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

It is easy then to see that \[ (p\Rightarrow q)\iff (\neg q\Rightarrow\neg p)\]

where \( \neg q\Rightarrow \neg p\) is trivially true (otherwise ’to be’ would not be necessary for thought).

Therefore \(p\Rightarrow q\) is true.