7

This is definitely closest to the gambler's fallacy. An example of this fallacy demonstrated in your example would be that the player, having killed 80 monsters without a coin, thinks that the next 20 monsters will have a higher probability of finding a coin with each kill. This is fallacious, as no matter how many monsters the player has killed, even after ...


6

There are plenty of issues with subjective probability assignments to degrees of belief discussed e.g. in SEP's Subjective Probability Theory. I will only address the one outlined in the OP. For a book length treatment see Fundamental Uncertainty: Rationality and Plausible Reasoning volume edited by Marzetti and Brandolini. The idea of distinguishing ...


4

It's a strange question, if you really look at it. "The Universe" is not a random variable. Probability means nothing. Either the universe is or is not complex. There is no probability to be had unless you define the problem with a random variable. We could treat this as a Bayesian inference question. You are asking if P(C | M) > P(C) where C is a ...


3

In colloquial terms, conditional probability tries to capture the idea that context matters. For instance, if we ask how likely it is we will be robbed in the coming year, we can do the math: I've seen numbers like a 0.15% chance that any given person will be robbed in any given year. But obviously that's not the same for everyone, everywhere. Someone who ...


3

Wikipedia may be a good place to go for initial information on this. Here is what it says: In probability theory, conditional probability is a measure of the probability of an event occurring given that another event has occurred. This tells us that there are two events involved. We want to find a measure for the probability of one event, A, given that ...


3

Let me point out, first, that Occam's Razor is not a law; it's a rule-of-thumb that has more to do with pragmatics and aesthetics than necessity. It's a good rule of thumb, sure, but it is based on an a priori belief that the universe as a whole conforms to what human minds count as parsimony. That being said, the main issue with applying Occam's Razor to ...


3

Your argument rests on a number of unsupported assumptions, chiefly this one: smaller universes are created more often than larger universes. So perhaps it's better phrased as so: If there are many universes, and the majority of them are smaller than this one, then does the anthropic principle indicate that the size of this universe is decisive in ...


3

It is important to distinguish between axiomatisation and interpretation. The mathematical formalism is nailed down by Kolmogoroff's axioms, but this only puts slight restrictions on the philosophical interpretation. All three major philosophical interpretations are consistent with Kolmogoroff's axioms. Secondly, what Kolmogoroff did was not actually an ...


2

It depends on the definition of knowledge. My definition of knowledge would come down to this: an assumption that a belief which is correct, is correct Is it posssible to know apples exist? I'd say it could be possible. I'll explain why I think so. According to my definition there are really two things you have to do: (1) to believe that apples exist, and (...


2

Quine's account of probability is motivated by the same concerns as his account of modality, distrust of intensional notions and metaphysical largesse. Hintikka characterized Quine's distrust of modality as "one-world view", and argued that it is contrary to his own maxim of accepting what is indispensable in science. Quine does offer a stripped down ...


2

Most physicists don't care about the interpretation of probability. Nor do they care about the controversy over the "interpretation" of quantum mechanics. The philosophy of probability is not in a good state. It is mostly divided between frequentists who think that probability is defined by long run frequency and Bayesians who think that probability has ...


2

Solution: As we sorted out in the comments below, everything until your conclusion prob(A)=prob(B) is correct. So I will start there. You have shown: By (5-2) des A∨B = (prob A * des A + prob B * des B) / (prob A + prob B) = 1, since prob A = prob B. But to apply (5-2), one has to show that prob(A∨B)≠0: if this were the case, then 0=prob(A∨B)des(A∨B)+...


2

Jimit, let me say first you have my condolences. Here I will provide another way to look at unlikely tragedies. In my previous career I had to deal with finding the root causes of catastrophes in our factories. Fortunately, none of these involved loss of life, but they had huge consequences for our business. What I discovered was that these disasters were ...


1

I suspect the underlying problem you are concerned about is whether it's justifiable to assign probabilities to claims with insufficient evidence, and if so, how can such probabilities be assigned? For some responses to Pascal's Wager, this comes in the form of assigning a probability to the existence of God. Often, it is justifiable to assign probabilities....


1

I'm not sure what you mean by people "arguing in favour of IQ"; perhaps you mean people advocate specific policies because they seem liable to increase cognitive abilities, such as improved education of removing lead from the environment. OK, I grant people do that: we want to give people as much of whatever IQ tests measure as we can, but also want them to ...


1

As to Heaven, I don't expect anyone to be able to validly infer the laws of any non-physical world, real or imaginary, from the laws of the physical world. Why would time in Heaven necessarily be physical time? Why expect a transition from the physical to the non-physical to follow the laws of the physical? If heat death, particle decay and all the laws ...


1

I think at least in your titular question, you're mangling terms in a way that is unhelpful. In logic and critical thinking, valid refers to when a deductive argument is such that if all of its premises are true, then its conclusion must be true (there are other similar but more exotic formulations -- e.g. must be constructable as a model -- but those don't ...


1

See page 76 : For the impossible proposition, the proposition which is false in all cases, we shall use the special symbol F and set prob F=0. Thus, to say that XY=F means to say that XY is never true. Axiom 5-1(c) says : prob is additive: if XY = F, then prob (X v Y) = prob X + prob Y. See page 81; using Ax.5-1(c), Jeffrey proves (5-1)...


1

I'm not sure this is exactly what you're asking, but it's very much possible to use Occam's razor with religion. Of these two hypothesis: Humans made a mix of the beliefs and legends of their time about the world and its origin, based on their current knowledge, it stuck orally, and eventually got written in a book that was then described as the original ...


1

It may be useful to keep track of what terms mean or at least state a definition. Wikipedia defines probability as follows: Probability is a measure quantifying the likelihood that events will occur. In the case of being pregnant or not, the current measure of the event of being pregnant is 0.5. That is all that number refers to. It is the current ...


1

Well she learned something new in the sense that the state of her beliefs changed from holding the belief that she is not pregnant, to holding the belief that she might be pregnant. I would also say that in light of Bertrand' paradox, the situation is a bit more complicated than saying P(e) = 0.5 should always mean maximum ignorance. For example, if we have ...


1

The famous 1964 paper of John Stewart Bell, in which "Bell's inequality" is established, begins by assuming two things. (The paper can be found here: https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf) One of them is "locality", which means (non-mathematically) that distant objects cannot affect one another instantaneously. Mathematically, Bell ...


1

Firstly, one would need to distinguish between a proposition being certain and a person being certain of it. All kinds of propositions might be certainly true (e.g. mathematical or logical theorems) but being certain of them requires sufficient competence on the part of a person to recognise it. Since you are contrasting certainty with knowledge, I assume ...


1

You change the theoretical space. The two Hcs are different, the two hypothesis spaces are different. You begin with: dog vs not dog, then go dog vs cat vs not dog minus cat, a new set of three, only 'dog' remaining the same. Consider for the purpose of generalising, the Buddhist device of the catuskoti, which sets aside the principle of the excluded ...


1

Wikipedia provides a useful stake in the ground for this query insofar as it notes the probabilistic grounding of frequentism (e.g., see link 1 below). That is where I would suggest the OP begin his exploration. Not being one to make fine and hard distinctions between disciplines I would only note that Wiki's summaries move the debate away from the ...


1

The sort of empirical support Marbe seems to have been looking at can be explained quite easily An Introduction to Probability and Inductive Logic, By Ian Hacking There's no empirical support for something so radical. I suppose that it can't be refuted logically because the assumption is about nature, how likely it is that natural events will occur, not ...


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