I thought you were going to talk about complexity. A finite set of object types and modes of combination can give rise to an infinity of possible structures, and so there will be no upper bound on the complexity that an individual structure might exhibit, even when the rules are simple. This might be conceived of as “messiness”.
And I think Heraclitus and Thales deserve more than zero points. In the three-way contest you describe, they are the advocates of substance, and Pythagoras is the platonist. What do you think of Anaximander—“All is apeiron”? It is a more sophisticated version of the Heraclitus-Thales position, one that does not identify the hypothesized universal substance with any particular observed substance, like fire or water, as if it were more fundamental than other observed substances. I suppose Anaximander’s opposite would be Empedocles, who may have introduced the idea that there is more than one fundamental substance.
The problem with saying that “all is mathematics” is that, like all platonism, it tries to short-circuit the relationship between substance and property, by focusing solely on properties.
I thought you were going to talk about complexity. A finite set of object types and modes of combination can give rise to an infinity of possible structures, and so there will be no upper bound on the complexity that an individual structure might exhibit, even when the rules are simple. This might be conceived of as “messiness”.
And I think Heraclitus and Thales deserve more than zero points. In the three-way contest you describe, they are the advocates of substance, and Pythagoras is the platonist. What do you think of Anaximander—“All is apeiron”? It is a more sophisticated version of the Heraclitus-Thales position, one that does not identify the hypothesized universal substance with any particular observed substance, like fire or water, as if it were more fundamental than other observed substances. I suppose Anaximander’s opposite would be Empedocles, who may have introduced the idea that there is more than one fundamental substance.
The problem with saying that “all is mathematics” is that, like all platonism, it tries to short-circuit the relationship between substance and property, by focusing solely on properties.