Actually, it’s not the
attempt to mathify that I find problematic—I find that encouraging. It is, though, the results.My (awesome) university philosophy professor had us do a very interesting exercise that was, though more logical than mathematical in nature, similar to what the author of TFA was going for. It goes like this…Write down a belief that you have. For people new to this process (the entire class), this should be a strongly held belief…doesn’t matter how controversial. Let’s say, for example:
I think abortion should be a woman’s choice. (For you controversy-hounds out there, please don’t mistake this for
my actual belief—I’m intentionally not going to define my actual belief on this topic here.) Don’t worry about getting the wording just right—you’re free to revisit your initial statement as many times as you like throughout and revise it to more concisely represent your intent.
Now write down the set of “sub-beliefs” that you have which form the basis of your belief. For our example: 1. Life begins at conception. 2. Every life is equally valuable. 3. A life has no quantifiable value, but is inherently precious and ought to be protected if at all possible. Etc. Next we iterate, applying the same process to each belief listed. Obviously, you will very quickly diverge into an explosion of statements that resist corralling at every effort. Do not fret—I haven’t told you about the thrust of the exercise yet.
(I should mention here that we did an entire section on identifying context-free statements, and we were asked to make our best effort to ensure that each statement was context-free, or as free of context as possible. “Context-free” means that the statement is true of our beliefs regardless of the circumstances in which the statement is tested. If that’s not possible—and it’s not often possible—we’d go for “generally” true, where “common sense”—whatever that is—dictates obvious exceptions.)
You will find it unnecessary to list each and every belief supporting your initial statement, which would quite likely fill several thick volumes if you did so exhaustively. Luckily, you don’t have to do this to satisfy the point of the exercise, which is: where necessary, skip down to “lowest level” beliefs…that is, at some point you will mentally reach a point where you have identified a belief for which you have no further basis beliefs. When you reach this point, you have identified an axiomatic belief—that is, something you accept essentially on faith, on gut feeling, because you think it is correct. If possible, identify the key beliefs that go from your initial statement to the set of axiomatic beliefs identified.
The next step is to look at your beliefs, both axiomatic and intermediate, for consistency. In every case in carrying out this exercise, one will invariably find a whole host of contradictory statements. Then we did an iteration that attempts to resolve these conflicts by tweaking our initial statement, etc…provided we were tuning up the language to indicate real intent and not moving the statements further away from our actual beliefs, great. The ultimate idea is to identify our beliefs in all their gory, inconsistent, warty detail.
Then, we make up a list of so-called axiomatic beliefs and they are given to 5 random classmates (all double-blind, of course). You then are tasked with taking home those 5 lists of axiomatic beliefs and attempt to drill down further. If they are truly axiomatic, you won’t be able to do this—the idea here is that you ultimately get back 5 people’s analysis of your list and given another chance to continue the process—most of the time, it turns out you realize your axiomatic beliefs weren’t axiomatic for you after all, and that you can actually drill down even more.
Anyway, it goes on like this, the ultimate point being that you arrive at some network of beliefs which you apparently do accept as axiomatic. The focus here is not on the logic that leads you down the path from the initial statement to the final list…the point is to show that your beliefs are not rigorously logical, even after you’ve done your level best to identify all the logical flaws, ultimately you wind up with a list of axiomatic beliefs that either directly or indirectly contradict each other to some extent. What these beliefs are, where the conflicts are, and how you resolve these conflicts all roughly correspond to your worldview.
As an entertaining add-on at the end of the course, the prof provided us with some very mild statistical metrics that told us how self-contradictory our beliefs were when pegged against our classmates, previous years, different types of statements (it was generally true that the more strongly held / the more controversial the statement, such as the abortion example above, the less self-consistent the foundational beliefs identified).
For a couple of years after doing this exercise, I found it very difficult to make strong statements of opinion about controversial topics. My mind would involuntarily start this process, identifying all the biggest logical hurdles and inconsistencies built into the statements I was about to make. This reflex also made me annoying to others with strongly held beliefs. 
