From 29a570918721fd5d73bb140a9fb3bfa3e5647b9f Mon Sep 17 00:00:00 2001 From: aethrvmn Date: Sat, 30 Aug 2025 15:18:29 +0200 Subject: added content --- content/theses/misc/cogito-ergo-sum.md | 31 +++++++++++++++++++++++++++++++ 1 file changed, 31 insertions(+) create mode 100755 content/theses/misc/cogito-ergo-sum.md (limited to 'content/theses/misc/cogito-ergo-sum.md') diff --git a/content/theses/misc/cogito-ergo-sum.md b/content/theses/misc/cogito-ergo-sum.md new file mode 100755 index 0000000..e3cb024 --- /dev/null +++ b/content/theses/misc/cogito-ergo-sum.md @@ -0,0 +1,31 @@ +--- +title: "cogito ergo sum" +weight: 20 +--- + +*'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. -- cgit v1.2.3