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 I have adapted this explanation from Appendix D of Carnap's Meaning and Necessity. If I subsequently pass to a more rigorous explanation, it will be independent of Carnap.
 I consider the philosophic status of non-actual possibility to be a deep question which belongs academically in foundations of physics. I am the only author who has explored the question. The treatment of non-actual possibility in mathematical logic is only a formal scheme resting on a set theory in which there is no non-actual possibility.
 To experience the waterfall illusion, turn around and around in place with your eyes open. Then stop and gaze at a fixed area.
 Books published in 1975 by Feyerabend and myself independently cited the waterfall illusion as an anomaly which belies the vacuousness of inconsistency. I attempted to present an entire theory of "admissible contradictions," but my treatment was premature.
 Ultimately, mathematical logic is concerned only with infinities; its only ultimate ontological commitment is to the empty set--Zermelo's fiction.
 Actual first publication was in Fluxus cc V TRE No. 3, New York, March 1964. See also "The Flaws Underlying Beliefs," in Blueprint for a Higher Civilization. My last revision of "Primary Study" was in 1979.
 There is a full list of my pertinent manuscripts at the end.
 That is the conclusion I defend. Cf. my "Intuitive Objections to Numerical Infinity and Irrational Numbers."
 I have my own exposition of Brouwer's proof, written to be as accessible and confrontational as possible.
 Found in the essay now titled "Personhood and Destabilization."
 I used the paradoxical cube in "Logically Impossible Space," the room which I showed at the 1990 Venice Biennale.
 Touch the little finger of your right hand to the tips of the crossed middle and ring fingers of your left hand. Close your eyes. You should feel the little finger as one finger in your right hand and two fingers in your left hand.
 It is curious that for mathematical logic, a contingent paradox is just as dangerous as a paradox in tenets which one takes seriously. That is because of the issue of completeness: a theory may not have a legal sentence which cannot be stably classified as true or false.
 Disregarding the use of the phrase as a trope to describe in a cute, literary way a husband who avoids his wife. This can be expressed literally and consistently as de facto separation.
 But note the foolishness when Tarski comes to the question of whether there can be an infinity of linguistic expressions in the "real" world. (Logic Semantics Metamathematics, p. 174, fn. 2.) The scientistic formalists will not get what they want painlessly after all.
 In "The Apprehension of Plurality," Io #41.
 H. Flynt, "History of Logical Norms" (Jan. 1984), unpublished.