We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures with degrees (...) of categoricity is $\Pi_{1}^{1}$-complete. (shrink)

Herodotus. Custom is king.--Engels, F. Ethics and law: eternal truths.--Sumner, W. G. Folkways.--Ross, W. D. The meaning of right.--Duncker, K. Ethical relativity?--Herskovits, M. J. Cultural relativism and cultural values.--Kluckhohn, C. Ethical relativity: sic et non.--Taylor, P. W. Social science and ethical relativism.--Ladd, J. The issue of relativism.--Redfield, R. The universally human and the culturally variable.--Bibliography (p. 145-146).

It is immensely difficult to give a philosophically adequate account of mental imagery. Peter F.R. Haynes, pp. 709–19) objects to the standard accounts, and offers one of his own which avoids the standard difficulties. Unfortunately it in turn seems to lapse into incoherence.Haynes rejects Cartesian accounts which would make images private objects in non-physical space. He also rejects current alternative views: both Rylean or behaviourist ones; and also intentionally complex ones, which assert that the relevant terms change their meaning. He (...) thinks that J. J. C. Smart's “topic neutral” approach may supply “the basis for a correct, intentionally simple, intuitively satisfying account of mental imagery”. But an adequate account must also be neutral, as Smart's is not, between different theories of mind. In addition to avoiding these difficulties an adequate theory has certain other desiderata; in particular Haynes places valuable emphasis on the need to explain the fact that we can sometimes mistake images for real perceptions or, more real perceptions for images. (shrink)

It is immensely difficult to give a philosophically adequate account of mental imagery. Peter F.R. Haynes, pp. 709–19) objects to the standard accounts, and offers one of his own which avoids the standard difficulties. Unfortunately it in turn seems to lapse into incoherence.Haynes rejects Cartesian accounts which would make images private objects in non-physical space. He also rejects current alternative views: both Rylean or behaviourist ones; and also intentionally complex ones, which assert that the relevant terms change their meaning. He (...) thinks that J. J. C. Smart's “topic neutral” approach may supply “the basis for a correct, intentionally simple, intuitively satisfying account of mental imagery”. But an adequate account must also be neutral, as Smart's is not, between different theories of mind. In addition to avoiding these difficulties an adequate theory has certain other desiderata; in particular Haynes places valuable emphasis on the need to explain the fact that we can sometimes mistake images for real perceptions or, more real perceptions for images. (shrink)

En el ámbito de la lógica matemática existe un problema sobre la relación lógica entre dos versiones débiles del Axioma de elección (AE) que no se ha podido resolver desde el año 2000 (aproximadamente). Tales versiones están relacionadas con ultrafiltros no principales y con Propiedades Ramsey (Bernstein, Polarizada, Subretículo, Ramsey, Ordinales flotantes, etc). La primera versión débil del AE es la siguiente (A): “Existen ultrafiltros no principales sobre el conjunto de los números naturales (ℕ)”. Y la segunda versión débil del (...) AE es la siguiente (B): “Existen ultraflitros sobre ℕ”. Se sabe que A implica B, pero se desconoce si B implica A. Di Prisco y Henle conjeturan en los artículos ([1], [2]) que esto no ocurre, es decir, conjeturan que B no implica A, en otras palabras, conjeturan que A es más fuerte estrictamente que B, que A es independiente de B, pero esto no se ha podido demostrar todavía aunque se ha intentado hacer desde hace aproximadamente 21 años. Una descripción detallada de este problema abierto puede encontrarse en esta ponencia (dictada en el marco del Día Mundial de la Lógica 14-01-2022) y en el artículo [3]. [1] C. Di Prisco y H. Henle. “Doughnuts, Floating Ordinals, Square Brackets, and Ultraflitters”. Journal of Symbolic Logic 65 (2000) 462-473. [2] C. Di Prisco y H. Henle. “Partitions of the reals and choice”. En “Models, algebras and proofs”. X. Caicedo y C.M. Montenegro. Eds. Lecture Notes in Pure and Appl. Math, 203, Marcel Dekker, 1999. [3] F. Galindo. “Tópicos de ultrafiltros”. Divulgaciones Matemáticas. Vol. 21, No 1-2, 2020. (shrink)

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.