Questions tagged [probability]
Use for questions about chance and likelihood, and attempts to define "probability" logically and metaphysically.
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Why is the gambler's fallacy a fallacy?
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" has "no memory."
At each toss, the ...
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Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?
I've seen a few different formulations of this, but the most famous is "monkeys on a typewriter" - that if you put a team of monkeys on a typewriter, given infinite time, they will ...
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Why would infinite monkeys not produce the works of Shakespeare?
Apologies if this is a very basic/obvious question. I have no training in philosophy, but have been making my way through Peter Adamson's History of Philosophy podcast.
Recently I listened to his ...
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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 ...
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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 ...
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Does every possible event have non-zero probability?
Almost every human being would agree that 2 + 2 != 5. In a sense, this is a logical impossibility.
However, almost every human being would also agree that pigs can't fly. Some, however, are adamant in ...
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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?
We think of someone winning five ...
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Does the "Sniper Firing Squad" analogy undermine the anthropic principle’s objection to the fine-tuning argument for God's existence?
The anthropic principle, also known as the "observation selection effect", is the hypothesis, first proposed in 1957 by Robert Dicke, that the range of possible observations that could be ...
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The implication if we discovered that natural abiogenesis is statistically nearly impossible
If we were to discover somehow that (sentient) life was so unlikely that it were almost impossible that it forms even once in the whole universe, does that imply anything about creation e.g.?
My logic ...
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Is the notion of "Complex System" a philosophy of science? Is it the opposite of Reductionism? Is it related to Holism?
I have tried to come to terms with the notion of "complex systems" of which I heard in one of the lessons at school though without too much depth. I grasp that a complex system is such that ...
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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 ...
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Is the SETI project built on false premises?
The SETI project analyzes signals and looks for patterns, some of which include prime number sequences that have an absurdly low improbability of occurring. It does this to detect intelligent life.
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Can Bayes' theorem be used non-fallaciously to argue for miracles?
NOTE: Originally this was a sub-question asked within Did Thomas Bayes truly develop Bayes' theorem in an effort to rebut David Hume's arguments against miracles?, but some commenters ...
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Is there any rigorous definition of just one single random choice?
The theory of probability uses random variables, which avoids the need to define what one single random choice means.
Yet in everyday conversations about probability, even professional probabilists ...
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Is all of probability fundamentally subjective and unneeded as a term outright?
What is the real probability that a person will be murdered tomorrow somewhere in the world? It seems like there should be a right answer to this. In fact, most of us would bet tens of millions of ...
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Should the evidence of OBEs and NDEs increase our epistemic probability of non-physicalist views of consciousness?
Should reports of out-of-body experiences (OBEs) and near-death experiences (NDEs) increase our epistemic probability of non-physicalist views of consciousness? In other words, should we judge non-...
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Does single case chance actually exist?
Does chance actually exist for a single case? Even for a coin, what does it mean to say that there is a 50% chance that the next coin toss will land on heads?
Someone might say that this means that if ...
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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 ...
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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 ...
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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 ...
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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 - ...
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Is plausibility more fundamental than probability?
There seem to be many contexts in which it makes sense to define a probability or atleast an approximate one and attach that to a certain proposition. If that is very low, it is often taken to be ...
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Depending on one's philosophy, is Bayes' theorem actually an axiom?
In the frequentist philosophy, probabilities refer to the relative frequencies of our outcomes in a large number of trials. Using this definition, it is possible to prove Bayes' theorem as simply a ...
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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. ...
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Is there a term for a fallacy in which one believes something to be divinely inspired due to being improbable?
Consider the following argument:
I have been born on Earth, during a time of relative prosperity. The probability that I was born at this moment, of all moments, is very small. Therefore, this is ...
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Does the halfer position in the Sleeping Beauty problem make for an irrational gambler?
It's my understanding that the Sleeping Beauty problem doesn't have a consensus answer, with major camps along the lines of "halfers," "thirders," and "the-question-statement-...
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Epistemic value of multiple eyewitness accounts: single event vs. multiple events given a fixed number of eyewitnesses?
Intuitively speaking, multiple independent eyewitness accounts of a single event are more convincing than a single eyewitness account. For example, multiple independent eyewitness accounts of a loud ...
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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 ...
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If someone clearly believes that he has witnessed something extraordinary very clearly, why is it more reasonable to believe that they hallucinated?
I'd first like to make the following point: there is definitely a point at which evidence does make it reasonable to believe extraordinary claims. For example, if all of Europe claims to have seen the ...
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Should X, if there’s no evidence for X, be given a non zero probability?
There may be no evidence that a fairy is sitting on a table. Many argue that one cannot prove a fairy doesn’t exist. Thus, many decide to attach an (infinitesimal) probability to it existing, as many ...
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Is there a reasonably up-to-date (as of early 2020s) review article on the Sleeping Beauty problem?
EDIT: I apologise for the lack of detail and clarity in the original post; I hope that my newly edited version will be clearer, and I particularly thank Conifold for useful feedback in the comments.
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Is it ever rational to stumble onto the conjunction fallacy in probability?
The conjunction fallacy is the phenomenon where many people believe that the probability of the event (A AND B) is strictly greater than the probability of the event A. It is usually thought of as an ...
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How important is explanatory power when it comes to assessing the likelihood of a hypothesis?
Suppose I predict that John will get into a fight tomorrow and he does. Almost noone will think I can read the future. It seems to be "within" the bounds of chance.
Suppose I instead ...
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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 ...
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Are there probabilistic facts of the matter about the universe? [closed]
Consider a factual claim, X. For instance, suppose I examine evidence E at a crime scene and hypothesize that the evidence is most likely explained by a murderer. We could pose the following ...
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What principle protects the objective nature of the prior and the conclusion in Bayes’s theorem?
The Bayesian analysis begins with the "prior": some assumption about the world and the probability that the assumption is true.
But the prior seems to be based on nothing. The hypothesis and ...
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Can we ever infer design purely from improbability? [duplicate]
Is it ever reasonable to come across an event that is very improbable and then infer that it must have been designed?
Note that my question is referring to cases where we make this inference purely ...
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Is it ever reasonable to infer impossibility from high improbability?
For context, please refer to the section Biological Information: Beyond the Reach of Chance (pages 10-12) in DNA by Design: An Inference to the Best Explanation for the Origin of Biological ...
user80226
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What is a philosophical interpretation of Bayes’s theorem when one of the probabilities is zero?
Bayes' Theorem
P(H) = probability of a hypothesis
P(E) = probability of evidence
P(E|H) = probability of evidence given the hypothesis
P(H|E) = probability of hypothesis given the evidence
P(H|E) = P(...
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Is probability physical or idealistic? Is probability an inherent part of nature/reality?
I asked this question a while back: Is entropy physical or idealistic?
Now, I am back to ask if the subject that entropy built around is inherently real i.e., probability in itself being inherent not ...
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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 ...
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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 ...
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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 | ...
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Implicit Models and Probability - are degrees of belief/truth/existence a complete free-for-all?
Or, to put it another way, as long as you model your statements using the grammatical framework of our modern logical idioms, is it appropriate practice to assign a probability to any utterance at all,...
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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 ...
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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 ...
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Extraterrestrial organisms similar to humans and design [closed]
If we ever confirm that intelligent extraterrestrial organisms similar to ourselves are living on other planets, is that a fact which would make our being designed along with them more probable? For ...
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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 (...
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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 ...
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Bayesian conditional probability and material implication
I was reading E. T. Jaynes' Confidence Intervals vs Bayesian Intervals (available here), and I came across this statement regarding Boole's The Laws of Thought:
Boole's own work on probability theory....
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