There are two different concepts of function that will be important to us. The first is the mathematical concept: a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. [From Wikipedia]. Thus, any task can be considered a function wherein the mechanism is abstracted away, leaving only the inputs and associated outputs
The second concept of function refers to working or operating in a proper or particular way. Thus, we say the function of the eyeball is to relay visual information to the brain.
When we speak of “function” here we will mean function in the mathematical sense, and when we want to discuss an entity operating in a proper way, we will say the function is associated with a purpose. Note that this “purpose” is essentially an explanation of why the entity came to exist. So we can refer to either “Natural” purpose, which is relevant to functions generated by natural selection, or to intentional purpose when discussing functions that were intentionally designed.
Now why do we care about function? The answer is that 1. it helps to explain dualism, and 2. it helps to explain qualia. Both of these concepts hinge on the “subjective” perspective. So the question becomes, where does a subjective perspective fit into a mechanistic theory? And the answer is: the subjective perspective is simply the operations of the functions of the Mechanism in question.
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