Functional accounts of organisms: divided between imaginary and symbolic

Gertrudis Van de Vijver (Ghent University), Levi Haeck (Ghent University)

The notion of ‘function’ has for a long time been conceived in two different but closely related ways: a biological function attributed to the organization of living organisms (Aristotle, Kant), and a mathematical function that is taken to be underlying judgments (Kant, Frege).

The former is ontological (about beings), the latter is logical (about thinking). Additionally, the former is of the order of the imaginary – we need to presuppose that the (observable) parts of the organism stand under the idea of a whole, which is unobservable – while the latter is symbolic – focusing on symbolic structure at work in the act of speaking and writing, namely, function (f) and argument (x) (and value (y)). We call the former of the order of the imaginary because we imagine ourselves into functional organizations of wholes and parts, which is what mereology is all about. This is not the case in the latter; we do not imagine ourselves into the symbolic structure, we read it off of the sentences we utter or the formal systems we write.

Our claim is that it makes a difference to explicitly take into account the symbolic, logical function, to the extent that it is what allows to capture the specificity of the imaginary, mereological function. In other words, we need the symbolic realm to explain the imagination of the whole, in its position as both necessarily an object and necessarily non-objectifiable. As Woodger states: formalization (formal functionalization, logics) is what allows to give a place, on the one hand to what is always already counted as an object (“knowledge about the object”) and on the other hand to what is the place from where something is counted as an object (“knowledge about knowledge”).

We discuss the various forms of confusion that can arise by not clearly distinguishing both takes on function.