Questions tagged [probability]

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105
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21answers
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Why don't fair coin tosses “add up”? Or… is “gambler's fallacy” really valid?

I have always been perplexed by a seeming paradox in probability that I'm sure has some simple, well-known explanation. We say that a "fair coin" or whatever has "no memory." At each toss the odds ...
18
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12answers
21k views

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

If the universe is analog, there must exist an infinite number of positions. This raises an interesting question. Let me boil it down to something familiar: a table and an ashtray. I'll let the ...
18
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8answers
3k views

Interpret Bayesian probability as frequentist probability?

It is usually said that the Bayesian probability is a subjective concept, quantifying one's degree of belief in something, while the frequentist probability is the the fraction of certain outcomes ...
10
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7answers
2k views

Is a “fair coin toss” a logical contradiction?

A previous question asked about the reality of the gambler's fallacy, in which logic appears to offend common sense. In light of the answers, I am now wondering about the other side of the coin, so to ...
10
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1answer
191 views

Is there any literature on the relationship between responsibility and probability?

If A causes B and I am doing A (willingly, knowingly, ...), then I can be held responsible for B. But what if probabilities are involved? Thought experiment: If you roll a 1 on a die you win. You ...
8
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6answers
1k views

Why are homologies evidence for evolution instead of common design?

I have seen some creationists arguing that when evolutionary biologists use homologies (anatomical or genetic) as evidence for evolution, they are committing the fallacy of affirming the consequent. ...
8
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8answers
601 views

Why do people perceive the randomness of events so poorly?

People who are not trained in statistics and randomness (and even sometimes those who are) tend to draw horrible conclusions about whether an event is random or caused. Fundamentally my question is - ...
8
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2answers
559 views

Hilbert's Sixth Problem: Is Kolmogorov's solution the last word?

The demand for axiomatization of probability was put forward by Hilbert at the very beginning of the past century: it was the sixth problem in his famous twenty three problems he deemed of high ...
8
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4answers
515 views

Is there a term for the position “no determinism but no free will”?

Often when free will is discussed, there are three main positions espoused: Libertarian: The universe is not deterministic and there is free will Hard-determinism: The universe is deterministic and ...
8
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3answers
251 views

What justifies probability in the case of a onetime experiment?

If I have an "experiment", the results of which can be classified clearly into "outcomes" (like rolling a die), then I can make a concrete and verifiable empirical claim that "if you repeat this ...
6
votes
3answers
717 views

Applying Bayes' theorem to Sleeping Beauty

Suppose we believe the "thirder" position of the Sleeping Beauty Problem. That is, we believe that P(Heads | Waking up) = 1/3. Applying Bayes' theorem, we get P(Heads | Waking up) = P(Waking up | ...
6
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3answers
444 views

Does Cox's theorem implicitly assumes the three classic laws of thought?

I read about Cox's theorem a long time ago in "Jaynes Probability Theory: The Logic of Science". It was used to justify the so-called "logical" interpretation of probability. My impression was that ...
6
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2answers
195 views

Bayesian statistics versus inductive skepticism

This is a question replicated here as advised by the statisticians' StackExchanged - see also https://stats.stackexchange.com/questions/178857/bayesians-positions-on-inductive-skepticism Philosopher ...
5
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5answers
5k views

What is the difference between a probability and a possibility?

I ask this in a fairly naive way. I understand that "probabilities" can be quantified in frequencies, degrees of belief, etc. with some defined "space" of probability.But I know little about modal ...
5
votes
3answers
319 views

When is it not possible to assign a probability?

I know only a little about set theory and probability, and struggle to infer their implications for many traditional metaphysical concepts and questions. I was surprised to read the statement, "......
5
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1answer
155 views

Is there a name for the fallacy: 1/100 chance == 100 times guaranteed success?

Let's say someone is playing a computer game in which the chance for some item to drop is 1 out of 100 each time he kills a monster. The player concludes that if he kills 100 monsters then it is ...
5
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1answer
48 views

Is the criterium of admissibility a valid requirement for probability interpretations?

One argument that is often raised against hypothetical frequentism, as e.g. developed by Reichenbach or Von Mises is that limiting relative frequencies can violate the axiom of countable additivity (...
5
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1answer
176 views

What is Quine's perspective on probability?

I am curious about what Quine's perspective on probability may be and if we can say that the quinean viewpoint on modality can be considered similar to his viewpoint on probability. Is probability ...
4
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6answers
2k views

Can playing lotteries be rational?

Suppose you have to choose between: a. getting 1$ b. getting a ticket of the lottery L(p) which gives you 1'000'000'000$ with probability p and 0 with probability (1-p), with p such that the expected ...
4
votes
5answers
197 views

Questioning determinism (example)

Questioning the world's deterministic behaviour, I shall present an example which seems to defy any certainty about the recurrence of events and is (obviously) a result of faulty logic, but I would ...
4
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1answer
150 views

Does the propensity interpretation of probability rely on the principle of indifference?

According to the late Popper, among others, probability is the propensity of a set of conditions to produce certain long run relative frequencies. Therefore if we say that a certain set of conditions ...
4
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2answers
127 views

Question about the “catch-all” hypothesis as a response to the “bad lot” objection

In response to van Fraassen's "bad lot" objection, I have seen in multiple papers (and in the response of Lipton, from what I remember) refer to the idea of the use of a 'catch-all' hypothesis which ...
4
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1answer
253 views

Can encrypted information be sent back in time while avoiding the Unproven Theorem Paradox?

Background: The Unproven Paradox involves sending a mathematical proof to individuals in the past that is obtained from the fact that there is a recipient in the past that publicly reveals the proof. ...
4
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1answer
561 views

Almost Sure Mind Transfer via Parfit's Identity Theory (interesting thought experiment)

Under Derek Parfit's theory of identity, we should direct our concern to future selves not because they are identical to us, but because they bear some special relation to our current self. He used ...
3
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2answers
240 views

Did something improbable happen when I became conscious?

Let's take that person's subjective experience of the universe is given. If we take for example one particular person - lets say the person that is reasoning about this question (denoted with I in the ...
3
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5answers
223 views

Are there probability distributions that are analytically derived?

Consider the simplest example, flipping a coin. Is the relationship between the symmetry of the coin and the 50-50 probability synthetic or analytic?
3
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5answers
220 views

Can there only be one success in an infinite amount of trials?

The premise is basically that there is an infinite amount of trials and a trial could either be a success or a failure. In this trial set, is it actually possible for there to be one and only one ...
3
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3answers
93 views

Is it a problem for Frequentism that infinite sequences do not exist?

Hypothetical frequentists defined probability as limiting long run frequencies of hypothetical random infinite sequences, such as an infinite sequence of coin tosses. One argument against this ...
3
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5answers
367 views

Are more parsimonious theories harder to falsify?

Occam's razor states that, everything else being equal, the theory with the least number of assumptions is more likely to be true. This has been formalized as Solomonoff's theory of inductive ...
3
votes
1answer
224 views

If our world is mathematical، Does not this increase the probability of being complex as well?

Tegmark's mathematical universe hypothesis, posits that reality is a mathematical structure. This mathematical nature of the universe, Tegmark argues, has important consequences for the way ...
3
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1answer
157 views

Probability and logic

Is probability theory (using Kolmogorov's axioms) an extension of the propositional calculus, or an extension of first order logic?
3
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2answers
126 views

Why is probability used to make decisions?

If I am offered two bets to choose one from, and either wins $100 or losses $100, I would want to know the chances of winning in order to decide which one to pick. For example, if one bet has a 90% ...
3
votes
1answer
111 views

Is the “measurement problem” really about Quantum Mechanics?

Philosophers (Popper in particular) have long debated the interpretation of probability as applied to the world. Their concerns echo those of physics (frequency, preparation, ensembles, ). It would ...
3
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3answers
638 views

Does Probability come before Scientific Method?

I am interested in the following epistemological problem. Usually, Probability is seen as a mathematical theory that we use to describe the physical world. Precisely, following the Scientific Method ...
3
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1answer
74 views

Please explain Good's solution to why we should make new observations

IJ Good's paper (1967) gives a solution to Ayer's problem on why we should make new observations. I'm trying to follow the steps in his solution. His assumptions are that: There are r mutually ...
3
votes
2answers
249 views

What defines “lack of evidence” and is it irrational to believe in something without evidence?

It is commonly accepted that the lack of evidence for a particular proposition makes belief in said proposition irrational. However, imagine the following proposition, P: An object exists for ...
3
votes
1answer
76 views

Is there a name for the following gambling fallacy?

I'm writing a paper on the game of blackjack and I'm trying to make a point about how a common player's attitude is a logical/statistical fallacy in the following situation: When any common person ...
3
votes
1answer
230 views

Is philosophical (total) skepticism compatible with the modern scientific world view?

I've been interested in philosophical skepticism lately as I've just recently learned about the close relationship between certain schools of ancient skepticism and fallibilism, which I'm told is the ...
3
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2answers
95 views

What is frequentism?

I am studying for an exam and I ran into frequentism. Honestly, I don't understand anything about that. Is frequentism related to probability only? Why are probabilities understood as frequencies? I ...
3
votes
2answers
292 views

What is the name of this logical fallacy involving probabilities of two unrelated events?

I've often heard that you have better chances of winning the lottery than you do where X is some unhappy event. Occasionally, I hear people who have actually experienced X say they should buy a ...
3
votes
4answers
130 views

Emergent Complexity In Probability Distributions

I originally posted this in Physics SE but was told it's more appropriate here... In quantum mechanics we describe waves of probability or probability distributions. Does this have to or should it be ...
3
votes
3answers
206 views

What does it mean to “conditionalize a probability distrubition”?

What does it mean to "conditionalize a probability distrubition"? In case relevant, I've been reading about "Adam's Thesis", and that's where this phrase has been thrown about.
2
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4answers
143 views

How does it make sense to infer the existence of a group from a sequence of events?

Just read an interesting section in The Drunkard's Walk - L. Mlodinow and this section made me think: [people]... confuse[ing] the probability that a series of events would happen if it were the ...
2
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5answers
375 views

How do you prove probability? [closed]

I have this thought that has bugged me for a couple of days and could not find any answers on the internet. I thought this would be the best place to consult. How does one go about proving ...
2
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1answer
65 views

Frequentist notion of probability

The or rather one of the Frequentist interpretations of probability claims that the statement "The next coin toss )that is executed under conditions X) has a probability of 90% to land heads" simply ...
2
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3answers
173 views

Thinking that all individuals pursue “selfish” interest is equivalent to assuming that all random variables have zero covariance

I read that: Thinking that all individuals pursue "selfish" interest is equivalent to assuming that all random variables have zero covariance. -- Nero What does that mean, and what does it have to do ...
2
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1answer
174 views

Finding desirabilities and probabilities in Jeffrey's Logic of Decision

I'm trying to solve problem 16 (Ch. 5) of Jeffrey's Logic of Decision. The problem says: Suppose that A and B are pairwise incompatible propositions, and suppose that the preference ranking is as ...
2
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3answers
109 views

Probability calculus and Quantum Mechanics [closed]

I am not an expert and probably this question highlights this. Anyway, is the probability calculus used in Quantum Mechanics? Does the concept of probability adopted in Quantum Mechanics satisfy the ...
2
votes
1answer
115 views

Is 'interpretation' in quantum mechanics the same as 'interpretation' in probability? [closed]

I heard all 'interpretations' of quantum mechanics give exactly the same answer to every measurement so they are all equally correct. Is that the same 'interpretations' as in probability? Context: ...
2
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3answers
919 views

Is there a middle ground between determinism and libertarianism?

Is it possible that we live in a universe where some things are truly deterministic and other truly random and the difference between those two things is how their particles are arranged? For example,...