It's true because things in such situations behave in such ways. I don't know why this is supposed to entail laws-as-habits. — Michael

If there are no real tendencies or habits that govern things in such situations, then what constrains them to behave in such ways?

I'm not the one saying that physical laws are habits, so I don't know why you're asking me. — Michael

If laws of nature are not real tendencies or habits, then what are they?

I don't see how a counterfactual can be considered a physical-law-as-habit. — Michael

Do you deny the truth of the proposition, "If I were to let go of a stone, then it would fall to the ground"? If not, how do you explain it? What else would "a physical-law-as-habit" be, if not this kind of conditional necessity?

There v is no law of gravity, there are just some tentative equations which may be useful for synchronizing clocks. — Rich

The law of gravity is not the same thing as the mathematical model that we often use to represent it. Again, it is a real tendency or habit that governs actual things and events such that if certain conditions were to obtain, then certain outcomes would follow.

Successful, precise predictions never occur. — Rich

Who said anything about precision? We make successful predictions all the time, since success does not require absolute precision.

This is why I prefer Sheldrake's preferred use of habit as opposed to law, allowing for approximate repetitive events but not precisely what is predicted. — Rich

I am not familiar with Sheldrake, but Peirce had the same preference; hence my references to "tendency or habit" above. I suspect that it is also why he consistently talked about "generals" rather than "universals" when discussing nominalism vs. realism.

Suppose that I am holding a stone. If I were to let go of it, then it would fall to the ground. This proposition is true, regardless of whether I ever actually let go of the stone. It expresses a tendency or habit - a conditional necessity - that really governs the stone's behavior in an inexhaustible continuum of possible cases, so it is not reducible to any actual occurrence or collection thereof.

Probability is always conditionalized on something ... — SophistiCat

And I am simply suggesting that if it is conditionalized solely on someone's knowledge (or lack thereof), background or otherwise, then we should not call it "probability." Again, I recognize that this is a futile quest.

To rephrase, what is gravity if not the law of gravity? Are you defining it as the actual behavior, or is it a real tendency or habit that governs that behavior without being reducible to it?

So it's not that there's gravity, our mathematical model which describes gravity, and a law of gravity. There's just the first two. — Michael

How are you distinguishing "gravity" from the "law of gravity"?

The perfect circle though cannot be a real, or natural figure, and this is indicated by the irrational nature of pi. — Metaphysician Undercover

As I have noted before, the perfect circle can be real, just not actual. The irrational nature of pi has nothing to do with it - the circumference of a circle is incommensurable with its diameter, which just means that the two cannot be measured by a common unit.

My suggestion is that a law just is a description. — Michael

That would be the nominalist view; by contrast, a realist would say that a "law of nature" is a real tendency or habit that governs actual things and events, but is not reducible to them. If a law is merely a description, then there is no good reason to think that it would apply to future behavior, since different things and events are involved; yet we make successful predictions all the time, not just in science, but in everyday living.

I already acknowledged that I am swimming upstream on this. I think that "probability" should be reserved for when we are making predictions about populations and/or random samples, and not applied to events that have already happened such that the only uncertainty about the result is due to ignorance.

Even after the coin has been flipped, the correct answer to the question "what is the probability that it's heads?" is "0.5" ... — Michael

No, again, at that point the correct answer is 1 if it came up heads and 0 if it came up tails. Someone's personal ignorance of the result is irrelevant once it is actual, rather than potential.

Again, my issue is not so much with doing the kinds of calculations that you are describing, it is with calling this "probability" rather than "confidence," "degree of belief," or "plausibility," depending on the context. And I realize that I am swimming upstream here, since people refer to it as "probability" all the time.

I obviously disagree, but I see no point in arguing about it. There is a reason why the scientific method is also called the hypothetico-deductive method. Newton's laws were just explanatory hypotheses (retroduction) until they produced testable predictions (deduction) that were subsequently corroborated by experiments and observations (induction).

So, GR was not inferred from data. We know this to be historically true. — tom

You are the one who insists on defining retroduction as "inferring from data." I describe it as "formulating an explanatory hypothesis," which is exactly what Einstein did.

Einstein worked out some crucial tests - the classical tests of relativity. — tom

That was deduction, and the actual testing was induction.

Science on the other hand works from problem to solution, without method. — tom

Claiming this over and over again does not make it true. There is no deterministic route from a perceived problem to a single "right" solution - not in engineering, and not in science.

Back to general relativity, what was the surprising observation, and how was the explanation inferred from it? — tom

I am not a historian of science, so you tell me - what motivated Einstein to develop his theory? What problem was he trying to solve? What reason did he have to doubt the theories that were already in place?

So you don't think the unification of GR and QM is a problem? — tom

What gave you that idea?

Each theory renders the other problematic due to certain mutual inconsistencies. There has never been an observation, surprising or otherwise, that calls either into question. — tom

How about the fact that each theory renders the other problematic due to certain inconsistencies? That seems rather surprising, hence the desire to find a way to unify them.

Relativity theory involved the inductive conclusion that all motions are relative. Einstein took another inductive conclusion, that the speed of light is always the same relative to physical objects, and produced consistency between these two, with the special theory of relativity. — Metaphysician Undercover

These were both retroductions (experience to hypothesis), not inductions (hypothesis to experience). Inductive experimentation requires a retroductive theory and its testable deductive predictions before it can even begin.

Maybe you'd care to give an example of it at work? How about a rough idea of how general relativity was induced? — tom

Einstein hypothesized it (retroduction), he and others worked out some of its experiential consequences (deduction), and then various scientists conducted further experiments and made observations to see whether those predictions were falsified or corroborated (induction).

Whatever you call it, it's still supposed to be a method of inference: theories from data. — tom

Not exactly; it is more like the formulation of a plausible explanation for an otherwise surprising observation on the basis of other background knowledge. It typically involves making connections that had not been recognized before.

Science on the other hand is problem solving, and there's no method for that. — tom

Engineering is problem solving, and there are all kinds of methods for that. The same basic pattern of retroduction (design), deduction (analysis), and induction (testing) is evident.

With the understanding that retroductive reasoning is a type of inductive reasoning. — Hanover

Not at all - retroduction (or abduction) is a distinct type of reasoning that provides explanatory conjectures for deductive explication and inductive examination. I prefer the term retroduction because it proceeds "backwards" relative to both deduction (consequent to antecedent) and induction (experience to hypothesis).

What is/are the common roles and functions of all national governments? What are the responsibilities of all governments? — TopHatProductions115

Thomas Jefferson's answer in 1776 still rings true to me.

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. — That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, — That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.

B can be 2(false). So again, can I make a claim that I've opened a new option [2. False] for the Liar statement which was written off in the original paradox? — TheMadFool

Again, nothing about B has any bearing whatsoever on what you can claim about A. They are two different statements.

Let me try to explain it as clearly as possible. — TheMadFool

Repeating the exact same argument is not an explanation, and it is certainly not any more convincing.

This statement is neither true nor false. This however is a TRUE statment about A. — TheMadFool

This is not a statement about A at all; it is a statement about B. As soon as you change "false" to "neither true nor false," you have a different statement, and the two are not equivalent.

Therefore the liar statement, which is equivalent to B, is also true. — TheMadFool

As others have been pointing out, the liar statement (A) is not equivalent to B. At the very least, you have to provide an argument for why the two statements are (supposedly) equivalent.

Thus we arrive at a substratum, or substance, view. — darthbarracuda

That is not one of the two options in this thought experiment. I was hoping to avoid debates about which (if either) is correct, and instead focus on how we would go about figuring that out, as well as the practical differences (if any) that would manifest between people who take each position.

A nominalist who would adopt realism for the sake of discussion is an extreme relativist. — jkop

I meant that each person within the thought experiment must choose either extreme nominalism or extreme realism, not that participants in the discussion have to pick a side.

If the principle holds when there are just two things to consider then it holds when there are a trillion things to consider. — Michael

Turn that around - if it does not hold when there are a trillion things to consider, then it does not hold when there are just two things to consider. See, whether we accept Bayesian values as an objective measure of confidence or degree of belief is itself a subjective matter.

And if you need the change to be sufficiently large enough then you just need to check a sufficiently large proportion of non-black things. — Michael

What would be "sufficiently large"? Can we identify some objective threshold, above which the increase in calculated plausibility would count as evidence, and below which it would not? Or is it a matter that each person has to determine subjectively?

With the example of eggs, having checked 9 of the 10 eggs should count as evidence. — Michael

Would most people guess that the 10th egg is also white? Sure, but the probability in that individual case is no different than it was for each of the first nine - 0.5. It is just as likely that the 10th egg is non-white as that it is white; neither guess is objectively better than the other. If you flipped a coin that you knew to be fair and got heads nine straight times, would you bet on the next flip also being heads? Notice how our intuition goes the opposite way in this case, even though the two scenarios are probabilistically identical - I suspect that most people would guess that the 10th flip will be tails, even though (again) neither guess is objectively better than the other.

You said it isn't frequentist probability being that the probability (or plausibility, if you prefer) is 0.5¹⁰, not either 0 or 1. — Michael

No, you are not making the distinction between the probability that any batch of ten eggs would be entirely white (0.5¹⁰) and the probability that this particular batch of ten eggs actually is entirely white (either 0 or 1).

Reasoning is fallacious if it doesn't guarantee validity, where validity is when it's impossible for the premises to be true and/or the conclusion false. — Terrapin Station

Only in deductive reasoning. Retroductive reasoning is valid when it produces an explanatory hypothesis that is capable of experiential testing. Inductive reasoning is valid when it proceeds in such a way that it will be self-correcting in the long run.

If green apples are relevant to the proposition "if something isn't black then it isn't a raven" then it's relevant to the proposition "if something is a raven then it is black". — Michael

I do not consider the observation of a green apple to be relevant to either of these propositions. Bayesian plausibility somehow counts it as evidence that all non-black things are non-ravens, but I do not - in this case, mainly because of the sheer number of non-black things. Even if we limit it to actual non-black things and assume that the quantity is finite, it will still be so large that the change in your calculated value is vanishingly small - certainly not sufficient to count as genuine evidence in my book.

Again, the maths I used in the example shows that the Bayesian probability of every egg being white just is 0.5¹⁰, and this is true even if I believe otherwise (hence the objectivity). — Michael

Again, this is not yet Bayesian plausibility, it is frequentist probability - the proportion of infinitely many ten-egg batches that would consist entirely of white eggs. It only becomes Bayesian plausibility when you claim that the increase to 0.5⁹ when you observe that the first egg is white increases your confidence that all of the eggs in this particular batch are white.

A thing can be evidence even if it isn't taken to be. That's why "ignoring evidence" is a thing. — Michael

This is simply what person A calls it when person B ignores something that person A counts as evidence, but person B does not. Is there some objective standard that dictates which of them is right? Bayesian plausibility somehow counts the observation of a green apple as evidence that all ravens are black, but I do not. I have other criteria for something to count as evidence, including relevance.

Again, there's the example of the eggs I gave earlier. It's an application of Bayesian probability (as I understand it), but it has nothing to do with how confident any particular person is. — Michael

Huh? Once the entire batch of ten eggs is produced, your calculations are only about how confident you are that all of them are white, as you observe them one by one. Again, objectively, either all of them white (p=1) or at least one of them is non-white (p=0).

But their actual confidence isn't relevant, as we're considering objective Bayesian probability ... each observation of a white egg is evidence that every egg is white. — Michael

Your premiss here is that anything that increases the Bayesian plausibility of a proposition should count as evidence for its truth. Only someone who agrees with this - i.e., attributes validity to it - will actually be more confident about the truth of a proposition by virtue of such calculations. Your original example, where the observation a green apple somehow counts as evidence that all ravens are black, demonstrates the implausibility of this whole approach.

And feel free to replace "probability" with "plausibility" if it really matters that much to you. — Michael

If you had just said this in the beginning, then we might not have had much of an argument at all. :D

I'm use Bayesian probability, as just mentioned. What I'm saying is that, given it's using objective values, it isn't something that will vary from person to person as you suggest. Hence it being objective Bayesian probability (as I understand it). — Michael

My point is that someone's actual confidence or degree of belief is not objectively measurable. Again, most people will never do this calculation, and only those who agree with its underlying assumptions will attribute any validity to it at all. In any case, my main contention is that we should avoid calling it "probability," because doing so encourages confusing what we think with how things really are.

If so then I think that the last issue of contention is my claim that evidence is anything that increases the objective Bayesian probability that a hypothesis is true. But then what else does it mean to count as evidence, I wonder? — Michael

Lots of different people have lots of different ways of counting something as evidence, and then weighing it with other evidence. Very few people have any idea what "objective Bayesian probability" is, let alone how to use it as a tool for mathematically gauging their confidence or degree of belief. Again, I personally would prefer that everyone use the latter terms or "plausibility," rather than calling it "probability" at all.

Then what about my example of the eggs? It certainly seems to make use of objective values and so won't vary from person to person, even though it's about confidence/plausibility. — Michael

I raised no objections to what you said in the post that you linked about the probability of all ten eggs being white before they are produced; or even the probability of all ten eggs being white after eight of them have already come out white, but before the other two eggs are produced. My objection was to your claim that the same reasoning still applies after all ten eggs have been produced. At that point, either all ten eggs are white (p=1) or at least one of them is non-white (p=0).

What we are calculating here is not confidence/plausibility, but the proportion of outcomes that would occur in infinitely many random trials. If you were to use the device to produce a batch of ten eggs a million times, then the number of batches with all white eggs would be approximately 0.5¹⁰ x 1,000,000 = 977. If you were to use the device to produce a batch of two eggs a million times, then the number of batches with both white eggs would be approximately 0.5² x 1,000,000 = 250,000. However, these values tell us nothing about the actual color of the eggs in a single batch of ten or two after the device produces it.

Yes, although there is more to the frequentist view than what you quoted. As its own Wikipedia article states:

In the frequentist interpretation, probabilities are discussed only when dealing with well-defined random experiments (or random samples) ... For any given event, only one of two possibilities may hold: it occurs or it does not. The relative frequency of occurrence of an event, observed in a number of repetitions of the experiment, is a measure of the probability of that event ... A claim of the frequentist approach is that in the "long run," as the number of trials approaches infinity, the relative frequency will converge exactly to the true probability ...

The frequentist interpretation is a philosophical approach to the definition and use of probabilities; it is one of several such approaches. It does not claim to capture all connotations of the concept 'probable' in colloquial speech of natural languages. As an interpretation, it is not in conflict with the mathematical axiomatization of probability theory; rather, it provides guidance for how to apply mathematical probability theory to real-world situations.

Personally, I think that even the "objective" Bayesian approach is fundamentally subjective, because it claims to measure confidence, degree of belief, or plausibility, all of which will vary from person to person.

Fallacies are part of the repertoire of our survival skills. — TheMadFool

Not fallacies per se, but rather types of reasoning other than deduction - e.g., retroduction (hypothesizing a plausible antecedent from an observed consequent) and induction (generalizing from individual cases).

Do you believe that an agent can have better or worse reasons for increasing or decreasing his confidence in a given hypothesis in the face of new evidence? That is, some types of evidence are "better" or "worse" than others? — Arkady

Objectively or subjectively? :D Yes, but I would prefer not to say that probability has anything to do with it, since we are clearly talking about one person's confidence. And I do think that someone's evaluation of evidence as "better" or "worse" typically has both objective and subjective aspects.

, ,

As I have stated repeatedly, probability does not apply to individual cases - only to populations (P) and samples randomly taken therefrom (S). Probability is simply the proportion of P or S that has a designated characteristic (C).

If we know that X% of P has C, then we can predict that approximately X% of S will have C; this is statistical deduction. If we know that Y% of S has C, then we can predict that approximately Y% of P will have C; this is quantitative induction. In both cases, the accuracy of the prediction increases as the size of S increases, until the error disappears completely when S is identical to P. By the way, this is what gives induction its distinctive (i.e., non-deductive) validity as a form of reasoning - it is self-correcting in the long run.

What we have primarily been discussing in this thread is a third type of inference. If we know that no S has C, then we can predict that no P has C, but it is meaningless to assign a probability value to such a prediction; this is crude induction. It is also self-correcting; in fact, it takes merely a single counterexample to falsify the prediction. Despite its obvious fallibility in this sense, it is the only way to "justify" a universal proposition inductively.

So universality - in practice, in the real world - obtains only by a failure to find otherwise. The absence of not-A as a particular, is inductive confirmation of the presence of A as a generality. — apokrisis

Or as Peirce succinctly put it, "A particular proposition asserts the existence of something of a given description. A universal proposition merely asserts the non-existence of anything of a given description." (CP 5.155; 1903)

Then you need to show where my admittedly incomplete calculation has gone wrong, because I think I have shown that the probability is greater than 0.5, and somewhere close to 0.9 — unenlightened

The calculation is fine as far as it goes; the interpretation is the problem. The last marble in the bag is either black (p=1) or non-black (p=0), we just do not yet know which. You have basically invented a clever mathematical way of measuring your level of confidence in your guess that the 17th marble is black, based solely on the fact that the first 16 were black.

That's the nature of probability, that one can be wrong. — unenlightened

If one can be wrong, then one is really talking about (subjective) confidence or degree of belief, rather than (objective) probability.

You did not stipulate any knowledge of how the marbles got into the bag. All we knew was that the first 16 marbles that we took out were black. This information alone is insufficient to calculate a meaningful probability that the 17th marble will also be black. Most people would indeed be likely to bet on it being black in that scenario, but again, they would be wrong if it turned out to be white.

If I say that nobody in my house is American I'm not saying that nobody in my house can ever be American. — Michael

Fair enough, but what you are really saying then is that nobody in your house right now is American.

Wait, so you're saying that it's unobjectionable to claim that a universal proposition has a greater than 0 but less than 1 probability of being true? — Michael

No, but I can see why you misunderstood me. The universal proposition is "if something is not black then it is not a raven"; i.e., "all non-black things are non-ravens." The proposition that I find unobjectionable is "for any randomly selected non-black thing, the probability is 0.5 that it will not be a raven." This is not the same (universal) proposition; it is instead a particular proposition, "some non-black things are non-ravens," with the additional information that the proportion of non-black things that are non-ravens is 50%.

If I say that all humans are shorter than 9 feet I'm not saying that all potential humans are shorter than 9 feet. — Michael

I think you are, unless you qualify it somehow. You are saying that anything taller than 9 feet cannot (ever) be human.

When I say that the probability that "if something is not black then it is not a raven" is true is 0.5 I mean that that for any randomly selected non-black thing, the probability is 0.5 that it will not be a raven. — Michael

Then this is a universal proposition after all, rather than a singular proposition; and it is, in fact, logically equivalent to "all non-black things are non-ravens." Your use of probability in this case is unobjectionable to me; you are simply saying that exactly 50% of all non-black things are non-ravens.