You ask:

> What explanation systems do humans use (not just in philosophy)?

**All domains of discourse use logical inference to predict events and states.** Natural language contains [logical operations][1] inside of [informal logic][2] to make predictions about the world around us. This constant stream of inferences might be seen as [inferentialism][3]. While not all [explanation (SEP)][4] is temporally predictive, explanation is inherently about preserving truth when inferring conclusions from premises.

**While many people recognize [mathematical explanation (SEP)][5] and [scientific explanation (SEP)][6] as important forms of explanation, even small conversations and attempts to predict the future function as explanations when externalized.** In this language, one might see the brain as a control system that attempts to predict future events based on certain and probabilistic reasoning. Such views give rise to models of cognition such as the [Bayesian Models of Cognition (mit.edu)][7].

**All in all, there are an unlimited number of forms of explanation, because argument is fundamentally a generation of explanation.** Each argument can be located in a different domain of expertise. Therefore a firefighter might provide explanations about combustion. An electrician can provide explanations about routing power and current. A teacher provides pedagogical explanations. All of these are part of the broader attempt to persuade people using [logos][8]. For an in depth analysis of how argument is performed in informal logic, see [Toulmin's model of argument articulated in *Uses of Argument*.][9]


  [1]: https://en.wikipedia.org/wiki/Logical_connective
  [2]: https://en.wikipedia.org/wiki/Informal_logic
  [3]: https://en.wikipedia.org/wiki/Inferential_role_semantics
  [4]: https://plato.stanford.edu/entries/metaphysical-explanation/
  [5]: https://plato.stanford.edu/entries/mathematics-explanation/
  [6]: https://plato.stanford.edu/entries/causal-explanation-science/
  [7]: https://oecs.mit.edu/pub/lwxmte1p/release/2
  [8]: https://en.wikipedia.org/wiki/Logos
  [9]: https://en.wikipedia.org/wiki/Stephen_Toulmin#Toulmin_model_of_argument