added small thesis

content/texts/theses/cogito/_index.md

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+---
+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.