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underneath Tool Thinking is the belief that there are things about thinking that need to be concealed
Why do you think this? By "things about thinking", do you mean like, the criteria for deciding which tool to use? If so:
I think people do sometimes deploy toolbox-thinking in cases where they want to conceal why exactly they chose one tool over another. Lots of ethical debates go this way. But more often, it's about complexity rather than concealment: we choose our tools based on a myriad of small, nebulous, overlapping patterns, learned from diverse sources, some difficult to express in words, and the collective mass of them too large to communicate.
This post reminded me of the discussion of creativity in Carse's Finite and Infinite Games. He wrote that finite games are games (in a loose sense) with definite rules, with beginnings and ends, for which one can speak of preference orderings and optimizations. Infinite games have no end but may include finite games, and can be played but not won; they are played for the sake of playing. It makes no sense to talk about optimizing on an infinite game.
Modern art's surface-level boundary breaking can certainly be thought of as a winnable competition, but I'd be much more hesitant to say the same of all of human life, the higher-level creative process that gave rise to modern art and the problem of transportation. I'm not convinced that optimization captures all the important properties of intelligence (or creativity). Perhaps someone with a better understand could elucidate this for me?