The Nature of Probability

[KevinDW78]

Thank you Grames, I have wanted to get both of those Peikoff lectures because I assumed they would have the answers I've been looking for. Just gotta find the time to justify the cost of buying them. Your notes definitely help shed light on the issue.

[Jake_Ellison]

Anyhow, in fact "probability" is not just formal combinatorics.

Of course not. In the example of using combinatorics to figure out that seven is a better guess than two, for the result of two dice thrown, I'm also basing that on previous experimentation with balanced dice, which resulted in an even spread. (in fact, the knowledge that it will result in an even spread in the future as well, if thrown many times, is based on understanding the causal relationships involved in throwing a die, not just on an inventory of previous throws)

[DavidOdden]

But that just takes me back to square one. HOW does one measure evidence against certainty? By what standard?

The standard is "everything that you know". If everything that you know points to a conclusion and nothing points to an alternative conclusion, then the conclusion is certain. If the evidence overwhelmingly points in the direction of the conclusion but you have one observation which points to a different conclusion, then the conclusion is "extremely probable".

For instance, suppose we look at charge non-conserving particle decays, which theoretically have a probability of 0. And yet you appear to have one charge non-conserving decay. That could be because the presumed physical law is wrong, or it could be because there was a measurement error (a negative particle was not detected). In order to say that, in this scenario, the law (a conceptual summary of everything that we know on the topic) is not true, we would have to be certain that the observation is reliable.

I am skeptical of attempts to assign specific numbers to our confidence in conclusions, since I have not seen a metaphysically sensible interpretation of what such numbers would be counting.

[KevinDW78]

I am skeptical of attempts to assign specific numbers to our confidence in conclusions, since I have not seen a metaphysically sensible interpretation of what such numbers would be counting.

ok that is more what I was looking for. An answer to the question of "is probability a quantitative concept or a qualitative concept?". Because I have the same objections you raise. To use a quip F.P. Ramsey made about Keynes' theory of probability, you would need some sort of psychogalvonometer in order to quantify degrees of belief.

Edited November 11, 2009 by KevinDW78

[softwareNerd]

But that just takes me back to square one. HOW does one measure evidence against certainty? By what standard? This is why this question has been so difficult for me to grapple with.

To clarify the issue, is this about the validity of induction: i.e. a question like: "if we see 100% of our observations 'fit' our knowledge, is that the basis for saying that our knowledge is certain?" Or, is this a different issue?

[DavidOdden]

To use a quip F.P. Ramsey made about Keynes' theory of probability, you would need some sort of psychogalvonometer in order to quantify degrees of belief.

An e-meter might be an appropriate tool.

[TLD]

To clarify the issue, is this about the validity of induction: i.e. a question like: "if we see 100% of our observations 'fit' our knowledge, is that the basis for saying that our knowledge is certain?" Or, is this a different issue?

Certainty is an assessment of evidence for a specific conclusion. I don't see "measuring evidence against certainty": you evaluate the evidence to determine if it is sufficiently consistent for certainty.

Knowledge is much broader - grasping the facts of reality.... And forming concepts from those facts and observations is the process of induction.

[KevinDW78]

To clarify the issue, is this about the validity of induction: i.e. a question like: "if we see 100% of our observations 'fit' our knowledge, is that the basis for saying that our knowledge is certain?" Or, is this a different issue?

No, I wouldn't be questioning the validity of induction, that'd just be silly. The question really is, does "probability" refer to a metaphysicical relationship or an epistemic relationship (i.e. degrees of ignorance). And then on top of that, is it a quantitiative measurement or a qualitatitive concept? Then finally, how would one form and apply probabilities to scenarios.

[softwareNerd]

... does "probability" refer to a metaphysicical relationship or an epistemic relationship (i.e. degrees of ignorance).

It is a concept in epistemology, but it is not a measure either of knowledge or of ignorance but a measure of observations, with a single added extension that assumes the pattern will stay the same in the future. Ignorance plays a role, because otherwise we would not need to make that best-guess assumption, but probability itself is not a measure either of knowledge or of ignorance. What we can have is a guess about the probable outcomes, based on the past observations; and, we can also have a measure of how consistent those past observations have been (a measure of "confidence" that really refers to the measure of how similar past patterns have been). In its role as a measure of past observations, it is quantitative.

[Grames]

Measurement is not the topic of the thread, but probability is fundamentally about counting things or in other words taking measurements. So I offer this.

Accuracy and Precision in measurement introduces a practical and realistic use of probability. Accuracy is the correspondence between the measured value and the true value. The problem in knowing how accurate a measurement is that if you knew the true value there would be no need to take a measurement. Repeated measurements and the central limit theorem are used together to infer a true value. Precision has to do with the repeatability of the method of measurement, and corresponds to the standard deviation of the measurements. Accuracy is metaphysical in claiming a true value exists, precision is epistemological in its attention to method, and the science of measurement applies probability to both.

[KevinDW78]

Thanks you SN and Grames. I think those points along with the others given are adequate for me to get a starting grasp on this subject.

[KevinDW78]

I'm in the process of writing my paper and missed one aspect of the scenario we have to use: the coin will only be flipped once and then destroyed. But I don't think that has any bearing on my thesis and where I am going to take it. But it does make me shake my head at the poinlessness of these silly hypotheticals that philosophy students are asked to endure.

[brian0918]

I'm in the process of writing my paper and missed one aspect of the scenario we have to use: the coin will only be flipped once and then destroyed. But I don't think that has any bearing on my thesis and where I am going to take it. But it does make me shake my head at the poinlessness of these silly hypotheticals that philosophy students are asked to endure.

Do you have to choose between seeing the result of the coin flip and killing a cat?