Fermat’s Least Time Principle has a long history. World’s foremost academies of the day championed by their most prestigious philosophers competed for the glory and prestige that went with the solution of the refraction problem of light. The controversy, known as Descartes - Fermat controversy was due to the contradictory views held by Descartes and Fermat regarding the relative speeds of light in different media. Descartes with his mechanical philosophy insisted that every (...) natural phenomenon must be explained by mechanical principles. Fermat on the other hand insisted an end purpose for every motion. For example, least time of travel and not the least distance of travel is the end purpose for motion of light. This implied a thinking nature, which was rejected by Descartes. Surprisingly, with contradictory assumptions regarding the relative speeds of light in different media, both Descartes and Fermat came to the same result that the ratio of sines of angles of incidence and refraction is a constant. Fermat’s result came to be known as the ‘Fermat’s least time principle’. We show in this article that Fermat’s least time principle violates a fundamental theorem in geometry – the Ptolemy’s theorem. That leads to the invalidity of Fermat’s principle. -/- . (shrink)

During 17th century a scientific controversy existed on the derivation of Snell’s laws of reflection and refraction. Descartes gave a derivation of the laws, independent of the minimality of travel time of a ray of light between two given points. Fermat and Leibniz gave a derivation of the laws, based on the minimality of travel time of a ray of light between two given points. Leibniz’s calculus method became the standard method of derivation of the two laws. (...) We demonstrate in this article that Snell’s law of reflection follows from simple results of geometry. We do not use the concept of motion or the time of travel in our demonstration. That is, time plays no role in our demonstration. (shrink)

I discuss Descartes’ metaphysics of selfhood, and relevant parts of contemporary philosophy regarding the first person. My two main concerns are the controversy that surrounds Descartes’ conception of conscientia, mistranslated as ‘consciousness’, and his conception of selfhood and its essential connection to conscientia. ‘I’-thoughts give rise to the most challenging philosophical questions. An answer to the questions concerning the peculiarities of the first person, self-identification and self-ascription, is to be found in Descartes’ notion of conscientia. His (...) conception of selfhood insightfully informs his conception of personhood. I offer a unified account of selfhood, conscientia, the first person, and personhood anchored in the self’s authority of reason and autonomy of freedom. (shrink)

The paper reconstructs the reception of Descartes's work by Scottish eighteenth-century philosophers. The Scots' image of Descartes was a by-product of a scientific controversy; philosophical arguments were brought into the picture more as asides than as a primary focus of interest. As soon as the Cartesian physics withered away as a real alternative to Newtonian physics, only the philosophical arguments were left, with no memory of the context out of which they originated, and the focus of the (...) discussion shifted from physics to the philosophy of mind and the theory of knowledge. (shrink)

In early modern times it was not uncommon for thinkers to tease out from the nature of God various doctrines of substantial physical and metaphysical import. This approach was particularly fruitful in the so-called beast-machine controversy, which erupted following Descartes’ claim that animals are automata, that is, pure machines, without a spiritual, incorporeal soul. Over the course of this controversy, thinkers on both sides attempted to draw out important truths about the status of animals simply from the (...) notion or attributes of God. Automatists – led by Nicolas Malebranche and Antoine Dilly – developed six such arguments, appealing to divine justice, providence, economy, glory (twice) and wisdom, while opponents to animal automatism developed two arguments, appealing to divine wisdom and goodness. In this article I shall examine the substance of all eight of these arguments, along with their origins, patronage, and variations, and the objections they elicited from opponents, with the aim of determining their suitability for use in contemporary debates about animal sentience and consciousness, and hence their relevance for contemporary philosophers. (shrink)

This article provides an analysis of Johannes Clauberg’s intentions in writing his Logica vetus et nova (1654, 1658). Announced before his adherence to Cartesianism, his Logica was eventually developed in order to provide Cartesian philosophy with a Scholastic form, embodying a complete methodology for the academic disciplines based on Descartes’ rules and a medicina mentis against philosophical prejudices. However, this was not its only function: thanks to the rules for the interpretation of philosophical texts it encompassed, Clauberg’s Logica was (...) meant to provide a general hermeneutics designed to put an end to the quarrels raised by the dissemination of Cartesianism. Such quarrels, according to Clauberg, were caused by the misinterpretation of Descartes’ texts in Revius’ Methodi cartesianae consideratio theologica (1648) and Statera philosophiae cartesianae (1650) and in Lentulus’ Nova Renati Descartes sapientia (1651), which criticized the apparent lack of a logical theory in Descartes’ philosophy and its supposed inconsistencies. Clauberg answers their criticisms by giving a clear account of Descartes’ logical theory and by undermining the interpretative criteria they assumed, in light of a general theory of error. Polemics over Cartesian philosophy, in this way, favored the development of a comprehensive Cartesian methodology for academic disciplines and of the first hermeneutics for philosophical texts. (shrink)

Nuestro recorrido será el siguiente. En el capítulo primero examinamos la noción de unión del cuerpo y el alma que Descartes formula desde el inicio de Las pasiones del alma (§2), noción anticipada por otros textos (Principia II §2) pero muy original, y que recusa todo dualismo, en tanto concibe una unión no substancial, en la que el alma está unida, de modo más o menos estrecho, a todos los cuerpos que la afectan, como "corps de dehors", de manera (...) tal que todos los sentimientos, internos o externos, en tanto referidos al cuerpo, pueden ser ubicados en una misma exterioridad respecto al alma (sección §1). Esta noción de unión: a) coincide plenamente con la experiencia del poder o capacidad del alma para actuar sobre el cuerpo, o recibir la acción del cuerpo, de manera tal de excluir definitivamente toda referencia a la substancia espiritual, corporal o compuesta; b) establece una diferencia meramente cuantitativa entre mi cuerpo y los cuerpos del mundo, porque la unión al cuerpo es más o menos estrecha, según sea más o menos inmediata la acción del cuerpo sobre el alma. La primera consecuencia de lo anterior es la siguiente: Las pasiones del alma no establece distinción alguna entre sentimientos interiores y exteriores, porque el lugar del agente (las partes de nuestro cuerpo, los cuerpos del mundo) no sirven ya más como criterio para la distinción entre los modos de la sensibilidad (sección §2). Es precisamente en este punto fundamental que la investigación cartesiana sobre las pasiones se distingue definitivamente del análisis de la sensibilidad realizado en la cuarta parte de Los Principios de la Filosofía, en donde la pasión era considerada como un sentimiento interior, junto con los apetitos naturales (IV §190), por oposición a los cinco sentidos exteriores (IV §§ 191-195). Luego del examen de la definición de pasión, en el próximo capítulo, podremos preguntar: dadas, por un lado, la interioridad de la pasión al alma, y por otro, el emplazamiento de todos los cuerpos en el mismo afuera, «dehors», respecto del alma, ¿cabe buscar, en la pasión, el sentimiento de un corps de dedans? Anticipemos que la reforma conceptual de la unión del cuerpo y el alma exige y a la vez resulta de una reforma lexical especialmente interesante porque, al excluir toda referencia a las substancias o a la substancialidad de la unión, a) identifica esta última con la capacidad o potencia del alma de afectar o ser afectada por el cuerpo (sección §3); b) debe describir la unión como un «estar (del alma) junto (al cuerpo), ( être jointe)», que califica la estrechez de la unión por la inmediatez de la acción (sección §4). Finalmente, esta conjunción del alma y del cuerpo anticipa de manera coherente la doctrina cartesiana del amor, el cual se define por la capacidad del alma de unirse (« se joindre ») a los objetos que la afectan en la apariencia de bondad. El capítulo segundo se dedicará a la definición de pasión (Pasiones §§21-28), el único sentimiento interior al alma misma porque el único que es tal como aparece, en una evidencia que no puede ser entendida mas que en relación, todavía indeterminada, con la evidencia primera ego sum, ego existo, en la Meditación Segunda, y especialmente con su última formulación, en la certeza del « creo ver » («videre videor»). El carácter inaugural de esta definición reside en los puntos siguientes: a) la relación con el alma convierte a la pasión en el único sentimiento que es tal como se siente, pero al mismo tiempo, b) inaugura una nueva forma de error posible, todavía indeterminado, pero de otro orden que aquél al que nos somete la naturaleza extrínseca del resto de las percepciones (sección §1). Ahora bien, la pasión es tal como se siente porque no es un « ver », videre, y por lo tanto no le corresponde revelar el ego sum (« ego sum qui sentio » VII, 29, 11), a través de un « creo ver », videre videor (sección §3). Quisimos probar que esto es perfectamente coherente con la doble enumeración de los modos del pensamiento, en la Segunda y Tercera Meditación, (VII, 28 y 35, respectivamente) y con la clasificación de los pensamientos (ideas, juicios, voluntades, afecciones), establecida en la Meditación Tercera (VII, 38) (sección §2). Pero la pasión, a la vez que inaugura una interioridad, se recibe en el alma, como algo que no proviene de ella (Pasiones §17). Es aquí, donde se da a conocer el carácter inaugural y a la vez paradójico de la pasión: en ella, la interioridad del alma a sí se conoce, por primera vez, en una modalidad particular de la recepción sensible. Examinamos esa doble condición, interioridad y recepción, en la sección §7, la última de este segundo capítulo. Dos consecuencias. La primera: a partir de la definición de pasión, la investigación sobre la cualidad sensible se independiza del examen de la realidad objetiva (sección §4). La pasión puede por lo tanto inaugurar una verdad y un modo de error que se separa definitivamente del objeto representado como cosa o privación de cosa. No seremos los primeros en decir que la pasión, el saber afectivo en general, sólo puede dirigirse a un no-objeto (F. Alquié). Pero hay que agregar que la definición de pasión, al recuperar su evidencia primera, abre a la meditación el campo de una realidad inobjetivable, o, mejor, de una modalidad de la objetividad definitivamente irreal, que ya ha sido descubierta por J-L. Marion, por lo menos para el caso particular de la admiración, y que sólo podrá ser de ser descripta en el momento de definir las pasiones particulares. La segunda consecuencia reside en la relegación definitiva de toda explicación de la pasión por la causa eficiente (sección §6). En efecto, Descartes deja de lado las funciones del cuerpo como criterio de clasificación de los modos de la sensibilidad, y la relega a la segunda parte de la segunda parte de su definición, de manera tal que la causa de la pasión no explica nada y por el contrario, es ella la que debe ser explicada. Si se admite una doble constitución de la metafísica cartesiana, nuestro esfuerzo conduce a mostrar que la noción de pasión, y la investigación que ella abre, pertenece a una metafísica presidida por su primera figura, cogitatio, antes que por la segunda, causa. La investigación sobre los efectos de la pasión, que comprende los artículos §§40 a 48 de Las pasiones del alma, y a la que dedicamos nuestro capítulo III, debe ser leída en continuidad al texto de la Meditación Sexta, en tanto viene a responder a la pregunta siguiente: ¿cuál es el modo de la pasividad que caracteriza a la pasión y la distingue de otros modos del sentimiento como de otros modos de constricción a la voluntad? Si la pasión, se recibe en el alma, ¿cómo se siente esa proveniencia, si por definición queda excluida toda relación al cuerpo como causa o como objeto? En primer lugar, aquello que caracteriza a la pasión es que ella tiene como efecto una disposición a querer. Pero, dado que la voluntad es esencialmente libre, la disposición a querer en el alma tiene a su vez un efecto igualmente necesario, este es, una respuesta del alma a la disposición a querer que es en ella, respuesta que Descartes llama (no) consentimiento a los efectos de la pasión (§46; §80). A partir del artículo §40, la investigación sobre las pasiones se introduce resueltamente en el ámbito de una moral, como una ciencia de los efectos (sección §1). En segundo lugar, y por lo anterior, la pasión, puede ser, en su interioridad y proximidad al alma, directamente contraria a la voluntad (365, 12-13), justamente, porque ella es el único sentimiento que tiene como efecto necesario en el alma una disposición a querer (§40). Lejos de presentar un mero obstáculo a una determinación del alma, la pasión se recibe como una invitación, a la cual el alma debe imperativamente responder. El punto a destacar (sección §2) es el siguiente: Descartes describe aquí una verdadera autoafección indirecta, por la cual el alma puede excitar en sí una pasión voluntaria (362, 28 ; 363, 2; 486, 6-9), autoafección de la cual es absolutamente incapaz en el caso del resto de los sentimientos, tal como quedaba establecido desde la Meditación Sexta. Así, el cuerpo que actúa inmediatamente sobre el alma, al cual ella está más estrechamente unida, abandona su condición de mero intermediario entre los cuerpos y el alma y pasa a ser, en una autoafección voluntaria, el intermediario entre una acción del alma y una pasión en el alma. En la sección §3 se agrega esto: la pasión, a diferencia de todos los sentimientos, no se siente en el instante. Por el contrario, en ella, el sentir se despliega en el tiempo y se hace por lo tanto independiente de la acción de los cuerpos sobre los sentidos internos o externos. Esto se debe a lo siguiente: primero, en la pasión, el cuerpo actúa como una totalidad indivisible. Segundo: el cuerpo actúa sobre sí. En la pasión, tercero, el cuerpo actúa de manera tal que su acción se presenta siempre como una exigencia al ejercicio efectivo de la libertad. Finalmente, en la pasión, la totalidad de las funciones del cuerpo se someten definitivamente a la voluntad, de manera que el alma puede afectarse a sí en una pasión voluntaria. Quisiéramos proponer (sección §3) que la experiencia del cuerpo en la pasión merece ser nombrada como la experiencia de un cuerpo de dedans, que se presenta en la repugnancia o el consentimiento y cuya acción no se siente en un lugar (en una internidad que no establece ninguna distinción con la exterioridad de los cuerpos del mundo), sino en el alma misma, en una interioridad que hace imposible la reducción del cuerpo sentido a la categoría común de objeto o causa. Ahora bien, la investigación sobre la pasión puede introducirse en el ámbito de la moral con una condición: que la pasión permita el acceso del ego a un alter ego, o según la fórmula tradicional utilizada por Descartes, a un «otro sí mismo», alter ipse. Es el problema que abordamos en el capítulo IV. Queda claro que las Meditaciones Metafísicas impiden, o mejor, ocluyen de modo parentemente definitivo, ese acceso. Pero, en Las pasiones del alma, Descartes, introduce un género muy particular de objeto , «otros objetos, que consideramos causas libres, capaces de hacer el bien y el mal » (§55, 374, 5-7). Más aún, la libertad del agente se erige en criterio de clasificación de segundo orden para todas las pasiones simples, con excepción del deseo. El punto a notar aquí (sección §1) es el siguiente: el ego no se ve afectado por la causa libre porque infiera que ella, a diferencia de otras, actúa moralmente sobre él, con independencia de toda determinación mecánica. Es al revés: el ego siente la acción de una causa libre porque se ve afectado por la libertad del agente; es esa afección la que otorga a los actos del otro el carácter moral de buenos o malos. Esto se prueba en el respeto o la veneración (§162): aquello que nos afecta no es la supuesta bondad o la maldad de los actos, sino inmediatamente aquello que los hace tales, esto es, la « capacidad » de hacer el bien o el mal. De aquí que el hijo, cuyos actos evidentemente no son morales, pueda nombrarse, entre los objetos de amor, como un « otro(s) sí mismo» (§82, 389, 15). A fin de precisar el sentido y los alcances de esta alteridad, debemos detenernos en la definición cartesiana del amor (secciones §§2-3). Esa definición debe, en primer lugar, distinguirse claramente de aquella que Descartes había ensayado dos años antes, en la carta a Chanut del 1 de febrero de 1647. El problema que preocupa a Descartes no es ya más la definición de un amor intelectual, sino la de un amor puro, que Descartes distingue precisamente de las pasiones que « participan del amor » (§82, título), mezcla de deseo y « otras pasiones particulares » (§82 389, 9-10). El amor puro es una pasión que no tiene relación alguna al cuerpo, porque se siente sin placer y es la primera de las pasiones « que pertenecen al alma », según la distinción establecida en los títulos de §137 y §139. Esta distinción se establece estrictamente dentro del ámbito del amor pasión porque no considera en ningún momento el alma en tanto separada del cuerpo, condición del amor intelectual (IV, 602, 4-8), sino como « nuestra mejor parte » (§139, 432, 5). El único que merece sin reparos el título de « amor puro » es el amor paterno, el único en el que se cumple la tríada, pureza, posesión perfecta, alteridad. En la sección §4 nos detenemos en los modos del engaño propio de las pasiones, en general, y del amor en particular, para entender el último rasgo que Descartes le otorga al amor puro, este es, el de ser un amor verdadero, que elude todas las formas de engaño a las que las pasiones pueden someternos, y puede por lo tanto ocupar el lugar del verdadero conocimiento. La teoría cartesiana del amor permite así dos conclusiones. Primera: la alteridad sirve para distinguir definitivamente el amor del deseo, el amor puro de las pasiones que participan de él, los grados de perfección del amor, amor paterno, amistad honesta, y, finalmente, la formas del amor, afección, amistad y devoción. Segundo, antes de toda reflexión sobre el deseo, es decir, antes de considerar la perfectibilidad del ego por la posesión de bienes que dependan exclusivamente de nuestra voluntad, Descartes escribe que el alma se perfecciona en el amor, por la unión al bien verdadero, mientras que se envilece y rebaja en su unión con un bien excesivamente estimado (§139, 432, 12-20 ; §142, 435, 18 –22). En la sección §5 examinamos el efecto del amor, la benevolencia, que Descartes, haciendo caso omiso de la tradición, define como una verdadera beneficencia, como un acto de donación, que no necesita de ningún deseo para hacerse efectivo. El punto a destacar aquí es que Descartes considera que el otro al que el alma se une es la « mejor parte » del todo que resulta de la unión (§82, 389, 16-17). Por este exceso, el generoso, sobre la estrechez de la unión al cuerpo, decide por la estrechez de la unión a otra alma, y privilegia el objeto de amor sobre el amor a la vida. Brevemente: la amistad cartesiana tiende a la devoción y rompe con toda noción de amistad fundada en la igualdad. Esto nos permite, en la sección §6 hacer notar cómo la teoría del amor resignifica un léxico que Descartes recibe de Aristóteles y Santo Tomás. La comparación, al menos inicial, con esos autores está dirigida a incluir a Descartes en una historia del amor. El quinto capítulo traza el largo itinerario de la noción de virtud, a través de la Correspondencia, y se detiene especialmente en las cartas mencionadas más arriba, ( a Elisabeth, 15 septiembre 1645; a Chanut, 1 febrero 1648) en las que Descartes ensaya y abandona una primera forma de moral definitiva, especialmente problemática, en tanto aspira, por primera vez, a deducir el amor a Dios de la idea de Dios, y se dirige a pensar al ego como parte de totalidades (familia, vecindad, Estado) que han sido, ellas también, creadas por Dios. Esta reflexión sobre el amor a Dios es todavía independiente de la reflexión sobre las pasiones, que recién comienza. Intentamos aquí despejar la intención cartesiana que puede resumirse así: de la misma manera que Dios, creador de toda verdad, es fundamento de toda ciencia y toda verdad se halla ya contenida en Su idea, es Dios, creador de totalidades físicas, sociales o políticas, el fundamento de todo amor, aunque no se lo conozca, o sólo confusamente, como tal; de modo que en todo acto de renuncia por la totalidad, amamos a Dios, en un amor sensible, aunque nada en Él sea imaginable. Sin embargo, una vez adquirida, en Las pasiones del alma, la definición de pasión e incluida la noción de consentimiento en la definición definitiva del amor, aquella vía de análisis, que parte de un ego ya incluido en las totalidades de las que forma parte como persona, agota definitivamente sus posibilidades y debe ser abandonada. Debemos preguntar, entonces: qué queda de esta ardua reflexión sobre el amor a Dios en Las pasiones del alma? Principalmente, Descartes recupera de aquellas cartas la reflexión sobre la Providencia divina, en los artículos §§146-147. Pero entre las cartas de 1645-1647 y el texto de Las pasiones del alma, hay una diferencia capital. La reflexión sobre la Providencia divina, en 1649, no hace mención alguna al amor, parece abandonar toda aspiración a fundar, en el amor a Dios, el amor a otros hombres y se dirige exclusivamente a establecer la regla del deseo, intermediario privilegiado entre pasión y acción (§143, 435, 26-29). Ahora bien, una moral que no tuviera otra regla que la del deseo presentaría dos características distintivas. Primero, la indagación sobre el bien verdadero se agota en la determinación del bien verdaderamente posible; son pues igualmente buenos todos los bienes igualmente estimables e igualmente posibles. De aquí, en segundo lugar, que la noción de virtud no pueda otorgar a la voluntad otro bien que su mero ejercicio, vacío de todo contenido. Ha sido pues posible interpretar que, la moral cartesiana, en el momento de alcanzar su fundamento, se independiza de ella, como otra potencia igualmente arbitraria, que no puede someterse a otro fin que el de imitar a Dios por la inmutabilidad de la decisión. En el capítulo sexto, dedicado a la definición de generosidad, nosotros propondremos, al contrario, que el texto de Las pasiones del alma, cuya teoría del amor aquella interpretación debe desconocer, permite otra lectura de la moral cartesiana. Sucede que Descartes cambia radicalmente el punto de partida de su reflexión : en las cartas de 1645-1647, la omnipotencia divina exigía considerar el ego como parte de distintas totalidades, a las que se haya ligado de hecho. En 1649, la unión no describe una situación existencial, impuesta por nacimiento, vecindad o juramento, porque no accede a una situación de hecho más que por el consentimiento libre y lúcido del ego a la unión efectiva con el bien amado. De aquí, proponemos, se siguen dos consecuencias. La primera (sección §2): una reformulación del problema del amor a Dios. La omnipotencia divina no se conoce como aquí como Providencia, es decir, en el decreto universal que determina la fatalidad de todas las cosas, sino en el acto singular de una donación personal y desmedida, la libre disposición de nuestras voluntades, por la cual la criatura se reconoce semejante a su Creador (§152). El generoso reconoce que el libre albedrío, el único bien por el cual puede estimarse a sí mismo, es, tal como quedaba establecido desde la Meditación Cuarta, un don divino y el reconocimiento por un don recibido es una pasión, la gratitud, la cual, a diferencia de la admiración, la esperanza o la seguridad, es una especie del amor, siempre virtuosa (§§193-194). En efecto, la reflexión sobre la Providencia, es apenas uno de los modos de reglar el deseo, el segundo, porque el primero es, justamente, la generosidad, que se define con total prescindencia del conocimiento de la fatalidad de todas las cosas (§145, 437, 27-438, 3). Investigamos aquí los tres rasgos del don divino: infinitud formal, pertenencia verdadera, distribución perfecta. La segunda consecuencia, que confirma la primera (secciones §§3-4), es la reformulación del amor a otros hombres. En efecto, no arriesgaremos demasiado al proponer que la definición de generosidad, lejos de agotarse en los artículos §§152-153, comprende los artículos §154 y §155 y culmina, finalmente, en el §156. Así entendida, la generosidad es una autoafección que, como tal, determina, prioritaria y precisamente, el modo en que el generoso es afectado por los otros hombres, en tanto causas libres, semejantes al ego, y por lo tanto semejantes a Dios. La generosidad se define pues en el horizonte de la alteridad porque el generoso no sería tal si no estimara a todos y cada uno de los hombres como generosos posibles (§154) y si no redescubriera su capacidad de hacer el mal por comparación al mal efectivamente realizado por ellos (§155). De aquí, finalmente, la regla definitiva de la moral cartesiana (§156), regla que, al definir la mejor acción posible, otorga un contenido definitivo a la firme resolución de hacer el bien, esta es: imitar la donación original, haciendo el bien a todos los hombres. Luego, la ausencia de una reflexión sobre el amor a Dios, en Las pasiones del alma, no es, todavía, una desaparición, ya que el acto de donación divina condiciona definitivamente la regla moral como una imitación, que se concibe como una repetición, igualmente gratuita, de aquella donación original. La relación entre ambos puntos se prueba en lo siguiente: Descartes afirma que el efecto necesario de la benevolencia generosa, la gratitud es uno de las principales vínculos de la sociedad entre los hombres (§194, 474, 13-15), la cual se funda pues en el mismo vínculo que une al hombre generoso con Dios: gratitud por la gratuidad de la donación (sección §6). La afirmación cartesiana es de un laconismo insalvable, pero recupera un texto hasta aquí descuidado, la Carta a Voetius de 1643, la primera reflexión cartesiana sobre el amor y la única dedicada a examinar las leyes que de él se deducen, como una jus caritatis (sección §7). Examinamos en la seccción §8 la problemática relación, o ausencia de relación, entre esas leyes de amistad y la ley civil, jus civile, basada en la autoridad del Príncipe. Finalmente, en la Conclusión, podemos detenernos en un problema ya dos veces pospuesto, este es, el que resulta de la equivalencia que Descartes establece entre amistad honesta y caridad cristiana. (IV, 309, 2-4; IV , 612, 14), equivalencia que la noción de generosidad está lejos de contradecir y que recupera la «gran afinidad» (VIII-2, 112, 24-25) entre las leyes de la amistad y las leyes de caridad, que Descartes había desarrollado en aquel capítulo séptimo de la Carta a Voetius. El carácter problemático de esta equivalencia es evidente: si el amor natural, por exceso, aspira a la caridad, es a riesgo que la caridad, por defecto, deje de ser cristiana. Esa afinidad no ha merecido mayor atención por parte de la metafísica y de sus historiadores. Pero, ha merecido la mayor atención por parte de la destitución de la metafísica que lleva a cabo Blaise Pascal quien descubre y acusa, en esa afinidad, el último esfuerzo de la filosofía cartesiana, dirigida a otorgarle al ego su última y más controversial primacía, la del acceso a Dios por el amor. -/- . (shrink)

Abstract The paper reconstructs the reception of Descartes's work by the Scottish Enlighteners, from Colin MacLaurin to Dugald Stewart. The Scots' image of Descartes was a byproduct of a scientific controversy; philosophical arguments were brought into the picture more as asides than as a primary focus of interest. As soon as the Cartesian physics withered away as a real alternative to Newtonian physics, only the philosophical arguments were left, with no memory of the context out of which (...) they originated, and the focus of the discussion shifts from physics to the philosophy of mind and the theory of knowledge. (shrink)

The impression we are often given by historians of philosophy is that the readiness of medieval philosophers to appeal to authorities, such as The Bible, the Church, and Aristotle, was not shared by many early modern philosophers, for whom there was a marked preference to look for illumination via experience, the exercise of reason, or a combination of the two. Although this may be accurate, broadly speaking, it is notable that, in spite of the waning enthusiasm for deferring to traditional (...) authorities, appeals to scripture remained commonplace in the work of early modern philosophers. In order to understand the philosophers of the early modern period, the philosophies they developed, and the debates they fought, we need to understand how they used scripture. This paper is intended to contribute to this desideratum by examining how scripture was used by those who engaged in a particular debate within natural philosophy, the so-called beast-machine controversy of the 17th and 18th centuries. (shrink)

This essay examines Descartes’s impact on medical faculties in the German Reformed context, focusing on the case of the Marburg physician Johann Jakob Waldschmidt (1644–89). It first surveys the wider backdrop of Descartes-reception in German universities, and highlights its generally conciliatory character. Waldschmidt appears as a counterpoint to this tendency. The essay then situates Waldschmidt’s work in the context of confessional politics at the University of Marburg, and specifically of the heightened controversy in Hesse around the teaching (...) of Descartes in the last years of Waldschmidt’s life. The second half of the essay details Waldschmidt’s ambitious program to reform medicine along Cartesian lines, in physiology, pathology, and therapy, and evaluates its merits and limits. (shrink)

Richard Baxter, one of the most famous Puritans of the seventeenth century, is generally known as a writer of practical and devotional literature. But he also excelled in knowledge of medieval and early modern scholastic theology, and was conversant with a wide variety of seventeenth-century philosophies. Baxter was among the early English polemicists to write against the mechanical philosophy of René Descartes and Pierre Gassendi in the years immediately following the establishment of the Royal Society. At the same time, (...) he was friends with Robert Boyle and Matthew Hale, corresponded with Joseph Glanvill, and engaged in philosophical controversy with Henry More. In this book, David Sytsma presents a chronological and thematic account of Baxter's relation to the people and concepts involved in the rise of mechanical philosophy in late-seventeenth-century England. -/- Drawing on largely unexamined works, including Baxter's Methodus Theologiae Christianae (1681) and manuscript treatises and correspondence, Sytsma discusses Baxter's response to mechanical philosophers on the nature of substance, laws of motion, the soul, and ethics. Analysis of these topics is framed by a consideration of the growth of Christian Epicureanism in England, Baxter's overall approach to reason and philosophy, and his attempt to understand creation as an analogical reflection of God's power, wisdom, and goodness, understood as vestigia Trinitatis. Baxter's views on reason, analogical knowledge of God, and vestigia Trinitatis draw on medieval precedents and directly inform a largely hostile, though partially accommodating, response to mechanical philosophy. (shrink)

Francisco Sanches (1551–1623) was an important figure in the history of philosophical scepticism, and most specifically in the later sixteenth and early seventeenth century. Sanches gained notoriety through his controversial text, That Nothing is Known. His skeptical ideas concerning what could be known of the phenomenal world, influenced the work of other philosophers like René Descartes. In fact, in the last twenty-five to thirty years, his work has at last been acknowledged as having served as a background source of (...) Descartes’ refutation of scepticism. Sanches was not only a philosopher; he was also a physician, and a professor of medicine – a fact that doubtlessly tempered his scepticism. In recent years, there has been a growing interest in Sanches, as he has come to be seen as a significant philosopher in the history of scepticism, along with Montaigne, Descartes, and Hume. Some contemporary thinkers have gone as far as comparing his notion of language and metaphysics to that of someone like Wittgenstein. (shrink)

Are living organisms--as Descartes argued--just machines? Or is the nature of life such that it can never be fully explained by mechanistic models? In this thought-provoking and controversial book, eminent geophysicist Walter M. Elsasser argues that the behavior of living organisms cannot be reduced to physico-chemical causality. Suggesting that molecular biology today is at the same point as Newtonian physics on the eve of the quantum revolution, Elsasser lays the foundation for a theoretical biology that points the way toward (...) a natural philosophy of organic life. Explicitly repudiating "vitalism" (the notion that the laws of nature need to be modified when applied to living organisms), Elsasser argues instead that the structural complexity of even a single living cell is "transcomputational"--that is, beyond the power of any imaginable system to compute. Beginning from this insight, Elsasser leads the reader through a step-by-step process that ultimately arrives at the conclusion that living and non-living matter are separated by "a no-man's land of irrationality." Trained in Germany as a physicist, Elsasser first pondered the implications of quantum mechanics for biology as early as 1951. The more closely he studied the inherent complexity of life, the more skeptical he became of the reductionist view of organisms as tiny machines. "An organism," he concluded, "is a source of causal chains which cannot be traced beyond a terminal point because they are lost in the unfathomable complexity of the organism." Like the physicist who works within the bounds of an unfathomable universe, Elsasser argues, the biologist must seek answers within a system that is no less unfathomable. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine – (...) Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

The theories of pre-existence and epigenesis are typically taken to be opposing theories of generation in the seventeenth and eighteenth centuries. One can be a pre-existence theorist only if one does not espouse epigenesis and vice versa. It has also been recognized, however, that the line between pre-existence and epigenesis in the nineteenth century, at least, is considerably less sharp and clear than it was in earlier centuries. The debate (1759-1777) between Albrecht von Haller and Caspar Friedrich Wolff on their (...) theories of generation is usually taken to be a debate between a pre-existence theorist and an epigeneticist, and the supposed fact that these two theories of generation are mutually exclusive explains (so the story goes) the divide between Haller and Wolff. However, it’s not clear that Haller endorsed an especially robust form of pre-existence, and nor is it clear that Wolff’s theory of generation -- once he considered it carefully -- is clear epigenetic. Rather, Haller’s theory of generation is marked by traces of epigensis and Wolff’s theory has elements of pre-existence theory. This is not to say that their theories of generation are basically the same, but the debate between the two ought not to be framed in terms of pre-existence versus epigenesis. Their points of difference must be explained in some other way. In this way, their controversy bears characteristics of similar disputes over generation in the nineteenth century more than it resembles those in the seventeenth century. In this paper, I argue that (a) Haller’s and Wolff’s theories both blend elements from pre-existence and epigenesis; (b) but there are still deeply-rooted differences between the two generation theories; (c) one source of these differences is that Haller and Wolff have divergent conceptions of what an adequate explanation is; (d) we can see that they have different conceptions of what constitutes an adequate explanation by paying heed to their evaluations of Descartes’ epistemology and methodology in his theory of generation (such as it is); and (e) this shows that one of the main differences between Haller’s generation theory and that of Wolff is the degree to which each thinks we need to (and indeed can) explain the nature of the causes -- both efficient and final -- at play during the formation of organic beings. (shrink)

The editor's introduction discusses Clarence I. Lewis's conceptual pragmatism when compared with post-empiricist epistemology and argues that several Cartesian assumptions play a major role in the work, not unlike those of Logical Positivism. The suggestion is made that the Cartesian legacy still hidden in Logical Positivism turns out to be a rather heavy ballast for Lewis’s project of restructuring epistemology in a pragmatist key. More in detail, the sore point is the nature of inter-subjectivity. For Lewis, no less than for (...) the Logical Positivists at the time of the Protocols Controversy and Husserl in the Cartesian Meditations, this is a problem without a solution. The reason is that all these philosophers are apparently unable to realize that the existence of a plurality of knowing subjects cannot be treated at once both as a speculative problem and a methodological one. Lewis, thanks to his pragmatist approach both comes closer to the right answer and offers an even more naïve unsatisfactory solution to the pseudo-problem under discussion. The fact that he has clear in mind that inter-subjectivity means not only a plurality of linguistic utterances but also a co-existence of different kinds of practical behaviour. Eventually, the very idea of mind, the key-idea in the book, suffers from the above mentioned tension. In fact, if inter-subjective communication and action is considered at a methodological level, the very idea of mind would not need an analysis, and no kind of ‘reflexive’ analysis. Methodology might be limited to a ‘naïve’ level where the existence of the world and a plurality of subjects be taken as a bedrock of uncritically accepted evidence. Philosophical reflection on ultimate evidence, instead, would take a different approach, maybe the one Wittgenstein was putting into practice in the same years when Mind and the world order was written, namely it would be bound to question the very meaning of the idea of ‘mind’ as an undue fiction – the same carried out by Descartes – when he assumed the Cogito to be at once a body of self-evident truths and a thing or substance, the familiar Platonic idea of psyche or soul. (shrink)

Kant’s pre-1770 philosophy responded to the mind-body problem by applying a theory of “physical influx”. His encounter with Swedenborg’s mysticism, however, left him disillusioned with any dualist solution to Descartes’ problem. One of the major goals of the Critical philosophy was to provide a completely new solution to the mind-body problem. Kant’s new solution is “perspectival” in the sense that all Critical theories are perspectival: it acknowledges a deep truth in both of the controversy’s extremes (i.e., what we (...) might nowadays call eliminative materialism and an absolutely ideal folk psychology), by viewing both as ways of considering the issue, rather than as the only correct approach. Once we take into account its perspectival character, a new way of understanding Kant’s philosophy of mind emerges. The mind is no longer separate from the body, but is a manifestation of it, viewed from another (specifically human, rational) perspective. Kant’s transcendental conditions of knowledge (spatio-temporal intuition, categorial conception, and principled schematization) do not portray the mind as somehow creating the physical world; rather, they imply the opposite, that knowledge of objects is necessarily structured by a set of unconscious assumptions about the physical world. Our pre-conscious (or pre-mental, in Descartes’ sense of “mental”) encounter with an assumed spatio-temporal, causal nexus is entirely physical. A reincarnated Kant’s solution to today’s mind-body problem would be: eliminative materialism is good science; but only the “explanatory idealist” can consistently be an eliminative materialist. Philosophically, multiple perspectives are necessary in order to understand anything we say or do. (shrink)

Nineteenth century Christian thought about self and relationality was stamped by the reception of Kant’s groundbreaking revision to the Cartesian cogito. For René Descartes (1596-1650), the self is a thinking thing (res cogitans), a simple substance retaining its unity and identity over time. For Immanuel Kant (1724-1804), on the other hand, consciousness is not a substance but an ongoing activity having a double constitution, or two moments: first, the original activity of consciousness, what Kant would call original apperception, and (...) second, the reflected self, the “I think” as object of reflection. Both are essential to the possibility of an awareness of a unified experience. Such an awareness is achieved only insofar as the self is capable of reflecting on its activity of thinking. As such, the possibility of self-consciousness, or the capacity to reflect on one’s own acts of thought is essential to the constitution of the self. This new model of the mind became the starting point to the thought of central 19th century figures such as Friedrich Schleiermacher (1768-1834), J. G. Fichte (1762-1814), Friedrich Hegel (1770-1831) and Søren Kierkegaard (1813-1855). This chapter will explore their reception of Kant’s model of self-consciousness, the controversies surrounding its development and exposition, and the advantages of this model for theological reflection. The idea of mind as essentially capable of reflection provided an account of how the self can stand in an ontologically immediate relation to God constitutive of the self, while at the same time allowing that the self’s consciousness of itself is distinct from this original moment, so that a limited or false consciousness of self is possible. As such the task of the self is to recognize (that is, to realize in and through self-consciousness) who it most truly is, both in relation to God, and in relation to self and other. (shrink)

Radical Enlightenment – Spinoza’s Demiurgic Role in the Formation of the Idea of Enlightenment? In his monograph devoted to the history of enlightenment, Radical Enlightenment. Philosophy and the Making of Modernity (1650-1750) British historian Jonathan Irvine Israel formulated a new theory of dating, sources, and the nature of this period of history. Israel attributed a major role in the formation of the concepts of enlightenment to the philosophy of Spinoza (1632-1677). The work has caused a series of controversies and criticisms (...) concerning the assessment of facts related to the history of ideas. In this article I refer to interpretations of the role of Spinoza’s philosophy and its early reception between 1663-1678 when it had a direct influence. The political situation in the Netherlands in the period of 1648-1677 (i.e. from the gaining of independence to the death of Spinoza) and the fate of the philosophy of Descartes (since 1650) are two significant factors that played an important role in shaping the initial reception of Spinozism and determined the fate of that philosophy for a long time. (shrink)

This paper focuses on Foucault's concept of the Panopticon. The Panopticon since time immemorial has been used as a concept in order to control society. Since this is being used as a tool to control society, this then is considered to be a form of technology of which is being used by individuals who hold power.

This is an excerpt of Aquinas' proof of the existence of God. In proving God's existence, Aquinas lays out a cosmological argument of which also sets that tone for his seminal work in epistemology.

Töz problemi Antik Çağ’dan bu yana farklı adlandırmalar, farklı yorumlamalar şeklinde tartışılmaktadır. Bu çalışma, modern felsefenin kurucularından ve rasyonalist düşünürler olan René Descartes’ın epistemolojisinde ve Benedictus Spinoza’nın ontolojisinde oldukça ciddi bir öneme sahip olan töz kavramının neye karşılık geldiğini ve ortaya çıkardığı temel problemleri ele almaktadır. Descartes’ın birden fazla tözün olabileceği fikri ile düalist bir töz anlayışı geliştirdiği yerde, Spinoza Descartes’a bir eleştiri olarak tek bir tözün kabulüne dayalı monist bir töz anlayışı geliştirmiştir. Doğal olarak bu çalışma (...) töz kavramına tarihsel bir çerçeve çizerek, Descartes’ın ruh-beden düalizmine dayanan töz anlayışı ile Spinoza’nın Tanrı temelli töz anlayışını karşılaştırmayı amaçlamaktadır. (shrink)

A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of n = 3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite (...) descent. The infinite descent is linked to induction starting from n = 3 by modus tollens. An inductive series of modus tollens is constructed. The proof of the series by induction is equivalent to Fermat’s last theorem. As far as Fermat had been proved the theorem for n = 4, one can suggest that the proof for n ≥ 4 was accessible to him. An idea for an elementary arithmetical proof of Fermat’s last theorem (FLT) by induction is suggested. It would be accessible to Fermat unlike Wiles’s proof (1995). (shrink)

In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case (...) for “n = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it. (shrink)

The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a (...) subspace of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart. (shrink)

The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. (...) The relevant mathematical structure is Hilbert arithmetic in a wide sense, in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem. (shrink)

In his Meditations Descartes concludes that he is a res cogitans, an unextended entity whose essence is to be conscious. His reasoning in support of the conclusion that he exists entirely distinct from his body has seemed unconvincing to his critics. I attempt to show that the reasoning which he offers in support of his conclusion. although mistaken, is more plausible and his mistakes more interesting than his critics have acknowledged.

Descartes is widely portrayed as the arch proponent of “the epistemological transparency of thought” (or simply, “Transparency”). The most promising version of this view—Transparency-through-Introspection—says that introspecting (i.e., inwardly attending to) a thought guarantees certain knowledge of that thought. But Descartes rejects this view and provides numerous counterexamples to it. I argue that, instead, Descartes’s theory of self-knowledge is just an application of his general theory of knowledge. According to his general theory, certain knowledge is acquired only through (...) clear and distinct intellection. Thus, in his view, certain knowledge of one’s thoughts is acquired only through clear and distinct intellection of one’s thoughts. Introspection is a form of intellection and it can be clear and distinct. Ordinarily, however, introspection isn’t clear and distinct but is instead confused with dubitable perceptions of bodies. To make introspection clear and distinct, we need to “sharply separate” it from all perceptions of bodies by doubting all perceptions of bodies. Without such radical doubt, introspection remains confused and we lack certain knowledge not just of the specific features of our thoughts, but even of the minimal claim that a thought exists. Far from being the high priest of Transparency, Descartes is radically opposed to it. (shrink)

This paper is on Descartes’ account of modality and, in particular, his account of the necessity of the laws of nature. He famously argues that the necessity of the “eternal truths” of logic and mathematics depends on God’s will. Here I suggest he has the same view about the necessity of the laws of nature. Further, I argue, this is a plausible theory of laws. For philosophers often talk about something being nomologically or physically necessary because of the laws (...) of nature, but this necessity is thought to be metaphysically contingent. However, they struggle to explain how the laws could be genuinely necessary while being metaphysically contingent. The chief advantage of Descartes view, I argue, is that God’s will can plausibly explain both the necessity of the laws and the contingency of the laws. So, Descartes’ theistic account of laws provides a plausible explanation, perhaps the best explanation, of the contingent-necessity of laws of nature. (shrink)

Descartes has a Clarity First epistemology: (i) Clarity is a primitive (indefinable) phenomenal quality: the appearance of truth. (ii) Clarity is prior to other qualities: obscurity, confusion, distinctness – are defined in terms of clarity; epistemic goods – reason to assent, rational inclination to assent, reliability, and knowledge – are explained by clarity. (This is the first of two companion entries; the sequel is called, "Descartes's Method for Achieving Knowledge.").

Conventional wisdom dictates that proofs of mathematical propositions should be treated as necessary, and sufficient, for entailing `significant' mathematical truths only if the proofs are expressed in a---minimally, deemed consistent---formal mathematical theory in terms of: * Axioms/Axiom schemas * Rules of Deduction * Definitions * Lemmas * Theorems * Corollaries. Whilst Andrew Wiles' proof of Fermat's Last Theorem FLT, which appeals essentially to geometrical properties of real and complex numbers, can be treated as meeting this criteria, it nevertheless leaves (...) two questions unanswered: (i) Why is x^n +y^n = z^n solvable only for n < 3 if x, y, z, n are natural numbers? (ii) What technique might Fermat have used that led him to, even if only briefly, believe he had `a truly marvellous demonstration' of FLT? Prevailing post-Wiles wisdom---leaving (i) essentially unaddressed---dismisses Fermat's claim as a conjecture without a plausible proof of FLT. -/- However, we posit that providing evidence-based answers to both queries is necessary not only for treating FLT as significant, but also for understanding why FLT can be treated as a true arithmetical proposition. We thus argue that proving a theorem formally from explicit, and implicit, premises/axioms using rules of deduction---as currently accepted---is a meaningless game, of little scientific value, in the absence of evidence that has already established---unambiguously---why the premises/axioms and rules of deduction can be treated, and categorically communicated, as pre-formal truths in Marcus Pantsar's sense. Consequently, only evidence-based, pre-formal, truth can entail formal provability; and the formal proof of any significant mathematical theorem cannot entail its pre-formal truth as evidence-based. It can only identify the explicit/implicit premises that have been used to evidence the, already established, pre-formal truth of a mathematical proposition. Hence visualising and understanding the evidence-based, pre-formal, truth of a mathematical proposition is the only raison d'etre for subsequently seeking a formal proof of the proposition within a formal mathematical language (whether first-order or second order set theory, arithmetic, geometry, etc.) By this yardstick Andrew Wiles' proof of FLT fails to meet the required, evidence-based, criteria for entailing a true arithmetical proposition. -/- Moreover, we offer two scenarios as to why/how Fermat could have laconically concluded in his recorded marginal noting that FLT is a true arithmetical proposition---even though he either did not (or could not to his own satisfaction) succeed in cogently evidencing, and recording, why FLT can be treated as an evidence-based, pre-formal, arithmetical truth (presumably without appeal to properties of real and complex numbers). It is primarily such a putative, unrecorded, evidence-based reasoning underlying Fermat's laconic assertion which this investigation seeks to reconstruct; and to justify by appeal to a plausible resolution of some philosophical ambiguities concerning the relation between evidence-based, pre-formal, truth and formal provability. (shrink)

Descartes’s cogito – I am thinking, therefore I am – is an intuitive deduction. Contrary to Transparency, certainty of I am thinking does not come easily; it’s achieved by making introspection perfectly clear through radical doubt. Scientia – rational immunity to doubt – comes with the habit of intuiting with perfect clarity that skepticism is false. (This is the second of two companion entries; the prequel is called, "Descartes's Clarity First Epistemology.").

Descartes's approach to practical judgments about what is beneficial or harmful, or what to pursue or avoid, is almost exactly the opposite of his approach to theoretical judgments about the true nature of things. Instead of the cautious skepticism for which Descartes is known, throughout his ethical writings he recommends developing the habit of making firm judgments and resolutely carrying them out, no matter how doubtful and uncertain they may be. Descartes, strikingly, takes irresolution to be the (...) source of remorse and repentance, of vice, and of a weak soul. In order to explain its dangerousness, this essay offers an analysis of irresolution as a failure of the will to determine itself to follow a judgment in the face of ignorance or uncertainty. This analysis connects irresolution to weakness of will and explains why Descartes regards resolution as an essential component of virtue. (shrink)

This paper examines Descartes' problematic relational theory of motion, especially when viewed within the context of his dynamics, the Cartesian natural laws. The work of various commentators on Cartesian motion is also surveyed, with particular emphasis placed upon the recent important texts of Garber and Des Chene. In contrast to the methodology of most previous interpretations, however, this essay employs a modern "spacetime" approach to the problem. By this means, the role of dynamics in Descartes' theory, which has (...) often been neglected in favor of kinematic factors, is shown to be central to finding a solution to the puzzle of Cartesian motion. (shrink)

This article examines how deduction preserves certainty and how much certainty it can preserve according to Descartes’s Rules for the Direction of the Mind. I argue that the certainty of a deduction is a matter of four conditions for Descartes. First, certainty depends on whether the conjunction of simple propositions is composed with necessity or contingency. Second, a deduction approaches the certainty of an intuition depending on how many “acts of conceiving” it requires and—third—the complexity or difficulty of (...) the acts of thinking, which is determined by the content of the thoughts and on external factors. Fourth, certainty depends on the intellectual aptitude of the person using the deduction. A deduction lacks certainty when it relies on memory such that it is not apprehended with immediacy. However, the mental capacity and speed of a mind can be increased by training the special mental faculties of perspicacity and discernment. Increasing one’s intellectual aptitude allows for more steps of a deduction to be inferred in fewer acts of conceiving, thereby helping preserve the certainty of a deduction. (shrink)

That Descartes’ God is not a deceiver is amongst the canonical claims of early modern philosophy. The significance of this (purported) fact to the coherence of Descartes’ system is likewise canonical, infused in how we teach and think about the _Meditations_. Though prevalent, both ends of this narrative are suspect. We argue that Descartes’ color eliminativism, when coupled with his analysis of the cognitive structure of our sensory systems, entails that God is a deceiver. It’s doubtful that (...) Descartes recognized this, given his insistence that God is not a deceiver, and the role this plays in his system. But this is a concession Descartes can grant if we are careful about the kind of deception at play—a kind Descartes _does_ recognize, albeit not without some ambiguity. On our story, Descartes’ metaphysics and epistemology are not driven by concerns about deception _per se_, but by concerns about God’s _benevolence_. (shrink)

In this paper, I present an interpretation of Descartes that deemphasizes his skepticism. I analyze a selection of remarks from Descartes’ correspondence in which he makes judgments about the skeptics. I argue that such remarks display Descartes’ attitude of contempt for skeptical philosophy. Since Descartes associates the skeptics with the activity of constant and total doubting and yet presents scenarios that seemingly arise from extreme doubt—like the malicious demon hypothesis—I look at what Descartes says in (...) the correspondence about his own use of doubt in his published works. Descartes distances himself from the skeptics because he claims that whereas they doubt everything and, in so doing, act heretically, he uses doubt for a noble purpose. I suggest that although Descartes is influenced by skeptical ideas and considers skeptical argumentation to be useful, his strategic use of such argumentation should not lead us to believe that he condones skepticism. Quite the contrary, most of his remarks on the subject show that Descartes is highly critical or dismissive of skeptical ideas. Therefore, I argue that it is more accurate to characterize Descartes as a philosopher generally opposed to skepticism. (shrink)

The paper advances the hypothesis that René Descartes presents a skeptical system of philosophy in Thomas Reid’s reading. There is a sort of ‘involun-tary’ or ‘accidental’ skepticism that results from the adoption by Descartes of both a skeptical method and a skeptical principle. The first section shows to what extent the Cartesian method of doubt – which focuses on the reliability of the faculties of the mind - is a skeptical demand that cannot be satisfied. The second section (...) shows how the principle of the Cartesian system – which establishes that ideas are the immediate objects of the operations of the mind – is not only skeptic but leads exactly and naturally to the most radical form of skepticism, namely, solipsism. The third section discusses the Cartesian sources of the doubt on the existence of external world according to Reid. (shrink)

I argue that Descartes' Second Causal Proof of God in the Third Meditation evidences, and commits him to, the belief that time is "strongly discontinuous" -- that is, that there is actually a gap between each consecutive moment of time. Much of my article attempts to reconcile this interpretation, the "received view," with Descartes' statements about time, space, and matter in his other writings, including his correspondence with various philosophers.

An early modern scholastic conception of moral possibility helps make sense of Descartes's own perplexing use of that concept and solves the exegetical puzzles surrounding Descartes's conflicting remarks about free will.

In this paper, I explore René Descartes' conception of human freedom. I begin with the key interpretive challenges of Descartes' remarks and then turn to two foundational issues in the secondary literature: the philosophical backdrop of Descartes' remarks and the notions of freedom that commentators have used to characterize Descartes. The remainder of the paper is focused on the main current debate: Descartes' position on the relationship between freedom and determinism.

How coherent is Descartes' conception of vacuum in the Principles? Descartes' arguments attacking the possibility of vacuum are difficult to read and to understand because they reply to several distinct threads of discussion. I separate two strands that have received little careful attention: the scholastic topic of annihilation of space, particularly represented in Albert of Saxony, and the physical arguments concerning vacuum in Galileo that are also continued after the publication of the Principles in Pascal. The distinctness of (...) the two sorts of opponent accounts for Descartes' odd habit of summarily declaring vacuum "contradictory" in some contexts, while providing extended conceptual and physical arguments meant to establish its "impossibility" in others. In several passages late in the Principles, Descartes also considers the physical ramifications of "empty space," including a discussion of the appearance of a star, were an empty space situated at the center of the celestial vortex. I argue that the discussion allows for a sensible conception of space with extension, but without matter, quite adequate to the physical discussions of vacuum among Descartes' contemporaries. (shrink)

Descartes is notorious for holding a strong anti-vacuist position. On his view, according to the standard reading, empty space not only does not exist in nature, but it is logically impossible. The very notion of a void or vacuum is an incoherent one. Recently Eric Palmer has proposed a revisionist reading of Descartes on empty space, arguing that he is more sanguine about its possibility. Palmer makes use of Descartes’ early correspondence with Marin Mersenne, including his commentary (...) on Galileo’s Two New Sciences. I argue that Palmer’s reading is mistaken, and that it relies on an understandable but faulty inference—i.e., that if Descartes considers the implications of an opposing view, he must find it at least coherent. Descartes, as I show from his correspondence and other texts, uses a variety of persuasive strategies, and levels charges of different logical strength, against positions which he takes to be incoherent. Thus we cannot infer from the fact that Descartes argues, e.g., that something is a superfluous theoretical entity, that he admits that entity’s coherence. He often chooses to argue a weaker thesis against an opponent so that he can use an argument to which the opponent is more likely to agree. (shrink)

In this paper, I aim to address a specific issue underpinning Cartesian metaphysics since its first public appearance in the Discourse right up until the Meditations, but which definitely came to the surface in the Second and Fifth Replies. It involves the possibility that to be thinking and to be extended do not actually contrast as two entirely different properties; hence, these two essences cannot serve as the basis for a disjunctive, real distinction between two corresponding substances, the mind and (...) the body. I dub this problem the ‘thinking matter issue.’ I suggest that Descartes’s concerns about the ‘thinking matter issue’ characterizes and structures the entirety of Meditation Two and its connection with Meditation Six, especially in the attempt to covertly implement what I refer to as Descartes’s ‘prejudice strategy.’ The core of the ‘prejudice strategy’ lies in the idea that the ‘thinking matter issue’ is just a false problem, one raised by the inadequate notions of the mind and the body that we apply to this problem. In section 1, I set out the way in which the ‘thinking matter issue’ emerged in Descartes’s philosophy after the first exposition of his metaphysics in the Discourse. Section 2 deals with the new argumentative path Descartes draws for the Meditations and with the new role that he assigns to the inference about the mind’s non-physical nature after the cogito. In section 3, I contend that the ‘prejudice strategy’ structures Meditation Two and, partially, Six. Section 4 shows that Descartes himself reveals this in his Replies to the Second and the Fifth Set of Objections. In section 5, I delve into Descartes’s foundational theory of the ‘prejudice strategy,’ i.e. his theory of infancy as set out especially in the Replies to the Sixth Set of Objections. -/- . (shrink)

Planteamos el problema siguiente: Descartes contesta la acusación irracional de Voetius interpretando, excepcionalmente, los Evangelios y afirma que las _leyes de caridad _son _afines _a las _leyes de la amistad natural _que rigen las funciones del pastor y del profesor. Proponemos que Descartes excluye el examen de las virtudes teologales e incursiona en el derecho privado y civil para probar que Voetius no es un _verdadero _profesor, ni un _verdadero _pastor, y usurpa las atribuciones del juez. Frente a (...) la irracionalidad, la búsqueda de la verdad se despliega en el alegato jurídico. -/- Descartes and the laws of charity. Public and private law in the Letter to Voetius Abstract. We pose this problem: Descartes responds to Voetius’ irrational accusation by resorting once, on his own initiative, to Gospel, an interpretation that reviews the laws of charity as akin to the laws of natural friendship governing pastor and teacher roles. We propose that the Letter be a legal argument. Descartes has no interest in theological virtues: facing irrationality, he delves into private law to prove that Voetius is not a true teacher, or a true pastor, and encroaches on the function of judge. (shrink)

RESUMEN En la Carta a Voetius, Descartes escribe que su enemigo es el diablo, el enemigo. La acusación es etimológicamente coherente e introduce una excepción a la metafísica, una voluntad de mal. Finalmente, la malignidad odia la verdad : es deliberadamente irracional. Examinamos aquí la oratoria del mal: primero, sus recursos retóricos ; segundo, las pasiones que excita y su combinación en una pasión particular, la cólera piadosa; tercero, sus efectos: la disolución del vínculo civil entre ciudadanos y amistoso (...) entre familiares. -/- ABSTRACT In his Letter to Voetius, Descartes writes that his enemy is the devil, the enemy. The accusation is etymologically coherent and introduces an exception to metaphysics, a will to evil. Finally, malignity hates truth : it is deliberately irrational. The article examines the oratory of evil: first, its rhetorical devices ; second, the passions it elicits and their combination with a specific passion, pious rage; and third, its effects: the dissolution of the civil bond among citizens and the friendship bond family members. (shrink)

This essay explores the vexed issue of individual corporeal substance in Descartes' natural philosophy. Although Descartes' often referred to individual material objects as separate substances, the constraints on his definitions of matter and substance would seem to favor the opposite view; namely, that there exists only one corporeal substance, the plenum. In contrast to this standard interpretation, however, it will be demonstrated that Descartes' hypotheses make a fairly convincing case for the existence of individual material substances; and (...) the key to this new found individuation is a long neglected set of passages in the Principles of Philosophy. (shrink)