A COURSE HANDOUT FROM DR. RON BARNETTE

OMNIPOTENCE AND SUPERTASKS

Presumably, there are countless tasks that an omnipotent, all-powerful, being could perform, that we, non-omnipotent creatures (strong as we may be), could not, if such a being could exist. Moreover, given our standards of what we take to be logical limits on what is possible and what is not, it might be argued that among the tasks performable by an all-powerful being are included some that we might judge to be seemingly impossible. Yet clarity demands some notion of logical possibility as the limit, even for omnipotent performances. What I would like to explore in this brief piece is the concept of a supertask, which is to be understood as a task that only an omnipotent being could perform.

The notion of a task is a helpful one, I submit, since it connotes an activity with an achievement, or terminus---an outcome or successful completion; in other words, a process of means to an accomplished end. Further, a task lends itself to a procedural explication popular in the terminology of logic and computational theory; viz., a flow-chart, or a general set of instructions which indicate, sequentially, just how the task can be performed to completion. From start to finish, there is precision, understanding, and theoretical description offered by a flow-chart, which characterizes a program of calculation. Now consider the following chart, which defines a particular task involving one's listing of natural numbers in series: 1, 2, 3, 4, and so on. We can then go on to discuss features of the task with regard to omnipotence, aided by the flow-chart.

INSTRUCTIONAL FLOW-CHART FOR THE LISTING OF ALL NATURAL NUMBERS

START

WITHIN 2 SECONDS OF THE START, WRITE DOWN THE NUMBER '1'

IN ONE-HALF THE TIME TAKEN TO PERFORM THE PREVIOUS TASK, WRITE DOWN THE NEXT NUMBER IN THE SERIES OF NATURAL NUMBERS

REPEAT THE PREVIOUS INSTRUCTION....then REPEAT, and REPEAT, and REPEAT, and so on...

STOP AFTER FIVE SECONDS HAVE ELAPSED FROM START AND THE LAST TASK WAS COMPLETED

Is the above a possible program? That is, could any possible being execute it? Think about what the task involves. You might even try running it yourself, although I suspect that you won't get too far before the five seconds runs out---maybe reach '5'? Maybe even '6'? But this is to be expected, since you're not omnipotent, after all. How would such a being fare, do you think? To '100'? Why not more? After all, omnipotence is at stake. How about '100,000', then? How about all the natural numbers? Why not? Let's agree that if a being could run the program (i.e., follow successfully all the instructions), and thereby not omit a single number, then such a being would be indeed omnipotent, and that such a task would be a supertask.

QUESTION: Is the above a possible supertask? Or: Is it logically possible for any being to successfully run the program described by the flow-chart? Or: Is an omnipotent being possible? Think about this....

Submit your reasoned case to Dr. Ron Barnette

Good luck!

(Special thanks to Emily Gung for preparing the original HTML version)