In Psychological Types §540, Jung says of Hegel:
As forerunners of Nietzsche’s intuitive approach I would mention Schopenhauer and Hegel, the former because his intuitive feelings had such a decisive influence on his thinking, the latter because of the intuitive ideas that underlie his whole system. In both cases, however, intuition was subordinated to intellect, but with Nietzsche it ranked above it.
Which means that T ranks higher than N in Hegel (and Schopenhauer). According to Jung, Hegel is thus either an ENTJ or an INTP.
As for Schopenhauer, Jung also says of him in Psychological Types §322:
Negation, therefore, is itself an attitude to the world, a particularly Schopenhauerian attitude that on the one hand is purely intellectual and rational, and on the other a profound feeling of mystical identity with the world. This attitude is introverted; it suffers therefore from its typological antithesis.
Taking these claims in conjunction, then, Schopenhauer can in Jung’s estimation can only be INTP.
* We are grateful to the users ‘Jungster’ and ‘DesmondPlusFaraday’ for working out the details of Jung’s claims here.
Update: May 2013: In The Psychology of C.G. Jung (1942), Jung’s associate Jolande Jacobi says:
“Kant, for example, was a pure thinking type, while Schopenhauer must be regarded as an intuitive thinking type.” (p. 13)
In making this statement, it would seem that Jacobi is alluding to Psychological Types §540 and §632) for these statements. What is interesting to us is that Jolande’s reading seems to be closer to the spirit of Psychological Types than the ever so many attempts to extract statements concerning specific function orders from that work. A tendency that we have been guilty of ourselves. – We should furthermore note that Jacobi had Jung himself to critique her work.
As a point of general interest, on the inferior function, she also quotes Jung to say: “You do not have it under your thumb; it has you.” (p. 17)