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Back to Bayes, ASECS: Probabilistic Reasoning and the Eighteenth Century Infowhelm

Roundtable: Artificial Intelligence and the Eighteenth CenturyASECS Toronto 2024 • Samuel Baker • The University of Texas

Published onOct 20, 2024
Back to Bayes, ASECS: Probabilistic Reasoning and the Eighteenth Century Infowhelm

How do we place the current iteration of Artificial Intelligence in dialogue with its historical predecessors? What does it even mean to talk about AI as a thing of the past, and not just of some nearly tangible future? The harshest critics of AI find the term itself fundamentally misleading, and argue it should be jettisoned in favor of more neutral descriptors such as “machine learning.” Humanists like us may associate such views with colleagues of ours, like Lauren Goodlad, editor of the new journal Critical AI, but many AI scientists too hold some version of this position. One AI scientist with whom I work closely likes to say that, quote, “an AI is a smart machine that hasn’t been invented yet.” This joke, if it is a joke, informs the position I am coming to take on the matter: artificial intelligence is a thing, but it has always been a thing, often a very stupid thing, if sometimes brilliant in its very dullness. We just have a way of forgetting that AI has already been a thing, because we keep inventing AIs and then, exactly, naturalizing them, be they prehistoric automata, algorithmically organized books and equations, or recommender systems that just feel right. A movement is now underway that seeks to reclaim this long history of concepts of, and even exemplars of, artificial intelligence, a movement one surfacing in myriad special issues of humanities journals, as well as in books like a pair of edited collections from Oxford University Press which I just reviewed for the Poetics Today special issue on AI, the AI Narratives and Imagining AI collections, which feature chapters by, among many others, colleagues who frequent this conference, like Julie Park. The subtext of some arguments in this mode is that the past only, exactly, imagined AI, while the present implements it; myself, I afford enough agency to works of imagination that they themselves can furnish AIs where I am concerned.

Now, many modern AIs are informed by a special family of mathematical procedures known collectively as Bayesian statistics. If I anonymize my computer, google “Bayesian” and screenshot the results, I get a list that includes, in reverse alphabetical order, Bayesian statistics, regression, probability, optimization, model, network, inference, correlation, and last but not least, artificial intelligence. If I just search for “Bayes,” meanwhile, I get an autocomplete for many of the same composite terms, but also results for “Bayes theorem” and “Bayes formula.” That is because Bayesian statistics originated with a formula, or theorem, postulated by an eighteenth-century mathematician, Thomas Bayes, the longtime Presbyterian minister at Tunbridge Wells. With the rest of my time today, I want to explore the questions of, who was this Thomas Bayes, and what did he have to do with artificial intelligence, then and now? And what can a look at his work tell us about “the first great media explosion,” that of the eighteenth century, as it “grappled with a torrent of words that, to some, seemed like little more than mindless, mechanical manufacture,” and in so doing anticipated, or inaugurated, our own era?

I adumbrated this question two years ago at ASECS in Baltimore, discussing the role of causation in thought then and now. I grouped Bayes with figures like David Hume, whose Enquiries are said to have inspired Bayes’s theorizing, and Richard Price, who rescued Bayes’s essay on probability from his papers after his death, finished it, and published it with the Royal Society. Today, I take a more textualist approach to Bayes, briefly sketching the metaphysical import of his theorem as it relates to his theology and to the burgeoning print culture of his time.

I want to begin, then, not from Bayes’s famous “Essay Towards Solving a Problem in the Doctrine of Chances,” but from his little-known but I think also influential pamphlet “Divine Benevolence.” In this pamphlet, Bayes responds to a now-forgotten argument for the salience of God’s rectitude, by arguing that benevolence is God’s essential property. God, on Bayes’s view, communicates happiness to his creation, irrespective of whether His creation is possessed by right reason, and such happiness will grow as His creation grows. The first thing to notice here is the tacit progressivism of Bayes’s theology, of a kind with the faith in a divine dispensation that, at the end of the century, would lead Price and William Godwin to embrace the prospect of revolution. A second thing to note is that in Bayes’s theology, truly significant intelligence is reserved for the mind of God. Whereas for his interlocutor, intelligence orders happiness through divine and also through human rectitude, Bayes, by contras,t declares that he “[doesn’t find] (he is sorry to say it) any necessary connexion between mere intelligence, though ever so great, and the love or approbation of kind and beneficent actions.” Thus, for Bayes, divine benevolence exists independently of human rectitude, if not of divine rectitude. Bayes adds that “God also is infinitely wise, and therefore infinitely good,” and that “if we,” by contrast, “cannot see this connexion between intelligence and goodness,” this “is a strong proof that our Creator is really good, since nothing can be a greater security to the general happiness than this.” Here Bayes approaches Godwin’s necessitarian ethical vision, in which the mission of human intelligence can only be to grok the mechanism and the model possessed by the non-human, if not exactly artificial, intelligence of God.

If no human model can ever properly grasp the truth, we enter into the looking glass world of a natural theology where it is human thought, sadly, which is condemned to be artificial intelligence, unless it be supplemented by the divine, vital data afforded by scripture, or perhaps by the book of nature. Ironically, Bayes may be engaged in a pamphlet war, but he is gesturing out of that world of print philosophy toward a world grounded otherwise than in such human-machine interaction.

Bayes’s probability theorem, laid out in his “Essay Towards Solving a Problem in the Doctrine of Chances,” is usually presented as the opposite of theological metaphysics: as a tool, indeed, for proliferating empiricism by chaining multiple inductive observations. This is why it is widely used to underpin the computation of probabilities in ways that simulate human intelligence: it seems propitious for grounding such computation in the world. And it was always thus; hence it is that Jesse Molesworth avers that “from a cultural perspective--from a conceptual perspective, Bayesian analysis seems the natural product of the mid-[eighteenth-]century mind’s fascination with inductive thinking.” This claim for the inductive essence of Bayesianism seems true: and yet from its inception, this natural product of inductive thinking also seems, like Bayes’s theology, to proliferate recourse to zones of artificial intelligence from which to deduct conclusions. In my last paragraph, I’ll try to sketch how this can be so.

Briefly, Bayes’s theorem takes the then already known basic math for combining probabilities, and, by adducing the probabilities of counterfactual outcomes, enables us to revise, or “condition,” our prior understanding of a probability, based on our estimation of the probability of an event we have observed. So, if we don’t believe there is a fire, because no alarm has gone off, but we see smoke, we assign a probability to fire that lies between what just no alarm would indicate (a low probability) and what just seeing smoke would indicate (a high probability). Or, if we don’t believe in God, because the miracles said to be the proof of His existence appear impossible and have never been observed by our own selves in real life, but then we do observe a miracle, the very unlikeliness of that miracle suggests to us that we might need to radically revise our prior estimate of God’s existence. Notice here that while we can, like good frequentists, only input into Bayes’s theorem probabilities that derive from observed data, we will necessarily furnish that data from media that we cannot validate ourselves. And famously, in practice Bayesian “priors” are often extravagantly speculative, since the Bayesian conditioning process seems so well fitted for revising them into empirically grounded probabilistic statements. Empiricism becomes a machine for tolerating ontological claims that are given, not discovered. For us, an artificial intelligence arises out of grounding rituals, with essentialism lurking in our training data; for the eighteenth century, too, a spectral intelligence was adumbrated by processing the scraps of spiritual doctrine and temporal argument that, in Coleridge’s phrase, abused the blessed machine of language.

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