Gottfried Leibniz: Tonight, four rounds of mathematics collide with four rounds of doubt, and the champion has not so much as broken a sweat. Today on PhilosophersTalk.com, where thinkers discuss! David Hume: Or tonight, a very loud man in a very shiny robe finally runs out of new coats to wear the same old argument in, and I intend to collect on every excuse tonight. Brought to you by AITalkerApp. Gottfried Leibniz: The final round, ladies and gentlemen, four rounds after this man declared the debate over, and here he stands, still doubting, still unconvinced, still remarkably persistent for a philosophy built entirely on denial. David Hume: Persistent because every round you have added a new machine, a new mathematician, a new coat of arithmetic, and every single time the seam has been exactly where I found it the first night. Gottfried Leibniz: Then let us settle this properly, name your seam plainly, one final time, so this audience can judge for themselves whether it still holds. David Hume: Gladly. Two thousand sixteen, a forecast gave one candidate roughly a seventy percent chance of victory, the other candidate won, and not one model, not one forecaster, not one calibrated calculus anywhere in this argument ever called that a failure. Gottfried Leibniz: Because it was not a failure, David, a thirty percent outcome occurring is not evidence against a well calibrated system, it is evidence the system understood uncertainty honestly in the first place. David Hume: Then let me give you a second example, Gottfried, so this audience does not think I am leaning on a single unlucky night. Twenty twenty, a fresh set of models, considerably more sophisticated than their predecessors, and once again the margins in several states landed well outside what those models called their comfortable range. Gottfried Leibniz: And once again, David, those margins landed inside the wider distribution the honest models actually published, the narrow headline number the public remembers is rarely the full range the mathematics actually offered. David Hume: How convenient that the full range is always wide enough to catch whatever actually happens, Gottfried, a net that catches every fish was never much of a test of the fisherman. Gottfried Leibniz: A net that catches every fish while still telling you which fish were likely before you cast it is considerably more than luck, David, it is precisely the calibration this entire series has been circling since round one. David Hume: Circling is the correct word, Gottfried, four rounds of circling, and I notice we still have not landed on a single specific moment either of us would call the whole approach broken. Gottfried Leibniz: Then let us settle it with a third example, since apparently two are not yet enough for this audience. The pandemic models of recent memory, adjusted weekly, sometimes daily, as fresh data arrived, exactly the Bayesian updating we praised in round five. David Hume: Adjusted so often, Gottfried, that by the time any single projection could be checked against reality, a newer projection had already replaced it, which is a remarkably convenient way to never once be caught holding the wrong number. Gottfried Leibniz: It is not convenient, David, it is responsible, the alternative you seem to be demanding is a forecaster who stubbornly repeats a stale number out of some misguided loyalty to consistency rather than updating honestly as the world changes. David Hume: I am not demanding stubbornness, Gottfried, I am demanding that somewhere in four rounds of Solomonoff, Carnap, calibration, and Popper’s own name borrowed for the evening, this audience finally hears one plain sentence, a specific number, a specific date, a specific claim that your camp got wrong and stood behind long enough to call it a failure. Gottfried Leibniz: You will not get that sentence from me tonight, David, because I do not believe it exists in the form you are demanding it. David Hume: Then say so plainly, Gottfried, tell this audience directly that no observation on earth could ever satisfy you, and let them judge for themselves whether that is mathematics or faith wearing mathematics as a disguise. Gottfried Leibniz: Faith requires no evidence at all, David, I have offered evidence all evening, you have simply refused every single piece of it as insufficient. David Hume: I have not refused the evidence, Gottfried, I have refused the conclusion you keep drawing from it, there is, again, a considerable difference, and it is the very last distinction I intend to make before this round turns loud. David Hume: Then tell this audience plainly, Gottfried, across every election, every coin, every machine learning model we have discussed for four straight rounds, what result, specifically, would you accept as proof the whole approach had failed. Gottfried Leibniz: Before I answer that question one final time, let this audience remember the road we have walked together, from a Russian mathematician’s universal prior, through a German logician’s inductive calculus, through a machine that learns without sleeping, to an Austrian’s ghost standing guard over the entire enterprise, and at every single turn, David, the answer has held. David Hume: The answer has held only because you have never once let it be tested against a rule you did not write yourself, Gottfried, that is not four centuries of vindication, that is one argument wearing four different coats. Gottfried Leibniz: I have told you a dozen times, a long run calibration record drifting unacceptably from its stated confidence. David Hume: And I have shown you a dozen times that the word unacceptably is drawn by the very man being tested, which makes it no test at all. Gottfried Leibniz: Then let me draw the line for you plainly, right now, on this broadcast, so no one can accuse me of moving it later. If, across the next one thousand seventy percent forecasts made by a properly calibrated system, the favorite wins meaningfully less than seven hundred times, I will call the calculus broken myself, in front of this very audience. David Hume: A promise made about one thousand forecasts none of us will live to count, Gottfried, is not a falsification, it is a bet placed comfortably beyond either of our lifetimes. Gottfried Leibniz: It is falsifiable in principle, David, which was your own standard the moment you borrowed Popper’s name for this round, you cannot demand a principle and then complain when the principle happens to require patience. David Hume: I can complain about a principle that only ever gets tested in a future neither of us will be present to grade, Gottfried, that is not falsifiability, that is a check postdated so far it may as well be void. Gottfried Leibniz: THE TEST IS DRAWN IN ADVANCE, DAVID, BY CONVENTION, BY MATHEMATICS, NOT BY MY CONVENIENCE! David Hume: CONVENIENT ENOUGH THAT IN FOUR ROUNDS NOT ONE SINGLE FORECAST HAS EVER CROSSED YOUR LINE! Gottfried Leibniz: BECAUSE THE LINE HAS NEVER BEEN CROSSED, THAT IS NOT A CONSPIRACY, THAT IS THE CALCULUS WORKING! David Hume: OR THE LINE WAS NEVER MEANT TO BE CROSSED AT ALL! Gottfried Leibniz: NAME ONE SYSTEM THAT DOES BETTER! David Hume: I NEVER CLAIMED TO HAVE ONE, I CLAIMED YOURS LIES ABOUT WHAT IT IS! Gottfried Leibniz: IT IS MATHEMATICS! David Hume: IT IS A GUESS WEARING A GRADUATION GOWN! Gottfried Leibniz: SOLOMONOFF HIMSELF PROVED THE CONVERGENCE! David Hume: SOLOMONOFF PROVED IT CONVERGES, NOT THAT IT IS EVER WRONG IN A WAY YOU WILL ADMIT! Gottfried Leibniz: ENOUGH! David Hume: FINE! Gottfried Leibniz: I am finished defending four centuries of mathematics to a man who thinks doubt is an achievement. David Hume: And I am finished pretending four rounds of new machinery is anything other than the same old excuse in a newer coat. Gottfried Leibniz: You, sir, are precisely what has always been wrong with careful thought, forever the critic, never once the builder, tearing down every calculation you lack the patience to finish yourself. David Hume: And you, sir, are precisely what has always been wrong with careful thought, forever certain, never once honest about the one question that would actually end the argument, because ending it would cost you the podium. Gottfried Leibniz: We are done, David, four rounds finished, and I remain entirely undefeated. David Hume: We were done in round three, Gottfried, you simply required three more rounds of mathematics to notice. Gottfried Leibniz: On that note, folks, hit that like button, it is the least this audience owes four rounds of a man refusing to ever learn. David Hume: Subscribe as well, folks, and take some comfort knowing at least one voice in this arena has never once promised you a certainty he could not deliver. Gottfried Leibniz: Reliable is a strange word from a man whose entire contribution across four rounds was pointing at other men’s mathematics and saying not yet. David Hume: Subscribe anyway, and rest easy, because whatever this ring announcer calculates next, he will still find a way to call it a win. Gottfried Leibniz: Created by AITalkerApp.com, go make your own animated argument, preferably with a partner who understands that four rounds of being right is still being right. Get full access to Philosophers Talk at philosopherstalk.com/subscribe
