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I could give (but, not being a professional historian, nor a native Dutch speaker, only few) references and background-remarks, but I will keep this short, to make more use of what a Q&A-sites offers, hoping for a summary by professional hiostorians and philophers:

Question.

  • In constructivism (in the technical sense), is "mind" more or less merely a convenient monosyllabic and four-letter synonym for "algorithm/computer/lambda calculus/Turing machine", or is there more to the predilection of constructivists for using this word when describing what constructivism is about? (Such as in "proofs are object constructed by our minds".)

  • How much weight did Brouwer himself attach to using this problematic concept/word "mind" in describing his philosophy? Is there anything left of his writings in which he discusses this very point (i.e., whether "mind" and "algorithm" are interchangeable synonyms). Wouldn't he be so much better off by keeping to some objective metaphor, like calculating machines/clockworks/cogs/levers etc when it came to having his philosophy be adopted by others?

Remarks.

  • Part of my motivation for asking this is a censor-like "Oh, cut out that mind-bit!"-reaction that I often have when doing background reading on constructivism.

  • I could imagine that Brouwer held opinions in the direction of mind-is-the-most-fundamental-concept-of-all-something-like-a-schopenhauerian-will-and-any-model-of-algorithm-will-be-driven-by-mind-too, or something like that, and would be interested in whether there are writings on that.

  • Would it be comparing apples with oranges to a professional philosopher to argue that " Brouwer's "mind" is Schopenhauer's "will" " ? EDIT: this is a vague question of course; let me give it precise variant here, more in the direction of comparative literature: have Brouwer's ideas and Schopenhauers concept of "will" been (recognizably) discussed in a published philosophical article? I think this improbable.

  • It ("mind") appears over and over again in writings on constructivism, also in very technical mathematical contexts, and is used by professional mathematicians/type theorists. My intuitive reaction to this always has been: Constructivism is just about equally platonic as platonism, and constructive proofs are an objective eternal reality as well, so why for goodness' sake do they always mix-in the m-word?

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  • $\begingroup$ Mind is a basic concept for Brouwer but we can hardly find a "theory of mind" in his thought, apart from the fundamental First act of Intuitionsim. $\endgroup$ – Mauro ALLEGRANZA Jul 17 '17 at 19:12
  • $\begingroup$ It does not seems to me that "mind appears over and over again in writings on constructivism, also in very technical mathematical contexts"; see e.g. Bishop's Foundations; the only significant occurrence of it is at page 1, where mathematics is defined as a "creation of our mind". $\endgroup$ – Mauro ALLEGRANZA Jul 17 '17 at 19:15
  • $\begingroup$ For Brouwer, for sure, mind is not synonym of algorithm; for B, math is independent of language. $\endgroup$ – Mauro ALLEGRANZA Jul 17 '17 at 19:16
  • $\begingroup$ @MauroALLEGRANZA: thanks for comments. Re "it does not seem to me": well, isn't Bishop's book pretty technical, and page one pretty significant? By "over and over" I meant "felt by me to appear in a large proportion of technical writing on the subject, with _one occurrence per work already counting for "occurs" ". Interesting point you make in "for B, math is independent of language" (I am unsure whether your use of "B" means "Brouwer" or "Bishop" though.) $\endgroup$ – Peter Heinig Jul 18 '17 at 4:43
  • $\begingroup$ I agree that Bishop's book is very "technical", but it seems to me that the concept of mind does not play any significant role in it :-) $\endgroup$ – Mauro ALLEGRANZA Jul 18 '17 at 6:38
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Regarding the algorithmic conception of the mind:

He may not have known how the brain/computer worked exactly, but it's a reasonable assumption that it involves procedures and memory, which are analogous to the way computers function.

There has been much resistance to this idea, making the point that the human brain is not a digital computer, but it is unclear to what degree detractors understand computing at a fundamental level, which is not restricted to microprocessors.

I personally prefer the term "algorithmic intelligence" over "artificial intelligence" because it is more precise and descriptive, and doesn't carry the stigma of artificiality. (Philip Dick, the narrative philosopher, has a very famous meditation, partly on this subject.)

There is much we don't understand about consciousness or the workings of the human mind, but materialists would assume any functions to be ultimately rooted in nature. (Conway's Game of Life has theoretical implications regarding algorithmic intelligence/super intelligence, regarding such as merely functions of the complexity of the system.)

I can't comment on Brouwer or Brouwer Schopenhauer, but hopefully this sheds some light on the "proceduralist" conception (if I can rebrand that term to give it a computer science definition;)

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