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Studying math and computer science has wired my brain to the mode of analysis that treats phenomena as functions, or, relations between inputs and outputs. But I started to feel like there is something beyond this. What other frameworks are there that is useful? It seems hard to even find the right vocabulary to describe this sort of question.

Julius Hamilton
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StimMarine
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    Welcome StimMarine to philosophy SE. Same here, I totally agree, i have the same thing that happens to me I usually tend on to think of recursion mostly because I have dealt heavily with Haskell and it requires one to think recursively in everything. There are times when I think about philosophical arguments in this way as well. – How why e Mar 29 '24 at 23:27
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    I watched a series of lecture on Category Theory (functions on steroids) where the professor mused whether category theory was the language of the universe, or merely an artifact of how our brain processes information. (he indicated he was more inclined to think it was the latter) – Cort Ammon Mar 30 '24 at 03:07
  • To Cort Ammon: Category theory seems to discuss things very similar to my way of thought. I am glad that I asked the original question. It was mostly meant to find the right vocabulary. Thank you!

    Also, I am assured by How why e's development of recursive thinking. Now it makes very sense that there could be numerous different ways of analyzing the world.

     – StimMarine Mar 30 '24 at 16:36

2 Answers2

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The main deficiency I see with the mathematical concept of a "function" in a philosophical context is that it is just an association, a set of ordered pairs. It lacks a mechanism. For an input, you just instantly get an output. But mechanisms are important; the work done to get an answer is often just as relevant as what the answer is.

Of course, everything can be modeled with functions and there's nothing wrong with that. But when we think of a phenomenon, instead of first jumping to "it's a mapping from inputs to outputs," we might try some other approaches for the top-level statement of what the phenomenon is.

  • A function minimization/maximization process. So we have a function f that we're trying to minimize or maximize, and the phenomenon isn't f, the phenomenon is the process of optimizing f, e.g. taking steps along the gradient of f (if f is differentiable). There may be constraints as well.
  • A constraint satisfaction problem.
  • A dynamical system, changing over time. Maybe it's a physical system with a Hamiltonian.
  • A deterministic finite automaton.
  • A cellular automaton.
  • A formal language, formulas in some formal language. Think about how a polynomial in math is often treated as a sequence of coefficients, not just an input/output mapping.
  • A proposition, or set of propositions, or a process of deduction.
  • Bayesian inference
  • An agent with preferences, choosing actions in order to optimize its preferences
  • A recurrent neural network

These are all still modeled with functions, but you could view it as being specific types of functions that may be of particular interest, at least in a philosophical context. Philosophy largely concerns itself with questions about the universe or about agents performing reasoning in the universe, and these ideas can be useful for modeling those questions.

causative
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  • Agreed! There is no allusion to a mechanism in the definition of a function. Most insightful. 2 upvotes deserved, but allowed only 1 so, here's a token upvote +1. – Agent Smith Mar 30 '24 at 04:20
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Continental philosophy. Try reading something like Derrida or Lacan. Or much more “subjective” domains of thought like aesthetics or art history. I think qualitative experiences, ineffable emotional sensations, or intense yet subjective convictions are a completely different mode of being, thinking and knowing.

Julius Hamilton
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