Un intento de disolución al problema de Gettier

Esta monografía cuestiona la validez de la crítica de Gettier a la suficiencia de lo que ha sido conocido como el análisis “tradicional” del conocimiento. Este análisis establece el conocimiento como creencia, verdadera justificada. Gettier en su famoso artículo "Is Justified True Belief Knowledge?" Propone una serie de contraejemplos que parecen cumplir con las tres condiciones recién establecidas, pero no puede ser considerado conocimiento. La monografía explora dos estrategias principales para responderle a Gettier: por un lado, me pregunto sí los contraejemplos realmente cumplen con las tres condiciones. Yo argumento que los contraejemplos de Gettier son imperfectos en cuanto a que no pueden cumplir con la condición de creencia; y si esto es así los contraejemplos no serían una amenaza al análisis “tradicional” del conocimiento ni tampoco serían una prueba de su insuficiencia. Por otro lado, si uno pudiera aceptar la validez de los contraejemplos uno podría aun cuestionar su relevancia. Esto es lo que pretendo hacer en la segunda parte de este trabajo. Intento mostrar que una solución al problema de Gettier no mejora para nada nuestra investigación metodológica, ni cambia de ninguna manera la forma en que nosotros adquirimos nuestras creencias y nuestro conocimiento en general. Por lo tanto, los contraejemplos de Gettier aun si pudieran funcionar correctamente (lo cual defiendo en la primera parte de la monografía que no es así) son irrelevantes y no son una amenaza real al análisis “tradicional” del conocimiento. La monografía se propone, entonces, efectuar una disolución más que una solución al problema de Gettier.

Putting the horse before the cart: a pragmatist analysis of knowledge

The definition of knowledge as justified true belief is the best we presently have. However, the canonical tripartite analysis of knowledge does not do justice to it due to a Platonic conception of a priori truth that puts the cart before the horse. Within a pragmatic approach, I argue that by doing away with a priori truth, namely by submitting truth to justification, and by accordingly altering the canonical analysis of knowledge, this is a fruitful definition. So fruitful indeed that it renders the Gettier counterexamples vacuous, allowing positive work in epistemology and related disciplines.

Counterexamples to some pointwise estimates of the maximal Cauchy transform in terms of the Cauchy transform

Motivated by the work of Mateu, Orobitg, Pérez and Verdera, who proved inequalities of the form $T_*f\lesssim M(Tf)$ or $T_*f\lesssim M^2(Tf)$ for certain singular integral operators $T$, such as the Hilbert or the Beurling transforms, we study the possibility of establishing this type of control for the Cauchy transform along a Lipschitz graph. We show that this is not possible in general, and we give a partial positive result when the graph is substituted by a Jordan curve.

Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces Hs(Ω) and tildeHs(Ω), for s in R and an open Ω in R^n. We exhibit examples in one and two dimensions of sets Ω for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if Ω is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.

Seeking compositionality in holistic proto-language without substructure – do counterexamples overwhelm the fractionation process?

In holistic theories of protolanguage, a vital step is the fractionation process where holistic utterances are broken down into segments, and segments associated with semantic components. One problem for this process may be the occurrence of counterexamples to any segment-meaning connection. The actual abundance of such counterexamples is a contentious issue \cite{smith06,taller07}. Here I present calculations of the prevalence of counterexamples in model languages.  It is found that counterexamples are indeed abundant, much more numerous than positive examples for any plausible holistic language.

A Survey of Counterexamples to Hilbert's Fourteenth Problem

We survey counterexamples to Hilbert’s Fourteenth Problem, beginning with those of Nagata in the late 1950s, and including recent counterexamples in low dimension constructed with locally nilpotent derivations. Historical framework and pertinent references are provided. We also include 8 important open questions.

Uniqueness and counterexamples in some inverse source problems

Uniqueness of a solution is investigated for some inverse source problems arising in linear parabolic equations. We prove new uniqueness results formulated in Theorems 3.1 and 3.2. We also show optimality of the conditions under which uniqueness holds by explicitly constructing counterexamples, that is by constructing more than one solution in the case when the conditions for uniqueness are violated.

The conserved quantity theory of causation and chance raising

In this paper I offer an 'integrating account' of singular causation, where the term 'integrating' refers to the following program for analysing causation. There are two intuitions about causation, both of which face serious counterexamples when used as the basis for an analysis of causation. The 'process' intuition, which says that causes and effects are linked by concrete processes, runs into trouble with cases of misconnections', where an event which serves to prevent another fails to do so on a particular occasion and yet the two events are linked by causal processes. The chance raising intuition, according to which causes raise the chance of their effects, easily accounts for misconnections but faces the problem of chance lowering causes, a problem easily accounted for by the process approach. The integrating program attempts to provide an analysis of singular causation by synthesising the two insights, so as to solve both problems. In this paper I show that extant versions of the integrating program due to Eells, Lewis, and Menzies fail to account for the chance-lowering counterexample. I offer a new diagnosis of the chance lowering case, and use that as a basis for an integrating account of causation which does solve both cases. In doing so, I accept various assumptions of the integrating program, in particular that there are no other problems with these two approaches. As an example of the process account, I focus on the recent CQ theory of Wesley Salmon (1997).

Contraexemplos e raciocínio dedutivo

Tese de Doutoramento apresentada ao ISPA - Instituto Universitário

RECASTING THE ELLIOTT CONJECTURE

Let A be a simple, unital, finite, and exact C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup which is obtained from the Elliott invariant in a functorial manner. We conjecture that this embedding is an isomor phism, and prove the conjecture in several cases. In these same cases - Z-stable algebras all - we prove that the Elliott conjecture in its strongest form is equivalent to a conjecture which appears much weaker. Outside the class of Z-stable C*-algebras, this weaker conjecture has no known counterexamples, and it is plausible that none exist. Thus, we reconcile the still intact principle of Elliott's classification conjecture -that K-theoretic invariants will classify separable and nuclear C*-algebras- with the recent appearance of counterexamples to its strongest concrete form.

The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-Algebras

We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C¤-algebras. In particular, our results apply to the largest class of simple C¤-algebras for which K-theoretic classification can be hoped for. This work has three significant consequences. First, it provides new conceptual insight into Elliott's classification program, proving that the usual form of the Elliott conjecture is equivalent, among Z-stable algebras, to a conjecture which is in general substantially weaker and for which there are no known counterexamples. Second and third, it resolves, for the class of algebras above, two conjectures of Blackadar and Handelman concerning the basic structure of dimension functions on C¤-algebras. We also prove in passing that the Kuntz-Pedersen semigroup is recovered functorially from the Elliott invariant for all simple unital C¤-algebras of interest.

Some conceptual difficulties regarding "net" multipliers

Multipliers are routinely used for impact evaluation of private projects and public policies at the national and subnational levels. Oosterhaven and Stelder (2002) correctly pointed out the misuse of standard 'gross' multipliers and proposed the concept of 'net' multiplier as a solution to this bad practice. We prove their proposal is not well founded. We do so by showing that supporting theorems are faulty in enunciation and demonstration. The proofs are flawed due to an analytical error but the theorems themselves cannot be salvaged as generic, non-curiosum counterexamples demonstrate. We also provide a general analytical framework for multipliers and, using it, we show that standard 'gross' multipliers are all that is needed within the interindustry model since they follow the causal logic of the economic model, are well defined and independent of exogenous shocks, and are interpretable as predictors for change.

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

Escenari, entorn, refugi : interiorisme domèstic i espais narratius

La casa és un conjunt de condicions físiques que en fan un habitatge, però també, és una xarxa de relacions que conformen la vida domèstica. Si bé el disseny disposa d’instruments molt efectius per garantir els estàndards d’habitabilitat, no es planteja, al mateix nivell, la qualitat de la domesticitat, la regulació de la qual, queda en el terreny dels usos dels habitants. L’estudi de cas de l’espai narratiu de les Peces de Cambra d’August Strindberg, analitzat a partir del conjunt d’àmbits comuns de la vida social, que proposa Peter Sloterdijk, permet establir quatre tipus ideals de cases sense llar i identifi car greus dèfi cits de domesticitat. Des d’aquests contraexemples s’obren perspectives que amplien l’horitzó del projecte d’espais domèstics.