Emergent phenomena are quite interesting and amazing, but they present two main scientific obstacles: to be rationally understood and to be mathematically modelled. In this paper we propose a powerful mathematical tool for modelling emergent phenomena by applying category theory. Furthermore, since great part of biological phenomena are emergent, we present an essay of how to access an emergence from observational data. In the mathematical perspective, we utilize constructs (categories whose objects are structured sets), their operations and their corresponding generalized (...) underlying functor (which are not necessarily faithful) to define emergence. From this definition, we elaborate several results concerning homomorphism between emergences, representability, pull-back, push-out, equalizer, product and co-product of emergences among other results. After we have presented such mathematical model, we utilize a hierarchical structure as example—from molecules to a flatworm—, in order to understand the relation between biological systems and its underlying emergence in a hierarchical model. (shrink)

in the euthyphro, socrates tells euthyphro that Meletus is taking him to court for impiety.1 Upon hearing Euthyphro’s claim to have knowledge of piety, Socrates asks Euthyphro to take him on as a pupil, so that he might acquire knowledge of piety himself. Although this may seem unsurprising, given Socrates’s high regard for knowledge in other dialogues, the reason that Socrates gives for wishing to acquire knowledge, in this case, is bizarre—for he says it is because knowledge of piety will (...) help him to secure his acquittal on charges of impiety.It is unclear, however, why Socrates believes that his learning what piety is should lead to the impiety charges against him being dropped, yet no one has ever made a.. (shrink)

A directory of archives and manuscript repositories, with links to web pages for the repositories and to online finding aids. Searchable by: collection name; city; state; National Inventory of Documentary Sources (NIDS) number; and National Union Catalog of Manuscript Collections (NUCMC) number.

In this essay I will try to show that there are what would appear to be some unnoticed consequences of the doctrine of divine foreknowledge. For the purposes of this discussion I will simply assume that future events are possible objects of knowledge and, hence, that foreknowledge is possible. Accordingly, I will not be concerned with discussing such questions as the status of truth-values for future contingent propositions or whether knowledge is justified true belief. Furthermore, I will not be concerned (...) with the issues involved in the claim that the doctrine of divine foreknowledge conflicts with doctrines concerning the properties of created beings, e.g., the doctrine of voluntary human action. (shrink)

La paradoja del mentiroso lleva siglos atormentando la mente de filósofos y lógicos. El presente texto intenta una solución siguiendo la siguiente tesis: la paradoja no puede ser resuelta por la lógica dado que lo implicado en ella trasciende las fronteras de esa disciplina. Lo que trasciende estas fronteras (establecidas en gran medida por Frege, en tanto padre de la lógica moderna) es el propio ser humano como ser capaz de articular sentido. De ahí la necesidad de explorar cómo la (...) fenomenología aborda al ser humano para reconcebir también al lenguaje y al tiempo. Este giro será crucial para entender por qué el problema de dicha paradoja es la autorreferencialidad, lo que también conlleva a reinterpretar qué se entiende por niveles de lenguaje (sea en la forma de Tarski o de Kripke). (shrink)