foundation of it I take to be, that Belief and Disbelief {by this Mill means taking something as true and taking something as false} are two different mental states, excluding one another. This we know by the simplest obser-vation of our own minds. (System of Logic, bk. 2, chap. 7)8
Thus it is a matter of the ability of our mind to observe in an experiential way; and this shows that taking a proposition as true and taking the same proposition as false are two different states of mind. We meet up with this in observing our minds or our inner life. Continuing:
And if we carry our observation outwards {i.e., in words}, we also find that light and darkness, sound and silence, motion and quiescence, equality and inequality, preceding and following, succession and simultaneous-ness, any positive phenomenon whatever and its negative, are distinct phenomena, pointedly contrasted, and the one {namely, affirmation} [40] always absent where the other {negation} is present. I consider the maxim in question to be a generalization from all these facts. (John Stuart Mill, Gesammelte Werke, 1884, vol. 2, p. 326)9
The principle of contradiction is merely a generalization of matters of fact, both physical facts in the outer world and mental states of affairs. There are physical incompatibilities, things that cannot subsist together.10 The same holds for facts of the mental world. States of belief and disbelief—i.e., holding something to be true and holding the same thing to be not true—these two acts are incompatible with each other. Affirming and denying the same proposition make it impossible for them to be co-present in one and the same mind.
The axiom [of non-contradiction] merely states these same facts in a general form when it speaks of propositions that can apply either to the physical or the mental.
Sigwart’s logic has essentially defined the inquiry into logic since
8. [John Stuart Mill, A System of Logic, Rationative and Inductive, in CW, vol. 7, pp. 277–278. The glosses by Heidegger do not show up in GA 21 and are taken from Moser, pp. 82–83.]
9. [This reference, which does not appear in Moser or Weiss, is to John Stuart Mill, Gesammelte Werke, 2nd edition, ed. Theodor Gomperz (Leipzig: Fues, 1884). In the Logische Untersuchungen, Husserl used Gomperz’s first edition (1872–1873), in which the cited text appears at vol. 1, p. 298, and where the reference is to §4 (§5 was added in the 1872 English edition of Mill’s work, which is not reflected in Gomperz’s first German edition). See LU, vol. 1, §25, p. 79 / tr. 111–112.]
10. [At this point in Heidegger’s own manuscript (as published in GA 21, p. 40.7) there appears the following: “(cf. Leibniz’s ‘intra’–the ‘simul’),” i.e., “(compare Leibniz: ‘between’ and the ‘at the same time’).” There is no evidence in Moser or Weiss that he spoke these words during this lecture.]