Reply #8: An argument against complete scientific explanation of consciousness

[Stunster]

Here's an argument by Christopher Small against the idea that consciousness can be "dissected by the formalized reasoning that underlies mathematics, logic and the empirical sciences".

The full article, extending over six longish pages, is available here, but the main statement of the argument follows below. It's a lengthy piece and relies on some technical, but still fairly well known, aspects of mathematical logic. I think it's well done, and quite plausible. One would need to read the whole thing to appreciate fully the excerpt I reproduce now, but here it is anyway:

Let us consider all computer aided scanners which can effectively answer questions posed about conscious states of a subject being scanned. Suppose we label such brain scanners. For any given brain scanner coupled with a computer program let us categorize brain processes into two kinds in relation to that scanner.

* We will say that a particular brain process is (S,A)-allointentional if an algorithm A for interpreting the information from a scanner S determines that the process does not correspond to a thought about that particular process.

For example, the process associated with thinking about a certain passage of the Jupiter Symphony would presumably be (S,A)-allointentional. On the other hand, if I start to think about the processes occurring in my brain at this very moment then I am having (S,A)-autointentional processes, provided that a scanner S can effectively determine this fact.

* We will say that a particular process is (S,A)-autointentional if the scanner S determines that the process does correspond to a thought about that particular process.

In response to an (S,A)-autointentional process, the algorithm A might report (in part): HE IS THINKING ABOUT HIS OWN BRAIN PROCESSES. Note:

* Thoughts about processes strictly other than the actual ones associated with that particular thought are (S,A)-allointentional and not (S,A)-autointentional.
* Brain proccesses which correspond to thoughts about themselves and also about other things are (S,A)-autointentional, not (S,A)-allointentional.

Now, consider the thought of all (S,A)-allointentional processes. If all thoughts correspond to processes interpretable by scanner S and algorithm A, then there is some process that corresponds to this. The hypothetical scanner S and its algorithm A should be able to report that this idea is the object of consciousness. Is a process corresponding to thinking about all (S,A)-allointentional processes itself (S,A)-allointentional or (S,A)-autointentional? Attempting either answer leads to a contradiction.