Próba aksjomatycznego ujęcia jaźni

Psychologists use identity’s and Ego’s conceptions. The first conception is not clear, the second one from logical point of view is not correct. The aim of this article is to provide the definition of these two conceptions. Let: 1. P(=) is psychological (logical) identity’s indication2. o, o 1 , o 2 ,.. (e, e 1 , e 2 ,..) are people’s (Ego’s) variables3. j is the function’s indication. The expressions: j(o) (j (o i )), dla i>0, we read:person’s Ego o (o i ).The psychological identity’s definition provided in the article is as follows:(P 1 ) ∀o (oPo),(P 2 ) ∀o 1 ∀o 2 (o 1 Po 2 → o 2 Po 1 ),(P 3 ) ∀o 1 ∀o 2 ∀o 3 (o 1 Po 2 ∧ o 2 Po 3 → o 1 Po 3 ),(P 4 ) ∀o∀o 1 ∀o 2 ∀o 3 ∀R [(oRo) ∧ (o 1 Ro 2 → o 2 Ro 1 ) ∧ (o 1 Ro 2 ∧ o 2 Ro 3 →o 1 Ro 3 ) ∧ (o 1 Po 2 → o 1 Ro 2 )].And the Ego is defined as follows:(I) ∀e (e = e),(J 1 ) ∀e∃o [j(o) = e],(J 2 ) ∀e∃o [j(o) = e],(J 3 ) ∀o 1 ∀o 2 [j(o 1 ) = j(o 2 ) ≡ o 1 Po 2 ],(J 4 ) ∀e∀o (e ≠ o),(J 5 ) ∀e∀o ~ (ePo),(J 6 ) ∀e 1 ∀e 2 ~ (e 1 Pe 2 ).