SingleDad

Evidentiary Arguments

An evidentiary argument is a particular type of argument used to prove what is actually the case out of what is possibly the case. It thus differs from a logical argument, which is used to prove what is or is not possible.

Logical arguments are useful; it is certainly valuable to explore what might be or could be, but the realm of possiblity (those collections of possible facts which are not logically contradictory) seems much larger than the realm of actuality, that collection of facts which are actually true. However, as this argument will show, an evidentiary argument must make use of contrafactual logical possibility.

We must first, of course, define what we mean by a fact. A fact is a statement that can be known directly to be true. We will further qualify fact into three categories:

1) actual fact: A statement actually known to be true
2) possible fact: A statement that, if true, would be directly known
3) actual nonfact: A possible fact that contradicts an actual fact

In order for evidentiary arguments to have any weight, we will assume that the reader accepts as true the objectivity of real world and the validity of perception in permitting us to make directly true statements about that objective world. While it is possible to deny these statements, such a denial says only that evidentiary arguments are not meaningful, it says nothing about the character of valid evidentiary arguments. Such a metaphysical discussion is beyond the bounds of this work.

We can define a method for establishing facts: perceptual observation. A statement is a fact if the truth of the statement could be established by direct perceptual observation. A statement is an actual fact iff it is directly observed to be true. A statement is an actual nonfact if it contradicts a fact directly observed to be true.

An evidentiary argument proposes that a particular hypothesis entails some actual fact. In formal notation we represent the hypothesis as H, an actual fact as F, a possible fact as F', and an actual nonfact as ~F, and the entailment claim of an evidentiary argument as H <-> F.

To make an evidentiary argument, we must use logical entailment, not logical implication. To be satisfying, an hypothesis must explain not only the facts we know, but explain why the facts are not somehow different. In other words, we must show that if the hypothesis were false, it would be logically impossible for the facts to be true. Logical entailment captures that intention; logical implication is silent on whether the facts might or might not be true if the hypothesis were false.

From a logical standpoint, we can prove entailment from implication using the logical inverse: H <-> F iff H -> F and ~H -> ~F. It is clear that we can show the truth of H from this entailment: (F & (H <-> F)) -> H. It is also necessary to assume the possibility qualifier: (~H -> F'). If the negation of an hypothesis does not imply a logically possible fact, then we are making a logical argument, not an evidentiary argument; we are essentially saying that the negation of an hypothesis is logically impossible.

It is relatively easy to prove that H -> F; usually an hypothesis is offered because the direct implication is obviously plausible. But proving that the hypothesis is the correct hypothesis means proving the entailment, not just the implication.

The possibility qualifier coupled with the contrapositive gives us a way to prove the entailment. If ~H -> F', then we can examine the possible fact and determine (by observation) whether it is an actual fact or an actual nonfact. If we determine that the possible fact is an actual nonfact, we can express this as an implication: F' -> ~F. Since F is an actual fact and known to be true, then we can transform this implication by the contrapositive to F -> ~F', therefore ~F' -> H. Since F is true, ~F' is true therefore F -> H is true, therefore, again by the contrapositive, ~H -> ~F. Since we have now shown that both H -> F and ~H -> ~F, we have proven the entailment and thus the truth of H.

This formulation shows why falsifiability is an important criterion to the establishment of an evidentiary argument. If it cannot be shown that the negation of an hypothesis leads to an actual nonfact, then we cannot prove the inverse formulation and we are left only with the unsatisfying direct implication H -> F, which doesn't tell us much about whether our hypothesis, H, is actually true because it is unknown whether ~H -> F is true or false.

We can restate these criteria in ordinary language:

1) Possibility Criterion: Does the negation of the hypothesis imply a logically possible fact?
1) Relevance Criterion: Is the implication itself true?
3) Determinability Criterion: Can the possible fact implied by the negation be determined to be either an actual fact or an actual nonfact?
4) Actuality Criterion: Is the possible fact implied by the negation an actual nonfact?

If all four of these criteria are met, then we can determine that the evidentiary argument is both well-formed (by criteria 1-3) and true (by 4).

Note that the generality of evidentiary arguments holds even if different facts are implied by the truth and the falsity of the hypothesis. In other words, the form and truth of an evidentiary argument still holds even if H -> F1 and ~H -> ~F2 where both F1 and F2 are actual facts. This feature is useful because it allows us to determine the truth of competing hypotheses that both imply a large set of actual facts by identifying a possible fact where the competing hypotheses differ in their implication. I.e. H1 -> F1 and H2 -> F1 but ~H1 -> F2 and ~H2 -> ~F2. If F2 is an actual fact, then it is obvious that H1 is false and H2 is true.

It should be noted that, given this definition of an evidentary argument, the truth of an hypothesis is always relative to the known facts. It is not meaningful to talk about the truth of an hypothesis established by evidentiary arguments without regard to the evidence; indeed it is the contention of an evidentiary argument that while an alternative hypothesis might be true (because it would entail logically possible facts), it is not actually true because it implies actual nonfacts.

We also see that we can talk about evidentially equivalent hypothesis. Two hypotheses are equivalent if they imply the same set of facts. This equivalence can be actual or complete. Two hypotheses are actually equivalent if they predict the same actual facts, but they predict different possible facts which are not yet known to be actual facts or nonfacts. Two hypotheses are completely equivalent if it can be shown that they always predict the same possible facts. For example, under general relativity, it is can be shown that in a gravitational field the hypothesis that space remains constant but objects change length is completely equivalent to the hypothesis that space changes shape but objects remain constant; both hypotheses imply the exact same observational facts. Therefore, evidentially speaking, these two hypotheses are not different, they are actually the same hypothesis. The metaphysical implications of this equivalence is left to the speculation of the reader.

Now it is obvious that in the real world facts and implications are not known with logical certainty. But we can use probability theory to recast the definition of evidentiary arguments into probabilistic form.

In probability theory, we continue to denote our predicates in logical form. H denotes the hypothesis, and F, F' and ~F denote an actual fact, possible fact and actual nonfact respectively. However, instead of the strict implication operator, we denote the relationship between two predicates with the general probability function P(). The expression P(A) denotes the a priori scalar probability that A is true; the value is usually the probability "size" of A divided by the size of A plus the size of all logically possible alternatives to A. The expression P(A|B) denotes the scalar probability that A is true given that B is definitely true. P(A|B) represents the probability that the implication B -> A is true; if the implication is certain, then P(A|B) = 1.

By this notation, we represent the implications in the evidentiary arguments as follows:

H -> F translates to P(F|H)
~H -> ~F translates to P(~F|~H)

Now we know the truth of F and ~F, so we would like to recast these probability statements in the reverse form; we would like to determine the value of P(H|F), i.e. what is the probability of H given the fact of F. To determine this value, we must use Bayes Theorem.

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

To evaluate this equation with confidence, we have to assign plausible numerical values to each of the terms.

Since we have (presumably) formulated our hypothesis intelligently, we can feel confident that P(F|H) is relatively high number; i.e. it is very probable that if our hypothesis were true, we would observe the actual facts known to be true.

More importantly, though, we want to make sure that P(F|~H) is a small number. Since P(~F|~H) = 1 - P(F|~H), we want to make sure that P(~F|~H) is a high number. In other words, we want to forumulate our falsifiabily criterion as generally as possible: We want to feel confident that if any other logically possible nonequivalent hypothesis were actually true, we would probably observe an actual nonfact.

Lastly, we see that our evidentiary criteria need to be stronger the lower the a priori probability of the hypothesis (without regard to the evidence), i.e. the lower P(H) is, the higher P(F|H) and P(~F|~H) need to be to determine that P(H|F) is high. This is the formalization of the emergent criterion that extraordinary claims require extraordinary evidence.


Evidentiary Arguments and Theism

We can see that many supposedly "evidentiary" arguments for theism do not fulfill the criteria for evidentiary arguments.

It is sometimes asserted that if a god did not exist, then nothing would exist. However, this is not an evidentiary argument, because the consequent is not a possible fact. It is not possible to know for a fact that nothing exists, because if nothing exists, we would not exist to know that fact. Although this argument can be made on metaphysical grounds, it is not an evidentiary argument.

Another argument that fails on evidentiary grounds is the argument from belief. The fact that many people believe in the existence of a god is held to be evidence that a god exists. Now it is certainly true that if a god existed, people would tend to believe in its existence. We can represent these predicates as G (a god exists) and B (belief in a god exists). Thus it is obvious that G->B (or P(B|G) is high). However, this argument fails because the inverse fails: It is not true that the nonexistence of a god would imply a lack of belief. In other words ~G -> ~B is not a plausible entailment (or P(~B|~G) is not very low). We know this implication is implausible because in the general case it can be proven (on evidentiary grounds) that people believe in things generally held to be false (such as UFOs, alien abductions, honest politicians and tasty British cooking). Worse yet, people hold contradictory beliefs. Generally it seems that lack of existence of something often has no effect on the fact of belief or lack of belief. If the theist wishes to use the fact of belief, he must show (via evidentiary arguments) that there is some special quality of theistic belief (B') that would persuade us that the actual nonexistence of a god would entail the nonexistence of that quality of belief (e.g. ~G->~B' or P(~B'|~G) is high).

[ December 14, 2001: Message edited by: SingleDad ]

[ December 15, 2001: Message edited by: SingleDad ]</p>

jpbrooks

Argumentation is a new and interesting area of study for me.
I have been curious about how arguments about historical events are to be carried out and assessed. For example, are historical events to be viewed as facts, (even though they cannot be directly observed), or as beliefs? Historical data that we only have access to from secondary sources seems to be more akin to beliefs than to facts.
But I'm interested in what others have to say on the topic of Evidentiary Arguments.

Ernest Sparks

Singledad,

Do you think any facts are known directly whose negations are untenable? For example, electrons exists, because radios, TVs and other equipment wouldn't work if they didn't exist. But does anybody really know whether or not some distinctly different explanations for these devices are not possible?

[ December 15, 2001: Message edited by: Ernest Sparks ]</p>

SingleDad

The existence of electrons (actually the relativistic electron "quantum field", of which actual electrons are epiphenomena) is a hypothetical proposition that is proven through evidentiary argument. We do not have direct perceptual knowledge of the existence of electrons, therefore their existence is not a "fact" according to my technical definition.

The actual facts that evidence the existence of electrons are our perceptual experiences, from the prosaic (such as turning on a light) to the esoteric (such as the outcomes of advanced physics experiments). If electrons did not exist as we believe them to, then our experiments would have turned out differently.

Indeed the the "truth" of the existence of electrons is relative to the known facts that evidence their existence. If some other hypothesis were to exist, it must either be actually or completely equivalent to the hypothesis of the existence of electrons and thus, on the basis of the evidence we have to date, the same hypothesis, merely worded differently.

Of course, if an alternative hypothesis implies a different determinable possible fact (perceptual experience), it would indeed be different, and we could distinguish between the existing hypothesis and the alternative based on the determination of that possible fact as an actual fact or nonfact.

It should be noted that an alternative hypothesis would still be actually equivalent to the existing hypothesis relative to the facts known today; the metaphysical implication seems clear then that today's hypothesis would be a true special case of the more general alternative hypothesis under the circumstances that distinguished today's facts from the relevant possible fact(s) that would support the alternative hypothesis.

Ernest Sparks

An example of a conceivable distinct theory on cathode ray experiments in the 1890s was ether breakdown by electical stress. But after Thompson's elegant ray bending and straightening in crossed magnetic and electrostatic fields was demonstrated, no one wanted to pursue this any more, except maybe Sir Oliver Lodge, who loved the ether concept. It is fun to consider a guided wave explanation of the bending of cathode rays possibly anticipating the 1920s wave theory of the electron, but the persistent electron particle had already prevailed by the start of the twentieth century.

I don't know if such an alternative could have survived later scrutiny, but I am not prepared to say that it would have been equivalent to the electron theory we know, except in the need to explain the same set of facts.

[ December 16, 2001: Message edited by: Ernest Sparks ]</p>

bd-from-kg

SingleDad:

I’m not sure where you’re going with this. It appears that you are trying to lay a foundation for rigorously “proving” scientific theories. This is impossible in principle. Much of what I have to say below just expands on this.

1. Logical formulation

First, as to the definitions of “facts”:

According to these definitions the domain of “possible facts” is very restricted; it consists entirely of statements to the effect that I am currently having a perception. Even a description of this perception would involve conclusions, and would therefore not be a “possible fact”, much less an “actual fact”. (None of this is a problem in itself; it only becomes so in view of what follows.)

But nothing about the “real world” is logically entailed by the fact that I am currently having a perception. Thus, let P be “I am currently having perception p” Clearly P does not logically imply anything about the “real world”. And since entailment is a symmetric relation (A entails B iff B entails A), it follows that no hypothesis about the “real world” can entail P (in your sense).

Not so. For example, take a simple hypothesis like “if you mix pure sodium and water you will always get an explosion”. The negation of this hypothesis is “If you mix pure sodium and water you won’t always get an explosion”. This doesn’t imply any “possible facts”. Yet the original hypothesis is clearly meaningful and not tautological. It is a scientific hypothesis (in fact, a very ordinary, typical one) capable of being tested.

From this point (until the next section) I will assume that the kind of hypothesis you have in mind is a scientific hypothesis – i.e., a hypothesis that there is some kind of regularity or pattern in one’s perceptions (which is taken to correspond to a regularity or pattern in the “real world” which is assumed to be causing the perceptions). Not only are such hypotheses interesting in themselves, but it is essential to establish some such hypotheses before you can get anywhere with establishing any other kinds of interesting empirical conclusions.

Quite true. That’s why it is a truism that scientific hypotheses (in fact, empirical hypotheses in general) cannot be proven. Indeed, it’s not clear what you mean by “the correct hypothesis”.

Not really. Falsifiability means only that there are possible facts F such that H -&gt; F, and therefore ~F -&gt; ~H. It says nothing about whether ~H implies anything.

Actually it’s almost always clear that ~H does not imply either F or ~F (in the sense that F or ~F can be deduced from ~H). Normally ~H is simply a denial that the regularity of pattern described by H exists. And from such a denial very little can be deduced. And yes, it’s “unsatisfying” that no specific hypothesis about the “real world” is implied by any perception or set of perceptions, but that’s the way it is.

More generally, no set of “actual facts” in your sense – i.e., true statements to the effect that certain perceptions are occurring – imply anything whatever about future perceptions. Not only do our current perceptions tell us nothing (in a strict logical sense) about the “real world”; they tell us nothing about the future.

Basically, in an empirical metaphysics you can’t get anywhere, ontologically speaking, without assuming the Principle of Induction and Occam’s Razor. They’re the only things that provide any kind of connection between different perceptions. And they cannot be “proved” or “justified” by any kind of empirical evidence. They simply have to be asserted as metaphysical axioms.

2. Probabilistic formulation

For most nontrivial cases this “definition” of P(A) is meaningless. This is particularly clear in the case in which A is a statement of a scientific law – i.e., of a universal correlation between events of a certain description, such as a cause/effect relationship.

Quite true. But what constitutes a “plausible numerical value”?

This is really a misuse of Bayes’ theorem. When this theorem is applied in the kind of context for which it was intended, the terms on the right side can be assigned values in some sensible way. For example, say that the population in a certain area is 80% white, 20% black, and that the crime rate for blacks is four times that of whites. If we ask “what’s the probability that this crime was committed by a black?” we can apply Baye’s theorem as follows. Let F be “the crime was committed”, H be “the crime was committed by a black”. Then we can plausibly set P(H) = 0.2, P(~H) = 0.8, P(F|H) = 4x, P(F|~H) = x (with x unspecified). We then get:

P(H|F) = (4x * 0.2) / ((4x * 0.2) + (x * 0.8)) = (0.8x)/(1.6x) = 0.5 .

The initial probabilities used in this reasoning can be questioned on various grounds, but at least they come from somewhere; they weren’t drawn from a hat. But if H is something like “God exists” or “A invariably causes B” there seems to be no nonarbitrary way to assign the initial probabilities. In fact, it isn’t even clear what “probabilities” would mean in such cases. Either God exists or He doesn’t; either the causal relationship between A and B holds or it doesn’t. There is no “domain” of possible “outcomes”. Thus the concept of a “probability” would seem to be meaningless for any universal statement – i.e., one without any “free variables” – because any such statement is either always true or always false.

In a vast number of cases, although P(H), P(H|F), etc. are theoretically meaningful, in practice their values are pretty much unknown. At best one might be able to say, for example, that P(F|~H) would seem to be much lower than P(F|H). The only real value of Bayes’ theorem in such cases is qualitative; it shows, for example, that if P(F|H) &gt; P(F|~H), then F is evidence for H in the sense that whatever initial probabilities are plugged in, P(H|F) &gt; P(H). It also shows, as you point out, that if P(H) is assigned a very low value, P(F|H) must be much greater than P(F|~H) to get any specified value of P(H|F). [For example, to get P(H|F) &gt; 0.5 you must have P(F|H)/P(F|~H) &gt; P(~H)/P(H).]

3. Evidentiary Arguments and Theism

But this is a good evidentiary argument: in general the fact that a great many people believe something really is good evidence that it’s true. For example, many people believe that Columbus is the capital of Ohio whereas few believe that Akron is. And it turns out that Columbus really is the capital of Ohio and Akron isn’t. Similarly, the great majority of people believe that an object dropped from an airplane will generally fall to the ground, that if a baby isn’t fed it will soon die, that eating veggies is healthy, and that using crack cocaine is a bad idea. Oddly enough, all of these widespread beliefs are true. In general, for any proposition X imagine two cases: (1) you have no evidence regarding it except that the great majority of people believe it; (2) you have no evidence regarding it except that almost everyone disbelieves it. Only a fool would suppose that he was not far more justified in believing X in the first case than in the second. Which is to say that widespread belief has strong evidentiary value. Your point that many false beliefs are widely held shows only that it is not an infallible indicator of truth.

In fact, we can express this point in terms of Bayes’ Theorem. Let F be “the great majority of people believe H”. Obviously P(F|H) &gt; P(F|~H) (i.e., widespread beliefs have a positive correlation with “reality&#8221 ) , and therefore P(H|F) &gt; P(H). That is, F constitutes evidence for H.

So this argument cannot be dismissed on these grounds. I think it can be dismissed on other grounds, though.

Since no one has the time to examine the evidence regarding every question, all of us take the “short cut” of accepting the popular opinion about lots of things. Thus, I believe that a Mercedes is likely to be a better-built car than a Hyundai, that it’s safer to fly in jumbo jets than in small private planes, that it’s wise not to buy anything from telemarketers, and lots of other things, because most people think so (in fact, because i have the impression that most people think so), and not because I’ve studied the evidence. There’s nothing wrong with this; it’s perfectly rational. But ultimately, to be justified, a belief must be based on evidence other than the fact that most people subscribe to it. If popular belief were to be accepted by everyone as an adequate reason for believing in something, false popular beliefs would persist indefinitely. Thus for each popular belief, it’s essential that some people examine it to determine whether it has any underlying evidentiary support. A person who does this is called a “skeptic”. Thus when a belief is examined from a skeptical standpoint the fact that it is widespread is automatically out of court. Now when a question is “put in play”, it is usually taken for granted that the idea is to discuss it from a skeptical point of view. In this context the state of public opinion may not be taken into consideration. If you are seriously examining whether lower speed limits save lives, you don’t accept the argument that most people think they do; you look at actual accident statistics. For the same reason, in a serious discussion of whether God exists, the popular opinion that He does is irrelevant.

[ December 19, 2001: Message edited by: bd-from-kg ]</p>

SingleDad

bd-from-kg

It seems to me that your rebuttal rests entirely on the grounds that it is impossible or implausible to believe that:

• perception has any relationship to reality
• useful facts can be known
• the real world has any regularity
• any false hypothesis would imply a contrafactual observation
• probability theory is meaningful

All of these assertions go against the presuppositions of my argument and are thus beyond its scope. It is frankly unclear why you have attempted a rebuttal of my argument when you are actually rebutting my presuppositions. However, the presuppositions are clear, and my intention is to analyze evidentiary arguments under these presuppositions. Indeed, these presuppositions are fairly close to your definition of rationality as posted in another thread, so it is doubly unclear why you would contravene them for the purposes of rebutting an argument that depends on them.

In this defense, I talk about the "presupposition" of objectivity, regularity, the ability to know facts perceptually. I'm using this term relative to my argument to denote beliefs that are not addressed, not as claims that these propositions must be metaphysically presupposed. I am frankly explicit in the OP that these sorts of questions are outside the scope of my argument.

This is a nitpick. One can extend the definition of "fact" to uncontroversial statements about actual perceptual experiences. My argument is not about the nature of facts, but rather about how we can reason from facts to hypotheses that can't be directly experienced.

I'm not sure if you're simply asserting that my argument is false as a prelude to a proof or attempting to show that it cannot be true. If you are doing the former, then it is probably better to simply state your intention.

I'm also not at all sure if you're claiming here that perception gives us no reliable information about the real world. If you're coming at this from a perspective of platonism, then the entire concept of the evidentiary argument is absurd, and a detailed critique of my argument is unnecessary; indeed it addresses issues entirely outside the scope my my argument.

It is not at all "clear" that perception cannot entail anything about the real world. Indeed, under the presupposition of objective reality (which can be concluded, but is beyond the scope of my argument) a perception does entail that objective reality caused that perception and no other possible perception. So your prima facie case fails.

The more general case is clearly not obvious. It is not at all obvious that perceptions about the world entail hypotheses. Were such the case, then my argument would be an exercise in triviality. But not everything that is true is trivially obvious.

You're misstating the hypothesis and mixing in the perceptual experience. All you are showing here is that it's possible to formulate imprecise hypotheses that aren't falsifiable.

Your version of the hypothesis is not only atypical, it is unfalsifiable and thus not a scientific hypothesis. We can form the hypothesis more scientificially by saying that, "pure sodium and water are reactive under laboratory conditions". We phrase the implication as, "if pure sodium and water are reactive under standard laboratory conditions then I will measure (experience) a rapid rise in temperature and pressure." The falsification would be, "if pure sodium and water are not reactive, I will measure a constancy in temperature and pressure." If I were measure a constancy of temperature and pressure, then I know that sodium and water are not reactive. Likewise, if I measure a rise in temperature and pressure, I know that it is not possible that sodium and water are reactive under the specified conditions.

Words like "always", "sometimes" or "never" are not scientific precisely because, as in your example, they are not falsifiable. This is why science requires a degree of talent: it is nontrivial to be able to frame hypotheses in a falsifiable manner.

As mentioned in the preamble to my argument, this sort of regularity is presupposed when examining evidentiary arguments, it is not the subject of scientific hypotheses. This sort of regularity must be presupposed to construct any plausible implication. Again, you are critiquing subjects that are beyond the scope of my argument.

Again, if scientific arguments cannot be proven, it is entirely unclear why you are bothering to critique an argument that presupposes things you don't hold to be true.

I disagree. Indeed this form of falsifiablity does not seem to allow us to draw any inferences about the truth of hypotheses. There is no a priori definition of falsifiability; we are better served to use a definition that will help us find the truth.

Not at all. Again the regularity of objective reality is not at issue in this argument; were it so, then no hypothesis could plausibly imply any set of facts, and, as I stated, evidentiary arguments would be generally useless.

Yes indeed, very little can be deduced; indeed, according to your formulation, we cannot deduce anything about the real world from our perceptions. Again I have to note, if you do not believe in the value of perception to construct true statements about the real world, your rebuttal would be more honestly and sincerely directed at the presuppositions of objectivity and realism than against this argument for a definition of evidentiary arguments.

I stated explicitly that one has to presuppose objective reality for evidentiary arguments to be able to speak the truth, and indeed such a conclusion can be made using induction and parsimony. Perhaps you didn't read the original argument carefully. I am not making a metaphysical argument for empiricism here, but rather arguing for a definition of an ontological method under empiricism.

It is unclear whether you are critiquing my argument or probability theory in general. P(A) denotes the general probability function, and probability theory assumes that we can determine probabilities in general with a reasonable degree of rigor. I do realize that my probabilistic argument is on the thin side; it is my intention to frame this argument on the logical basis of falsification. It will fall to another article to focus more heavily both on probability mathematics and a more rigorous definition of a priori probabilities of hypotheses. There are some metaphysical questions as well in the extention of the logical to the probabilistic which I have handwaved over.

It is also an error to assume that scientific hypotheses are "universal" statements. Rather, scientific statements are applicable to and relative to known facts. Because we presuppose that the universe is regular, we tend to believe that we can extend our hypotheses to unknown facts, but such an extension is again beyond the scope of my original argument.

Well, admittedly my case for the plausibility for assigning terms to the right-hand side of Bayes theorem is thin, but since I do make a case for their values, I cannot see how my argument "misuses" Bayes theorem.

Part of the implication of my argument is that if there's no way to assign any plausible numerical value to the a priori probability of an hypothesis, then it is indeed impossible to evaluate it evidentially, and thus the hypothesis is nonscientific. It should be noted that scientific hypotheses are not stated as "A invariably causes B", but talks rather about the probability of a causal relationship between A and B under specified cirucumstances.

Generally, these forms are more amenable to assigning an a priori probability. For instance if there is an observed correlation between two events, then the can count up the correlations and noncorrelations and assign that value to the a priori probability of a causal hypothesis.

More importantly, the a priori probability of an hypothesis is not the critical issue. To prove an hypothesis, one wants to make the falsification as general as possible. One should construct one's hypothesis so that any alternative hypothesis would imply something different about the actual facts. Given enough facts, any true hypothesis can be demonstrated to an arbitrarily high degree of probability.

Much work has been done on the interative use of Bayes theorem in evidentiary arguments and in assigning plausible values to the relevant terms. A survey of the existing literature will definitely be included on a more thorough examination of probability theory as it relates to evidentiary arguments.

I will address the remainder of the rebuttal at a later date.

[ December 19, 2001: Message edited by: SingleDad ]</p>

Synaesthesia

This strict logical sense doesn’t seem to tell us very much about perception, does it? As a matter of fact our perceptions do have quite a bit of information and they do allow us to anticipate future experiences. With our perceptions, we can evaluate how well we are able to anticipate the future and why.

We are not just fed a sequence of images. Each perception is developed by, and develops our theories about the world. There is a continuous interplay between how we understand the world and how we see it. That is why I think that we should be wary of too sharp and too clear a distinction between what is a “fact” and what is a “theory”, because the two are implicitly meshed together at every level of cognition.

The principle of induction is a theory about how human beings learn from the world. It’s a simplification for what goes on, there are many process at work in our minds rather than one, but philosophers have found it very useful. However, neither the epistemic principles upon which science operate nor the way humans interlink their perceptions are based upon this metaphysical presupposition.

Science goes by way of comparing different theories about this world of perception. A characteristic of scientific theories, those that survive the relentless selective pressures at work, are that they portray an evolving world with subtle and pervasive consistencies. These are simply the theories that have turned out the best. We don’t presuppose that the world has underlying constants, we observe it and we work with it. We are not statically grounded by a single notion of induction from the past to the future.

You know, a lot of people think that hearsay is not solid evidence - Especially people with a vested interest in getting accurate information. (Beyond the simple fact of opinion, does not the the demographic add much to our understanding?)

Despite my unfamiliarity with Baye’s theorem, (I’ve resolve to go back and look at SD’s proof of it.) it does seem right to suppose that F constitutes evidence for H. However, it also constitutes evidence for M, the theory that the notion of a guiding deity is comforting to people, that it is useful for the control of society and it is a belief that has persisted BECAUSE it’s good at persisting. Which theory is better is beyond the scope of simple popularity of belief.


Single Dad,
I can see the value in the perspective of empirically equivalent but logically contradictory theories being considered identical. However, as I mentioned earlier, I see perception as being a very large element of how we understand things. Different formulations or functional accounts of a theory may very well have a pivotal effect upon how we build upon the theory and relate it to the rest of our knowledge. However, in most cases, they would be the same FAPP.

Regards,
Synaesthesia

SingleDad

bd-from-kg

I argue that the question of what is or is not a good evidentiary argument is not whether there's a correlation between an hypothesis and a true conclusion, but whether the correllation can be expressed in a falsifiable manner.

I don't state that nonevidentiary arguments cannot be true, merely that evidentiary arguments are a particular type of true argumentation. Showing that a particular true argument is nonevidentiary is not a rebuttal of my argument.

The argument that people believe objectively true propositions is not an argument that belief constitutes evidence in the objective truth of propositions, because there are known examples where belief does not constitute evidence.

From a logical standpoint, if one wishes to use fact of belief as a falsification criterion of an hypothesis about an objective claim, one must construct the implication such that if the objective claim were false then belief would not exist. Since this implication is known to be false (in probabilistic terms, P(~F|~H) is not high), the argument is not evidentiary.

Certainly one can use opinion (in some cases) to have a reasonable assurance that a proposition is probably true, however this is a true nonevidentiary argument, and, as such, is not prima facie evidence that my construction of evidentiary arguments is false. Since I don't claim that only evidentiary arguments are true, it is again unclear why this example is discussed as a rebuttal.

To rebut my construction of evidentiary arguments, it seems that one must show that a valid evidentiary argument leads to a false conclusion, not that nonevidentiary arguments can lead to true conclusions.


Synaesthesia

Please note that I don't attempt to prove Bayes' Theorem. My intention is to show that Bayes' Theorem is the probabilistic equivalent of the inference of entailment from falsifiability. In the logical form, an evidentiary argument concludes the truth of F -&gt; H from the knowledge of F, using the implications that H -&gt; F and ~H -&gt; ~F. In the probabilistic version, an evidentiary argument concludes a high probability of P(H|F) from the certainty of F (P(F)=1) using high values of P(F|H) and P(~F|~H). The arguments are obviously symmetrical.

Essentially, I am arguing for the logical basis for using Bayes' Theorem. I show that falsification is a necessary step for proving entailment in the logical case and thus the falsification term of Bayes' Theorem is logically justified.

Well, the metaphysical implication of evidentiary equivalent but supposedly mutually contradictory logical theories seems to be that the supposed distinction itself is false. In the general relativistic case it seems to be a false distinction to talk about the length of an object and the gravitational field as if they were separate things. They are, evidentially speaking, the same thing, and the distinction is thus arbitrary or false.

[ December 20, 2001: Message edited by: SingleDad ]</p>

bd-from-kg

SingleDad:

I haven’t time to reply to your longer reply, nor to compose a new post for the “Nature of Metaphysical Axioms” thread at this time because of the Christmas rush. (I plan to do both later.) But I have time (barely) to respond to your last post now.

With respect to my comments about your statement, “Another argument that fails on evidentiary grounds is the argument from belief”, you say:

OK, I was a little sloppy in saying that the argument from belief is a good “evidentiary argument”, since you have defined this phrase in your own personal, idiosyncratic way.

To illustrate just how idiosyncratic your definition of an “evidentiary argument” is, consider the following: “Jones was killed here in this room at 3:15 on Nov. 2 by a 35mm bullet. Smith is known to have been in the area at that time, and he recently stole a gun that fires this type of bullet. A gun of this type, with Smith’s fingerprints on it, was found in a dumpster outside the building the next day, and lab tests show a good match between the fatal bullet and this gun. Moreover, traces of blood that lab tests show are almost certainly Smith’s were found on a shoe Smith wore that day. And Smith had just found out a couple of days earlier that Jones had bilked him out of so much money that he is bankrupt.” According to your definition, this is not an “evidentiary argument” for the hypothesis that Smith killed Jones, because this hypothesis does not imply (or even make it especially likely) that Smith stole a gun of the appropriate caliber, that a gun of this type would be found in the dumpster, that Jones’s blood would be found on Smith’s shoe, that Jones had defrauded Smith, etc. Yet this argument, which is based entirely on things that would ordinarily be called “evidence”, would most likely be good enough to convict Smith of murder.

But your original statement was not that the “argument from belief” is not an “evidentiary argument”, but that it “fails on evidentiary grounds”. Unless you also have a personal, idiosyncratic definition of “evidentiary grounds” that you haven’t told us about, this can only be interpreted as meaning that the widespread belief in God is not evidence that God exists. Now “evidence” is a very common word in the English language with a clear meaning: a fact F is evidence of a hypothesis H if F makes it more likely that H is true. Formally, F is evidence of H if P(H|F) &gt; P(H). If we are using the word “evidence” in its ordinary, everyday meaning, it’s obviously true that the fact that something is widely believed is evidence that it’s true. So the “argument from belief” fails on “evidentiary grounds” only if you define “evidentiary grounds in such a way that the argument in the last paragraph also “fails” on “evidentiary grounds”. This seems to me to be an abuse of language.

If your meaning was only that the “argument from belief” fails to satisfy your personal, idiosyncratic definition of an “evidentiary argument” rather than that it fails to support the conclusion, you’re perfectly right. But there would seem to be little reason why anyone but you should find this conclusion interesting.