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Dan Dolderman

SOPINOZA READING: Please read up to the top of page 8 where the short proof for existence of God ends. There is a longer proof presented further down in page 9. This reading is intended to help us see how philosophers after Descartes based the truth on Geometric proofs. In the words of Foucault it is the Episteme of the time that encourages the truth to be mathematically structured and proven (derived.) Please compare this writing with the geometry proofs (in the Greek constructions.) Along the way we also learn about the structure and format of a mathematical theory. Spinoza’s argument for proving existence of God is known as ‘geometric argument’ because it is modeled after Euclid’s style of axiomatization of geometry (remember axiomatization is about the priority of form/structure over the content, in establishing the truth.) A mathematical theory consists of the following elements: 1. There is an underlying language in which the theory is formulated, and the theory is about the objects defined in that language. For example in the theory of Euclidean geometry the objects are points, lines, circles, etc. In the case of Spinoza the objects of the theory are the concepts such as: ‘CAUSE OF ITSELF’, FINITE, SUBSTANCE, ATTRIBUTE, GOD, FREE, ETERNITY. We don’t need to know what they mean, but the only thing we know is the way Spinoza wants to use them. 2. This language has its syntax (rules that govern the formation of correct statements,) and semantics, (rules which determines how meaning is created and what truth-values in a language are.) In mathematic it is Syntax that is the form (which is prior to content and the source of truth.) Semantics is about the truth of a statement. In Spinoza’s case the syntax is how these concepts are to mingle; it is grammar of Latin (or whichever language he used), but also the way a philosopher used to combine the objects of language to compose loner statements. 3. And there are rules of derivation (for valid deductions,) which in the case of Spinoza or philosophical arguments we tend to refer to as common sense arguments! 4. And there are Axioms, which are a collection of statements that are taken to be true with no proof or justifications. Axioms are considered to be very trivial to our common sense, however beware that axioms in geometry and also in Spinoza’s work are very cleverly designed so that they make the proofs work. 5. Then we arrive at propositions or derivations: these are ‘true statements’ that can be deduced or proven from the definitions and/or axioms using the rules of derivation. 6. Armed with all these, a theory is the collection of all the ‘true statements’ (which includes propositions and axioms) of the particular language of the theory. Important ideas to watch for: When you read Spinoza please note that there is a reason for defining the concepts the way he defined them, and there is a reason for choosing the axioms the way he presented them. All these definitions and axioms are to fit together to form a proof. Think of the proof as a jigsaw puzzle, whose pieces nicely fit into one another to make up a complete picture. Do you think the jigsaw puzzle factory makes the pieces first, or that they make the full picture first and then they cut the full picture into jigsaw pieces? Perhaps Spinoza first designed his proofs and then added whatever he needed as axioms (true statements) of his theory. Please be prepared to comment on this. As the proofs progress please notice the following patterns and be prepared to comment on them. a. Language and the grammar actually force certain (proof) ideas on the theory builder. b. How does Spinoza, alter the shape of a word or the mode of a phrase or the usage of a vocabulary in order to achieve the desired format of a statement that fits into his definition. Here is his argument for proving existence of God: 1. God is a substance (by Spinoza’s definition of God, Definition VI) therefore it is sufficient to prove that any substance must exist. 2. Indeed he proves that a substance cannot be assumed not to exist (therefore any substance must exist!) Do you think that something that cannot be assumed not to exist must then exist?! 3. In fact Spinoza thinks that if he assumes that substance does not exist then he has conceived the substance as not existing. (Are these two concepts the same?) 4. Axiom VII: if something can be conceived as non existing then its essence must involve non existence, (that is, an attribute of that thing is non-existence.) For example dictionary definition of a unicorn is: a mythical horse-like animal with a single horn. As you see the mythical is part of the definition of a unicorn, therefore the essence of a unicorn, among other things, involves non-existence. 5. But the essence of a substance involves existence, therefore this would be a contradiction to the assumption that substance may not exist. But why does the essence of a substance must involve existing? Here we present Spinoza’s argument in this regard. Notice how this
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