge that view and support an independent, parallel processing model, which predicts that procedural and declarative knowledge can be acquired separately and that the former does not depend on the availability of working memory, whereas, the latter does. The behaviour of these two processes was manipulated (...) by providing or withholding visual (and auditory) appraisal of outcome feedback. Withholding feedback was predicted to inhibit the use of working memory to appraise success and, thus, prevent the formation of declarative knowledge without affecting the accumulation of procedural knowledge. While the first experiment failed to support these predictions, the second and third experiments demonstrated that procedural and declarative knowledge can be acquired independently. It is suggested that the availability of working memory is crucial to motor performance only when the learner has come to rely on its use. (shrink)

RésuméCet article a été inspiré par l'opposition qui semble exister entre les deux grands courants animant l'œuvre de M. Bachelard.Les auteurs rappellent la différence existant entre une organisation predicative et une organisation dialectique de la connaissance. La connaissance objective est de structure dialectique. Il en résulte que l'évolution de cette connaissance s'accompagne d'un processus obligé de dévalorisation et de revalorisation relative de ses formes antérieures.Ce même processus rend aussi compte des rapports de la pensée poétique et de la pensée objective (...) et scientifique.Dans cette perspective, l'unité d'inspiration de l'œuvre de M. Bachelard est parfaitement évidente. — F. et J.‐P. G. (shrink)

Sheldon adds his voice to the growing chorus of protest against theological "fideism." Religion is not an irrational commitment to what cannot be known. Rather "pure straight reason, impartially pursued, leads by logical necessity to worship of... supernatural deity...." This rather surprising thesis is defended by identifying "true" philosophy, the wise pursuit of goods, with religion and morality, whose core is compassionate love, impartial and universal in scope.--P. F. J.

The solution of the outer multiplicity problem in the tensor product of U(3) irreducible representations (irreps) developed by Biedenharn et al.(1–7) and realized through the well-known Draayer-Akiyama (DA) computer code(8) is extended to the quantum algebra Uq(3). An analytic formula for special stretched Uq(3) Wigner coefficients, $$\left\langle {(\lambda _1 \mu _1 ) H_1 , (\lambda _2 \mu _2 ) \varepsilon _2 \Lambda _2 m_2 \left| { (\lambda _3 \mu _3 ) H_3 } \right.} \right\rangle _{\max }^q $$ is derived using (...) a projection operator method.(9–10) In this expression Hi denotes the highest weight vector of the (λiμi) irrep; the subscript “max” means coefficients corresponding to a unit tensor operator with a maximal characteristic null space; and q is the usual quantum label so the standard U(3) Wigner coefficient, which is required in the DA code, can be obtained in the q→1 limit of the theory. To illustrate the theory, some Uq(3) Wigner coefficients for the tensor product (22)×(22) are calculated. The procedure for evaluating nonhighest weight Wigner Uq(3) coefficients follow the DA prescription. (shrink)

We introduce a linear analogue of Läuchli's semantics for intuitionistic logic. In fact, our result is a strengthening of Läuchli's work to the level of proofs, rather than provability. This is obtained by considering continuous actions of the additive group of integers on a category of topological vector spaces. The semantics, based on functorial polymorphism, consists of dinatural transformations which are equivariant with respect to all such actions. Such dinatural transformations are called uniform. To any sequent in Multiplicative Linear Logic (...) , we associate a vector space of“diadditive” uniform transformations. We then show that this space is generated by denotations of cut-free proofs of the sequent in the theory MLL + MIX. Thus we obtain a full completeness theorem in the sense of Abramsky and Jagadeesan, although our result differs from theirs in the use of dinatural transformations.As corollaries, we show that these dinatural transformations compose, and obtain a conservativity result: diadditive dinatural transformations which are uniform with respect to actions of the additive group of integers are also uniform with respect to the actions of arbitrary cocommutative Hopf algebras. Finally, we discuss several possible extensions of this work to noncommutative logic.It is well known that the intuitionistic version of Läuchli's semantics is a special case of the theory of logical relations, due to Plotkin and Statman. Thus, our work can also be viewed as a first step towards developing a theory of logical relations for linear logic and concurrency. (shrink)

A construction is described of a cartesian closed category A with exactly two elements out of a C-monoid such that can be recovered from A without reference to the construction.