34 lines
917 B
Markdown
34 lines
917 B
Markdown
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---
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title: "cogito ergo sum"
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weight: 20
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---
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# cogito, ergo sum
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*'cogito, ergo sum'* is a latin phrase used as a philosophical proposition, which became a fundamental axiomatic truth within the boundaries of western philosophy, and has been used to assert the reality of one's own mind.
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in this text, we try to review this statement using formal propsitional logic.
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the phrase *'cogito, ergo sum'* (*'je pense, donc je suis'* in the original French) can be trivially reduced to a logical sentence
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{{< katex display=true >}}
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p \Rightarrow q
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{{< /katex >}}
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It is easy then to see that
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{{< katex display=true >}}
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(p\Rightarrow q)\iff (\neg q\Rightarrow\neg p)
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{{< /katex >}}
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where
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{{< katex display=false >}}
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\neg q\Rightarrow \neg p
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{{< /katex >}}
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is trivially true (otherwise *'to be'* would not be necessary for thought).
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Therefore
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{{< katex display=false >}}
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p\Rightarrow q
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{{< /katex >}}
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is true.
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