St. Augustine, Thomas Aquinas, dogma and mathematics

A few weeks ago, I finally got around to reading “Between the Lord and the Priest”, a book-length conversation between Adam Michnik, Jozef Tischner and Jacek Zakowski. I came for the historical content, but stayed in part for certain disputes in Catholic theology in Poland in the 1960s and 70s. It’s not my usual cup of tea; Tischner himself acknowledges that all this was of very limited interest to the general public while trailing well behind contemporary Western European philosophy. It nonetheless describes beautifully some of the disagreements I’ve had with my fellow mathematicians with regard to life in general and social issues in particular.

The framework for the dispute is provided by the long-standing dichotomy between St. Augustine and St. Thomas Aquinas. The way Tischner explains it, Thomism posits eternal, unchangeable truths that must be accepted as dogma and followed in life. It prescribes synthesis, universality, vast generalizations, logical chains of cause and effect all the way back to deity. Augustine, on the other hand, is less sure of himself. Even if the truth, somewhere out there, might be eternal and unchanging, our understanding of it is grounded in history, tradition and experience, and in the end that understanding is all we can ever access. In practice, this is a more bottom-up approach to religion, starting with personal, individual existential questions and then seeking guidance in the Scriptures and the church’s intellectual tradition.

Now, here is where things get interesting. Tischner goes on to say that Thomism, in its methodology and spirit, is actually quite similar to Marxism. Marxists, too, had their axioms of class struggle and dialectical materialism. They presumed to shape human consciousness through class awareness, much as Thomists presumed to shape it through philosophical and religious dogma, with little regard to individual experience and understanding.

That was why Michnik, an atheist and a leftist at odds with communism, tuned into Tischner’s polemics with Thomists. Thomism, like Marxism, represented codified, linear thinking where “one thing always follows from another, and everything is perfectly arranged and therefore very simple.” Tischner found that he could not talk like that to his parishioners – people who’d fought in the war, lived through the horrors of Nazi occupation, made choices that most of us wouldn’t want to think about. Their experience defied the scheme. Michnik, then in his twenties and already a veteran of protests and prisons, trying to graduate from university before his next arrest, had no love for simple explanations of everything, either. He’d rejected Marxism already; he would go on to consider religion, but not if it offered no escape from the same kind of closed-minded thinking, not if it were perfectly arranged with one thing always following from another.

At times, Marxist-Leninist philosophy was almost comical in its straightforwardness. Michnik cites Lenin’s theory of cognitive reflection, asserting that

(1) a world exists “independent” of and “external” to consciousness, and (2)
knowledge consists of approximately faithful “reflections” of that world in consciousness.

The second part of that, understood literally as Lenin indeed intended, is, on a very basic level, at odds with science, and I could say much more along these lines just based on my experience with photography. What’s less funny is the underlying Thomist assumption that there can only be one intellectually correct interpretation and only one right set of conclusions, namely those espoused by the bearer of the dogma, and that any departure from that must be a result of either misinformation or bad faith. When communists censored dissenting opinions, part of it was a genuine conviction that such opinions were obviously nonsensical and therefore there was no reason to disseminate them. When they lost the 1946 referendum in Poland, they blamed it on “confused thinking” and “complete ignorance” among the population. In a similar vein, but centuries earlier, the Catholic Inquisition might first try intellectual arguments, but if the accused were not persuaded, that constituted proof that they were possessed by the devil, because how else could they not agree? Thomists responding to Tischner informed him on a regular basis that he did not really know St. Thomas, because had he known him, he’d love him.

I started drawing my own analogies long before the point where Tischner actually uses the word “mathematical.” Like a good Augustinian, I’ll start with specifics. A couple of weeks ago, in a comment section far away, a mathematician proposed to “solve racism” by generalizing it (to something he never quite defined) so that racism itself would follow easily as a special case. In a different comment section last year, several mathematicians insisted on a purely mechanistic solution to sexism in mathematics. They accepted it as a self-evident axiom that mathematicians were progressive and well-intentioned people who would automatically eliminate sexism from their ranks if it only were pointed out to them. One might of course wonder why it hasn’t worked yet; but one would then be doubting an axiom, an act that’s not only morally reprehensible but, worse, logically inexplicable.

I’m thinking of mathematicians who’ve argued with my blog posts by taking shots at some sentence pulled out of context, the way they might point to an incorrect formula in a math paper. I’m thinking of one person who started a discussion with me, then allowed reluctantly in response to my arguments that he might not be able to change my mind after all, because convincing people is hard in general. Apparently, the possibility of me convincing him had never been on the table. I’m thinking of those who expected I’d stop believing in that gender bias thing if they only could explain it all to me, almost like religious evangelists. Sorry, no. I’ve heard your arguments many times already. I disagree with them, not because I don’t understand them well enough, but because I do. They don’t address my experience, and they never will if you keep starting from your own axioms instead.

It became clear to me over the last couple of years that I’m not, and probably never have been, part of a “mathematical community” of any kind. Sure, some of my best friends are mathematicians. I do my expected share of “service to the community.” But after hours, I’d rather kick off my shoes with people who at least share my logic. I’d rather discuss experiences, not axioms. I’d rather debate someone who’s actually listening to me, not just building his own castles of abstraction.

It’s been claimed by some of those in question that mathematics itself supports Thomist thinking. (As in, “I’m a mathematician and therefore this is how I approach this problem.”) I’m not so clear on that. To some extent, sure: we’re all trained in binary logic and deductive reasoning, as we should be. But in my own research practice, I often work in the Augustinian direction, starting with specific examples and then working towards something more general. Freeman Dyson’s “Birds and Frogs” article comes to mind, except that I’ve met froggy types like me who are incredibly dogmatic on social issues, and birds who are not.

If I were a Thomist, I’d try for a diagnosis, conclusion, and a list of recommendations for my peers. Maybe the problem is when mathematicians Act Like Mathematicians, showing off their smarts where wisdom is called for. Maybe, too, it’s unexamined purchase into the letter of the deductive philosophy of Russell and Bourbaki, without stopping to consider the actual practice of mathematical research; but that argument becomes circular right there. So, instead, I’d rather just leave you with something to think about, and excuse myself from Math Overflow once again.

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