conceptual

Aun entre quienes piensan que la razón es valiosa, no hay consenso en para que sirve. Pregunta 1. Si la razón tiene valor epistémico, ¿ésto significa que podemos obtener conocimiento genuino a través de la razón sola? Empirismo : No. La razón es esencialmente inferencial y no la mejor inferencia puede darnos algo a partir de la nada. La mejor de las inferencias solo puede demostrar la verdad de algo a partir de otro conocimiento previo. Racionalismo : Sí. Ahí está nuestro conocimiento de lo divino, las matemáticas, la lógica, etc. por ejemplo. [Pasar a pregunta 2] Pregunta 2 . ¿Qué tipo de cosas y hechos podemos conocer a través de la razón pura? Respuestas Realistas : Sobre ideas, conceptos, formas, universales, entes abstractos, etc. Hechos necesarios, universales, formales, etc. [Pasar a pregunta 3] Respuestas Críticas : Ninguno. Es un error pensar al conocimiento puramente racional a semejanza del conocimiento empírico. Sí, el conocimiento empírico es de objetos y hechos, pero el ...

One of the main philosophical peeves of mine are philosophers confounding symbols and what they represent, and in particular mistaking features of logical notation with actual logical facts. For example, is d ouble negation  an actual logical rule or is it actually a notational convention of certain logical notations? It seems to be the later, since we can have expressively equivalent logical notations where double negation is not even expressible, for example, if we consider diagrammatic systems where negation is represented by a reversible transformation of diagrammatic elements (Monroy forthcoming). For similar reasons, one might consider the   c ommutativity  (of disjunction or conjunction) not as an actual logical rule but a notational convention of certain logical notations, since we can have expressively equivalent logical notations where commutativity is not even expressible , for example, if we consider expressions that are not sequences but sets of symbol...

  Like any other kind of visual representation, you will need to follow the golden rule :  use things that are patently related/similar/different to represent things that are relevantly related/similar/different First, you are going to need to represent the elements in the structure. Use itemised elements like points, geometric figures, letters, etc. This will be your terminal vocabulary, so to speak, corresponding to what Greenberg calls the first order  elements of the system and thus can be as iconic or symbolic as desired. Then you are going to need how to represent their properties and relations. The mechanisms you can use to represent them are of two types: intrinsic and extrinsic. Intrinsic [I was very tempted to call them Leibnizian but I think the reference may be too obscure for many. It’s a shame]: You can exploit similarities , relations and differences in the way you have decided to represent the elements in the structure to represent similarities, relat...

I. Introduction and Preliminary Remarks  This post aims at presenting two essential notions in Wittgenstein’s philosophical account of mathematics duting the middle period of his philosophical carreer: mathematical objects and concepts.  Let me start by making two preliminary remarks: First, to specify to which Frege and which Wittgenstein’s I refer to, and, second, to clarify the scope of Wittgenstein’s philosophy of mathematics during this period. First of all, it must be recognized that both Wittgenstein and Frege were thinkers whose philosophical views, specially on mathematics –a central topic for both of them–, radically mutated throughout their philosophical careers. In this paper, I focus on two particular periods of each of these philosopher’s careers. For Frege, I focus on his late XIXth century work, specially on The Foundations of Arithmetic (1884) and contemporary articles. For Wittgenstein, I consider only the work of his middle period, the early th...