I’d say evidence is that which provides support for the entirety of a claim, or part of that which provides support for an entire claim if you also have evidence from other experiments. I do feel that there is an amount of observations that’s sufficient to make a universal claim; I don’t have any problem with someone suggesting multiple, consistent observations are evidence for multiple consistent occurrences. And actually observing all cases would be evidence for all cases.
That 99 ravens may be black means nothing as to whether the 100th is, and is no more evidence that they all will be than if you had 98 or even just 1 observation. An observation must back up the entire premise to be considered evidence for that premise.
I would say the weaker, more appropriate phrasing would be “All our observations suggest that charges tended to act like this…”, since the entirety of the premise is thus reduced to the exact data used to support it.
That still leaves the underlying assumption that there is a consistensy, that we can predict unknown results from known. That’d be filled with data about the apparent unchanging nature of physical laws (though i’m no scientists myself, so I wouldn’t know what they’d be). You still end up with that assumption though that in general that which hasn’t been observed will tend to match up with what has been, to a greater or lesser extent depending on the uniformity of results. And that’s just that, an assumption.
No one’s ever taken me to the lab to check, though an awful lot of other humans (and other similar entities) have been observed: is there any evidence at all for the claim that my body is made up of carbon-bearing organic molecules?
So the difference between the strong and weak phrasings is the difference between using observations as support for the claim P and using observations as support for the claim “Observations appear to support the claim P”?
Well, presumably you’ve had injections or medical treatment which rely on your body being consistent with humans that have been studied; you could claim that as evidence that your body reacts as would one of carbon-bearing oxygen molecules. But if there was no such link to your particular case, i’d say no, there’d be no evidence.
Sort of. The strongest, informal phrasing which would probably be most common is “P is true”. A scientist would tend to use your latter example when talking about a particular case (and what I would consider the most accurate phrasing), and the former when talking about a theory.
I think I see the objection. Please correct me if I mess this up.
As long as there is at least one raven, if all ravens are black then some black things are ravens. However, some black things could be ravens without all ravens being black. Sound right?
(not that it matters! Sorry for the tangent, the thread is confusing enough…)
That seems a bit of a cop-out; I don’t feel any of my medical treatments have been worthy of consideration as direct observation of organic molecules, and if I didn’t feel less-than-universal observations supported universal claims, I would not feel any of the treatments I have had would indirectly establish my body to be made of organic molecules either (at best, they establish that whatever I am made of has, on certain occasions, reacted similarly to the way many organic molecules have on many occasions).
However, if it helps, I will reformulate the example (without any essential difference, of course): there is, in the yard right now, a chirping bird (not a raven, I’m afraid, but let that not deter us); as best I know, this particular bird has never been subject to medical treatment or injection or any more intense observation than a couple minutes of “Oh, there’s a bird in my way”. Certainly, I am unfamiliar with any previous experiment upon it. It is my steadfast contention that this bird, like all birds, possesses a heart, a brain, lungs, and so on; the reason I hold this is because I understand that every bird ever examined has been like so. However, I have never opened up this particular bird to actually check, and certainly the possibility exists that it is actually filled with candy instead. Do I have evidence for my contention, then? [And, if you consider the questions to be separate, let me also ask, do I have justification for making it/believing it?]
Well, alright, naturally, there is different phrasing when discussing particular cases and whole theories, as these are different things to talk about. My whole concern with science is as regards the discussion of scientific theories, so let us focus on that, rather than particular cases. Do we agree that scientific theories are unabashedly given as universal claims, then? Is it not also the case that scientists feel they have evidence for their theories?
Of course observing 99 black ravens doesn’t prove that the 100th raven will be also be black.
But which way are you going to bet?
Suppose I make a wager with you. I have a jar with 100 balls. I allow you to draw out 99 balls at random and observe their color. If you reached into my jar and pulled out 99 black balls, what odds would you give that the last remaining ball would be black as well?
Would you refuse to make such a bet? If I offered you an even money bet that the remaining ball was not black would you accept? It seems to me that after you’ve drawn out 99 black balls at random, odds of 99 to 1 that the remaining balls is not black would be fair. It would be foolish of you to refuse to bet if I gave you odds of 98 to 1 or better.
So the 99 black balls ARE evidence of the color of the remaining ball…if we are able to make certain assumptions about how those balls were selected. If we change the conditions and I don’t allow you to draw balls at random, but instead I look into the jar and hand you the ball of my choice, I’d agree that the 99 balls I showed you don’t provide evidence for the color of the remaining ball. Or if I was able to add extra balls after your 99 observations, or if I was able to change the color of a ball in your hand before you had a chance to observe it, and so on.
But human beings routinely bet their LIVES on things that aren’t “proven”. How do you know that apples aren’t poisonous? How do you know that the next time you step out of the house that you won’t fall into the sky? How do you know that when you turn around a leopard hasn’t crept up behind you? How do you know that when you say “Supercalifragilisticexpialidocious” it won’t cause the sun to explode?
All logic has to work this way, because for logic to “prove” anything, you have to accept the premises. All men are mortal, Socrates is a man, therefore that proves Socrates is mortal according to your logic. But how do you know that all men are mortal? How do you know Socrates is a man? What makes you willing to accept the premises? The only reason you have for accepting any premise is not deduction, but induction. You know that all men are mortal, but even if you deduced that from other premises, what caused you to accept those earlier premises? At some point you either have to throw up your hands and accept inductive reasoning, or declare that there are certain premises that you accept without proof.
And this is neccesary if you want to continue to survive, because how do you know that breathing and eating are neccesary for you to continue to survive? You can declare that you have no proof that human beings need to breathe to survive just because every living human being you’ve ever observed died if prevented from breathing. But if you don’t accept the need to breathe, you’re not going to be alive any more, and therefore you won’t be around to argue with any more. Every single living logician accepts inductive reasoning in their day to day life, the ones that didn’t wouldn’t be able to decide whether to drink water or hemlock.
OK, and I can illustrate this with the ball example again.
Suppose I have a jar with 100 balls, and I allow you to pull out balls at random and observe their color and label. You draw out 99 balls and observe that none of them are black, and they are labled various things…“apple”, “telephone”, “car” and so on, but none of them are labeled “raven”.
I then ask you to wager about the remaining ball. What are the odds that the remaining ball is not black but is labeled “raven”?
We know that at least 99 balls out of 100 were not black. If there were one black ball, the odds that it would be the last one picked are 99 to 1. Maybe there weren’t any black balls in the jar, but the odds that the last one is not black is at least 1 to 99.
Similarly, we know that at least 99 balls out of 100 were not labeled “raven”. So the odds that the last ball is labeled raven is AT LEAST 99 to 1. Since the labels have been all kinds of things, we have no idea what the last ball will turn out to be labeled…but we’re pretty confident it isn’t “raven”. And if we haven’t seen “soup” or “jam” we’re also exactly as confident that the last ball isn’t soup or jam. If we hypothesize that there are an infinite number of potential labels, then any label has a zero possibility. But for any real world label we’ve only got a finite number of possibilities. So infinity is out, but we’ve got some large but unknown number of possibilities. But since there were only 100 actual balls, the maximum possible odds for that one remaining ball is 99 to 1 for any potential label. It could be much smaller than that, but it’s at least 99 to 1.
So what are the maximum odds that the last ball is a non-black raven? .99*.01, or .0099. In other words, if I offered you odds better than 1 to 99, you should take the bet that the last ball won’t disprove the hypothesis that all ravens are black.
The reason looking at 99 black ravens and guessing that the 100th raven will also be black seems reasonable, while looking at 99 nonblack nonravens and guess that the 100th thing will also be a nonblack nonraven seems unreasonable, is that there are a lot more than 100 things in the world.
If there were only 100 things in the world, finding 99 nonblack nonravens would be just as good of evidence that all ravens are black as finding 99 black ravens. We have an intuitive sense that a sample of 100 ravens is a nontrivial sample of ravens–but a sample of 100 nonblack things is a pretty poor sample of nonblack things.
I’m afraid your probabilistic reasoning is flawed, Lemur866; in general, you couldn’t hope to justify inductive inference by the rules of probability alone, because the rules of probability are consistent with all kinds of probability distributions.
Specific steps that seem problematic:
Do you mean here to say that I’ve already picked 99 distinct balls out of the jar, with “the last one” being the sole ball I haven’t already picked? The only significant thing that having picked and returned 99 distinct black balls out of a 100-ball jar tells us, in terms of probability, is that the odds of picking a black ball next time are at least 99%… only because the odds are at least 99% that we’ll pick one of those same balls back up again. But it doesn’t automatically tell us anything about the probability of the one so-far unexamined ball being black; indeed, this depends heavily on the (as yet unspecified) probability distribution of barrel contents to begin with [i.e., what was the ratio between the a priori probability of the barrel containing 99 black balls and 1 non-black ball and that of it containing 100 black balls? This can run the full gamut from 0 to 1, and correspondingly will allow the probability we are interested in to run the full gamut from 0 to 1].
Same problem as above.
Same problem as above.
This assumes that all labels are equiprobable, which need not be the case. Again, it depends heavily on the a priori probability distribution of barrel contents our analysis uses. The assumption of equiprobability would also conflict with the style of argument above; after all, there are two possible blackness statuses for the last ball (IS BLACK and ISN’T BLACK), but you felt that (conditional on information about other balls) the probabilities of the two weren’t equal.
Same problem as above (the one about the assumption of all labels being equiprobable). Also, presuming as above that you are speaking here about the probability of a particular label appearing on the sole unexamined ball (rather than the probability of a particular label coming up on the next draw possibly by virtue of the next draw being of a ball already examined), there is no particular upper limit of of 99 (against) to 1 (for) [e.g., it may be the case that the probability distribution of 100-ball jars is such that, with probability 4/5, a jar contain 99 balls labelled “telephone1” through “telephone99”, along with 1 ball labelled “raven”, while, with probability 1/5, a jar contains 100 balls labelled “telephone1” through “telephone100”; in this case, obviously, having drawn 99 distinct non-“raven” balls, the probability of the sole unexamined ball being labelled “raven” is 4/5, much higher than 99 against to 1 for].
This assumes that being non-black and being a raven are not positively correlated. [To see the general problem with analyzing conjunctions by multiplying probabilities without establishing facts about probabilistic correlation, consider: the probability that a die roll gives a non-even number is 1/2 (“1”, “3”, or “5” count). The probability that a die roll gives a prime number is also 1/2 (“2”, “3”, or “5” count). However, the probability that a die roll gives a non-even prime is not less than or equal to 1/2 * 1/2 = 1/4. Rather, it is the higher 1/3 (“3” or “5” count).]
Anyway, to restate my position, I side with you in defending the reasonableness of inductive inference; however, I must take issue with any attempt to justify this from the axioms of probability without further (essentially contrivedly inductive) assumption, as this simply cannot be done: there are plenty of probability distributions which, taken as models of the universe, fail to validate anything like inductive inference.
Returning to this, I now think perhaps you were speaking of drawing balls from the jar without placing them back (thus, no risk of re-drawing the same ball). But, if so, this would still be a flawed analysis in pretty much the same way. I think what has happened here is perhaps the common mistake of conflating a conditional probability with the converse conditional probability. It’s true that the probability of the first 99 draws being black balls, given that there is precisely one non-black ball, is 1/100. However, it does not follow that the probability of there being precisely one non-black ball, given that the first 99 draws are black balls, is also 1/100, or in either direction bound by such. P(a|b) and P(b|a) are quite separate quantities, related only through Bayes’ Theorem [P(a|b) = P(b|a) * P(a)/P(b)]. They may diverge wildly in any which way.
As before (though I made a slip-up expressing it before), the ratio between the a priori probability of the jar containing 99 blacks and that of it containing 100 blacks can run the full gamut from 0:1 to 1:0, and correspondingly will allow the conditional probability of “All 100 balls in the jar are black, given that the first 99 drawn were” to run the full gamut from 0 to 1.
To illustrate this with one of the simplest, most natural probability distributions to consider, let us suppose our jar is initially filled by the following process: a fair coin is flipped 100 times, with a black or white ball being placed in the jar each time accordingly. We then give our jar a good vigorous shaking and start drawing balls from it at uniform random without replacement. Suppose we’ve drawn 99 balls from it and they’ve all been black. What is the probability that the sole remaining ball is black as well (i.e., that the jar was filled entirely with black balls)?
Answer: 1/2. Not shabby, but not particularly high either. Far short of 99%.
Proof: The a priori probability of the jar containing all blacks (with us then necessarily first drawing 99 blacks) is 1/2^100. The a priori probability of the jar containing precisely 99 blacks but with us happening to first draw those 99 blacks (that is, drawing its sole white ball last) is 100/2^100 * 1/100 [the first factor is because there are 100 coin flip sequences which would result in precisely 99 black balls]. Since these two are equal, the answer follows.
I would say that no, you have no evidence for that. Whether you have justification or not for saying it depends on whether or not you consider the assumption that things tend to be consistent is correct or not; I too have no trouble assuming that, but that doesn’t mean I have evidence.
I don’t, nor do I have any way to know other than eating the apple or being eaten by that leopard. That things will behave consistently is an assumption that I as well as pretty much everyone on the planet, as you point out, works by. But it’s still an assumption.
But that’s just the thing; I don’t accept the premise that things will act consistently. It’s a guess. I don’t have any problem saying that it’s probably (and hopefully, anyway) a pretty good guess, at least from my experience, but that doesn’t make it proved. Logic based on a premise that hasn’t been shown to be true means the conclusion can’t be taken as true, and evidence for a piece of logic whose premise hasn’t been shown to be true isn’t evidence.
Of course. But there’s a difference between what we’re willing to accept in science and what we’re willing to accept in everyday life. I don’t have a problem relying on the underlying assumptions of science in my everyday life, and going around eating apples on the assumption they won’t be poison. But evidence has to be held to a higher standard than that. We can act as if inductive reasoning works, but scrutinised most carefully we can’t know.
Ah. Well, we can speak of absolute evidence (i.e., evidence relative to no background assumptions), but we can also speak of evidence relative to some background assumptions, right (the same way you considered justification relative to certain background assumptions)? And since the assumptions being considered are ones generally left implicit, I think the natural convention would be to take discussion of evidence to implicitly be relative to those assumptions unless otherwise specified. Is that the only thing causing us to talk at cross-purposes?
[By considering evidentiary status relative to certain assumptions, what I mean is, as with justification, considering the question of whether something is evidence/justification modulo those assumptions, and thus, while so doing, not concerning oneself with the question of whether those assumptions themselves have any evidence or justification.]
Sort of. I think that’s definetly the point of contention - but while certainly I can recognise that discussion of “evidence” being relative to those assumptions being accepted, I personally don’t think that observations or the like which are based on prior assumptions which don’t have full (by which I mean fulfilling all of the premise) evidence to be evidence in turn.
In other words, I think you’re saying that should we assume the premise is correct, evidence from it is evidence. I’m saying that it doesn’t matter whether we assume the premise is correct or not (as far as calling something evidence goes); if there isn’t in turn full evidence to back up the premise, anything we might bring to back up a conclusion is not evidence itself. For me it seems like saying “Here’s something that backs up this particular answer, only we don’t know what the question is”.
You needn’t take me to be saying that the inductive premises are obviously correct; I’m saying that conventional speech is such that “evidence” is implicitly always relative to certain ubiquitous background assumptions unless otherwise specified, “justification” is always implicitly always relative to those, etc., and that the inductive premises are part of that conventional background theory. I’m saying, as far as determining what counts as evidence, justification, etc., it doesn’t matter whether that background theory is correct or not, since we are always implicitly only evaluating evidentiary status relative to it.
That having been said, it is woven into the fabric of our fundamental (extra-deductive) logic to speak this way, and there is no more use quibbling over the hesitation that those particular background premises (or equivalently, methods of inference) haven’t been validated by some nebulous external criterion than there is in worrying about the possibility that, say, “A and (B or C) implies (A and B) or (A and C)” or any other aspect of our logic isn’t actually legitimate. It is legitimate by fiat, legitimated by definition, by the empirically observable nature of the language-game of reasoning we play, the same way it is legitimate to use the word “raven” for a particular kind of bird rather than a barstool for no more reason than that that is the customary employment of that term; all reasoning must come to an end somewhere, and acceptance of inductive reasoning is, in the contexts of concern, part of that starting point.
I accept inductive reasoning. I just don’t accept inductive reasoning as it applies to what I would call evidence - you can reason from it, but if you’re reliant upon it as the base of your evidence, I don’t consider it evidence. That there is no such thing as “relative evidence” in the way you’re talking about - if the base isn’t held up by full evidence itself, then nothing building on that can be evidence, to me.
I certainly have no problems accepting consistency in those terms. We need to in order to do pretty much anything, really. But science and evidence are and should be held to a different standard than “Well, let’s just act as if it’s so”. It needs to be shown to be so, and I personally would not call anything that relies on that for which there is no full evidence of it being shown as evidence. In my eyes, you can’t just talk about relative evidence; it’s like saying full emptiness, if it’s full, it’s not empty.