Gray Area, the objections you list are objections from within a model. This is right and proper. A lot of people don’t reason the same way you do, though. Quick replies: (1) We know from sheerly physical considerations that you can build a brain at least a million times as fast as a human brain, which gives us many interesting results of itself. (2, 3) Barring a specific model of cognitive science one cannot disprove a magical upper bound which lies exactly above human intelligence, even though raw evolution encountered no apparent difficulty in accidentally building humans out of chimps using only a threefold increase in brain and a sixfold increase in prefrontal cortex. But the principle of mediocrity weighs heavily against such an arbitrary presumption, as well as the general notion that evolution doesn’t build optimal systems, plus all the known flaws we talk about on Overcoming Bias. Furthermore my own, specific model of cognitive science is already suggesting that we can go beyond human purely on the basis of writing better software, but this is too complex to justify in detail here—the common sense of this should be apparent, though.
Doug, it may help to think in terms of a log odds ratio, in which case a probability of zero corresponds to negative infinity. You could never get that much counterevidence—we are talking about a subjective probability, not an objective frequency. Perhaps you are hallucinating or deluded or a toy in a computer simulation of mathematical error. Infinity is not a number, and 0 is not a probability.
Jonvon, there is only one human superpower. It makes us what we are. It is our ability to think. Rationality trains this superpower, like martial arts trains a human body. It is not that some people are born with the power and others are not. Everyone has a brain. Not everyone tries to train it. Not everyone realizes that intelligence is the only superpower they will ever have, and so they seek other magics, spells and sorceries, as if any magic wand could ever be as powerful or as precious or as significant as a brain.
If you work hard at it, you can have a personal subjective probability of one that the Rangers will win the World Series next year. They might even win. In which case...nothing. You still shouldn’t have thought that.
It may be best to act as if the probability was one, for lack of ability to represent near-one probabilities in your mind. But I recommend acting and committing to act as if it were impossible to blackmail you, even though you probably (rightly) think the chances someone could successfully do it against you are high enough to be representable.
If an angry empty crack pipe demands you stop daydreaming, then it should be thought more likely than before that the memory isn’t of something that really happened.
If you are thinking that you are thinking of something, you could be wrong. Thinking the thought “Mouse” is what it feels like to think of a mouse, thinking “I’m thinking of a mouse” is what it feels like to think of thinking of a mouse.
Ideally, whenever you discover that you have mis-remembered something, you should lower your overall confidence in the accuracy of your memories.
Or perhaps you mean it in the sense of “What is the probably that I (the person hearing this sentence in an internal monologue) exist?”. That one is tricky. But, however you resolve the anthropic dilemma there, you still shouldn’t assign it a probability of 1, if only because, very occasionally, other things that seemed just as ludicrously obviously true in the past have later been shown to be false.
You misunderstood, not that the stimulus correlated to anything, but that I myself experienced the memory of the stimulus. This does not mean i had the stimulus, nor that I hallucinated it, simply that I now have the experience of having remembered the stimulus. How could I be wrong about that? What sense does it make to question if you recall something? Again, not if you recall it accurately, but if you recall it all. How might I think I remember one stimulus, and find that i actually remembered another?
Okay, so you mean something like from my second paragraph, right?
The reason you shouldn’t assign a probability of exactly 1 to any belief, even to things that you can’t imagine being wrong about, is that in the past, intelligent and well-educated people have also believed things that they also couldn’t imagine being wrong about. And then later, been wrong. Usually because they were making some assumption that they weren’t even aware of.
Setting a probability of 1, for a Bayesian, is saying “I will never ever ever adjust my subjective probability for this belief downwards, no matter what.” Putting yourself in that position is not a good idea.
Furthermore, the belief in question has a lot to do with consciousness and internal experience. This is a poorly understood field, so beliefs in this area deserve special scrutiny.
Gray Area, the objections you list are objections from within a model. This is right and proper. A lot of people don’t reason the same way you do, though. Quick replies: (1) We know from sheerly physical considerations that you can build a brain at least a million times as fast as a human brain, which gives us many interesting results of itself. (2, 3) Barring a specific model of cognitive science one cannot disprove a magical upper bound which lies exactly above human intelligence, even though raw evolution encountered no apparent difficulty in accidentally building humans out of chimps using only a threefold increase in brain and a sixfold increase in prefrontal cortex. But the principle of mediocrity weighs heavily against such an arbitrary presumption, as well as the general notion that evolution doesn’t build optimal systems, plus all the known flaws we talk about on Overcoming Bias. Furthermore my own, specific model of cognitive science is already suggesting that we can go beyond human purely on the basis of writing better software, but this is too complex to justify in detail here—the common sense of this should be apparent, though.
Doug, it may help to think in terms of a log odds ratio, in which case a probability of zero corresponds to negative infinity. You could never get that much counterevidence—we are talking about a subjective probability, not an objective frequency. Perhaps you are hallucinating or deluded or a toy in a computer simulation of mathematical error. Infinity is not a number, and 0 is not a probability.
Jonvon, there is only one human superpower. It makes us what we are. It is our ability to think. Rationality trains this superpower, like martial arts trains a human body. It is not that some people are born with the power and others are not. Everyone has a brain. Not everyone tries to train it. Not everyone realizes that intelligence is the only superpower they will ever have, and so they seek other magics, spells and sorceries, as if any magic wand could ever be as powerful or as precious or as significant as a brain.
Do I not have a personal subjective probability of one that I just recalled the stimulus of writing this sentence?
No, you don’t.
If you work hard at it, you can have a personal subjective probability of one that the Rangers will win the World Series next year. They might even win. In which case...nothing. You still shouldn’t have thought that.
It may be best to act as if the probability was one, for lack of ability to represent near-one probabilities in your mind. But I recommend acting and committing to act as if it were impossible to blackmail you, even though you probably (rightly) think the chances someone could successfully do it against you are high enough to be representable.
What evidence could I observe that would lower my probability that I remember a stimulus?
If an angry empty crack pipe demands you stop daydreaming, then it should be thought more likely than before that the memory isn’t of something that really happened.
If you are thinking that you are thinking of something, you could be wrong. Thinking the thought “Mouse” is what it feels like to think of a mouse, thinking “I’m thinking of a mouse” is what it feels like to think of thinking of a mouse.
If you can demonstrate that I can be wrong about thinking I’m thinking something I’ll retract my OP.
Of course that I remember the appearance of the crack pipe, does not need for it to be that there was a crack pipe.
Ideally, whenever you discover that you have mis-remembered something, you should lower your overall confidence in the accuracy of your memories.
Or perhaps you mean it in the sense of “What is the probably that I (the person hearing this sentence in an internal monologue) exist?”. That one is tricky. But, however you resolve the anthropic dilemma there, you still shouldn’t assign it a probability of 1, if only because, very occasionally, other things that seemed just as ludicrously obviously true in the past have later been shown to be false.
You misunderstood, not that the stimulus correlated to anything, but that I myself experienced the memory of the stimulus. This does not mean i had the stimulus, nor that I hallucinated it, simply that I now have the experience of having remembered the stimulus. How could I be wrong about that? What sense does it make to question if you recall something? Again, not if you recall it accurately, but if you recall it all. How might I think I remember one stimulus, and find that i actually remembered another?
Okay, so you mean something like from my second paragraph, right?
The reason you shouldn’t assign a probability of exactly 1 to any belief, even to things that you can’t imagine being wrong about, is that in the past, intelligent and well-educated people have also believed things that they also couldn’t imagine being wrong about. And then later, been wrong. Usually because they were making some assumption that they weren’t even aware of.
Setting a probability of 1, for a Bayesian, is saying “I will never ever ever adjust my subjective probability for this belief downwards, no matter what.” Putting yourself in that position is not a good idea.
Furthermore, the belief in question has a lot to do with consciousness and internal experience. This is a poorly understood field, so beliefs in this area deserve special scrutiny.