Las definiciones ocupan un lugar muy importante en la _Ética_ de Spinoza, sin embargo, su naturaleza y su función permanecen aún en gran medida bajo un manto de oscuridad. Tal es así que numerosos comentadores han abordado el tema aunque nunca se ha llegado a un acuerdo definitivo. En el presente trabajo revisitaremos esta vieja cuestión comenzando por una reconstrucción de la doctrina spinoziana de la definición expuesta en diferentes partes del _corpus_. Para ello tomaremos como punto de referencia la (...) oposición entre definición real y definición nominal tal como aparece delineada en la doctrina de la _Lógica_ de Port Royal. Luego ofreceremos un examen de la naturaleza y función de las definiciones de la _Ética_. El recorrido realizado aquí nos permitirá, por un lado, determinar cuál de las interpretaciones en juego tiene mejores fundamentos y, por el otro, arrojar luz sobre la función de las definiciones en la metodología spinoziana. (shrink)

Spinoza scholars have claimed that we are faced with a dilemma: either Spinoza's definitions in his Ethics are real, in spite of indications to the contrary, or the definitions are nominal and the propositions derived from them are false. I argue that Spinoza did not recognize the distinction between real and nominal definitions. Rather, Spinoza classified definitions according to whether they require a priori or a posteriori justification, which is a classification distinct from either the real/nominal or the intensional/extensional classification. (...) I argue that Spinoza uses both a priori and a posteriori definitions in the Ethics and that recognizing both types of definitions allows us to understand Spinoza's geometric method in a new way. We can now understand the geometric method as two methods, one resulting in propositions that Spinoza considers to be absolutely certain and another resulting in propositions that Spinoza does not consider certain. The latter method makes use of a posteriori definitions and postulates, whereas the former method uses only a priori definitions and axioms. (shrink)

Like many of their contemporaries Bernard Nieuwentijt and Pieter van Musschenbroek were baffled by the heterodox conclusions which Baruch Spinoza drew in the Ethics. As the full title of the Ethics—Ethica ordine geometrico demonstrata—indicates, these conclusions were purportedly demonstrated in a geometrical order, i.e. by means of pure mathematics. First, I highlight how Nieuwentijt tried to immunize Spinoza’s worrisome conclusions by insisting on the distinction between pure and mixed mathematics. Next, I argue that the anti-Spinozist underpinnings of Nieuwentijt’s distinction between (...) pure and mixed mathematics resurfaced in the work of van Musschenbroek. By insisting on the distinction between pure and mixed mathematics, Nieuwentijt and van Musschenbroek argued that Spinoza abused mathematics by making claims about things that exist in rerum natura by relying on a pure mathematical approach. In addition, by insisting that mixed mathematics should be painstakingly based on mathematical ideas that correspond to nature, van Musschenbroek argued that René Descartes’ natural-philosophical project abused mathematics by introducing hypotheses, i.e. ideas, that do not correspond to nature. (shrink)