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Descartes' Project Descartes’ Project (Rene Descartes, 1596-1650) Descartes’ Project. • His central philosophical project was to build a theory of knowledge, a theory that would apply to our knowledge of the ordinary physical objects and events around us. • This project was influenced by three very NEW ideas (for his time) —actually one old idea (the notion of mathematical proof), and two new ones (the notion of scientific proof and the his own invention of algebra). 1 A. The notion of a mathematical proof. How do you prove that the sum of the interior angles of a triangle is always equal to 180 degrees? 1. Draw two parallel lines. 2 1. Draw two parallel lines. 2. Draw two lines that intersect the parallel lines to form a triangle 1. Draw two parallel lines. 2. Draw two lines that intersect the parallel lines to form a triangle 3 3. Name the angles of the triangle for convenience. A B C To begin any proof, you must start with a set of axioms—some set of rules you know to be true. A B C 4 Here are two “indubitable” facts of geometry. A. A straight line subtends 180 degrees. You know this because a circle subtends 360 degrees (by definition) and if we divide the circle in half with a line then 1/2 X 360 = 1800 Here are two “indubitable” facts of geometry. A. A straight line subtends 180 degrees. B. When a line intersects two parallel lines, the two interior angles on opposite sides of the line, are equal. A A 5 So, start with a triangle, ABC. A B C So, start with a triangle, ABC. 1. Angle B = Angle B’ B’ A B C 6 So, start with a triangle, ABC. 1. Angle B = Angle B’ 2. Angle C = Angle C’ C’ B A B C So, start with a triangle, ABC. 1. Angle B = Angle B’ 2. Angle C = Angle C’ 3. Angles A, B’ and C’ together equal 1800 4. The interior angles of the triangle, A + B + C = 1800 C’ B’ A B C 7 To form a proof—any sort of proof—you need two things: 1. A set of axioms that are self-evidently true. 2. A set of logical rules that, when applied to the axioms, will yield conclusions that are also true. e.g. If p then q, p, therefore q. If you have these two things—premises you know to be true and rules for moving beyond the premises, preserve the truth of the premises—then you are assured true conclusions. Your proof is truth-preserving: starting with true premises, you are guaranteed true conclusions. The Principle of Deductive Closure: If you have two premises, A and B, and if you know A and you know B, and if from A and B together, C follows logically, then if you believe C, you know C. 8 Given the Principle of Deductive Closure, it is easy to see why Descartes is so attracted to a foundational system of knowledge—because if he starts with the right axioms, and proceeds using the rules of logic, he is guaranteed that his system will get him truths about the world. That’s the good news. 9 That’s the good news. Here’s the Bad News. That’s the good news. Here’s the Bad News. Why would ANYONE think that it would be possible to make such a system for proving facts about the nature of the world as opposed to facts about mathematics? About the common objects we run into — about people and trees and plants and chairs? How is THAT supposed to work? 10 The Answer: Descartes’ is counting on the truth of two more views about the nature of science. A. A mechanistic/causal view of the world in which we can explain the behavior of large-scale visible objects in terms of the properties of very small, invisible objects —the ultimate constituents of reality, and; B. Each of us “comes with” certain innate knowledge about the nature of those ultimate constituents which we can discern by careful thought. The Old View: Aristotle’s View (384 -322 BC) The Nature of Objects according to Aristotle Aristotle thinks of objects, not just as existing at a single time, but as existing through time—as having a beginning or birth, a life span, and an end or death. In this sense, Aristotle’s view is quite organic; we can make sense of it best if we think about living organisms as the paradigms of objects. 11 A Substance (an object) = Form + Matter A “substantial form” is the form which any object has throughout its entire life span, the form which defines that object at each moment at which it exists. How and why do objects change the way they do? What accounts for the patterns of change we see in objects? The Famous Ham Sandwich Question. There are two things, a ham sandwich and you. You take the ham sandwich, put it into your mouth, chew it up and ingest it. Some of the ham sandwich becomes a part of you; other parts of the ham sandwich which the body cannot use are excreted. WHY? 12 Of course this is usual sequence of events—this is what usually happens. But WHY? Couldn’t it the story have turned out differently? Of course this is usual sequence of events—this is what usually happens. But WHY? Couldn’t it the story have turned out differently? There are two things, a ham sandwich and you. 13 Of course this is usual sequence of events—this is what usually happens. But WHY? Couldn’t it the story have turned out differently? There are two things, a ham sandwich and you. You take the ham sandwich, put it into your mouth, chew it up and ingest it. Of course this is usual sequence of events—this is what usually happens. But WHY? Couldn’t it the story have turned out differently? There are two things, a ham sandwich and you. You take the ham sandwich, put it into your mouth, chew it up and ingest it. Parts of you turn into the ham sandwich, making a bigger (and no doubt) better ham sandwich. 14 Of course this is usual sequence of events—this is what usually happens. But WHY? Couldn’t it the story have turned out differently? There are two things, a ham sandwich and you. You take the ham sandwich, put it into your mouth, chew it up and ingest it. Parts of you turn into the ham sandwich, making a bigger (and no doubt) better ham sandwich. Other parts of you are not needed for the bigger and better ham sandwich, and they are excreted from the ham sandwich. If this alternative scenario is possible (i.e. if there is a possible world in which this occurs), then we need to explain why what does happen is what happens — why the ham sandwich turns into you and not the other way around. 15 Aristotle’s Answer There are four kinds of causes in the world — I.e. things that affect or bring about change. Material causes: what the object is made of Efficient causes: the events that brought it into being Formal cause: what it is; its substantial form Final cause: what it is for, its role in the world The process of change is not random: it is governed by the formal and final causes of a substance (object). The goal of science according to Aristotle is the discovery of formal and final causes. Formal and final causes are discoverable by observation. By observing an object over the course of its lifetime, we can see: • what it is (essentially) or its formal cause; • what it is for, its final cause. In other words, although such causes are not sensible (immediately apparent to the senses), they are none the less known by observation: by the careful observation of the life events of the object. Therefore, the challenge of science is to explain the observable events/properties of the world in terms of other observable properties. 16 The new conception of science a. the advent of experimental method in the sciences; the postulation of hypotheses which are then tested. b. the explanation of the observable features of the world in terms of their hidden constituents (Galileo’s Corpuscular theory) The final element: Descartes’ own discovery/invention of algebra What analytic geometry does, in effect, is to “translate” geometric forms into algebraic equations. Its gives us a way of describing, using an equation, a geometric form. And of course, once we have these equations, we can use them in mathematical proofs. 17 PUTTING IT TOGETHER. Descartes’ Great Idea PUTTING IT TOGETHER. Descartes’ Great Idea 1. The New Science. What science is about is describing the nature and interaction of the ultimate constituents of reality. 18 PUTTING IT TOGETHER. Descartes’ Great Idea. 1. The New Science. What science is about is describing the nature and interaction of the ultimate constituents of reality. 2. The Thesis of Rationalism. We come into the world with, in some sense, knowledge of the most basic principles of physics—of the notion of a cause, of the understanding that matter must take up space, that one things cannot be in two different places at one, etc. PUTTING IT TOGETHER. Descartes’ Great Idea 1. The New Science. What science is about is describing the nature and interaction of the ultimate constituents of reality. 2. The Thesis of Rationalism. We come into the world with, in some sense, knowledge of the most basic principles of physics—of the notion of a cause, of the understanding that matter must take up space, that one things cannot be in two different places at one, etc.
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