SingleDad

bd-from-kg

Perhaps you should take your time so as not to embarrass yourself as badly as you do here. My own time is also limited; I am frankly resentful that I have to spend it refuting your pseudointellectual bullshit.

I guess your personal enmity towards me has clouded your judgement.

Your personal enmity towards me has apparently caused you to apparently abandon logic and common sense to levels shown by christian theists in an attempt to embarass me. I am frankly irritated and have lost my tolerance of having you say black every time I say white. I don't know what I did to piss you off, and at this point I frankly don't care.

Firstly, according to your idiosyncratic definition of knowledge, we can never show that Smith killed Jones because you apparently don't trust perception to give us any knowledge, nor can we use our induction of regularity as a fact to show entailment. Since, given the facts, it is logically possible that Smith did not kill Jones, it is your epistemic basis that cannot give us this knowledge.

However, stipulating those common sense presuppositions, we see that all of the facts you give us can be used in an evidential argument.

You stipulate several facts; We will first examine the case logically, assuming all our facts are true and our hypotheses determinate; the math is much simpler that way. We can then frame the argument in the corresponding probabilistic cases; I will leave the solution as an exercise to the reader (because I'm too lazy to do all the algebra).

<ol type="1">[*]Jones is dead[*]Time of death is 3:15[*]Cause of death is a gunshot wound[*]9 mm bullet*[*]Smith is known to be in the area (presumably seen by a reliable witness).[*]Smith is known to be in possession of a pistol of the same type as the bullet[*]A gun of this type was found near the scene[*]The gun has Smith's fingerprints on it[*]The gun fired the bullet[*]Traces of Jones's blood were found on Smith's shoe*[*]Smith had a motive to murder Jones[/list=a]

There are evidentiary and nonevidentary arguments here.

Firstly, we have evidentiary arguments that you made some errors in your description. I hypothesize that you made an error (H) the contravention of implies some actual nonfacts. There's no such thing as a 35mm gun (that's a bullet almost 1 1/3" in diameter ). If you had not made an error ~H, that would imply that there was such a thing as a 35mm pistol. Since the existence of a 35mm pistol is an actual nonfact, the hypotheses that you have made an error is proved evidentially. Additionally, you claim that Smith had Smith's blood on his shoes. Again, had you not made an error, then that would imply that having one's own blood on one's shoes is a remarkable event. Again, since that's an actual nonfact, the hypothesis holds evidentially.

Now some of the facts above are evidentiary arguments that Smith killed Jones, and other facts are rebuttals to evidentiary arguments to a defense.

The evidentiary arguments for the prosecution are Smith's fingerprints on the gun, and a chain of evidentiary arguments showing that Smith killed Jones. In logical terms, it is unlikely to the point of absurdity that:

• If the cause of death were anything other than a gunshot wound, Jones would not have a gaping hole in his chest.
• If the cause of the gunshot wound had been anything other than that specific bullet, that bullet would not have been found on the scene.
• If the gun that fired the bullet had been any other than the gun found nearby, it would not have matched the rifling tests
• If Smith had not handled the gun, his fingerprints would not have been on it.
• If Smith had not been near Jones when he was bleeding, he would not have Jones' blood on his shoes.
• If Smith had not murdered Jones, he wouldn't have been nearby when Jones was bleeding

Again, we consider these in the ideal logical sense. In no cases is the implication perfect, but without abandoning ideas that the universe is regular (e.g. Smith's fingerprints did not "magically" appear on the gun), the implications are strong enough to simplify (for the sake of argument) logically.

The other evidence relates to the hypotheses that if Smith didn't murder jones, then Smith would be a reasonable defense on one of any number of grounds:

• The facts of the case might not implicate Smith
• Smith might have an alibi
• Smith might have no motive

In logical terms ~H -&gt; (D1 | D2 | D3).

However, we see that Smith has no valid defense, so again we have an evidentiary argument.

Now in probabilistic terms, we represent these arguments using Bayes' theorem.

Let us look at a simple example. Let us take it as fact that Smith was killed by a bullet with Jones' fingerprints on it.

P(H) = Smith killed Jones
Since somebody killed Jones, the a priori probability is 1 / (the number of people that could possibly have killed him). Let's say that there are 1,000,000, so P(H) = 1e-6.; P(~H) = 1 - P(H) = 0.999999

P(F|H) = If Smith killed Jones (known to have been killed by a gunshot wound caused by a gun Smith handled), it is certain that Smith handled the gun. P(F|H) = 1

P(~F|~H). What is the probability that if Smith did not kill Jones with the murder weapon, his fingerprints would not appear on the gun? This probability also seems very high; 999,999 people out of a million did not kill Jones, and their fingerprints were not on the gun. So we can say that the probability of P(~F|~H) = 0.999999, thus P(F|~H) = 1e-6.

Therefore, by Bayes Theorem,

P(H|F) = (P(F|H) * P(H)) / ((P(F|H) * P(H)) + (P(F|~H) * P(~H)))

P(H|F) = (1 * 1e-6) / ((1 * 1e-6) + (1e-6 * 0.999999))

P(H|F) = 1e-6 / (1e-6 + 0.999998)

P(H|F) = 0.5

We have now raised the probability of P(H) to .5.

Given this finding, we can do the same thing with the probability that the blood would be found on the shoe. We'll use the same reasoning, but the a priori probability P(H|F) has been raised to 0.5 (we are just subsituting P(H|F) for P(H)).

P(H|F') = (1 * 0.5) / ((1 * 0.5) + (1e-6 * 0.999999))
P(H|F') = .999998

After two pieces of evidence, we are virtually certain that Smith killed Jones.

Indeed, when this case is tried, the defense will attempt to undermine the evidentiary basis of these assertions, either by arguing that the probability of the hypothesis is low in general (i.e. that if the murder occurred, it is unlikely to believe that the fingerprints would be on the weapon) and that the probability of the inverse is high (that even if Smith did not murder Jones, it is probable that his fingerprints would be on the weapon).

The rest of the probability calculations will be left as an exercise to the reader.

bd-from-kg, please don't waste my time like this in the future.

[ December 21, 2001: Message edited by: SingleDad ]</p>

Richard Carrier

The following is from an anonymous reviewer with substantial experience in the field (i.e. I didn't write this, so don't shoot the messenger). I have also sent it out to be reviewed by some professors, and am awaiting their response. Also, I have received complaints by important persons that Mr. Hamelin has descended into the use of foul language and personal attacks and, to put it simply, we don't like that. I haven't had time to review those complaints, but they come from credible sources, so I suggest shaping up the behavior.

The anonymous review follows:

In my opinion, his essay is NOT EVEN CLOSE to being suitable for the library because I think it suffers from serious problems (to put it mildly). However, I seem to be having problems putting the majority of my worries into words.

What I can tell you is this: the author doesn't appear to have a basic grasp of the proper terminology. He uses the word "evidentiary" when he should be using the word "evidential." In the literature of the philosophy of religion, I am not aware of a single authors who uses the former expression but I can think of countless authors who use the latter expression (e.g., witness the entire body of literature about the evidential argument from evil). Moreover, the author's attempt at explaining the distinction between evidential and logical arguments (in his words, 'what is actually the case' vs. 'what is possibly the case') is unsuccessful. His definition of so-called logical arguments is correct, but his definition of evidential arguments misses the mark. The point of evidential arguments is to show what is the best explanation for some fact. More importantly--and this is a point the author doesn't even seem to be aware of--evidential arguments often appeal to facts that are consistent with a denial of the conclusion of the evidential argument in question. This feature of evidential arguments is what gives them their strength, yet there is no discussion at all about this in the article.

This feature of evidential arguments is best illustrated by an example. Paul Draper's argument from the biological role of pain and pleasure (widely considered to be the strongest formulation of the atheistic argument from evil) appeals to known facts about the biological role of pain and pleasure. Those facts, by themselves, are consistent with both metaphysical naturalism and theism. However, Draper's evidential argument shows how, nevertheless, those facts are antecedently much more probable given naturalism than given theism. Hence, naturalism offers a better explanation for those facts than theism.

The author's essay is an incompetent treatment of this issue. Please don't embarrass the Secular Web by posting it in the library.

I will make the following additional objection to Larry's argument. Larry's contention that there could not be an evidential argument for theism is ludicrous. Just what exactly does he think the fine-tuning argument is? No theist presents the fine-tuning argument as a so-called "logical argument," in the sense that the alleged 'fine-tuning' of the universe is logically incompatible with the nonexistence of God. On the contrary, ALL theists who promote the fine-tuning argument admit the alleged fine-tuning is logically compatible with atheism. Instead, they claim that the alleged fine-tuning is vastly more *probable* on the assumption of theism than on the assumption of atheism. Thus, by definition, the fine-tuning argument is an evidential argument. It may be (and I would argue, is) an unsound argument, but it is an evidential argument.

[ December 30, 2001: Message edited by: Richard Carrier ]</p>

SingleDad

Richard Carrier

I will, of course, respond to legitimate criticism intended to arrive at the truth. However, it seems unfair to both remain anonymous and assert one's expertise.

I apologize for the (singular) personal attack. It should be noted that this attack is:

• Limited to a single message (in this thread)
• Provoked by my irritation from a criticism that that is entirely unsupported and seems trivially false
• Accompanied by a substantive refutation
• On a message board and not in a professional or academic journal
• Occurs in a context of longstanding personal animosity that I maintain has been initiated and perpetuated by the person to whom my inappropriate remarks are directed
• uses only one instance of "foul language" consisting of the word "bullshit", a term ordinarily permitted on this message board

In any case the criticism of my behavior on a message board seems an ad hominem attack on the value of my work. If bd-from-kg (the "victim" of my remarks here) wishes to request official censure for my behavior on this thread, he is welcome to post a complaint in the Bugs, Problems and Complaints thread where it will be evaluated by the administration of this board; naturally I would recuse myself from participating such an evaluation and accept the decision of the remaining administrators without complaint.

I am not a professional philosopher, so I apologize for my familiarity with professional terminology. Evidentiary and evidential are synonyms. The paper does not change substantively from changing "evidentiary" to "evidential"; if this change would make the work more acceptable, I have no objection. Again, as I am an amateur, I will have to rely on the judgement of those better versed in the field.

To rebut a possible future charge of hubris, it should be noted that I was solicited to assemble this article for the library.

I don't understand this criticism. Presumably if we are attempting to show which of two explanations is "best", we are implicitly agreeing that both explanations are logically possible, and that the best explanation is the one more likely to actually be the case.

It seems for any partial hypothesis (one that does not attempt to explain all facts), there will be an infinite number of facts that are consistent with both the hypothesis and its negation. Such a case is implicit in the rules of material implication.

Again, I fail to understand this criticism. The logical form of evidentiary arguments is explicitly noted as an ideal case, and is presented, albeit possibly not as clearly as possible, as the underpinnings of using Bayes Theorem in the probabilistic case.

I will examine Drange's argument in more detail, but on first glance it appears directly compares the falsification probabilities for the existence of pain and pleasure under theism and naturalism. He shows that (stating naturalism as N, theism as ~N and the fact of the existence of pain and pleasure as F) that P(~F|~N) is rather high, whereas P(~F|N) is rather low: In other words the exist of pain and pleasure tends to falsify theism more than it tends to falsify naturalism.

If we could know the truth of the implications with certainty, and if indeed Drange's conclusion were true, we would indeed find that ~N &rarr; ~F and the falsification criterion would prove the the truth of naturalism and the falsity of theism.

I am uncertain whether this contention is the reviewers or Mr. Carrier's. And I agree that it would indeed be ludicrous for me to claim that there could not be an evidential argument for theism.

Regardless, the author of this contention should at least read my essay carefully: I do not make such a claim. My claim is much narrower: that two particular arguments for theism, the argument from existence and the argument from belief, are not valid evidential arguments according to the criteria and structure I describe. My essay attempts to show why such arguments are invalid and do not tend to rationally persuade one to the conclusion asserted.

As I do not address the fine tuning argument, this criticism seems misplaced at least. However, it can be shown that the Fine Tuning argument falsifies neither theism nor naturalism, and neither on a logical nor probabilistic basis, and thus cannot form the basis of a valid evidential argument for either position.

This seems to me to be a quibble. Again, I assert that arguments such as the fine tuning argument are invald and unsound precisely because they fail to show, neither logically nor probabilistically, that the negation of a hypothesis leads to the improbability of an actual fact. Perhaps it would be more precise to state that these arguments appear to be evidential, but fail because they do not sucessfully meet the criteria for a valid evidentiary argument.

It seems as yet unproven whether my essay is "incompetent" and "embarassing". While I certainly welcome criticism intended to strengthen the precision of my work, a quibble of terminology, an uncharitable reading ignoring the explicit inclusion of the probabilistic form of the evidentiary argument, and a vehement criticism of a claim not actually made, and an quibble between the finding the form is deficient or the conclusion invalid on the basis of form does not demonstrate my "incompetence" or that the article is "NOT EVEN CLOSE" to suitability.

It seems that to show that my essay is deeply flawed (rather than showing it to merely have some instances of imprecision), the author should show that either a valid evidential argument according to my criteria could be false, or that an invalid argument could be true.

And while the use of strongly pejorative language in this paragraph does not excuse my own behavior, it does appear that both parties to this discussion are not above personal language thinly veiled as criticism of the issue.

[ December 30, 2001: Message edited by: SingleDad ]</p>

Kenny

Just for the heck of it, here’s a proof of Bayes’ theorem:

1.) P(A/B) = P(A&B)/P(B)

This is just the intuitive definition of conditional probabilities: The probability that A is true given B is true is equal to the probability that both A and B are true divided by the probability that B is true.

2.) P(B/A) = P(A&B)/P(A)

This is just the definition of conditional probabilities again.

3.) P(A/B)P(B) = P(B/A)P(A)

Isolate P(A&B) to set both equations equal to one another

4.) P(A/B) = P(A)P(B/A)/P(B)

Rearrange and !viola!, you have Bayes’ theorem in its most basic form.

5.) Let X = P(A)P(B/A) +P(~A)P(B/~A)

If I can prove that X = P(B), I will have proven the expanded version of Bayes’ theorem which SingleDad uses.

6.) X = P(B)P(A/B) + P(B)P(~A/B)

I used line three to substitute out the first term and the substitution for the second term follows by analogy.

7.) X = P(B)P(A/B) + P(B)[1-P(A/B)]

This is just a simple probability expansion

8.) X = P(B)P(A/B) + P(B) – P(B)P(A/B) = P(B)

Just distribute and cancel and you’re done.

Q.E.D.

God Bless,
Kenny

[ December 31, 2001: Message edited by: Kenny ]</p>

bd-from-kg

SingleDad:

This is basically a (belated) response to your post of Dec. 19. I plan to post a response to your Dec. 21 outburst very soon.

But before doing so I have to say that I agree with many of the comments that Mr. Carrier reported. I’ll refer to a couple of the ones relating to substantive issues here; the others speak for themselves.

By the way, I have no idea where you got the impression that I thought that it was “impossible or implausible” to believe that “perception has any relationship to reality” or that “useful facts can be known”, etc. – at least in any sense in which the same cannot be said of most people doing philosophy of science. Perhaps you could cite the statements that led you to these conclusions.

1. Logical formulation

I note again that your exposition seems to be divided into (1) a discussion of how one might go about demonstrating the truth of a hypothesis about the “external world” logically and (2) how one might go about demonstrating it probabilistically. This interpretation seems to be confirmed by your statement:

If this means anything at all, it means that you intend, at least in part, to show how “real-world” hypotheses can be supported without resorting to “probabilistic” arguments. So far as I know, the only such arguments are those based on logical deduction. If you have some third type of argument in mind, perhaps you would explain what it is. In the absence of such an explanation I must assume that the exposition in the first part of the OP was intended to describe what a logically rigorous “evidentiary argument” would have to look like. It would seem to be self-evident that no such argument is possible in principle, but you seem to be of a different opinion, since you say:

With this understanding, let’s now consider some of your comments.

My main point was not that perceptions are not necessarily caused in some way by “external reality”, but that we cannot know what aspect of external reality is responsible for any given perception. For example, a man suffering from delirium tremens might “see” rats under the porch, but this does not “entail” that there are rats under the porch that caused this perception. It can be argued that it was caused by “external reality” (i.e., events in the man’s brain), but it was not caused in the way he presumably thought it was. So any conclusions about the “real world” that he draws from this perception will likely be wrong. We can never know that we are not in essentially the same position on any given occasion, or that our perceptions are not creating a false picture of “external reality” in more subtle ways.

Say what? To claim that this hypothesis is unfalsifiable is preposterous. To falsify it one need only mix sodium with water and observe that no explosion occurs. (To be sure, I haven’t stated the hypothesis very precisely for the sake of brevity.)

This is neither more nor less scientific than the original hypothesis; it’s just a different one. (The rest of your discussion here is irrelevant, since it discusses only how your hypothesis might be tested.)

But it is not presupposed that the specific pattern described by the hypothesis exists, which of course is what I meant.

As I said before, it is a truism that scientific hypotheses cannot be proven. It is entirely unclear why you are bothering to critique a staightforward statement which virtually all philosophers of science agree with.

The fact that one cannot draw logically rigorous inferences about the truth of hypotheses about the “external world” is in the natue of things; it is not the result of sloppy or ill-considered definitions.

In your OP you used the term “falsifiability” without defining it. I naturally assumed that you were using it with the meaning which is standard in philosophy of science. This meaning is explained admirably in the Encyclopedia Britannica entry for Karl Popper:

The meaning of “falsifiability” here is obviously the one I defined earlier. (Lots of other references can be found for this; the EB happened to be close at hand.) Evidently you have a different meaning in mind, since you “disagree” with this definition. Perhaps you would like to give your own definition of this term. Until then I have little choice but to use this term the way everyone else doing philosophy of science uses it.

But what we are talking about is not implication but entailment (in your special sense). This requires both that the hypothesis imply the facts and that the facts imply the hypothesis. The latter is practically never true in the case of a scientific hypothesis. The most that can be said of a hypothesis is that it is the “best” explanation of the known facts, where “best” is loosely defined in terms of simplicity, elegance, and parsimony. The fact that your requirement of “entailment” is rarely met by arguments that anyone else would call “evidentiary” is perhaps what prompted the anonymous reviewer to comment:

To say that the facts (F) that support the conclusion (H) are consistent with a denial of the conclusion is to say that ~H does not imply ~F, which according to your definition means that the argument in question is not an “evidentiary argument” – a conclusion which the reviewer (like me) apparently finds absurd.

My point was simply that little can be deduced regarding any specific “possible fact” from the mere denial that a specified regularity or pattern exists. This is really self-evident. I don’t understand why you’re disputing it.

2. Probabilistic formulation

In this section you attempt to lay a foundation for showing that the “probability” that “real-world” hypotheses are true can at least be estimated in practice. I think that, in the case of scientific hypotheses at least, this program is doomed from the start because, the “probability” that such a hypothesis is true is not even a meaningful concept. Let’s see how you tried to define it and go on from there:

I’m critiquing your definition of P(A) as “the probability ‘size’ of A divided by the size of A plus the size of all logically possible alternatives to A”. In most interesting cases, including the case where A is a scientific hypothesis, this definition is meaningless. The “size” or “probability size” of A has no definable meaning.

More seriously, I don’t think that it is possible to give a meaningful definition of what it means to say that that the probability that a scientific hypothesis is true is p. That is, I deny that the expression P(H) means anything when H is a scientific hypothesis.

Since this is a crucial point, I will take the liberty of quoting my own comments on it from an <a href="http://ii-f.ws/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=14&t=000475" target="_blank">earlier thread</a> which were made in response to your statement “The objective existence of quarks seems to have been established ...”:

This is a very real difficulty. Unless you can offer an interpretation of statements like “the probability that X is true is Y” that make sense when X is a scientific hypothesis, any attempt to describe the nature of evidentiary arguments for scientific hypotheses in terms of probabilities cannot even get off the ground.

Not so. Probability theory assumes nothing about whether or when it is possible to assign a priori probabilities, or what (if anything) constitutes a non-arbitrary assignment. In order for probability theory to be applicable to the real world it is necessary only that such an assignment is sometimes possible.

Indeed.

Come again? The whole point of a scientific hypothesis is that it claims to “extend” (i.e., apply) to unknown facts. If this is beyond the scope of your argument, your argument is of little interest.

For example, suppose that you mix two substances in the laboratory (under specified conditions) and they combine to form a new substance. (E.g., you might mix sodium and chlorine and get table salt.) Do it again; same result. Repeat a hundred times; same result every time. These results can be summarized by saying that every time you mixed sodium and chlorine you got salt. But this not a scientific hypothesis; it is an observation. The scientific hypothesis that you will probably formulate based on these experiments is that whenever sodium and chlorine are mixed under these conditions they will combine to form salt. This is a “universal” statement, and it is precisely the kind of hypothesis that scientists come up with over and over again. Of course, one might be more conservative and advance the weaker hypothesis that when sodium and chlorine are mixed under these conditions they usually combine to form salt. But this is still a universal statement in that it implies that, whenever these substances are mixed under these conditions, it is more likely than not that they will combine to form salt. Indeed, it’s precisely because scientific hypotheses extend to, and are meant to be applied to, “unknown facts”, that they are called “hypotheses” or “theories”.

So far as I can see, you haven’t made any case for assigning values to terms such as P(H) and P(F|~H). I don’t believe that there is any meaningful way to define either of these expressions. And even if it’s possible to define the latter meaningfully, I don’t believe there is any practical, nonarbitrary way to assign it a value. This is why I consider it a misuse of Bayes’ theorem to “apply” it in this fashion.

In that case, if your argument is correct there are no scientific hypotheses.

As a statement of fact this is obviously incorrect. Scientific hypotheses are routinely stated as “A invariably causes B”, or if you prefer, “B invariably follows A”. Lots of other scientific hypotheses are equally “absolute” or universal. for example, the hypothesis that gravity is inverse-square is a statement that a rather precise causal realtionship holds universally. (It’s false, but in a way that’s the point. Because it is precise and universal, it is falsifiable, and eventually it was in fact falsified.) Similarly, the statement that the measured spins along a given axis of two particles created simultaneously from the same photon are perfectly correlated is a universal statement. Moreover, a statement that a certain relationship will hold (under specified conditions) a specified percentage of the time is a perfectly good scientific hypothesis, but it is also a statement that a certain causal relationship always holds[/i], but is intrinsically statistical. Thus such a hypothesis is just as “universal” as the former type.

On the other hand, a “hypothesis” regarding the supposed probability of the existence of a causal relationship would be meaningless.

First, this wouldn’t be an a priori probability. Second, that simply isn’t how these things are done. If one observes a correlation of 0.95 between the outcome of the Super Bowl and how the U.S. economy performs that year, one does not assign the corresponding value as the a priori probability that there is a causal relationship between the two, nor (as I suspect you meant) as the a priori probability that this relationship will hold again next year. To do the latter would be to assume that the observed correlation is actually the product of a causal relationship of some kind. Anyway, nothing remotely like this is done (by rational people) unless the nature of the two types of events is such that it seems plausible that there might be a causal relationship involving them. Unfortunately, “seeming plausible” is not the sort of thing that can be quantified in a probabilistic sense.

Well, it’s one of the critical issues. If you can’t justify assigning any value to the a priori probability of a scientific hypothesis (as I argue), then Bayes’ theorem is inapplicable, and any attempt to formulate the nature of “evidentiary arguments” on this basis must fail.

It’s pointless to say that one “should” do what is impossible in principle. For example, say that your hypothesis is that the current “standard theory” of particle physics is correct, and my hypothesis is that it isn’t. If my hypothesis yielded a contrafactual statement, it would be possible to prove that it is false, thereby proving that the standard theory is correct in all respects. But it is well known that this cannot be done. Therefore my hypothesis does not yield any contrafactual statements. The same argument applies to any scientific theory.

Now of course you can argue that my hypothesis doesn’t really qualify as an “alternative hypothesis”, because it doesn’t imply any “actual facts” at all. But in that case, no doubt you would say the same of a hypothesis that did imply actual facts, but none that are not implied by yours. In that case you would say that it is either a “subhypothesis” (if it doesn’t imply all of the facts that your hypothesis does) or the same hypothesis in disguise (if it does). But that would mean that any alternative hypothesis would by definition have to imply something different about the “actual facts” than your hypothesis, so your statement that one “should” construct a hypothesis so that this is so is meaningless.

Not so. For example, consider the hypothesis “For every body with a mass greater than X, there is another such body within a distance Y from it”. (We will assume that “mass” and “distance” have been defined by specifying a coordinate system.) Let’s assume that this is actually true for some given values of X and Y. You might find any number of bodies with the requisite mass and verify that each one is a distance less than Y of another such body, but no matter how many you found you would have failed to show that there are no bodies that violate the hypothesis. At what point would you be justified in saying that the probabiity is greater than p that the hypothesis is true? What would this statement even mean?

Now suppose that the hypothesis is “No such body ever has existed or ever will exist”. How do you go about demonstrating this with any degree of probability? The past is known only very imperfectly; the future isn’t known at all. Even if we change the hypothesis to say that no more than one body in a billion (of those with the requisite mass) has ever been or ever will be this isolated, there is no way to demonstrate the truth of this hypothesis, or even to arrive at a meaningful estimate of the probability that it’s true.

I don’t think that even true scientific hypotheses can be demonstrated to any “degree of probability”. I think that the best that can be done is to show that it is rational to accept a given hypothesis (provisionally) on the basis of the known facts, and irrational not to (at least if one is in a position where one has to act either on the assumption that it’s true or that it isn’t).

Oddly enough, this is very similar to the position that you have taken in the past. For example, in the <a href="http://ii-f.ws/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=21&t=000012" target="_blank">Reformulation of Empiricism</a> thread you said:

This is a far more realistic, sophisticated, and defensible position than the one you have taken here. Why have you abandoned it?

SingleDad

bd-from-kg

Such is not my intention, as I have stated several times in this thread. And, as I have said, I am perfectly willing to clarify this point. To continue to harp on this uncharitable interpretation seems entirely redundant.

The philosophical and scientific treatment of hallucination, again as stated in my article and clarified by my later comments, outside the scope of my essay; such a point belongs in a more basic treatment of empiricism. It is a basic presupposition of science and empiricism that careful examination of perception and invocation of basic regularities of nature, such as causality, forms a valid epistemological basis. Again, continued criticism of this side issue seems nonproductive in the present context.

My apologies, I meant the hypothesis is unconfirmable.

Right. It is necessary to form hypotheses in both a confirmable and testable way.

Agreed. My point is that one can make a probabilistic argument that, in the ideal case and given the overall reliablity of perception and the assumption of regularity, can approach the ideal of a logical proof.

Again, the point of the argument is to show the ideal logical form that one attempts to approach.

So I am disagreeing with Popper, or at least this summary of his ideas. &lt;shrugs&gt; Popper is not the Pope and his ideas are not true by his authority. It is not impossible (however unlikely) that I am actually doing original work.

The meaning of "Under this method, a scientist seeks to discover an observed exception to his postulated rule" means that the scientists attempts to find an actual fact such that H &rarr; ~F. However, this criterion is merely abductive, and essentially requires the scientist to test (in the ideal case) every predicted fact according to his hypothesis.

It is not my observation, from my investigations into the actual way that scientists prove theories, that they actually do this. Rather, they try to eliminate alternative hypotheses, either directly or indirectly. In the direct form, they try alternative theories and try to show that the alternative implies an actual nonfact, and thus discardable. "When the impossible has been eliminated, whatever remains, however improbable, must be the truth."

Directly, they try to find some critical prediction of their theory that (ideally) would be impossible if some central tenet of their theory were false. The confirmation of general relativity by actually observing the changing rate of a clock in a different gravity disconfirms any absolutist version of time. Even if general relativity is somehow false, it is known that a correct theory must include a relationship between time and the presence of gravity.

To claim that I make no definition of "falsifiability" in my essay is astonishing, since my entire essay defines a criterion of falsifiability.

The "anonymous reviewer leaves "best" entirely, and your definition of "simplicity, elegance, and parsimony" completely leaves out the most important criteria: falsifiable and in accordance with the facts.

You are definitely prone to sweeping generalizations without any actual evidence that the generalization is warranted. You have not yet given a single counterexample of a persuasive evidential argument which can be shown does not meet the probabilistic form of the falsifiablity criterion I describe, nor could be described, in the ideal case, with the logical form. You simply assert that such arguments are never of the form I describe.

You simply assert that a statement is absurd without actually showing the absurdity. Why is it absurd to believe that the facts are not (in the ideal case) consistent with a denial of the conclusion or to say that the facts do not (in the probabilistic case) lower the probability of the denial of the conclusion?

This seems to claim that, for instance, the fact that every time I jump I only achieve about a foot of vertical leap is entirely consistent with the denial of the conclusion that I am a poor basketball player. Even in the logical case, you would have to assume dishonesty or the failure of causality to believe I could jump higher during an actual basketball game.

The argument is simpler if I refer, in the general case, to a specific fact. No loss of generality occurs if one extends the argument to some finite and tractable fact set. This is really self-evident; I don't understand why you're disputing it.

The use of Bayes Theorem in probabilistic scientific arguments and the assignment of a priori probabilities to hypotheses has a certain degree of controversy, but as noted, such controversy beyond the scope of my essay.

And I really wonder: if you claim that scientific theories cannot be justified on logical grounds, and they cannot be justified on probabilistic grounds, how do suggest that they be judged? It seems that the only criteria you suggest are entirely aesthetic ("simplicity, elegance, and parsimony").

Or perhaps you merely object to the use Bayes Theorem. If so, it would be useful to see a rigorous treatment of how one can use probabilistic reasoning to distinguish between different scientific theories without using Bayes Theorem.

Again this seems to indicate that you claim that neither logical nor probabilistic reasoning can distinguish between scientific hypothesis. Science is just another aesthetic endeavor, it is nothing more than poetry.

Again, are you arguing that it is not possible to use probability theory in distinguishing scientific theories?

Why is this a problem? The argument explicitly assumes the metaphysics of empiricism. I'm not trying to justify empiricism vs. platonism. The metaphysical examination of empiricism is indeed beyond the scope of my article, which is about distinguishing between scientific theories assuming the truth of empiricism. It seems puzzling at best that if your intention is to argue against empiricism, that you would choose this venue to do so, as my essay is entirely devoid of any arguments for or against empiricism.

If my argument is of little interest, then why are you bothering to respond to it in such detail?

My argument is not about the general applicability of scientific theories, but how one distinguishes between good and bad theories on the basis of the facts. It simply cannot be known if a scientific theory will be true according to unknown facts, and still we go about distinguishing between good and bad scientific theories all the time.

Again, you are addressing epistemological issues far outside the scope of this article.

Again, you make a sweeping generalization. We seem to feel that we can make distinguish between good and bad hypotheses. Is this feeling simply erroneous? Or is there another method by which we can distinguish them?

Again you are conflating the universal application of a scientific theory with the method of its determination. What we know about a scientific theory is conditioned on the known facts. Indeed when new facts come in, we test the theory against this new fact: If we find it false then the theory is wrong in its more general application. But a new scientific theory must still account for why the old theory is in accordance with the previous facts.

[quote]Oddly enough, this is very similar to the position that you have taken in the past. For example, in the Reformulation of Empiricism thread you said:

We can ... create an ontology that purports to describe the world underlying perception from simpler premises. We call the ontology true if it can derive true statements of perception ...
I'm explicitly rejecting ontology as real knowledge...

Causality is an ontological construct, as is objective reality...

There is no "problem" of induction because we're no longer claiming that we're gaining actual knowledge from induction. We're just constructing pragmatically useful ontological constructs.

Now it is an emotionally satisfying interpretation of empirical ontology to believe that the ontology has some sort of special relationship with the world as it "really" is, but I don't think we have any basis to make that claim epistemologically.

This is a far more realistic, sophisticated, and defensible position than the one you have taken here. Why have you abandoned it?

This statment makes it clear that you are addressing the philosophical underpinnings of empiricism itself; since I make no arguments in my original essay supporting empiricism, it seems your entire rebuttal is entirely inappropriate.

For reasons unrelated to your responses to me here, I will be leaving the Internet Infidels Discussion Board. Additional criticism is unnecessary and will go unread by me.

-DM-

For the record, I want it understood that I am NOT the author of the anonymous critique of SingleDad's article which was posted by Richard Carrier, above.

--Don--

bd-from-kg

1. On “evidentiary arguments”

Since SingleDad has apparently left these boards, there is little point in making a detailed reply to his latest posts. However, for the record I would like to make it clear why I think he was on the wrong track in this thread.

I believe that:

1. It is impossible to prove, in a rigorous logical sense, any proposition whatsoever about “external reality”, even if we presuppose that an external reality exists, that all perceptions are caused by it, that there are patterns and regularities to our perceptions that are caused by corresponding patterns and regularities in this “external reality”.

2. It is impossible to make a probabilistic argument for any such proposition except on the basis of patterns and regularities that are presupposed (by the argument in question) to exist.

3. The denial that any specified pattern or regularity exists implies little or nothing about “external reality”.

SD expressed the obvious objections to this point of view pretty well:

The answer to the final question is “yes”. Of the hypotheses that fit the facts, a rational person prefers the more useful ones to the less useful ones. In this context, by a “useful” hypothesis I mean one that is helpful in predicting future events, including the effects of my possible actions. Simplicity, elegance, and parsimony are not aesthetic criteria, but criteria of usefulness. Hypotheses with these properties are easier to understand, and allow us to derive predictions more easily, than those that lack them. Simple, elegant hypotheses allow us to conceptualize the world, and organize our perceptions into a coherent structure, whereas complex, messy ones don’t.

In practice we do not merely form hypotheses; we create an elaborate conceptual scheme (what SD calls an “ontology&#8221 ) for understanding or making sense of our perceptions, which we have a natural tendency to assume “corresponds” in some sense to “external reality”. But we have no way of knowing whether it does or not, and in view of this it is questionable whether it is even meaningful to ask whether such a correspondence exists. All that we can really know is that our ontology has often yielded correct predictions in the past, and any incorrect predictions can be explained on the basis of imperfect knowledge. We can also continue to search for simpler, more elegant ontologies that also have this property. And of course, since the value of an ontology lies entirely in its predictive power, it is irrational to adopt an ontology that yields clearly false predictions.

But we should never forget that none of this really constitutes knowledge. What we really have is a way of thinking about the world that has (hopefully) worked pretty well up to now in terms of generating correct predictions, and that’s all that we have. In no sense do the facts that went into forming our ontology imply that it is “correct”. There are always infinitely many ontologies that are consistent with all known facts.

[Note: All of this might sound weird and unsettling to those unfamiliar with the philosophy of science, but it is actually (as I understand it) well in the mainstream of current thinking in this area. In fact, as I commented in my last post, it appears to have been essentially SD’s position until very recently.]

This is why “entailment” in SD’s sense is an unreasonable requirement for an “evidentiary” (or evidential) argument. If the hypothesis in question is a scientific one (i.e., if it asserts the existence of some pattern or regularity that holds universally) no finite set of facts can logically imply it, and (IMO) it is meaningless to talk about the “probability” that it’s true. The only real question is whether to make it part of our ontology. On the other hand, a non-scientific hypothesis – for example, that a specific event occurred at a specific time and place, is “supported” by facts only in the sense that these facts imply it or make it probable in the context of the ontology we have already adopted. Moreover, for this type of hypothesis we typically have the opposite problem: normally it does not imply the facts that support it, or even make them especially probable. (Such a hypothesis normally has little or no “predictive power”, since it does not assert the existence of a pattern or regularity.) In either case we do not have “entailment” in SD’s sense.

Of course, by “entailment” one might mean only that the supporting facts should be more probable assuming the hypothesis is true. Formally, P(F|H) should be greater than P(F). However, it is trivial to show that whenever P(H|F) &gt; P(H), we have P(F|H) &gt; P(F) (and vice-versa). In this sense, requiring that the facts support the hypothesis is logically indistinguishable from requiring that the hypothesis support the facts. On the other hand, a more stringent requirement – e.g., that P(H|F) and P(F|H) should both exceed some “threshold value” such as 0.5 – excludes too much. On the one hand, there are lots of perfectly good evidential arguments for which P(H|F) is very high but P(F|H) is very low (though significantly higher than P(F) ), and on the other, when H is a scientific hypothesis, both P(H) and P(H|F) are meaningless (or if they are meaningful after all, both are very low).

Thus it appears that the concept of “entailment” is useless to any description of the nature of evidential arguments.

2. On Mr. Carrier’s post

I mentioned in my last post that I agreed with some of the comments reported by Mr. Carrier in his post on this thread. In view of SD’s unexpected departure I feel that I should clarify this statement. The comments that I agreed with were essentially these:

However, I agree with SD that it was unfair to quote an anonymous reviewer, and inappropriate to post publicly what was essentially a peer review, especially one so disparaging. The final comment (apparently by Mr. Carrier) that “Larry's contention that there could not be an evidential argument for theism is ludicrous” was particularly unreasonable, since SD had not made any such claim; he had said only that “many supposedly ‘evidentiary’ arguments for theism do not fulfill the criteria for evidentiary arguments”.

3. On SD and me

In explaining his rather intemperate comments toward me, SD claimed that they were prompted in part by a “longstanding personal animosity that ... has been initiated and perpetuated by the person to whom my inappropriate remarks are directed”.

Now while SD has obviously developed a personal animosity toward me, I have never felt any such animosity toward him. As to whether my comments to him warranted his animosity, or his false impression that it was reciprocated, this will have to be left to the reader to judge.

SD’s impression of “personal animosity” seems to have been based originally on my comments in the <a href="http://ii-f.ws/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=14&t=000333&p=" target="_blank">Objective vs. Subjective</a> thread last April. But it appears to have been greatly reinforced by my response to his comments in the thread he titled <a href="http://ii-f.ws/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=14&t=000383&p=" target="_blank">Inferences concerning the motives of the anti-abortion position</a>, which I considered to be an ad hominem attack on religious pro-lifers.

I have great respect for SD’s intelligence and his opinions (other than his opinions about members of the “religious right&#8221 ) . If I didn’t, I wouldn’t have bothered to engage in long exchanges with him. In fact, we agree on far more than we disagree on, although this has not always been apparent since our discussions have naturally tended to focus on the latter.

A major reason for my participating in forums like this one is to test my ideas by debating them with people with differing views. SD has helped me to clarify my thinking in many areas as well as providing a great deal of intellectual stimulation. He will be greatly missed. Let’s hope that he eventually decides to return.

[ January 02, 2002: Message edited by: bd-from-kg ]</p>

thefugitivesaint

bd-from-kg said:

I say, "Here, Here!" *claps hands with great enthusiasm*

Mageth

Great post, bd-from-kg. I hope SD somehow reads it.