WEBVTT 00:00:00.000 --> 00:00:03.819 Hi, this week we have been exploring truth. We've 00:00:03.819 --> 00:00:06.299 seen that truth gives us something solid to stand 00:00:06.299 --> 00:00:09.080 on. We've seen that it can be discovered and 00:00:09.080 --> 00:00:12.900 even surprise us. But that raises another key 00:00:12.900 --> 00:00:17.059 question. In math, truth does not stand alone. 00:00:17.300 --> 00:00:21.379 It depends on where we start. Every proof begins 00:00:21.379 --> 00:00:24.980 with assumptions, and those assumptions shape 00:00:24.980 --> 00:00:28.440 what follows. We saw this with geometry in the 00:00:28.440 --> 00:00:31.920 previous week. For centuries, Euclid's geometry 00:00:31.920 --> 00:00:36.479 was considered the truth. But when mathematicians 00:00:36.479 --> 00:00:40.020 changed just one assumption, something quite 00:00:40.020 --> 00:00:43.359 remarkable happened. New geometries appeared. 00:00:43.740 --> 00:00:47.820 Literally, new worlds were created. Different 00:00:47.820 --> 00:00:52.299 conclusions, yet still completely logical. The 00:00:52.299 --> 00:00:56.140 reasoning did not break. The starting point changed. 00:00:56.439 --> 00:01:00.240 And that changed everything. Math makes this 00:01:00.240 --> 00:01:03.359 crystal clear. If you change the assumptions, 00:01:03.619 --> 00:01:07.400 you can change what is true within that system. 00:01:08.799 --> 00:01:11.060 Now, let's consider how this shows up beyond 00:01:11.060 --> 00:01:14.299 math. Clearly, we all have starting points, assumptions 00:01:14.299 --> 00:01:18.340 about the world, about people, about truth itself. 00:01:18.939 --> 00:01:22.599 And those assumptions shape what we believe. 00:01:23.140 --> 00:01:25.819 You can see this clearly in how people approach 00:01:25.819 --> 00:01:28.870 something like the Bible. Some begin with the 00:01:28.870 --> 00:01:32.370 assumption that it must be read literally, like 00:01:32.370 --> 00:01:35.829 direct statements of truth. Others begin with 00:01:35.829 --> 00:01:38.150 the assumption that it is a collection of writings, 00:01:38.310 --> 00:01:41.969 stories, and poetry, and history that need to 00:01:41.969 --> 00:01:45.530 be understood in context. Different starting 00:01:45.530 --> 00:01:49.890 points, different conclusions. And often the 00:01:49.890 --> 00:01:52.469 disagreement is not just about the conclusion, 00:01:52.670 --> 00:01:56.900 it is about the assumptions underneath it. And 00:01:56.900 --> 00:01:59.040 sometimes it's not just the assumptions that 00:01:59.040 --> 00:02:03.540 matter, it is how we reason from them. In math, 00:02:03.760 --> 00:02:07.480 we are careful about that. We do not just say 00:02:07.480 --> 00:02:12.219 something is true. We show why it follows. But 00:02:12.219 --> 00:02:15.900 outside of math, it is easy to slip into a different 00:02:15.900 --> 00:02:20.800 pattern. Sometimes, something is treated as true 00:02:20.800 --> 00:02:24.780 simply because it comes from a trusted source. 00:02:25.610 --> 00:02:29.389 and then that source is trusted because it is 00:02:29.389 --> 00:02:33.090 assumed to be true. That kind of reasoning circles 00:02:33.090 --> 00:02:37.150 back on itself. Now, that does not mean the conclusion 00:02:37.150 --> 00:02:40.270 is wrong, but it does mean we have not really 00:02:40.270 --> 00:02:44.210 examined how we got there. And when we do not 00:02:44.210 --> 00:02:47.229 examine our reasoning, we can become more focused 00:02:47.229 --> 00:02:50.810 on defending conclusions rather than understanding 00:02:50.810 --> 00:02:55.319 them. Math invites something different. It invites 00:02:55.319 --> 00:02:59.259 us to slow down, to look carefully at our starting 00:02:59.259 --> 00:03:03.180 points, and to ask whether what follows truly 00:03:03.180 --> 00:03:07.039 makes sense. Because truth does not just depend 00:03:07.039 --> 00:03:11.259 on logic. It also depends on where we begin and 00:03:11.259 --> 00:03:16.680 how honestly we follow the path from there. I've 00:03:16.680 --> 00:03:20.199 noticed when I become aware that something shifts 00:03:20.199 --> 00:03:26.280 or changes in me, I become less defensive, and 00:03:26.280 --> 00:03:32.139 more curious. So my question today is, what assumptions 00:03:32.139 --> 00:03:35.979 am I starting with? And how is my reasoning shaping 00:03:35.979 --> 00:03:37.979 what I believe is true?