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^{2}*The Logical Syntax of Language*, p. 5.

^{3}Paul Lorenzen emphasizes this in "Methodical Thinking,"
*Ratio*, June 1965. For more from Lorenzen, see *Constructive
Philosophy* (1987).

^{4}I don't want to adduce a sheaf of references to support this. It
is enough to add Kurt Gödel, "Russell's Mathematical Logic," in *The
Philosophy of Bertrand Russell*, ed. Paul A. Schilpp (1944), p. 137.

^{5}K.G. Binmore, *The Foundations of Analysis*, Book 1, p. 5.

^{6}F.P. Ramsey, *The Foundations of Mathematics* (1931), pp.
20-21.

^{7}I introduced the notion of a Failure Theorem in "Anti-Mathematics"
(1980).

^{8}Cf. Michael Dummett, *Elements of Intuitionism* (1977),
p.10.

^{9}*From Frege to Gödel*, p. 460.

^{10}Whittaker & Watson, *A Course of Modern Analysis*, p.
3.

^{11}Brouwer's objective, infinitary solipsism was no help.

^{12}*The Logical Syntax of Language*, page 6. Incidentally, this
led me to propose moments of the person-world as propositions. Critical Notes
on Personhood, Part V.

^{13}Ibid., pp. 5-6.

^{14}Karl Menger, *Selected Papers* (1979), especially pp. 53-7.
On page 51, Menger notes that Sierpinski invented the method of defining a real
number by an unsolved problem.

^{15}Menger, *Selected Papers*, p. 57.

^{16}Menger, *Selected Papers*, p. 55.

^{17}Remark: In the classroom, Quine gave an example of a system with
only one symbol. Information is coded as the number of times the symbol is
repeated. But in this case more than ever, you have to be able to perform
real-world enumeration to read the system.

^{18}Cf. "The Flaws Underlying Beliefs," *Blueprint for a Higher
Civilization* (1975).

^{19}The last version of this exercise was called "A Refutation of
Arithmetic" (1988).

^{20}Again, as we are in the orbit of a negative universal result, the
explanations here are too casual. They have to be supplemented with more
rigorous treatments in other places, such as *Io* #41.

^{21}published in *Blueprint for a Higher Civilization*.

^{22}One could say that "semantics" came into concept art from the time
of "Subjective Propositional Vibration" (acronym SPV). *Blueprint for a
Higher Civilization*, p. 201.

^{23}Speculative sidelight: compare Gentzen's "consistency proof."

^{24}But Carnap told himself that he could pass to pure
combinatorics.

^{25}This is a notion supported by *The Logical Syntax of
Language*, p. 27, which has the term **'directly derivable'**.

*^{}published in *An Anthology*, ed. La Monte Young; see both
1963 and 1970 editions.

^{26}*Blueprint for a Higher Civilization*, pp. 87-94.

^{27}Not until 1987 would I begin to make new concept-art pieces, whose
framework-breaking features were far more focused and explicit.

^{28}already cited

^{29}or derivation, if you wish