Jochen Szangolies writes to us:
"The source of the homunculus fallacy is glossing over whom a given symbol is supposed to have meaning to: we imagine that the internal picture is simply intrinsically meaningful, but fail to account for how this might come to be--and simply repeating this 'inner picture'-account leads to an infinite regress of internal observers."
In this way we are warned of circularity and circular arguments.
But Lawrence Moss and the late Jon Barwise some years ago wrote:
"In certain circles, it has been thought that there is a conflict between circular phenomena, on the one hand, and mathematical rigor, on the other. This belief rests on two assumptions. One is that anything mathematically rigorous must be reducible to set theory. The other assumption is that the only coherent conception of set precludes circularity. As a result of these two assumptions, it is not uncommon to hear circular analyses of philosophical, linguistic, or computational phenomena attacked on the grounds that they conflict with one of the basic axioms of mathematics. But both assumptions are mistaken and the attack is groundless." (Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena. Center for the Study of Language and Information, Stanford California. CSLI Lecture Notes Number 60.)
For example, consider "self = (self)." It's the language of "hypersets," which is the subject of the above lecture notes.
However, instead of a simple object-- like a ball suspended in space-- think of an algorithm running on a computer.
To adopt a convention, say that when the algorithm runs, it exists. And when it does not run, it does not exist-- only the static code, or the formal specification for a computer program, then exists.
Now say that the algorithm "self = (self}" calls another algorithm when it is running, which runs and then returns execution to "self = (self)". In some sense that I won't try to make formal here, other algorithms like this are "part" of the algorithm "self = (self)." Now say that the last line of code which the computer runs in this algorithm is to call the algorithm itself. Hence "self = (self)" and "self" must be a "part" of itself.
Ideas like this led to formalizing the idea of a "non-wellfounded set." And then with non-wellfounded sets worked out, set theory could be successfully applied to the study of algorithms.
In engineering terms, the above "call to self" is a "feedback loop." For example, place a karaoke microphone next to the speaker. You get a squeal. It's a "runaway feedback loop."
Runaway feedback is usually a bad thing, but every self-driving car needs a well designed "feedback loop" in order to exist at all as a self-driving car. Likewise spacecraft reach Mars by means of well-designed feedback loops.
It therefore seems to me like the idea of "homunculus" implicitly models the homunculus as an object, like the ball suspended in space.
But if the "homunculus" is NOT an object, but a process, then we can use non-wellfounded sets or hypersets to model this process in a rigorous way.
Which by the way leads to a testable hypothesis: "The Dream Child Hypothesis." The question becomes this: On which feedback loop does the existence of "self" depend? (Implying that "self =(self)" needs a feedback loop in order to exist.)
1. Is the feedback loop for "self= (self)" the enteroceptor feedback loop, on which the heartbeat depends? Or,
2. Is the feedback loop for "self = (self)" the proprioceptor feedback loop, on which breathing depends?
After performing an experiment to test this hypothesis (on lab animals, using neuro-imaging) we would then be in a position to ask about processes like "self = (thinking, self)."
...the transformation to meaning in her life which Helen Keller so famously described.