Information as the core of Structuralism

Structuralism is a philosophical concept that says that all objects are defined by their relationship to other objects within the system. Although different fields have varying interpretations of structuralism, the above definition more or less captures the overall essence of the concept. This (w)holistic notion of the nature of objects has also enabled structuralism to become the predominant philosophy when it comes to mathematics, linguistics, and philosophy of science.

In mathematics, objects are exhaustively defined by their place in the system. For instance, structuralism holds that the number 1 is exhaustively defined by being the successor of 0 in the structure of the theory of natural numbers. Consequently, structuralism also maintains that objects do not have any intrinsic properties but are defined by relation to other objects within the system. If we agree to this, then it should follow from this that the quest for structuralism is first a quest for information.

For eg. In the case of Freg-ian 'Julius Caesar', the question is not whether the Frege-ian 'Julius Caesar' can ever be seen as a number, but what information would it provide. From a structuralist standpoint, it should be fairly straightforward to construct a system where 'Julius Caesar' represents the number seventeen and the system should work just fine.

Here is another example where 'information' dominates the narrative when it comes to structuralism:

Note that not one of these elements can individually give us all the information. It is as if each element is chosen to play a part in this triadic relationship and only after the relationship is realised can one gather any information at all.

Notes

1. Structuralism, in its strictest form, encourages fungibility. Not ideal when you think in terms of computation and causation.

References

1. Joel David Hamkins. (2021). Lectures on the Philosophy of Mathematics
2. Greimann, D. (2003). What is Frege's Julius Caesar Problem? Dialectica, 57(3), 261-278. Retrieved July 12, 2021, from http://www.jstor.org/stable/42971497