Euclid-proof

Synthetic a priori Judgments and Geometry

In the Prolegomena, Kant uses geometry as an example to show that we do have synthetic a priori knowledge. He argues that grasping how this kind of knowledge is possible there can lead to insights concerning the possibility (and the limits) of synthetic a priori knowledge in other areas, such as metaphysics. We will focus…

Photo of bust at Versailles, posted by Wally Gobetz https://www.flickr.com/photos/wallyg/1532378233

Meditations III and IV

In the first Meditation, we are trying as hard as we can to prevent ourselves from falling back on the comfortable acceptance of our long-held, customary beliefs; e.g., the belief that bodies exist, they cause our perceptions, and our perceptions resemble their causes (as Aristotelians and ‘common sense’ would have it); our belief that we…

https://upload.wikimedia.org/wikipedia/commons/8/83/Descartes3.jpg

Meditations I and II

Reading Questions for 1/21 For Thursday, 1/21, read the first two Meditations with the following questions in mind: What, according to Meditation I, can be called into doubt? How does the Meditator call into question beliefs about particular existing things that were acquired through the senses? How does the Meditator call into question beliefs about…

Modern Philosophy

Cartesian Ontology and First Philosophy

In my PHIL 202: Modern Philosophy course, we just finished a segment looking at Descartes in Context. We read Don Rutherford’s “Innovation and orthodoxy in modern philosophy”1, and some texts from Montaigne, Bacon, and Galileo, which are included in Ariew & Watkins’ Modern Philosophy anthology2, before working through the Meditations, selected Objections and Replies, Book I…

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ANP on Matter and Form

For those of you who still have some questions about what Aristotelian Natural Philosophy has to say about matter and form, here are some things that might help: Step 1. Forget everything you think you know about matter (free your conceptual apparatus from the particular determinate ways you have learned to characterize the physical matter…

Public Domain

If I were Galileo…

Here are some more things to think about in preparation for the short-answer portion of the mid-term, which we will be taking on Wednesday. If we get all the way through Innovation or Orthodoxy on Monday, I might ask you to talk me through the main points here as well: Imagine you are Galileo. You are…

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Descartes and Geometrical Demonstration

Reproduction of a proof from Euclid’s Elements (Public Domain: via Wikipedia Commons)   Those long chains of utterly simple and easy reasonings that geometers commonly use to arrive at their most difficult demonstrations had given me occasion to imagine that all the things that can fall within human knowledge follow from one another in the…