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43 votes

Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?

It looks like you've hit upon the concept of almost surely in probability theory. Something occurs "almost surely" if it happens with probability 1, but there still exist situations where that thing ...
Nuclear Hoagie's user avatar
39 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, ...
Zayn's user avatar
  • 640
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 ...
CriglCragl's user avatar
29 votes

Is this a statistical argument for reincarnation being almost inevitable?

The specific statistical error you're probably intuiting is that your sample is not representative. Even if you are non-existent for a million years, and existent only for a day, there's a 100% ...
Chris Sunami's user avatar
  • 30.2k
27 votes

Have I found a paradox, or is the universe digital? Or am I just plain wrong?

We run into essentially the same problem almost any time we try to combine the real numbers as described by mathematics with probability theory. When applying probability theory to something like a ...
aschepler's user avatar
  • 371
24 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 ...
Marco Ocram's user avatar
24 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 ...
minnmass's user avatar
  • 401
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 ...
Marco Ocram's user avatar
20 votes

What is unique about the quantum state of superposition?

I recently answered a similar question on physics.SE here. What is special about the probabilities of quantum mechanics is that the randomness cannot be explained by a theory of nature that is both ...
ACuriousMind's user avatar
20 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 ...
Christian Hennig's user avatar
19 votes
Accepted

Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?

Here, I think, is a more succinct answer: Let's say we have a dice with 1 trillion sides. Then, the probability of a given outcome on the next roll of the dice is one-in-a-trillion. On the other ...
AmagicalFishy's user avatar
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 ...
Graham's user avatar
  • 2,360
17 votes

The implication if we discovered that natural abiogenesis is statistically nearly impossible

If, and it's a big if, it could be proved that the probability of the emergence of life through natural causes was exceedingly close to zero, then you could still assume life emerged by chance. Before ...
Marco Ocram's user avatar
16 votes

Is there any rigorous definition of just one single random choice?

It's best to think of randomness as a model, not as a 'thing'. When we talk about a 'random event', we mean that at some time t0 we cannot predict with certainty the state of a system at time t1 (t1 &...
Ted Wrigley's user avatar
  • 20.1k
16 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 ...
Bumble's user avatar
  • 26k
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 ...
g s's user avatar
  • 6,209
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, ...
causative's user avatar
  • 13.6k
15 votes
Accepted

What is a philosophical interpretation of Bayes’s theorem when one of the probabilities is zero?

Bayes' Theoreom has P(E) != 0 as one of its pre-conditions. As with any other theorem, if any of the premises is not true you cannot validily deduce the conclusion. So the math thing to say is not &...
JonathanZ's user avatar
  • 451
15 votes

Should the evidence of OBEs and NDEs increase our epistemic probability of non-physicalist views of consciousness?

Near death experiences seem to largely be culturally and theologically neutral, and when they'renot they match the beliefs of the person having them, which suggests to me it's an entirely ...
TKoL's user avatar
  • 3,468
15 votes

Does the "Sniper Firing Squad" analogy undermine the anthropic principle’s objection to the fine-tuning argument for God's existence?

To me, a more accurate "sniper analogy" for fine-tuning would be: You run between 2 points of cover in a heavy firefight. There was probably hundred bullets hitting somewhat near you without ...
NotThatGuy's user avatar
  • 10.5k
14 votes

The implication if we discovered that natural abiogenesis is statistically nearly impossible

[This is a complete rewrite of my answer.] If I understand you're question, you're presuming that we somehow determine that the chance of all the conditions necessary to result in intelligent life is ...
Barmar's user avatar
  • 1,740
13 votes

Have I found a paradox, or is the universe digital? Or am I just plain wrong?

Zeno's Paradox is not a paradox. It is an attack on loose thinking. By emphasising the infinite nature of one thing, and not mentioning the infinite nature of another, it confuses people into thinking ...
ThinkSimple's user avatar
13 votes

Is getting 100 Heads in a row from a fair coin a miracle or not?

Yes, but only because every possible sequence of flips is a miracle. Consider. Suppose I flip a fair coin 10 times in a row. Say I get HTTHTTHTHT. Now that seems pretty normal, nothing remarkable ...
user4894's user avatar
  • 2,957
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 ...
R.M.'s user avatar
  • 1,293
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 ...
gnasher729's user avatar
  • 5,620
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 ...
kutschkem's user avatar
  • 2,290
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? ...
Dikran Marsupial's user avatar
12 votes

How Probable is the Philosophical Significance of Numerical Patterns in Religious Texts?

Apophenia describes (among other things) the human propensity to see questionable patterns in random data. That, in a nutshell, is what basically all of numerology is. The basic process tends to go ...
NotThatGuy's user avatar
  • 10.5k
11 votes

Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?

"If you made 1,000,000 similar decisions, the probability of that final outcome being reached at any one moment is 1 in a million." That quote represents the root of your misconception. If a coin is ...
Uueerdo's user avatar
  • 267

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