Constructive mathematics and unbounded operators -- a reply to Hellman (Q1902560)

The paper is an answer to \textit{G. Hellman} [``Constructive mathematics and quantum mechanics: Unbounded operators and the spectral theorem'', J. Philos. Logic 22, 221-248 (1993; Zbl 0801.03040)], who claims that constructive mathematics cannot cope with unbounded closed linear operators on a Hilbert space. The answer is based on showing that Hellman's analysis of a result of \textit{M. B. Pour-El} and \textit{J. I. Richards} [Computability in analysis and physics (1989; Zbl 0678.03027)] is wrong and that his ideas on the nature of acceptable domains for functions within constructive mathematics are inadequate. The paper contains some interesting reflections about the nature of constructive mathematics and may be useful for mathematicians not involved in the specific dispute but interested in a better understanding of constructive mathematics.