The framework presented here was inspired by, and aspires to be consistent with, David Deutsch’s Constructor Theory Deutsch’s Theory was created by and for physicists, including the requisite esoteric mathematics. Nevertheless, I have found it useful as a grounding basis for much of philosophy, including ontology, epistemology, teleology, causation, and Consciousness.
The basic premise of Constructor Theory is that all physical theories can be described in terms of which transformations of matter (processes or tasks) are possible, which are impossible, and why. For the purpose of the current framework, a “task” consists of an input configuration of matter (which can be described by a finite set of physical variables), an output configuration of matter (ditto), and a Constructor (which I will sometimes replace with the words Mechanism or Context) which performs the task by generating the output when presented with the input. While it’s possible to contemplate one-off processes which physically alter the system we call the Context or Mechanism, for our purposes here we (like Constructor Theorists) will be concerned entirely with tasks wherein the Constructor/Mechanism/Context remains essentially unchanged and able to repeat the task.
A task will typically be diagrammed as follows:
where x1, x2, etc. are the input variables and y1, y2, etc. are the output variables.
If Constructor Theory is true, then anything that happens, and anything that has happened, can be described in terms of tasks, because Constructor Theory purports to describe any physical transformation as possible or not, and clearly all physical transformations that have happened were possible ones.
One important implication which follows from this framework is that the outputs of transformations can become the inputs of other transformations. Mechanisms can be combined such that any regular network of tasks can be considered a new, higher level task with a new higher-level (super) Mechanism.
Thus, individual atoms can be considered Mechanisms, and certain combinations of such Mechanisms can be considered a super Mechanism. Note: the sub-Mechanisms are still Mechanisms in their own right.
Another important implication which follows from this framework will be what we mean by causation. For the time being we can put aside the baggage that philosophers have added to the idea of causation. For now, we can say that a Mechanism causes Output when presented with Input. Also, any system of matter can be considered the Output of one or more tasks. Thus, any system of matter, including any Input, will have a Causal History which includes all of the tasks that led up to that system and going all the way (at least) to the Big Bang.
There are two different concepts of function that will be important to us. The first, (from Wikipedia), is the mathematical concept: a relation between a set of inputs and a set of permissible outputs with the property that each set of input is related to exactly one set of outputs. 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.
In the current Theory, “function” will [usually] 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.