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There is an anecdote in which the participants were Wittgenstein and Carnap (or Hempel). One of the two had a book on parapsychology/paranormal stuff. The other scolded him for this. The book owner answered ‘It’s just an empirical matter’, meaning that the book made a set of claims and it was simply that reality was going to either confirm or disconfirm them, and that was it, there was no shame in hearing and testing claims. Can anyone help me with the details or source of this anecdote?

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See Vasso Kindi, Wittgenstein and Philosophy of Science, into Hans-Johann Glock & John Hyman (editors), A Companion to Wittgenstein (Blackwell, 2017), page 589:

Wittgenstein had studied science and engineering and appreciated the rigor and sharpness of the scientific way of thinking. It was Wittgenstein who dismissed Carnap’s scientific interest in parapsychological phenomena as not serious. Carnap thought that he would examine an important scientific problem with the impartiality and unprejudiced patience of a dissecting scientist. Wittgenstein “was shocked that any reasonable man could have any interest in such rubbish” (Carnap, 1963, [Intellectual Autobiography] p.26).

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Let me give the full citation:

"Rudolf Carnap: Intellectual Autobiography" in The Philosophy of Rudolf Carnap, edited by Paul Arthur Schilpp, The Library of Living Philosophers, vol. 11, Open Court, La Salle, III., and Cambridge University Press, London, 1963.

You may wish to search the Web for the mentioned book, somewhat poor quality pdfs of it are freely circulating on the Internet.

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