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Paranoid-schizoid and depressive positions will from now on be called by me, ‘the Positions’, as a matter of convenience.
The Positions are emotional experiences intrinsic to work. All anxiety is related ultimately to The Anxiety, which has two roots:
the contents of the Oedipal situation, which has as its scientific deductive system (s.d.s.) the Theorem of Pythagoras and as its calculus the relevant portions of algebraic geometry;
fear of the Positions, which have as their s.d.s. the Pons Asinorum, Euclid I.5, and its associated algebraic calculus.
Both theorems have always engaged the attention of mankind and have been confused with each other by name, e.g. the French call I.47 the Pons Asinorum (see Heath [1956], Euclid, p. 417).
The I.47 Oedipus and I.5 Pons Asinorum belong to different axes in human knowledge, but they intersect: one is related to content of knowledge (I.47 Oedipus), the other to acquisition of knowledge (I.5 Positions).
The Oedipal situation may occupy different positions in the hierarchy of hypotheses in different s.d.s's. In some it may be an initial formula; in others, a derived formula according to the function which the associated calculus is intended to fulfil.
There must be a counterpart to this in non-scientific discipline, and the same difference in hierarchical positions will be observed.
The s.d.s. associated with Euclid I.5 and the algebraic calculus associated with it are all associated with the Positions.
The Oedipal situation is associated with Euclid I.47 and its associated s.d.s. (if different from the theorem itself) and its associated algebraic calculus.