33 lines
917 B
Markdown
33 lines
917 B
Markdown
---
|
|
title: "cogito ergo sum"
|
|
weight: 20
|
|
---
|
|
|
|
# cogito, ergo sum
|
|
|
|
*'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.
|
|
|
|
in this text, we try to review this statement using formal propsitional logic.
|
|
|
|
the phrase *'cogito, ergo sum'* (*'je pense, donc je suis'* in the original French) can be trivially reduced to a logical sentence
|
|
|
|
{{< katex display=true >}}
|
|
p \Rightarrow q
|
|
{{< /katex >}}
|
|
|
|
It is easy then to see that
|
|
{{< katex display=true >}}
|
|
(p\Rightarrow q)\iff (\neg q\Rightarrow\neg p)
|
|
{{< /katex >}}
|
|
|
|
where
|
|
{{< katex display=false >}}
|
|
\neg q\Rightarrow \neg p
|
|
{{< /katex >}}
|
|
is trivially true (otherwise *'to be'* would not be necessary for thought).
|
|
|
|
Therefore
|
|
{{< katex display=false >}}
|
|
p\Rightarrow q
|
|
{{< /katex >}}
|
|
is true.
|