Oh, no, I didn't mean that rationality is a religion. I was referring to a movement, mostly based in Silicon Valley, that calls itself "Rationality" (and is only ostensibly about rationality; if you read their materials you'll see), and might qualify as a religion.
> This "different kinds of truth" leads right off the cliff of being unable to evaluate truth claims
Absolutely not. Hamlet really does kill himself, but that truth is not the same kind of truth as Hitler killing himself. Call it different logical theories (i.e. sets of axioms) or different simulations if you're more drawn to a mathematical or computational description of different kinds of truth. Of course, it is possible to reduce all those truths to the same system, but doing so is not very useful.
> Hamlet really does kill himself, but that truth is not the same kind of truth as Hitler killing himself. Call it different logical theories (i.e. sets of axioms) or different simulations if you're more drawn to a mathematical or computational description of different kinds of truth.
Axioms give us truth, but truth is inaccessible to us in the real world. Reality gives us probabilities, and our ideas about how the world works are good or bad based on how well they allow us to predict the world.
So saying that "Hitler killed himself" is not a "Truth" in that definition of the word, in that it does not follow from axioms, which means it can, conceivably, be disproven. "Hitler killed himself" is, at best, a fact, and facts are statistical in nature; of course, some probabilities are so close to 1 that denying them, or pretending they're uncertain, is insanity.
For more context on what I mean about facts being statistical, read this review of "Surfing Uncertainty":
Hamlet's suicide is a fact about a fictional world, in that it's possible to interpret the text such that it didn't happen, and interpretation shapes meaning. Again, though, some interpretations have so little going for them, textually and logically, that they're non-starters.
So both come down to the same thing, a three-part summary where some people seem bound and determined to ignore, misinterpret, and outright lie about the third part:
1. Truth is only available to us from axiom systems, where it follows inescapably, such that it is impossible to come to any other conclusion within that system.
2. Real life isn't an axiom system. Real life is perceived exclusively as a statistical interpretation of incomplete and flawed sensory data. Compare this to quantum mechanics and I walk you through a mathematical interpretation of Heisenberg's Uncertainty Principle with reference to waves and linear mechanics, I swear to God.
3. However, and this is the part some people refuse to understand and I mean screaming-match level refuse to get, just because we don't have absolute certainty doesn't mean we don't know anything at all. All probabilities are not 50/50, everything is not equally likely, and it is possible to know enough about reality to predict what's likely to happen. That is what the brain does on a moment-to-moment basis and most people live in the same reality as everyone else, and the same reality as inanimate objects. Reality isn't purely a figment of our collective imagination, it isn't purely a matter of opinion, and there's no way to walk on thin air.
1. I don't understand what any of this has to do with what I said.
2. Beware of learning philosophy from slatestarcodex. What he writes may sound very smart and convincing to people who have not studied philosophy, but Scott Alexander is often very, very misleading and extraordinarily simplistic. Much of what he brings up has been debated intensely among philosophers, with more interesting insights than his. For example, the entire exposition you laid out, with its distinction between deductive proof and inductive/probabilistic extrapolation, had already been worked out, pretty much in full, but the 17th century (see, e.g. Leibniz). We've learned a thing or two since then. In general, Alexander (and, in fact, the Rationality movement with which, I believe, he is associated) represent more or less the state of philosophy in the 17th and 18th centuries. The choice of stopping at the 18th century is, of course, one of the many ideological choices made by the Rationality movement, so take with a huge grain of salt anything you read by an author associated with that movement. Not that it's not true -- it's just very inaccurate and so, misleading. As you brought up quantum mechanics, the philosophy of the Rationalists, let's call them, amounts to Newtonian mechanics. True, but inaccurate and misses (or, in their case, chooses to ignore) some interesting and important phenomena. Of course, Newtonian mechanics just sounds better to most people, as it fits with their observations, and that is precisely what the Rationalists count on: that their 18th century philosophy would sound "common sensical" to their philosophically-lay readers, while more modern philosophy would sound, like qunatum mechanics, bizarre and foreign, and so likely to be discounted or even ridiculed by their readers.
Oh, no, I didn't mean that rationality is a religion. I was referring to a movement, mostly based in Silicon Valley, that calls itself "Rationality" (and is only ostensibly about rationality; if you read their materials you'll see), and might qualify as a religion.
> This "different kinds of truth" leads right off the cliff of being unable to evaluate truth claims
Absolutely not. Hamlet really does kill himself, but that truth is not the same kind of truth as Hitler killing himself. Call it different logical theories (i.e. sets of axioms) or different simulations if you're more drawn to a mathematical or computational description of different kinds of truth. Of course, it is possible to reduce all those truths to the same system, but doing so is not very useful.