37
votes
Accepted
Why would infinite monkeys not produce the works of Shakespeare?
Yes, the monkeys will do it. No, they don't have to.
It's mathematically true that after removing all logistical constraints - which is what we mean when we say there are infinitely many monkeys, ...
- 620
33
votes
Is the SETI project built on false premises?
Scientists use statistical significance measures all the time, discussed here: How improbable does an event have to be before we can say it didn't happen by chance?
"Life occurring on earth ...
- 20.5k
23
votes
How does probability constitute as knowledge in justified belief theory?
There is no paradox here. What you knew for certain before the lottery was that there were 100,000 possible outcomes, in only one of which you would win. The result of the lottery does not change the ...
- 13.5k
23
votes
Does Bayesianism give an out for pseudoscience that it shouldn’t deserve?
The first issue is that the presented hypothesis is actually two hypotheses. While the sentence "Adam can guess, using psychic powers, what the price of each stock in the world will be at the end ...
- 359
21
votes
Accepted
Does every possible event have non-zero probability?
The answer is no. Mathematically, if you have a continuous random variable, the probability of getting any one of its values is zero, but you can still get one, so zero probability does not ...
- 13.5k
19
votes
Accepted
Is all of probability fundamentally subjective and unneeded as a term outright?
In fact there is no way to define unique objective probabilities for anything that happens (or not) in the real world. Every definition of probability requires model assumptions that cannot be ...
- 573
19
votes
Isn’t everything absurdly improbable?
The probability of getting 100 straight heads is the same as any other sequence, yet the other sequences aren’t seen as improbable.
Yes they are, if you put a piece of paper in a sealed envelope ...
- 1,728
16
votes
Isn’t everything absurdly improbable?
Isn’t every event by definition improbable in the sense that each
event precedes an infinite series of causes that could have
(theoretically atleast) been different?
Specific events don't have ...
- 3,575
15
votes
Does every possible event have non-zero probability?
In Bayesian theory, the principle that every logically possible proposition has a probability that is never exactly zero, nor exactly one, is called the Cromwell Rule.
The idea behind the principle is ...
- 22.9k
15
votes
Accepted
Is it ever rational to stumble onto the conjunction fallacy in probability?
Well, the conjunction fallacy is a fallacy, so it's not rational to believe it. However...
Suppose Dave tells you he was just robbed and that's why he's were late to meet with you. You are skeptical, ...
- 11.1k
13
votes
Should X, if there’s no evidence for X, be given a non zero probability?
You mention Bayesians, so I'll reply in that context.
The Bayesian framework is (roughly) a way to take a "prior probability" of a statement, multiply it by a factor accounting for new ...
- 1,214
12
votes
How does probability constitute as knowledge in justified belief theory?
In a lottery, the expectation that you will definitely lose is not justified. The expectation that you are very likely to lose with a tiny chance of a huge win is justified.
Now the fact that you will ...
- 5,243
12
votes
How does probability constitute as knowledge in justified belief theory?
It is irrational to buy a lottery ticket, not simply because the chance of winning are low. The expected value of the money you gain is negative. In other words, if you had enough money to buy all ...
- 2,232
12
votes
Can a coincidence be evidence of a god?
Suppose for example that a person is standing on stage and says “God, if you exist, strike me with lightning right now” and a lightning strike occurs that barely misses him, is this evidence of God? ...
- 1,458
11
votes
Isn’t everything absurdly improbable?
Yes, it's extremely improbable for practically anything to happen in the exact manner that it does. You are correct.
But then what do you do with that information? So it was very improbable for those ...
- 11.1k
10
votes
Does single case chance actually exist?
You've hit upon a frequently debated topic in statistics, that is, what does "probability" actually mean?
At the moment, the philosophical arguments tend to boil down to two main camps: ...
- 1,214
10
votes
Is the SETI project built on false premises?
Let's focus on this part of the question: "On what basis can we ever
say, even if this pattern was detected, that this was generated by
intelligent lifeforms outside earth?"
Bayesian ...
- 367
9
votes
Does every possible event have non-zero probability?
Your mistake is thinking that probability is relevant
one asserts that the probability of pigs flying is 1 in 10^50
... and one has made one's first mistake which makes everything that follows moot.
...
- 1,728
9
votes
Does every possible event have non-zero probability?
Given that continuous random variables are perfectly well-defined, it follows trivially that there are logically possible events with probability zero. As an example, consider the probability that a ...
- 813
9
votes
Can a coincidence be evidence of a god?
No it doesn't imply a god exists. Think about it scientifically. How do physicists go about developing hypotheses and testing them? If you wanted to apply scientific reasoning, you would need to ...
- 13.5k
9
votes
Accepted
Is there a term for a fallacy in which one believes something to be divinely inspired due to being improbable?
See the Divine Fallacy:
The divine fallacy is a logical fallacy that occurs when someone assumes that a certain phenomenon must occur as a result of divine intervention or a supernatural force, ...
- 4,107
9
votes
How can one make sense of the gambler’s fallacy if probability is ill defined?
In the cases of independent events (...) the next (outcome's) probability does not depend upon previous ones.
This is general probability calculus. It's not confined to a specific interpretation of ...
- 573
8
votes
How should one treat probability in taking a decision?
I would first argue that there is no such thing, and that if a machine is trying to spit out a "true" probability of Islam being true, it would simply be wrong if it displayed 50.1, since ...
- 8,278
8
votes
Isn’t everything absurdly improbable?
This kind of problem arises when there is an attempt to apply probability to the real world. The theory of probability is about precise sample spaces and probabilities and events. The real world, on ...
- 688
8
votes
Can we fully expunge the notion of probability from philosophy?
Probability is an extremely useful concept, both within science and within epistemology and there is no good reason to want to expunge it. Most of your complaints about it are based on ...
- 22.9k
7
votes
Can a coincidence be evidence of a god?
If I experience a coincidence or a coincidence happens in the world that seems to be at extremely low odds, does this imply that God exists?
No. Why would it? To make such an assumption would be a ...
- 4,107
7
votes
Isn’t everything absurdly improbable?
The questions you need to ask are "improbable given what?", and "improable relative to what?"
Suppose I flip a coin. The probability that it will be heads, is 0.5.
Suppose I flip ...
- 1,273
7
votes
Can we fully expunge the notion of probability from philosophy?
No, probability is a foundational concept in philosophy. But not only that: it is an essential concept of language. Every sentence about the future is essentially an statement of probability: "he ...
- 6,831
7
votes
Does Bayesianism give an out for pseudoscience that it shouldn’t deserve?
This seems to be less about Bayesian probability analysis and more about forming testable hypotheses.
If we limit your hypothesis to "Adam knows the closing stock prices ahead of time.", ...
- 653
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