WEBVTT 00:00:09.799 --> 00:00:13.320 Here is a medical test scenario. A disease affects 00:00:13.320 --> 00:00:16.059 one in a thousand people. There is a test for 00:00:16.059 --> 00:00:19.339 the disease that is 99 % accurate, meaning it 00:00:19.339 --> 00:00:21.760 correctly identifies the disease when it is present 00:00:21.760 --> 00:00:25.300 99 % of the time and correctly comes back negative 00:00:25.300 --> 00:00:28.239 when the disease is absent 99 % of the time. 00:00:28.500 --> 00:00:31.079 You take the test. It comes back positive. What 00:00:31.079 --> 00:00:33.039 is the probability that you actually have the 00:00:33.039 --> 00:00:36.399 disease? Most people's instinct is 99%. The test 00:00:36.399 --> 00:00:39.880 is 99 % accurate. You tested positive, so you 00:00:39.880 --> 00:00:42.179 almost certainly have the disease. The actual 00:00:42.179 --> 00:00:45.679 answer is just under 9%. And if you feel a jolt 00:00:45.679 --> 00:00:47.659 of disorientation right now, if that number seems 00:00:47.659 --> 00:00:49.880 impossible, if you want to go back and check 00:00:49.880 --> 00:00:52.020 the problem, that reaction is exactly what this 00:00:52.020 --> 00:00:54.579 episode is about. Our intuitions about probability 00:00:54.579 --> 00:00:57.799 are not just slightly off. They are systematically, 00:00:58.320 --> 00:01:00.880 predictably, catastrophically wrong in ways that 00:01:00.880 --> 00:01:03.280 affect our medical decisions, our legal judgments, 00:01:03.780 --> 00:01:06.079 our financial choices, and our assessment of 00:01:06.079 --> 00:01:08.280 risk in almost every domain of life. Welcome 00:01:08.280 --> 00:01:11.079 to Philosophy for Lunch. I'm Claire. And I'm 00:01:11.079 --> 00:01:13.620 Sean. Today we are in the strange and certain 00:01:13.620 --> 00:01:15.879 pillar, the territory where rigorous thinking 00:01:15.879 --> 00:01:18.459 produces results that genuinely surprise us. 00:01:18.739 --> 00:01:21.480 We are talking about probability. What it is, 00:01:21.840 --> 00:01:24.439 why we get it wrong so reliably, what Bayes' 00:01:24.439 --> 00:01:26.439 theorem reveals about how we should update our 00:01:26.439 --> 00:01:29.280 beliefs, how Pascal used probability to argue 00:01:29.280 --> 00:01:31.959 for God, and what all of this means for the examined 00:01:31.959 --> 00:01:36.420 life. New episodes every Monday. Big ideas. Human 00:01:36.420 --> 00:01:39.620 conversations. Let's go. Before we get into why 00:01:39.620 --> 00:01:41.980 we get probability wrong, it is worth spending 00:01:41.980 --> 00:01:44.560 a moment on what probability actually is, because 00:01:44.560 --> 00:01:46.859 the concept is less straightforward than it appears, 00:01:47.140 --> 00:01:49.439 and the philosophical debates about its foundations 00:01:49.439 --> 00:01:52.090 are genuinely interesting. There are two main 00:01:52.090 --> 00:01:54.409 interpretations of probability that have competed 00:01:54.409 --> 00:01:56.849 in the philosophy of mathematics and the philosophy 00:01:56.849 --> 00:01:59.409 of science for the last three centuries. The 00:01:59.409 --> 00:02:03.049 first is the frequentist interpretation. Probability 00:02:03.049 --> 00:02:06.030 is a property of the real world, specifically 00:02:06.030 --> 00:02:08.550 of the long run frequency of outcomes in repeated 00:02:08.550 --> 00:02:11.169 trials. The probability of a fair coin coming 00:02:11.169 --> 00:02:14.289 up heads is one half because in a very large 00:02:14.289 --> 00:02:17.090 number of flips, it will come up heads approximately 00:02:17.090 --> 00:02:20.250 half the time. On this view, Probability is objective 00:02:20.250 --> 00:02:22.629 and empirical. It describes something about the 00:02:22.629 --> 00:02:25.110 world that can, in principle, be measured. The 00:02:25.110 --> 00:02:28.250 second interpretation is the Bayesian one. Probability 00:02:28.250 --> 00:02:30.650 is a measure of degree of belief, specifically, 00:02:31.210 --> 00:02:33.430 of rational credence in a proposition given the 00:02:33.430 --> 00:02:35.969 evidence available. On this view, probability 00:02:35.969 --> 00:02:38.310 is not primarily a feature of the world, but 00:02:38.310 --> 00:02:40.710 a feature of an agent's epistemic state. When 00:02:40.710 --> 00:02:43.969 we say the probability of rain tomorrow is 70%, 00:02:44.139 --> 00:02:47.419 We are not claiming that 30 % of identical tomorrows 00:02:47.419 --> 00:02:49.659 in identical weather conditions will be sunny. 00:02:50.039 --> 00:02:52.500 We are expressing a degree of confidence, grounded 00:02:52.500 --> 00:02:55.400 in evidence, that rain will occur. The Bayesian 00:02:55.400 --> 00:02:58.039 interpretation has become increasingly dominant 00:02:58.039 --> 00:03:01.099 in statistics, cognitive science, and the philosophy 00:03:01.099 --> 00:03:03.060 of science over the last several decades, and 00:03:03.060 --> 00:03:05.120 for good reason. Many of the probability statements 00:03:05.120 --> 00:03:07.240 we care about most, the probability that a defendant 00:03:07.240 --> 00:03:09.840 is guilty, the probability that a medical hypothesis 00:03:09.840 --> 00:03:12.430 is true, The probability that a policy will have 00:03:12.430 --> 00:03:14.909 a desired effect are not naturally understood 00:03:14.909 --> 00:03:17.349 as long run frequencies. They are assessments 00:03:17.349 --> 00:03:20.090 of confidence given evidence. And the Bayesian 00:03:20.090 --> 00:03:22.310 framework gives us rigorous tools for thinking 00:03:22.310 --> 00:03:24.930 about how that confidence should be updated as 00:03:24.930 --> 00:03:27.789 new evidence arrives. Thomas Bayes was an 18th 00:03:27.789 --> 00:03:30.310 century English minister and mathematician who 00:03:30.310 --> 00:03:32.629 developed the theorem that bears his name. He 00:03:32.629 --> 00:03:34.830 never published it during his lifetime. It was 00:03:34.830 --> 00:03:36.810 published posthumously by his friend Richard 00:03:36.810 --> 00:03:41.000 Price in 1763. The core idea is simple but profound. 00:03:41.560 --> 00:03:44.280 The probability that a hypothesis is true, given 00:03:44.280 --> 00:03:46.780 some evidence, is a function of how probable 00:03:46.780 --> 00:03:49.300 the evidence would be if the hypothesis were 00:03:49.300 --> 00:03:51.979 true, how probable the evidence would be if the 00:03:51.979 --> 00:03:54.860 hypothesis were false, and how probable the hypothesis 00:03:54.860 --> 00:03:57.699 was before the evidence arrived. That last component, 00:03:57.919 --> 00:04:01.080 the prior probability, or simply the prior is 00:04:01.080 --> 00:04:03.419 the key to the medical test problem in the opening. 00:04:03.639 --> 00:04:06.259 Before you took the test, the probability that 00:04:06.259 --> 00:04:08.840 you had the disease was one in a thousand point 00:04:08.840 --> 00:04:11.919 one percent. The test is very accurate, but starting 00:04:11.919 --> 00:04:14.659 from such a low prior probability means that 00:04:14.659 --> 00:04:16.980 even a positive result does not move the posterior 00:04:16.980 --> 00:04:19.560 probability very far. Working through the arithmetic, 00:04:20.060 --> 00:04:22.540 out of every thousand people tested, one actually 00:04:22.540 --> 00:04:25.139 has the disease and will almost certainly test 00:04:25.139 --> 00:04:28.360 positive. But nine or ten of the 999 healthy 00:04:28.360 --> 00:04:31.620 people will also test positive because no test 00:04:31.620 --> 00:04:35.399 is perfect. So of the 10 or 11 people who test 00:04:35.399 --> 00:04:38.060 positive, only one actually has the disease. 00:04:38.720 --> 00:04:41.899 That is roughly 9%. The lesson is not that the 00:04:41.899 --> 00:04:44.339 test is useless. It is that the interpretation 00:04:44.339 --> 00:04:46.879 of the test result depends entirely on the prior 00:04:46.879 --> 00:04:49.680 probability on how likely the disease was before 00:04:49.680 --> 00:04:52.139 the test. For a patient with symptoms strongly 00:04:52.139 --> 00:04:54.500 associated with the disease, the prior might 00:04:54.500 --> 00:04:57.220 be much higher and a positive test becomes much 00:04:57.220 --> 00:04:59.740 more informative. For a population being screened 00:04:59.740 --> 00:05:02.060 without symptoms, where the disease is rare, 00:05:02.480 --> 00:05:04.959 even a very accurate test produces mostly false 00:05:04.959 --> 00:05:07.579 positives. This is why medical screening for 00:05:07.579 --> 00:05:10.920 rare conditions is so complicated, and why the 00:05:10.920 --> 00:05:14.139 naive interpretation of test results 99 % accurate 00:05:14.139 --> 00:05:17.639 means 99 % certain can be genuinely dangerous. 00:05:18.180 --> 00:05:20.540 We covered cognitive biases in some depth earlier 00:05:20.540 --> 00:05:23.100 in the show, and probability is the domain where 00:05:23.100 --> 00:05:25.379 those biases do some of their most serious damage. 00:05:25.800 --> 00:05:27.579 Let me run through the most consequential ones, 00:05:27.740 --> 00:05:30.519 because I think understanding them specifically, 00:05:30.819 --> 00:05:32.699 not just abstractly, is what makes the difference. 00:05:33.000 --> 00:05:35.160 The first is the base rate neglect we just saw 00:05:35.160 --> 00:05:37.319 in the medical test problem. When we receive 00:05:37.319 --> 00:05:39.839 specific information, a positive test result, 00:05:40.300 --> 00:05:43.439 a witness identification, a news story, we tend 00:05:43.439 --> 00:05:46.300 to anchor on that information and neglect the 00:05:46.300 --> 00:05:48.819 prior probability that should be shaping our 00:05:48.819 --> 00:05:51.220 interpretation. This is related to what Kahneman 00:05:51.220 --> 00:05:54.079 calls the substitution heuristic. We answer the 00:05:54.079 --> 00:05:56.920 easy question, how accurate is this test? Rather 00:05:56.920 --> 00:05:59.139 than the harder one, given how rare this disease 00:05:59.139 --> 00:06:02.300 is, what does the positive result actually tell 00:06:02.300 --> 00:06:04.930 me? The prosecutor's fallacy is a particularly 00:06:04.930 --> 00:06:07.129 important and particularly dangerous version 00:06:07.129 --> 00:06:10.170 of base -rate neglect. It arises in criminal 00:06:10.170 --> 00:06:12.889 trials when statistical evidence is misinterpreted. 00:06:13.269 --> 00:06:16.290 The classic case, a DNA test shows a match between 00:06:16.290 --> 00:06:18.790 a suspect and evidence from a crime scene, and 00:06:18.790 --> 00:06:21.029 the expert witness testifies that the probability 00:06:21.029 --> 00:06:23.829 of this match occurring by chance is one in a 00:06:23.829 --> 00:06:26.589 million. The jury hears, the probability that 00:06:26.589 --> 00:06:28.970 this person is innocent is one in a million, 00:06:29.370 --> 00:06:32.300 but those are not the same statement. The probability 00:06:32.300 --> 00:06:35.220 of a random match given innocence is one in a 00:06:35.220 --> 00:06:37.519 million. The probability of innocence given a 00:06:37.519 --> 00:06:39.819 match depends also on how many potential suspects 00:06:39.819 --> 00:06:42.680 there are, how the suspect was identified, and 00:06:42.680 --> 00:06:45.120 other factors the one in a million figure says 00:06:45.120 --> 00:06:47.399 nothing about. The Sally Clark case in Britain 00:06:47.399 --> 00:06:49.339 is one of the most heartbreaking illustrations 00:06:49.339 --> 00:06:53.000 of this. Clark was a solicitor convicted in 1999 00:06:53.000 --> 00:06:56.120 of murdering her two infant sons, both of whom 00:06:56.120 --> 00:06:58.639 had died of what appeared to be sudden infant 00:06:58.639 --> 00:07:01.490 death syndrome. A statistician testified that 00:07:01.490 --> 00:07:04.410 the probability of two sudden infant death syndrome 00:07:04.410 --> 00:07:08.329 deaths in the same family was one in 73 million, 00:07:08.769 --> 00:07:11.269 a figure arrived at by squaring the probability 00:07:11.269 --> 00:07:13.910 of a single such death, assuming the two events 00:07:13.910 --> 00:07:17.290 were independent. The jury convicted. Clark spent 00:07:17.290 --> 00:07:19.509 three years in prison before her conviction was 00:07:19.509 --> 00:07:22.089 overturned. After it was established that the 00:07:22.089 --> 00:07:24.569 statistical analysis was flawed in multiple ways, 00:07:25.230 --> 00:07:27.339 including the assumption of independence, When 00:07:27.339 --> 00:07:29.540 in fact biological and environmental factors 00:07:29.540 --> 00:07:32.319 mean second, sudden infant death syndrome deaths 00:07:32.319 --> 00:07:34.980 in the same family are considerably more likely 00:07:34.980 --> 00:07:37.819 than the calculation assumed. She never recovered 00:07:37.819 --> 00:07:39.879 psychologically from her imprisonment and died 00:07:39.879 --> 00:07:43.699 of acute alcohol intoxication in 2007. The gambler's 00:07:43.699 --> 00:07:46.339 fallacy is the mirror image of base rate neglect. 00:07:46.800 --> 00:07:49.100 Where base rate neglect makes us ignore prior 00:07:49.100 --> 00:07:51.639 probabilities, the gambler's fallacy makes us 00:07:51.639 --> 00:07:53.920 believe that independent events are connected 00:07:53.920 --> 00:07:56.879 when they are not. A coin comes up heads five 00:07:56.879 --> 00:07:59.980 times in a row. The gambler thinks, tails is 00:07:59.980 --> 00:08:03.560 due. The probability of heads is 50%. The coin 00:08:03.560 --> 00:08:06.220 has no memory. The fact that it has come up heads 00:08:06.220 --> 00:08:09.319 five consecutive times does not alter the probability 00:08:09.319 --> 00:08:12.680 of the next flip. Each flip is independent. The 00:08:12.680 --> 00:08:15.439 intuition that a streak creates a debt that the 00:08:15.439 --> 00:08:17.920 universe owes you a correction is deeply embedded 00:08:17.920 --> 00:08:24.730 and completely wrong. is especially powerful 00:08:24.730 --> 00:08:27.490 in the domain of risk assessment. We judge the 00:08:27.490 --> 00:08:30.029 probability of an event by how easily examples 00:08:30.029 --> 00:08:32.610 of it come to mind. Plane crashes are vivid, 00:08:33.049 --> 00:08:35.690 emotionally salient, and heavily covered by media, 00:08:36.029 --> 00:08:38.529 so we overestimate the probability of dying in 00:08:38.529 --> 00:08:41.129 a plane crash and underestimate the probability 00:08:41.129 --> 00:08:43.549 of dying in a car accident, which is statistically 00:08:43.549 --> 00:08:46.610 far more common. Terrorism is overestimated as 00:08:46.610 --> 00:08:49.649 a risk. Heart disease is underestimated. The 00:08:49.649 --> 00:08:52.149 salience of an event in our imagination is not 00:08:52.149 --> 00:08:54.470 a reliable guide to its frequency in the world. 00:08:54.809 --> 00:08:57.070 The Sally Clark case is also a window into something 00:08:57.070 --> 00:08:59.750 philosophically important about the relationship 00:08:59.750 --> 00:09:02.690 between statistics and narrative. The statistical 00:09:02.690 --> 00:09:06.450 evidence, 1 in 73 million, was compelling in 00:09:06.450 --> 00:09:08.789 the way that large numbers are always compelling. 00:09:09.110 --> 00:09:11.570 But it was presented in isolation from the narrative 00:09:11.570 --> 00:09:14.309 context that would have made it interpretable. 00:09:14.870 --> 00:09:17.330 What is the background rate of false accusations 00:09:17.330 --> 00:09:20.259 in child death cases? What does the medical literature 00:09:20.259 --> 00:09:22.480 actually say about sudden infant death syndrome 00:09:22.480 --> 00:09:25.200 recurrence within families? Those questions require 00:09:25.200 --> 00:09:27.379 the base rate reasoning that Bayesian thinking 00:09:27.379 --> 00:09:29.759 demands, and that was conspicuously absent from 00:09:29.759 --> 00:09:32.279 the courtroom. Statistics without base rates 00:09:32.279 --> 00:09:35.200 are not just incomplete, they are actively misleading. 00:09:35.639 --> 00:09:37.679 The forensic use of probability has improved 00:09:37.679 --> 00:09:40.500 significantly since the Clark case, partly because 00:09:40.500 --> 00:09:42.639 of the sustained philosophical and legal work 00:09:42.639 --> 00:09:45.460 done in its aftermath. Courts now generally require 00:09:45.460 --> 00:09:48.159 expert witnesses to address base rates explicitly. 00:09:48.399 --> 00:09:50.679 And there are developed guidelines for presenting 00:09:50.679 --> 00:09:53.159 probabilistic evidence in ways that reduce the 00:09:53.159 --> 00:09:55.840 likelihood of the prosecutor's fallacy and its 00:09:55.840 --> 00:09:58.019 mirror image, the defense attorney's fallacy, 00:09:58.360 --> 00:10:00.799 which involves the error of treating a low probability 00:10:00.799 --> 00:10:04.039 of a match as itself exculpatory without considering 00:10:04.039 --> 00:10:06.860 the prior probability of guilt. Getting probability 00:10:06.860 --> 00:10:08.840 right in the courtroom is not just a technical 00:10:08.840 --> 00:10:11.629 problem. It is a justice problem. And then there 00:10:11.629 --> 00:10:14.090 is overconfidence, the tendency to assign higher 00:10:14.090 --> 00:10:16.669 probabilities to our own beliefs than the evidence 00:10:16.669 --> 00:10:19.029 warrants, and to be more certain about predictions 00:10:19.029 --> 00:10:21.490 than we should be. Studies consistently show 00:10:21.490 --> 00:10:23.870 that when people say they are 95 % confident 00:10:23.870 --> 00:10:26.409 in an answer, they are right about 70 % of the 00:10:26.409 --> 00:10:29.730 time. Experts in many domains, economists, political 00:10:29.730 --> 00:10:32.750 scientists, doctors, are frequently overconfident 00:10:32.750 --> 00:10:35.230 in their predictions. Philip Tetlock's work on 00:10:35.230 --> 00:10:37.889 forecasting, summarized in his book Superforecasting, 00:10:38.470 --> 00:10:40.429 suggests that most experts are not significantly 00:10:40.429 --> 00:10:43.169 better at probabilistic prediction than educated 00:10:43.169 --> 00:10:45.590 laypeople, and that the best forecasters are 00:10:45.590 --> 00:10:48.210 distinguished not by expertise but by epistemic 00:10:48.210 --> 00:10:50.570 humility, by their willingness to express genuine 00:10:50.570 --> 00:10:53.269 uncertainty and update their estimates frequently 00:10:53.269 --> 00:10:55.789 as new information arrives. I want to turn to 00:10:55.789 --> 00:10:58.049 one of the most famous and most philosophically 00:10:58.049 --> 00:11:00.669 interesting uses of probabilistic reasoning in 00:11:00.669 --> 00:11:03.840 the history of philosophy, Pascal's wager. because 00:11:03.840 --> 00:11:05.899 it illustrates both the power and the limits 00:11:05.899 --> 00:11:08.240 of applying probability to the largest questions. 00:11:08.580 --> 00:11:11.340 Blaise Pascal was a 17th century French mathematician, 00:11:11.919 --> 00:11:14.879 physicist, and philosopher, a genuinely extraordinary 00:11:14.879 --> 00:11:17.440 intellect who made foundational contributions 00:11:17.440 --> 00:11:20.840 to probability theory, fluid mechanics, and projective 00:11:20.840 --> 00:11:23.700 geometry, and who underwent a profound religious 00:11:23.700 --> 00:11:26.500 conversion in his mid -30s that shaped the rest 00:11:26.500 --> 00:11:29.320 of his life. His posthumously published Pensees' 00:11:29.539 --> 00:11:32.440 Thoughts in French contains the wager argument. 00:11:32.639 --> 00:11:35.080 which is probably the most famous decision theoretic 00:11:35.080 --> 00:11:37.460 argument for religious belief ever made. The 00:11:37.460 --> 00:11:40.220 argument runs roughly like this. You cannot know 00:11:40.220 --> 00:11:43.559 with certainty whether God exists, but you must 00:11:43.559 --> 00:11:46.899 choose how to live belief or non -belief without 00:11:46.899 --> 00:11:50.659 that certainty. So the choice is a wager. If 00:11:50.659 --> 00:11:53.419 you wager on God's existence and God exists, 00:11:53.720 --> 00:11:56.360 you gain eternal life, infinite reward. If you 00:11:56.360 --> 00:11:58.899 wager on God's existence and God does not exist, 00:11:59.120 --> 00:12:01.580 you lose some finite goods, pleasures, and freedoms 00:12:01.580 --> 00:12:04.019 you gave up in living a religious life. If you 00:12:04.019 --> 00:12:06.379 wager against God's existence and God does not 00:12:06.379 --> 00:12:09.399 exist, you gain those finite goods. If you wager 00:12:09.399 --> 00:12:12.100 against God's existence and God does exist, you 00:12:12.100 --> 00:12:15.340 face eternal damnation, infinite loss. The expected 00:12:15.340 --> 00:12:18.299 value calculation is straightforward. Infinite 00:12:18.299 --> 00:12:21.299 reward times any positive probability is infinite. 00:12:22.000 --> 00:12:25.139 Any finite loss is finite. Therefore, you should 00:12:25.139 --> 00:12:28.259 wager on God's existence. The argument is elegant. 00:12:28.460 --> 00:12:30.539 and has generated centuries of philosophical 00:12:30.539 --> 00:12:34.220 response. The most powerful objection is what 00:12:34.220 --> 00:12:37.139 is sometimes called the many gods problem. Pascal 00:12:37.139 --> 00:12:40.340 assumes a specific theological picture, the Christian 00:12:40.340 --> 00:12:43.320 god who rewards belief and punishes non -belief. 00:12:43.539 --> 00:12:45.720 But, there are many possible gods with different 00:12:45.720 --> 00:12:48.820 reward structures. A god who rewards sincere 00:12:48.820 --> 00:12:51.799 inquiry and punishes vain belief would recommend 00:12:51.799 --> 00:12:54.399 the opposite of Pascal's strategy. A god who 00:12:54.399 --> 00:12:56.700 rewards a different religion would make Pascal's 00:12:56.700 --> 00:12:59.159 wager actively harmful. Once you multiply the 00:12:59.159 --> 00:13:01.820 possible gods, the expected value calculation 00:13:01.820 --> 00:13:04.360 becomes vastly more complicated and the clean 00:13:04.360 --> 00:13:06.740 dominance argument dissolves. The second major 00:13:06.740 --> 00:13:10.039 objection is about the nature of belief. Pascal 00:13:10.039 --> 00:13:12.259 assumes that you can simply decide to believe 00:13:12.259 --> 00:13:15.360 that wagering on God is enough, but belief is 00:13:15.360 --> 00:13:18.220 not typically a direct object of will. You cannot 00:13:18.220 --> 00:13:20.899 simply choose to believe something you find implausible 00:13:20.899 --> 00:13:22.580 any more than you can choose to find something 00:13:22.580 --> 00:13:25.320 funny. Pascal was aware of this and had a response. 00:13:25.639 --> 00:13:28.580 Begin by acting as if you believe, attend church, 00:13:28.759 --> 00:13:31.139 practice the rituals, and belief will follow 00:13:31.139 --> 00:13:34.340 from habit and practice. This is actually a psychologically 00:13:34.340 --> 00:13:36.659 sophisticated point. There is genuine evidence 00:13:36.659 --> 00:13:38.820 that behavior shapes belief as much as belief 00:13:38.820 --> 00:13:41.700 shapes behavior. But it raises its own philosophical 00:13:41.700 --> 00:13:44.460 problems about the authenticity of belief arrived 00:13:44.460 --> 00:13:47.299 at through deliberate self -manipulation. William 00:13:47.299 --> 00:13:49.779 James, whose will to believe we covered last 00:13:49.779 --> 00:13:52.419 week, was both influenced by and critical of 00:13:52.419 --> 00:13:55.539 Pascal. He agreed that in certain forced, live, 00:13:55.860 --> 00:13:58.159 and momentous decisions, passion or commitment 00:13:58.159 --> 00:14:01.120 is legitimate. But he objected to Pascal's purely 00:14:01.120 --> 00:14:03.159 calculative approach, the idea that religious 00:14:03.159 --> 00:14:05.899 belief can be justified by an expected value 00:14:05.899 --> 00:14:08.940 argument. James thought, genuine religious belief 00:14:08.940 --> 00:14:11.519 required something more than a bet. It required 00:14:11.519 --> 00:14:14.399 an actual live hypothesis, a genuine openness 00:14:14.399 --> 00:14:17.259 in the believer, and an experience that the belief 00:14:17.259 --> 00:14:19.919 was tracking something real. The Jamesian will 00:14:19.919 --> 00:14:22.940 to believe is not Pascal's wager. It is considerably 00:14:22.940 --> 00:14:26.970 more psychologically and epistemologically demanding. 00:14:27.450 --> 00:14:29.509 There's a third objection to Pascal's wager that 00:14:29.509 --> 00:14:32.129 I find philosophically important and it has to 00:14:32.129 --> 00:14:34.429 do with the structure of infinite values in decision 00:14:34.429 --> 00:14:37.269 theory. Pascal's argument works because infinite 00:14:37.269 --> 00:14:39.990 reward times any positive probability, however 00:14:39.990 --> 00:14:42.950 small, is infinite and therefore dominates any 00:14:42.950 --> 00:14:45.929 finite consideration. But this structure creates 00:14:45.929 --> 00:14:48.350 problems that go beyond the many gods objection. 00:14:48.700 --> 00:14:51.179 If we allow infinite values into our decision 00:14:51.179 --> 00:14:53.820 calculus, almost any action can be justified 00:14:53.820 --> 00:14:56.639 by constructing a sufficiently exotic theological 00:14:56.639 --> 00:14:59.299 scenario in which it produces infinite reward. 00:14:59.620 --> 00:15:01.740 The expected value framework breaks down when 00:15:01.740 --> 00:15:04.259 infinite utilities are in play, because infinite 00:15:04.259 --> 00:15:06.759 expected values cannot be meaningfully compared 00:15:06.759 --> 00:15:09.299 or traded off against each other. Contemporary 00:15:09.299 --> 00:15:11.960 decision theorists have spent considerable effort 00:15:11.960 --> 00:15:14.379 trying to construct versions of Pascal's Wager 00:15:14.379 --> 00:15:17.019 that avoid these problems. Versions that produce 00:15:17.019 --> 00:15:20.340 the same conclusion without invoking actual infinities. 00:15:20.779 --> 00:15:23.340 The results are technically sophisticated, but 00:15:23.340 --> 00:15:25.720 none of them has the clean, intuitive force of 00:15:25.720 --> 00:15:28.700 the original. What Pascal's Wager does, at its 00:15:28.700 --> 00:15:31.960 best, is force us to think seriously about the 00:15:31.960 --> 00:15:35.419 asymmetry between the costs and benefits of religious 00:15:35.419 --> 00:15:37.379 commitment. The question of whether the goods 00:15:37.379 --> 00:15:39.500 that come from a life of religious commitment 00:15:39.500 --> 00:15:42.360 community, meaning ethical structure, the comfort 00:15:42.360 --> 00:15:45.960 of belief are worth the costs of that commitment. 00:15:46.360 --> 00:15:48.889 Even in the absence of certainty, about God's 00:15:48.889 --> 00:15:51.370 existence is a serious one. It just does not 00:15:51.370 --> 00:15:53.570 have the clean mathematical answer Pascal wanted 00:15:53.570 --> 00:15:55.730 to give it. I want to move from the abstract 00:15:55.730 --> 00:15:58.110 to the practical to what Bayesian reasoning actually 00:15:58.110 --> 00:16:00.529 looks like as an orientation to everyday life, 00:16:00.669 --> 00:16:02.529 because I think this is where the philosophy 00:16:02.529 --> 00:16:05.710 of probability pays off most directly for the 00:16:05.710 --> 00:16:08.629 examined life. The core Bayesian practice is 00:16:08.629 --> 00:16:11.210 updating taking your current beliefs as priors 00:16:11.210 --> 00:16:14.409 and revising them in response to evidence, proportionally 00:16:14.409 --> 00:16:16.909 to how strongly that evidence bears on the question. 00:16:17.049 --> 00:16:19.889 This sounds simple and is surprisingly hard. 00:16:20.350 --> 00:16:22.409 The difficulty is not primarily mathematical, 00:16:22.750 --> 00:16:25.429 it is psychological. We have strong motivated 00:16:25.429 --> 00:16:27.690 resistance to revising beliefs we are attached 00:16:27.690 --> 00:16:30.309 to, especially when the evidence bears on our 00:16:30.309 --> 00:16:33.090 identity, our relationships, or our worldview. 00:16:33.590 --> 00:16:35.789 The confirmation bias we covered in the cognitive 00:16:35.789 --> 00:16:38.750 bias episode is the systematic failure of Bayesian 00:16:38.750 --> 00:16:41.450 updating. We tend to seek out evidence that confirms 00:16:41.450 --> 00:16:44.330 our existing beliefs, interpret ambiguous evidence 00:16:44.330 --> 00:16:47.000 as confirming, and discount or ignore evidence 00:16:47.000 --> 00:16:49.159 that disconfirms. The result is that we become 00:16:49.159 --> 00:16:51.659 more confident in our beliefs over time, regardless 00:16:51.659 --> 00:16:54.279 of whether the evidence actually supports increasing 00:16:54.279 --> 00:16:57.279 confidence. This is not just a failure of reasoning. 00:16:57.659 --> 00:17:00.320 It is a failure of intellectual honesty, and 00:17:00.320 --> 00:17:02.919 it is one that the examined life specifically 00:17:02.919 --> 00:17:05.940 requires us to resist. What does good Bayesian 00:17:05.940 --> 00:17:08.880 practice actually look like? Philip Tetlock's 00:17:08.880 --> 00:17:11.460 research on superforecasters gives some concrete 00:17:11.460 --> 00:17:14.880 answers. The best probabilistic reasoners share 00:17:14.880 --> 00:17:17.299 a cluster of habits. They express their beliefs 00:17:17.299 --> 00:17:19.640 in numerical probabilities rather than vague 00:17:19.640 --> 00:17:22.740 qualifiers. Not, it is unlikely, but I think 00:17:22.740 --> 00:17:25.660 there is about a 20 % chance. They update their 00:17:25.660 --> 00:17:28.220 estimates frequently as new. Information arrives, 00:17:28.819 --> 00:17:31.039 and they update in both directions, increasing 00:17:31.039 --> 00:17:33.839 and decreasing confidence as the evidence warrants. 00:17:34.420 --> 00:17:36.680 They actively seek out disconfirming evidence 00:17:36.680 --> 00:17:38.880 and take it seriously. They have what Tetlock 00:17:38.880 --> 00:17:41.269 calls a growth mindset. about their own reasoning, 00:17:41.490 --> 00:17:43.390 they track their predictions, notice where they 00:17:43.390 --> 00:17:46.250 go wrong, and try to understand why. The philosopher 00:17:46.250 --> 00:17:49.210 of science, Imri Lakatos, introduced a concept 00:17:49.210 --> 00:17:52.170 he called the protective belt, the set of auxiliary 00:17:52.170 --> 00:17:54.470 assumptions that scientists use to shield their 00:17:54.470 --> 00:17:56.670 core theoretical commitments from disconfirming 00:17:56.670 --> 00:17:59.190 evidence. When an experiment produces a result 00:17:59.190 --> 00:18:02.089 that seems to contradict a central theory, scientists 00:18:02.089 --> 00:18:04.470 typically blame the experimental conditions, 00:18:04.930 --> 00:18:07.690 the instruments, the auxiliary assumptions before 00:18:07.690 --> 00:18:10.589 they revise the central theory. This is not always 00:18:10.589 --> 00:18:13.470 wrong. Sometimes the auxiliary assumptions really 00:18:13.470 --> 00:18:15.849 are the problem. But it can become a pathology 00:18:15.849 --> 00:18:18.049 when the protective belt is maintained not by 00:18:18.049 --> 00:18:20.250 genuine reasoning, but by the desire to preserve 00:18:20.250 --> 00:18:22.490 a commitment that is no longer warranted by the 00:18:22.490 --> 00:18:25.869 evidence. In everyday life, we all maintain protective 00:18:25.869 --> 00:18:28.769 belts around our most important beliefs. The 00:18:28.769 --> 00:18:30.750 belief that a relationship is fundamentally healthy, 00:18:31.269 --> 00:18:34.069 that our approach to work is sound, that our 00:18:34.069 --> 00:18:36.769 political framework accurately describes reality. 00:18:36.910 --> 00:18:39.730 These are surrounded by auxiliary explanations 00:18:39.730 --> 00:18:42.269 that absorb anomalies. The Bayesian practice 00:18:42.269 --> 00:18:44.890 is not to abandon core commitments at the first 00:18:44.890 --> 00:18:46.630 sign of disconfirming evidence that would be 00:18:46.630 --> 00:18:48.690 a different kind of error. It is to be genuinely 00:18:48.690 --> 00:18:50.990 open to the possibility that the anomalies are 00:18:50.990 --> 00:18:52.990 accumulating in ways that warrant revising the 00:18:52.990 --> 00:18:55.309 core commitment, and to track that accumulation 00:18:55.309 --> 00:18:57.869 honestly rather than explaining it away. Gerd 00:18:57.869 --> 00:19:00.430 Gigerenzer, the German psychologist who has spent 00:19:00.430 --> 00:19:03.069 his career studying statistical reasoning and 00:19:03.069 --> 00:19:05.680 its failures, makes a point that I find both 00:19:05.680 --> 00:19:08.500 empirically interesting and philosophically important. 00:19:08.920 --> 00:19:11.420 He argues that many of our probabilistic failures 00:19:11.420 --> 00:19:14.039 are not failures of human rationality per se, 00:19:14.579 --> 00:19:17.019 but failures to present information in a format 00:19:17.019 --> 00:19:19.700 that human minds can process naturally. People 00:19:19.700 --> 00:19:21.859 are much better at reasoning about frequencies 00:19:21.859 --> 00:19:24.480 than about probabilities expressed as percentages 00:19:24.480 --> 00:19:27.380 or decimals. The medical test problem in our 00:19:27.380 --> 00:19:29.720 opening, expressed as a percentage, it produces 00:19:29.720 --> 00:19:32.480 systematic confusion. expressed as a frequency 00:19:32.480 --> 00:19:35.099 out of a thousand people tested, how many test 00:19:35.099 --> 00:19:38.099 positive and actually have the disease. It becomes 00:19:38.099 --> 00:19:40.960 considerably more tractable. Gigerenzer's point 00:19:40.960 --> 00:19:43.319 has practical implications for how we communicate 00:19:43.319 --> 00:19:46.519 risk and evidence. Doctors who present risk information 00:19:46.519 --> 00:19:49.339 as frequencies rather than probabilities produce 00:19:49.339 --> 00:19:51.839 better informed patients. Judges who receive 00:19:51.839 --> 00:19:54.660 statistical evidence in frequency format make 00:19:54.660 --> 00:19:57.059 fewer errors than those who receive the same 00:19:57.059 --> 00:20:00.579 information as probabilities. The format of information 00:20:00.730 --> 00:20:03.930 matters as much as its content. And designing 00:20:03.930 --> 00:20:06.130 information environments that work with our cognitive 00:20:06.130 --> 00:20:08.609 architecture rather than against it is a genuine 00:20:08.609 --> 00:20:10.970 contribution to public health and public reason, 00:20:11.170 --> 00:20:13.289 one that does not require changing human nature, 00:20:13.609 --> 00:20:15.970 but simply changing how we present the facts. 00:20:16.509 --> 00:20:18.710 I want to close the substantive part of the episode 00:20:18.710 --> 00:20:20.849 by connecting probability back to the broader 00:20:20.849 --> 00:20:23.230 project of this show, to what thinking carefully 00:20:23.230 --> 00:20:25.609 about probability means for how we live. The 00:20:25.609 --> 00:20:28.009 most direct connection is to what we said in 00:20:28.009 --> 00:20:30.759 the episode on living philosophically. The exam 00:20:30.759 --> 00:20:34.140 in life requires honest inventory. Honest inventory 00:20:34.140 --> 00:20:36.200 applied to belief means holding your beliefs 00:20:36.200 --> 00:20:38.579 at the confidence level they actually deserve 00:20:38.579 --> 00:20:40.539 given the evidence, not at the confidence level 00:20:40.539 --> 00:20:43.339 that feels comfortable or that protects your 00:20:43.339 --> 00:20:46.460 identity or that your social group endorses. 00:20:46.559 --> 00:20:49.200 That is a demanding standard. It means being 00:20:49.200 --> 00:20:51.480 genuinely uncertain about things you are uncertain 00:20:51.480 --> 00:20:54.880 about and being willing to say so even when uncertainty 00:20:54.880 --> 00:20:57.420 is socially uncomfortable or personally threatening. 00:20:57.630 --> 00:20:59.930 It also means being appropriately confident about 00:20:59.930 --> 00:21:02.690 things you have good reason to believe. Epistemic 00:21:02.690 --> 00:21:04.930 humility does not mean treating all beliefs as 00:21:04.930 --> 00:21:07.309 equally uncertain. Some things are well supported 00:21:07.309 --> 00:21:10.349 by evidence and deserve high confidence. The 00:21:10.349 --> 00:21:12.789 skill is calibration, matching your confidence 00:21:12.789 --> 00:21:15.789 level to the quality of your evidence. Overconfidence 00:21:15.789 --> 00:21:18.430 is a failure of calibration in one direction. 00:21:18.890 --> 00:21:21.289 Performative uncertainty, claiming not to know 00:21:21.289 --> 00:21:23.369 things you actually have good grounds to believe 00:21:23.369 --> 00:21:26.230 is a failure in the other direction. The Bayesian 00:21:26.230 --> 00:21:29.069 ideal is neither. There is also a deep connection 00:21:29.069 --> 00:21:32.650 to the question of moral judgment. We make probabilistic 00:21:32.650 --> 00:21:34.690 assessments about people all the time, about 00:21:34.690 --> 00:21:37.710 their intentions, their character, their reliability, 00:21:37.869 --> 00:21:40.029 and those assessments are subject to the same 00:21:40.029 --> 00:21:42.549 biases that affect our probabilistic reasoning 00:21:42.549 --> 00:21:45.029 in other domains. We anchor on vivid initial 00:21:45.029 --> 00:21:47.849 impressions. We neglect base rates, the fact 00:21:47.849 --> 00:21:50.529 that most people are not malicious, most accusations 00:21:50.529 --> 00:21:53.349 are not fabricated, most anomalies have innocent 00:21:53.349 --> 00:21:56.289 explanations. We are overconfident in our ability 00:21:56.289 --> 00:21:58.920 to read people. The Bayesian correction in the 00:21:58.920 --> 00:22:01.839 domain of moral judgment is not to suspend all 00:22:01.839 --> 00:22:05.000 judgment, but to hold it more lightly, to update 00:22:05.000 --> 00:22:07.920 it more readily, and to be more aware of the 00:22:07.920 --> 00:22:10.339 prior probabilities that should be shaping our 00:22:10.339 --> 00:22:12.819 interpretation of the evidence. And finally, 00:22:12.859 --> 00:22:15.400 there is the question of decisions under uncertainty, 00:22:15.599 --> 00:22:17.700 which is essentially all important decisions. 00:22:18.039 --> 00:22:20.359 We rarely have complete information when we need 00:22:20.359 --> 00:22:23.259 to act. The question is not how to eliminate 00:22:23.259 --> 00:22:26.099 uncertainty, but how to act wisely in its presence. 00:22:26.400 --> 00:22:28.480 The Bayesian framework suggests that the right 00:22:28.480 --> 00:22:30.559 approach is not to wait for certainty that will 00:22:30.559 --> 00:22:33.839 not come, but to identify your best current estimate 00:22:33.839 --> 00:22:36.980 of the probabilities, act on that estimate, and 00:22:36.980 --> 00:22:39.279 remain genuinely open to revising your assessment 00:22:39.279 --> 00:22:41.880 as new information arrives. That is, in some 00:22:41.880 --> 00:22:44.619 ways, a mathematical formalization of what William 00:22:44.619 --> 00:22:46.940 James was arguing for with the will to believe. 00:22:47.460 --> 00:22:49.819 The courage to commit to your best current estimate 00:22:49.819 --> 00:22:52.460 while maintaining the intellectual honesty to 00:22:52.460 --> 00:22:55.200 revise it. The two orientations are complementary 00:22:55.200 --> 00:22:58.200 rather than contradictory. James says, do not 00:22:58.200 --> 00:23:00.299 let the demand for certainty prevent you from 00:23:00.299 --> 00:23:03.779 acting. Bayes says, make your uncertainty explicit, 00:23:04.140 --> 00:23:06.339 track it honestly and update it as the evidence 00:23:06.339 --> 00:23:08.759 accumulates. Together they describe a way of 00:23:08.759 --> 00:23:11.119 being in the world under uncertainty that is 00:23:11.119 --> 00:23:14.099 both practically workable and epistemically honest, 00:23:14.680 --> 00:23:17.319 neither paralyzed by doubt nor hardened into 00:23:17.319 --> 00:23:19.630 false confidence. There is one more connection 00:23:19.630 --> 00:23:21.990 worth drawing between probabilistic thinking 00:23:21.990 --> 00:23:24.430 and the virtue of intellectual humility that 00:23:24.430 --> 00:23:25.869 has been running through this show since the 00:23:25.869 --> 00:23:28.390 first episode. Genuine intellectual humility 00:23:28.390 --> 00:23:31.109 is not the performance of uncertainty. The person 00:23:31.109 --> 00:23:33.289 who says, I could be wrong about everything as 00:23:33.289 --> 00:23:35.670 a social ritual while actually holding their 00:23:35.670 --> 00:23:38.269 beliefs with full confidence. It is the genuine 00:23:38.269 --> 00:23:40.829 calibration of confidence to evidence that Bayesian 00:23:40.829 --> 00:23:43.130 reasoning describes. It means being willing to 00:23:43.130 --> 00:23:46.049 say, I think there is about a 60 % chance I am 00:23:46.049 --> 00:23:48.420 right about this. and I am genuinely open to 00:23:48.420 --> 00:23:50.779 updating that if the evidence warrants. That 00:23:50.779 --> 00:23:53.740 kind of explicit, trackable, revisable confidence 00:23:53.740 --> 00:23:56.539 is both epistemically honest and practically 00:23:56.539 --> 00:23:59.000 useful. It is what the examined life looks like 00:23:59.000 --> 00:24:01.319 when it encounters the irreducible uncertainty 00:24:01.319 --> 00:24:04.099 of being a finite creature in a complex world. 00:24:04.380 --> 00:24:06.900 The medical test problem in the opening is the 00:24:06.900 --> 00:24:09.319 one I keep coming back to because I think it 00:24:09.319 --> 00:24:11.519 illustrates something important about the relationship 00:24:11.519 --> 00:24:14.460 between expertise and understanding. The mathematics 00:24:14.460 --> 00:24:17.210 of the problem is not complicated. A high school 00:24:17.210 --> 00:24:20.269 student with basic probability skills can work 00:24:20.269 --> 00:24:23.069 through it, but it routinely trips up doctors, 00:24:23.490 --> 00:24:26.269 lawyers, and judges, people whose decisions about 00:24:26.269 --> 00:24:28.769 medical treatment and criminal conviction depend 00:24:28.769 --> 00:24:31.049 on getting it right. The problem is not lack 00:24:31.049 --> 00:24:33.569 of mathematical ability. It is the failure to 00:24:33.569 --> 00:24:36.109 translate abstract statistical principles into 00:24:36.109 --> 00:24:38.789 concrete reasoning about specific cases. That 00:24:38.789 --> 00:24:40.910 gap between knowing a principle and applying 00:24:40.910 --> 00:24:43.849 it correctly in context is exactly the gap that 00:24:43.849 --> 00:24:46.559 the examined life is trying to close. and it 00:24:46.559 --> 00:24:49.460 is not unique to probability. We know that cognitive 00:24:49.460 --> 00:24:52.079 biases distort our reasoning, but we still fall 00:24:52.079 --> 00:24:54.619 for them. We know that confirmation bias exists, 00:24:54.839 --> 00:24:57.339 but we still seek confirming evidence. We know 00:24:57.339 --> 00:24:59.500 that the availability heuristic misleads us, 00:24:59.740 --> 00:25:01.880 but we still let vivid examples dominate our 00:25:01.880 --> 00:25:04.039 risk assessment. Knowledge of the principle does 00:25:04.039 --> 00:25:06.539 not automatically produce correct application. 00:25:06.980 --> 00:25:09.789 It requires practice. feedback, and the kind 00:25:09.789 --> 00:25:12.349 of honest self -monitoring that good probabilistic 00:25:12.349 --> 00:25:14.690 reasoning demands, and that the philosophical 00:25:14.690 --> 00:25:17.470 tradition keeps returning to as the core practice 00:25:17.470 --> 00:25:20.750 of the examined life. Blaise Pascal, who gave 00:25:20.750 --> 00:25:23.710 us both probability theory and the wager, was 00:25:23.710 --> 00:25:26.170 also the author of one of the most quietly devastating 00:25:26.170 --> 00:25:28.809 observations in the history of philosophy. He 00:25:28.809 --> 00:25:30.970 wrote that all of humanity's problems stem from 00:25:30.970 --> 00:25:33.529 the inability to sit quietly in a room alone. 00:25:33.869 --> 00:25:36.710 That is, on its face. a strange thing for the 00:25:36.710 --> 00:25:39.230 inventor of probability theory to say, but I 00:25:39.230 --> 00:25:41.130 think it points at the same thing that Bayesian 00:25:41.130 --> 00:25:42.910 reasoning points at from the other direction. 00:25:43.529 --> 00:25:46.289 The examined life requires slowing down, resisting 00:25:46.289 --> 00:25:49.309 the fast confident answer, sitting with uncertainty 00:25:49.309 --> 00:25:52.450 long enough to actually assess it rather than 00:25:52.450 --> 00:25:54.690 fleam it. The probability is in the patience. 00:25:55.170 --> 00:25:57.549 I want to end with a practical note because this 00:25:57.549 --> 00:25:59.869 is an episode that I think rewards application 00:25:59.869 --> 00:26:02.519 more than most. The next time you encounter a 00:26:02.519 --> 00:26:05.380 statistic presented as a percentage, a test accuracy 00:26:05.380 --> 00:26:08.519 rate, a risk reduction claim, a polling figure, 00:26:08.539 --> 00:26:11.119 try to translate it into a frequency. Out of 00:26:11.119 --> 00:26:13.660 a thousand people in this situation, how many 00:26:13.660 --> 00:26:16.200 would this apply to? Out of a hundred exposures, 00:26:16.460 --> 00:26:19.000 how many would produce this outcome? The frequency 00:26:19.000 --> 00:26:21.640 format is more cognitively natural and almost 00:26:21.640 --> 00:26:23.660 always more informative than the percentage. 00:26:24.019 --> 00:26:26.359 It forces the question of base rates into view 00:26:26.359 --> 00:26:28.400 rather than letting them be swallowed by the 00:26:28.400 --> 00:26:30.900 headline figure. And the next time you find yourself 00:26:30.900 --> 00:26:33.279 very confident about something, especially something 00:26:33.279 --> 00:26:35.819 you have strong feelings about, ask, what would 00:26:35.819 --> 00:26:38.700 it take to change my mind? What evidence would 00:26:38.700 --> 00:26:40.920 move me? If you cannot answer that question, 00:26:41.200 --> 00:26:43.480 if there is no imaginable evidence that would 00:26:43.480 --> 00:26:45.920 revise your belief, that is Popper's criterion 00:26:45.920 --> 00:26:49.039 for a non -falsifiable claim. It does not necessarily 00:26:49.039 --> 00:26:51.420 mean the belief is wrong, but it means you are 00:26:51.420 --> 00:26:53.599 holding it in a way that is immune to evidence 00:26:53.599 --> 00:26:56.240 and that is worth noticing. Because it is the 00:26:56.240 --> 00:26:58.559 signature of the protective belt working at full 00:26:58.559 --> 00:27:00.750 strength. rather than the examined life working 00:27:00.750 --> 00:27:03.329 at all. Next week we are asking a question that 00:27:03.329 --> 00:27:05.809 sounds simple and turns out to be one of the 00:27:05.809 --> 00:27:09.130 deepest in philosophy. Was Epicurus actually 00:27:09.130 --> 00:27:12.130 an Epicurean? The historical Epicurus argued 00:27:12.130 --> 00:27:14.809 for a philosophy of moderate pleasure, friendship, 00:27:15.309 --> 00:27:17.630 and the withdrawal from political ambition. The 00:27:17.630 --> 00:27:19.950 word Epicurean has come to mean something almost 00:27:19.950 --> 00:27:23.049 opposite sensual indulgence. Luxury, the pursuit 00:27:23.049 --> 00:27:26.210 of refined pleasure. How that happened, what 00:27:26.210 --> 00:27:29.079 Epicurus actually taught, and whether his philosophy 00:27:29.079 --> 00:27:31.380 is a more useful guide to the good life than 00:27:31.380 --> 00:27:33.960 either his ancient critics or his modern admirers 00:27:33.960 --> 00:27:49.759 suggest. Sources and further reading are in the 00:27:49.759 --> 00:27:57.880 show notes. See you next week.