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Philosophy

PHL210Y1

Dan Dolderman

Summer

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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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