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Why care about the interpretation of mathematical diagrams

Judges use  photo finish to determine who won a race, a driver stops at a corner to ask a passer by for directions, a radiologist examines a patient’s x-ray before giving diagnosis, a traveller checks the screen at the airport to get information about her flight, a scientist checks the reading on her nanometer to determine the length of her samples, a mathematician looks at a diagram to gain insight into a new conjecture, etc. What all these cases have in common is that in all of them a person tries to get information about the world not by direct observation but by the use of representations of different sorts. Just as the radiologist need not have any direct contact with the patient, we usually do not need direct contact with whatever aspect of the world we want to know about. In every case, the information might be more or less accurate, the method we use more or less reliable, but in all of them the information is mediated by a representation: a photograph, some words, an x-ray...

Randomness, Explanation, Parfit and the Cosmos

It is widely accepted that explanation is a factive relation, that is, that it holds among facts (or true propositions, the distinction is not relevant for our purposes): if A explains B, A and B must be actual facts. Beyond that, it is a huge puzzle to determine what else is required for A to explain B. Some philosophers have defended the view that necessitation is another necessary condition for explanation, that is, that for A to explain B, A must necessitate or metaphysically entail B. The rationale for this condition is simple: for A to explain B, A must tell us why B happened instead of anything else that could have happened. If A does not entail B, then A is consistent with some possible outcome C different from B and this cannot explain why B happened instead of C. I (in Barceló 2015) and others have argued against the necessity condition. An interesting counterexample to the hypothesis that necessitation is required for explanation are what I will call explanations b...

Making Quantified truths True

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Available now! http://www.springer.com/us/book/9783319183619

Naturalismos Moderados y Exacerbados

Podemos identificar dos tipos de naturalismos en filosofía: Un naturalismo exacerbado y otro moderado. La primera noción de naturalismo la encontramos, por ejemplo, en el volumen editado por Steven Wagner y Richard Warner, Naturalism, A Critical Appraisal (1993). En su introducción, los editores escriben: We take naturalism to be the view that only natural science deserves full and unqualified credence. (Wagner y Warner 1993, 1. Énfasis mío) Es también esta noción de naturalismo la que aparece en The Oxford Companion to Philosophy (1995), editado por Ted Honderich, donde naturalismo se define como . . . the view that everything is natural, i.e. that everything there is belongs to the world of nature, and so can be studied by the methods appropriate for studying that world. (Honderich 1995, 604) Este naturalismo exacerbado se distingue por cuatro tesis radicales: Naturalismo (Ontológico): Todo es natural. No existen objetos ni sucesos fuera del ámbito de la natu...

Am I a philosopher or a logician?

Last week, I was invited to a workshop on logicality, where Ives Beziaú mentioned that it was a shame that we used the same word “logic” to name both the philosophical discipline and its subject matter. This, he insisted, is a problem common to other disciplines like history and geography. Other disciplines, like ornithology or meteorology – my example, not his – do not have this problem and thus we can say what their subject of study is without sounding tautological: ornithology studies birds and meteorology studies the atmosphere. But what can we say about what logic studies? Well, it studies logic, of course! just like history studies history and geography studies geography. That is why it is very important to make a difference between logic as a philosophical discipline, with its theories, problems, concepts, etc. and logic as an aspect of reality, with its proper phenomena of propositions following one another, sets of them being consistent or inconsistent, etc. Just ...

Wittgenstein contra Jackson sobre percepción de colores

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Para Wittgenstein, los colores obedecen a una gramática, es decir, a una serie de reglas – expresadas en enunciados necesarios como “ningún color es mas claro que el blanco” o “todo color tiene un único inverso’, etc. – que definen el contenido de nuestros conceptos cromáticos. En otras palabras, mientras que algunas de las cosas que decimos sobre los colores son contingentes, como que verde es la mezcla de azul y amarillo, o que cierto tono de verde es el más puro, etc. otras son necesarias. Algunos filósofos consideran esta distinción espúrea, pues piensan que, dado que el color es un fenómeno natural en el mundo, todo lo que decimos de los colores es, a final de cuentas, contingente. No hay, por lo tanto, nada cómo una gramática de los colores. Uno de los argumentos (a priori) mas famosos en contra de la existencia de dicha gramática consiste en considerar, como nos lo pide Jackson, el caso hipotético de Alfredo quién es capaz de distinguir un tono que nadie más puede di...

Wittgenstein and Frege on Arithmetical Objects and Concepts

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...