Is there an “algorithm” philosophy? Perhaps between relativism and pragmatism?

Question

I’m looking for philosophy that has the agent as central in characterizing knowledge, but is not as relative as relativism as knowledge will come from algorithms, and before pragmatism. I don’t think algorithms are explained by or restricted to science either historically. They seem cross discipline and broad, and not platonic either.

I think we can go back to the Meno and doubling the square to find an example of an algorithm (I know they come before this too). Meno because an algorithmic road seems presented but then not taken and algorithm is present in one of the founding stories of knowledge.

My tertiary summary of the slave boy in Plato’s Meno is that Socrates believes/demonstrates the boy is able to learn to double the square by being progressively reminded of truths his soul already knows.

Why is that a good example for supporting Plato’s metaphysics of static forms and truths, when what Socrates has done could be seen as simply sharing an algorithm (a clear series of steps)?

(It’s also a great story because it defines what knowledge is, knowledge of eternal forms/truths). I don’t know of a paradigmatic story which defines what algorithmic knowledge is.

I can’t find much in philosophy about algorithms as ways to characterize knowledge and philosophy. And yet they were hugely important to Ancient Greeks, and titans today say no complete definition of algorithm has been given (Yuri Gurevich, a philosophically inclined computer scientist).

Why algorithm and not just fold into pragmatism or relativism? Because relativism seems too against framework (e.g. I want to make algorithm shared and central) and pragmatism took till the 1800s, while algorithms existed to Ancient Greeks and were philosophically important already. Or maybe this is relativism, algorithm relativism where all knowledge is relative to algorithms?

Answer 1

I'm not sure exactly what you mean, however...

Algorithm is a term that is strongly associated with computer science these days, however any repeatable, goal-oriented behavior is algorithmic. As such, philosophies of math and science that formerly examine and embrace algorithmic and heuristic thinking explicitly might satisfy your search. To me, constructivist approaches to knowledge seem to be what you are looking for.

Constructivism

Some philosophies use algorithms in more prominent ways. One example is mathematical constructivism which relies on algorithms and proofs to establish the existence of mathematical objects:

In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists.

An advantage of constructivizing measure theory is that if one can prove that a set is constructively of full measure, then there is an algorithm for finding a point in that set (again see Bishop (1967)). For example, this approach can be used to construct a real number that is normal to every base.

The notion that proofs and algorithms are central to ontological claims is the salient feature of such an approach to mathematics. In fact, in a broader vein, scientific constructivism as an epistemological position relies on that general notion, that knowledge constructed generally understood as justified, true belief+ is a human-centric, pluarlistic set of processes:

According to constructivists, there is no single valid methodology in science but rather a diversity of useful methods.

Constructivists maintain that the dichotomy between discovery of the objective, and invention of the subjective is a false one with the emphasis being on pluralistic approaches, processes, methodologies, or if you prefer, algorithms which are central to the nature of what an entity is. From IEP's article "Constructivism in Metaphysics":

Constructivists are united first in their opposition to certain forms of Realism—namely, those that claim that x exists and is suitably independent of us. Constructivists about x agree that x exists, but they deny that it is suitably independent of us. Constructivism is distinguished from other versions of anti-Realism by the emphasis it places on the constructing relation. Constructivists are united by all being anti-Realists about x and by believing this is due to x’s being, in some way, constructed by us.

This emphasis on 'constructive relations' focuses on the processes and formulas for building knowledge to establish entities in the world.

Lastly, for some constructivists, the very algorithmic nature of concept manufacture is the heart not only of a philosophical position, but of philosophy itself. From IEP's Deleuze, Gilles:

As we have seen, a certain doctrine of empiricist constructivism runs through Deleuze’s work from the beginning, and on a number of levels. In What is Philosophy? this becomes the central and explicit theme: “philosophy is the art of forming, inventing, and fabricating concepts”.

Hence, for constructivists, the act of achieving goals through explicitly examining the human processes of algorithms and heuristics is one of the central epistemological, ontological, and metaphysical concerns.