Simple Cartesianism
Problems and Prospects
Descartes’s Most Basic Argument
1. I can doubt that my body exists.
2. I cannot doubt that my mind exists.
3. Hence, my body is not the same as my mind; or
conversely, my mind is not the same as my body.
Made Valid
1. I can doubt that my body exists.
2. I cannot doubt that my mind exists.
3. So, my body has a property that my mind lacks, viz.
being able to be doubted by me as to whether it exists.
4. LL (or, the Indiscernibility of Identicals)
5. Hence, my body is not the same as my mind; or
conversely, my mind is not the same as my body.
A Refutation by Analogy (?)
1. Mindy believes that Gus Hall is a communist.
2. Mindy does not believe that her uncle is a communist.
3. So, Gus Hall has a property lacked by Mindy’s uncle, viz.
being believed by Mindy to be a communist.
4. LL (or, the Identity of Indiscernibles)
5. Hence, Mindy’s uncle is not the same as Gus Hall.
—Oh, but he is: Mindy’s father, a virulent anti-communist, has
shielded her from the horrible truth that Gus Hall is his brother.
Another (?)
1. Ralph cannot doubt that 17 is odd.
2. Ralph can doubt that the only prime number between 15 and 19
is odd.
3. So, 17 has a property lacked by the only prime number between
15 and 19, viz. being such that its being odd cannot be doubted
by Ralph.
4. LL (or, the Identity of Indiscernibles)
5. So, 17 is not the only prime number between 15 and 19.
—Hmm, is there another?
What has gone wrong?
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Common answer: LL does not apply in intensional
contexts.
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An intensional context is opaque opposed to
transparent.
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A context is transparent iff it is extensional
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A context is extensional iff co-referential terms
can be substituted salva veritate
Illustrations
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Consider the sentence:
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‘Jakub dropped a vase that he believed had been bequeathed to him by his Polish grandmother.’
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‘Jakub’ and ‘vase’ refer to objects—namely, Jakub, a man, and his vase, an artefact.
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Two terms are co-referential when they refer to the same object.
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Jakub is Jan’s father. So, ‘Jakub’ and ‘Jan’s father’ are co-referential.
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The word ‘Jakub’ occurs in an extensional context.
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So, we may say, without altering the truth value of our sentence, ‘Jan’s father dropped a
vase that he believed had been bequeathed to him by his Polish grandmother.’
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Compare, however, two more co-referential terms ‘Jakub’s Polish grandmother’ and ‘the
most renown pianist in Krakow in the 1920s’.
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The phrase ‘his Polish grandmother’ appears in a non-extensional, or intensional context.
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We may not say, then, without threat of altering the truth value of our sentence: ‘Jakub
dropped a vase that he believed had been bequeathed to him by the most renown
pianist in Krakow in the 1920s.’
A Second Feature of Extensional Contexts
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Existential Generalisation yields acceptable results.
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That is, we can infer (b) from (a):
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(a) ‘Jakub dropped a vase.’
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(b) ‘Jakub dropped something.’
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And thence to (c):
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There is something that Jakub dropped.
Compare:
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(a) ’Jakub believed that there was a man hiding in the woods, waiting to ambush him and steal his
vase.’
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(b) ’Jakub believed that there was something hiding in the woods, waiting to ambush him and steal
his vase.’
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And thence to (c):
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‘There was something hiding in the woods, believed by Jakub to be waiting to ambush him and
steal his vase.’
The Logic of these Features
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Substitution salva veritate:
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Fa; a = b; therefore, Fb.
Existential Generalisation:
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Fa; therefore, ∃x(Fx)
The Main Complaint about Descartes’s Argument
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LL applies only in extensional contexts.
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Descartes applies LL to an intensional context.
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Hence, Descartes’s basic argument is unsound.
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If we accept that, an interesting pair of questions
remains:
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Precisely which premiss should we reject?
Why?