Confirmation

[aleph_0]

Here's a paradox presented by Carl Hemple, pretty famous, wondering what everyone thinks: Take the scientific hypothesis that all ravens are black. We intuitively take the existence of a black raven to confirm this sentence, the existence of a red raven disconfirms, and that all other evidence is irrelevant (so for instance, it should be irrelevant that there is a non-black non-raven like a yellow pen, or that there is a black non-raven like a black dog).

However, any sentence of the form

"All P are Q"

is logically equivalent to the sentence

"All non-Q are non-P."

I.e. these two sentences should be true in exactly the same situations. For instance, the first one is true if you check every P and see that it's a Q. Likewise, if you check every P and see that it's Q, and then find something which is not Q, then it can't be P (i.e. it turns out that all non-Q are non-P). If it were P, then you'd have an instance of a P which is non-Q, which is impossible in light of the already verified fact that all P are Q. Also, the first sentence is false when there is some P which is non-Q. The second sentence is false when some non-Q is P, but this is exactly the same situation as described in the previous sentence.

So in some sense, these two sentences should express the same proposition, just with different words. They share the same "truth-conditions" (which is just a fancy way of saying they are true and false in the same situations, as I described above).

Yet if the existence of a P which is Q confirms the hypothesis that all P are Q, then by the same rule, the existence of a non-Q which is non-P should confirm the second hypothesis. Yet the two hypotheses are logically equivalent! To use our example, the existence of a non-black non-raven would confirm the hypothesis that all ravens are black. Thus the existence of a yellow pen would confirm the hypothesis.

Ach! I'm all verklempt! Talk amongst yourselves. I gave you a topic.

[Edit: for further completeness on describing the logical relation. I note here that I know I have only shown the entailment in one direction, for anybody sufficiently sophisticated. I leave it as a homework exercise to demonstrate the contrapositive.]

Edited October 22, 2009 by aleph_0

[Grames]

This is easy. You ran off the rails at 'intuitively'. There is no crying in baseball, and no intuition in logic. The only thing that can confirm all ravens are black is a reason, a cause that creates the effect of a black raven. Also required is a context of knowledge, the specified circumstances under which that cause is operative.

[Rockefeller]

I think this is where the problem lies (as Grames pointed out too):

We intuitively take the existence of a black raven to confirm this sentence

[...]

Yet if the existence of a P which is Q confirms the hypothesis that all P are Q

How does the finding that one P is Q confirm the hypothesis that all P are Q?

[Jake_Ellison]

Take the scientific hypothesis that all ravens are black. We intuitively take the existence of a black raven to confirm this sentence

We don't, that would be a mistake on our part. There are two logical ways to conclude anything about ravens, neither is just by looking at one, and then intuitively drawing conclusions:

1. The only thing that could confirm that sentence would be to look at all ravens. From that, we could deduce that all ravens are black. That's practically impossible.

2. Or, we could instead rely on integration, and decide to form the concept raven, based on all the ravens we have seen, and others have seen, and documented. In the course of this process, we will have understood that ravens are generally black, unless there's something wrong with a specimen, in which case the feathers might be white. (at least that's how I heard it, but I'm by no means a biologist)

To use our example, the existence of a non-black non-raven would confirm the hypothesis that all ravens are black.

All ravens are black things. The equivalent of that is that: All non-black things are not ravens.

The existence of a non black non raven would not confirm or deny the second statement. In order to confirm the second statement, you'd have to look at all non-black things, not just one, and make sure they are all non-ravens.

P.S.

I remember reading about the Raven Paradox, by Carl Gustav Hempel, onOO.net, before:

http://en.wikipedia.org/wiki/Raven_paradox

I'll try a search, until then here's the wiki link to it. If the wiki is correct, then the answer is simple, Hempel was unaware of induction as defined by Rand, and he was wrong in thinking that it is the same as intuition. Induction doesn't rely on the color of one raven to determine what ravens are.

Also, the "paradox" described in the wilki page is not a paradox at all. For a paradox, you need a contradiction. And yet, Hempel presents none.

Edited October 22, 2009 by Jake_Ellison

[aleph_0]

Fair enough, you're a Hemplean bullet-biter. I might be too. But I'm not sure I understand what you mean when you say a cause confirms a hypothesis. Usually we take it that observations confirm or disconfirm and you can never observe a cause. You can observe evidence that supports the claim that A caused B, but you can never observe the cause itself. For instance, I may claim that the ball broke the glass, and cite as evidence that the observation that as the ball passed through the glass, it broke. But there all I have is the observation of the event: the ball passing through the glass, and it breaking. I don't observe the causal relationship between the two.

[aleph_0]

I think this is where the problem lies (as Grames pointed out too):

How does the finding that one P is Q confirm the hypothesis that all P are Q?

We don't, that would be a mistake on our part. There are two logical ways to conclude anything about ravens, neither is just by looking at one, and then intuitively drawing conclusions:

1. The only thing that could confirm that sentence would be to look at all ravens. From that, we could deduce that all ravens are black. That's practically impossible.

2. Or, we could instead rely on integration, and decide to form the concept raven, based on all the ravens we have seen, and others have seen, and documented. In the course of this process, we will have understood that ravens are generally black, unless there's something wrong with a specimen, in which case the feathers might be white. (at least that's how I heard it, but I'm by no means a biologist)

All ravens are black things. The equivalent of that is that: All non-black things are not ravens.

The existence of a non black non raven would not confirm or deny the second statement. In order to confirm the second statement, you'd have to look at all non-black things, not just one, and make sure they are all non-ravens.

I think there's a general equivocation on the use of the term "confirm", which I should make precise. To confirm a hypothesis, in the sciences, does not mean to prove conclusively but merely to lend evidence to. So the observation that the planets obey Newton's laws of gravity confirms but does not prove his hypothesis that all celestial bodies obey them.

[Jake_Ellison]

To confirm a hypothesis, in the sciences, does not mean to prove conclusively but merely to lend evidence to.

The existence of one black pencil does not lend evidence to the statement that all pencils are black. The same is true with ravens.

There is nothing to be gained from bringing into this more complex issues, such as what is science, or Newton and planets.

[edit]

Correction: the sight of one black raven does not lend evidence....The existence of one might, if it is studied, and the reason for the black feathers is found. But that's a lot more information than "look a black raven!", which is what Hempel is talking about.

Edited October 22, 2009 by Jake_Ellison

[DavidOdden]

The observation of a black raven confirms the hypothesis because it is entirely consistent with the hypothesis, and the correlation is entailed by the hypothesis. The hypothesis, in crude form, is that there is a causal relationship between being a raven and being black, meaning that it is in the nature of raven's that they are black. Modus tollens doesn't really work -- there is no causal connection between not being black and not being a raven. That is why seeing a yellow pen is irrelevant to the hypothesis that ravens are black.

It is immaterial that causality is not something that can be sensed, in the way that heat can be sensed. What matters is that it can be known.

[aleph_0]

So if I claim that the path of light is bent by gravity, it is not confirming evidence to observe an instance of the path of a light wave being bent by gravity? I have to establish some causal relationship between the two? Or if I claim that all of the apples in the basket are red, it is not confirming evidence to produce evidence of seven of them being red and there are eight apples in the basket? Would it not be confirming evidence to demonstrate that eight of the eight apples are red? I would somehow have to give a causal explanation as well?

Also, the correlation of non-black things being non-ravens is also entailed by the hypothesis. There was nothing in the hypothesis that expressed a causal relationship, as far as I can tell. You might think that causality explains the correlation between ravens and being black, but it is not necessary for confirmation. The claim was just that the set of all ravens is a subset of the set of black things.

Now whether modus tollens works might not be at issue. Forgetting the formalism and any correlation to natural English language that you might have with a material conditional, if it is claimed that all P are Q, can it be that some non-Q is P?

I take it that it's important to note that causation cannot be sensed, since what we are talking about is what evidence can count toward confirming a hypothesis. So if you have evidence for a causal relationship, and this causal relationship bears on the likelihood of a hypothesis, then that evidence confirms the hypothesis. So to be precise, the causal relationship does not confirm, but rather it implies (or necessitates, or makes likely), and the evidence confirms--but a causal relationship isn't need for confirmation. For instance, the relationship of confirmation might involve non-causal statistical laws.

[Edit: Made the last paragraph readable.]

Edited October 22, 2009 by aleph_0

[Grames]

Fair enough, you're a Hemplean bullet-biter. I might be too. But I'm not sure I understand what you mean when you say a cause confirms a hypothesis. Usually we take it that observations confirm or disconfirm and you can never observe a cause. You can observe evidence that supports the claim that A caused B, but you can never observe the cause itself. For instance, I may claim that the ball broke the glass, and cite as evidence that the observation that as the ball passed through the glass, it broke. But there all I have is the observation of the event: the ball passing through the glass, and it breaking. I don't observe the causal relationship between the two.

The usual practice is wrong. That causes are never observed is despicable sophistry. Some clearly are. You observed the ball breaking the glass with your eyes, that is all there is to say and all that ever could be said. Any investigation into the properties of glass, the mass and velocity of the ball, etc.. would all rely on the same eyes. If you are going to flatly deny the evidence of your senses you have no business claiming to observe anything at all in the first place.

The technical definition of confirm escaped me, thank you for spelling that out. So, observing a black raven lends a small amount of evidence. Observing a million more black ravens says nothing more. Identifying the cause of a raven being black lends conclusive evidence to the hypothesis. If ravens are black because of a specific gene, then the hypothesis should be stated as "all ravens are black unless their color gene is altered or blocked." An albino raven with alteration of the color gene is a confirmation of this hypothesis.

A bald statement that "all ravens are black", lacking any conditions or context can never be proven. It is only relations and context that ties things down, makes them true and keeps them true long enough to speak of them before they could change again.

The notes I provided on Dr. Peikoff's Induction in Physics and Philosophy cover statements of the form "All S is P" and what counts as evidence for such propositions. Check the link in my sig.

edit: (No need to go beyond the first and possibly second lectures.)

Edited October 22, 2009 by Grames

[brian0918]

Identifying the cause of a raven being black lends conclusive evidence to the hypothesis. If ravens are black because of a specific gene, then the hypothesis should be stated as "all ravens are black unless their color gene is altered or blocked." An albino raven with alteration of the color gene is a confirmation of this hypothesis.

A bald statement that "all ravens are black", lacking any conditions or context can never be proven. It is only relations and context that ties things down, makes them true and keeps them true long enough to speak of them before they could change again.

I see a possible regression in your argument. Rather than relying on all ravens working the same way (as one does when observing a bunch of black ravens and concluding "all ravens are black"), you are now relying on all raven color genes working the same way (either as on/off switches for color) - so one would have to add a further clarification of "all ravens are black unless their color gene is altered or blocked, so long as [some requirement on color gene internal functionality]", which in turn would presumably shift the reliance back further, to something more fundamental. Does this make sense? How far back must you go, and where does it stop?

Maybe I'm asking this out of confusion about what constitutes a true statement. If I observe hundreds of ravens, all black, can I truthfully say "all ravens are black" unless and until such time that I observe an albino one, forcing me to understand the biology that causes this raven to be white - to do this, I might eventually observe 100 ravens with gene ABC123 turned on that are black, and 100 ravens with gene ABC123 off or blocked that are white, and make a new conclusion from this - "all ravens are black so long as ABC123 is on" - is this statement then true, unless and until some time in the future when we find a raven with ABC123 on that is purple? Are all these statements "true"? If not, what are they, and what are some examples of true statements?

Edited October 22, 2009 by brian0918

[Plasmatic]

Until your "all" is encased in a causative context you don't have a valid generalization.

[Grames]

I see a possible regression in your argument. Rather than relying on all ravens working the same way (as one does when observing a bunch of black ravens and concluding "all ravens are black"), you are now relying on all raven color genes working the same way (either as on/off switches for color) - so one would have to add a further clarification of "all ravens are black unless their color gene is altered or blocked, so long as [some requirement on color gene internal functionality]", which in turn would presumably shift the reliance back further, to something more fundamental. Does this make sense? How far back must you go, and where does it stop?

What you are calling regression is also called expanded context. A first explanation counts as an explanation so long as it accounts for the context without contradiction. Finding a contradiction means you've got to figure out the qualification on the explanation. So long as there is no contradiction you have nothing to work with to advance your knowledge, so you have stopped because you are blocked.

Maybe I'm asking this out of confusion about what constitutes a true statement. If I observe hundreds of ravens, all black, can I truthfully say "all ravens are black" unless and until such time that I observe an albino one, forcing me to understand the biology that causes this raven to be white - to do this, I might eventually observe 100 ravens with gene ABC123 turned on that are black, and 100 ravens with gene ABC123 off or blocked that are white, and make a new conclusion from this - "all ravens are black so long as ABC123 is on" - is this statement then true, unless and until some time in the future when we find a raven with ABC123 on that is purple? Are all these statements "true"? If not, what are they, and what are some examples of true statements?

If all you have access to is a bunch of black ravens you are not able to say "all ravens are black". Rather, if you do say it anyway it is an arbitrary statement with no truth value because there is no way to evaluate it. All the ravens you have seen are black, but you have no epistemological right to claim any other ravens are black. You cannot pass from the particulars of your experience to a universal claim without knowing what universal cause acts on every raven to make it black.

If 100 ravens with gene ABC123 turned on are black, and 100 ravens with gene ABC123 off or blocked are white, and this is the only difference, then - "all ravens are black so long as ABC123 is on" - is true in that context of knowledge. A raven with ABC123 on that is purple is evidence of an additional factor that affects color; the context has changed. Figure out the new qualification that resolves the contradiction.

[brian0918]

If 100 ravens with gene ABC123 turned on are black, and 100 ravens with gene ABC123 off or blocked are white, and this is the only difference, then - "all ravens are black so long as ABC123 is on" - is true in that context of knowledge. A raven with ABC123 on that is purple is evidence of an additional factor that affects color; the context has changed. Figure out the new qualification that resolves the contradiction.

Why is it that seeing only black ravens does not allow you to make a truth statement that all ravens are black, but seeing 100 black ravens with ABC123 on and 100 white ravens with it off allows you to make a truth statement that all ravens are black so long as ABC123 is on? Remember that we can't say for sure that ABC123 is the determining factor for color, or the only one. It's just that that's the only evidence we have. It's possible that we happened to pick all only ravens that also have some other gene XYZ789 enabled, just as it's possible in the first case that we happened to pick all ravens that have ABC123 on.

In other words, and replying to Plasmatic who said: "Until your "all" is encased in a causative context you don't have a valid generalization", we do not yet know what causes ABC123 to make ravens black (or if it even does). All we have are examples of black ravens with ABC123 on, and white ravens with ABC123 off.

To me it seems like, so long as we know nothing about genes and have no evidence of anything but black ravens, we can truthfully say - "all ravens are black, given the evidence at hand". If at some point we find an albino raven, that forces us to find more context.

Edited October 22, 2009 by brian0918

[DavidOdden]

There was nothing in the hypothesis that expressed a causal relationship, as far as I can tell.

There should be. That is the point of scientific inquiry. The goal is to inquire about the identity of existents subsumed by concepts.

[aleph_0]

The usual practice is wrong. That causes are never observed is despicable sophistry. Some clearly are. You observed the ball breaking the glass with your eyes, that is all there is to say and all that ever could be said. Any investigation into the properties of glass, the mass and velocity of the ball, etc.. would all rely on the same eyes. If you are going to flatly deny the evidence of your senses you have no business claiming to observe anything at all in the first place.

You observe the ball move through space and as it does, you observe the glass breaking. That doesn't mean, necessarily, that the ball broke the glass. You could have an object that is able to permeate glass and flow through it, or the impression of glass could be an illusion, etc., and the coincidence of the impression of glass breaking while the ball passes through the glass doesn't actually cause the breaking. Now you can then investigate the ball before or after the event to find out whether it's able to permeate solid objects, you could touch the glass to see if it's an illusion, and this will all add increasing evidence to the conclusion that the ball broke the glass. But in your observation, there is only ball and glass--no third thing, the "cause", that pokes up out of the two.

So, observing a black raven lends a small amount of evidence. Observing a million more black ravens says nothing more.

So if you had two competing claims--say, all ravens are black, and all ravens are between two and three lbs.--and you had one observations for the first but one million for the second, you wouldn't be more certain of the latter? Suppose you have two hypotheses, A and A', where A & A' is a contradiction so they are mutually exclusive. Yet we don't have any evidence for either. But we know that A entails B and A' entails B'. B & B' is not a contradiction, but B confirms only A and B' confirms only A'. If you observed just one instance of B but one million instances of B', ceteris parabus, you wouldn't be more inclined to believe A'?

Identifying the cause of a raven being black lends conclusive evidence to the hypothesis.

Perhaps if you were ever to be able to produce perfect evidence for a hypothesis about the cause, but that hypothesis will always require some amount of evidence which might, at some point in the future, fail to obtain--meaning you'd have to scrap the causal law.

A bald statement that "all ravens are black", lacking any conditions or context can never be proven.

How about by looking at all black ravens?

There should be. That is the point of scientific inquiry. The goal is to inquire about the identity of existents subsumed by concepts.

So when researchers just collect data without yet attempting to make causal hypotheses, they are not doing science? Or when they analyze their data to find patterns (like noting the peculiar fact that, of every raven they observed, it was black--though still invoking no notion of a cause) they are not doing science? I'd disagree, but then, this might just be a semantic difference.

[Plasmatic]

Alepho your stealing the concept "cause". Causality is perceptually induced by observing entities in dynamic relation. Yours is the standard skepticism of induction.

[aleph_0]

So we see a bunch of things in dynamic relations and that imposes into our consciousness the concept of a causal relation between them?

[brian0918]

Alepho your stealing the concept "cause". Causality is perceptually induced by observing entities in dynamic relation. Yours is the standard skepticism of induction.

How isn't it also a skepticism of induction to not permit oneself to conclude that "all ravens are black" given the observation of only black ravens?

[DavidOdden]

So when researchers just collect data without yet attempting to make causal hypotheses, they are not doing science?

In order to buy a quart of milk, you must first get off your butt, find your wallet, pull out a couple of dollars, get your coat, go to the store, find the milk, take it to the cashier and plunk down the money. Getting off your butt is not your end, it is a means to the end. Trolling for data is preparation for hypothesis formation and testing. But we're talking about the advanced stage, with a hypothesis. When you have a real scientific hypothesis (and I flatly reject the view that a hypothesis is just "guessing"), that hypothesis -- an assertion about the nature of reality -- properly includes concepts of causation. If you really don't know what ravens are, then you are not deal with a hypothesis, you're just dealing with a hunch.

[TheEgoist]

How isn't it also a skepticism of induction to not permit oneself to conclude that "all ravens are black" given the observation of only black ravens?

Because there are strong and weak inductive inferences. No one denies that you can be mistaken. A categorical denial of induction is that you can always be mistaken, so induction really isn't a valid method of reasoning.

Observation that all ravens are black is passive, perceptually evident. There is nothing scientific about noticing that x has y characteristic simply by looking at it.

The fact that every observed raven has the attribute of blackness doesn't even guarantee that every raven forever will have that attribute. "It is the genetic predisposition for all ravens to have black feathers.".

"Well I saw a raven that has every other attribute needed to be a raven, except it was light gray.".

It's at this point you could form a hypothesis; the most likely being that it is a genetic anomaly. Animals are interesting cases to use in induction, because they're special. Nothing is guaranteed in animal-to-animal generations. For example the rabbit we know today was nothing like the rabbit of 10,000 years ago. It takes a bit of a background in biology to comment on it precisely, IMO. However just the generalization that all ravens are black IS a pretty weak gen.

I think these same issues of evolving knowledge are explained quite well by Rand in the Q&A portion of IOE. I believe the whole section is actually called "Induction" and it deals with the more permanent induction of water boiling. Peikoff also explains this issue in OPAR. I can't cite page number, but it is in the chapter on Reason under "Certainty as Contextual"

(Note: I noticed once I put crow instead of raven. It may have happened elsewhere, don't have time to proof read atm. This post was put together in a bit of a flurry, so sorry for some unclear aspects)

Edited October 22, 2009 by TheEgoist

[DavidOdden]

How isn't it also a skepticism of induction to not permit oneself to conclude that "all ravens are black" given the observation of only black ravens?

You know (or should know) that some cats are black, some dogs are black, some cows are black and some horses are black. You also know that some dogs, cats, cows, horses are not black. And you know that all polar bears are not black.

From this you know that color can, but need not, be an aspect of the identity of a animal species. This is sufficient evidence to leave open the question of whether one black raven or one white swan is "one of the types that exist" versus "is typical in this respect of all members".

[TLD]

Rockefeller

How does the finding that one P is Q confirm the hypothesis that all P are Q?

It doesn't! But philosophically, one does not need to see all Ps to conclude that all P are Q.

If all the Ps seen are Q, then the evidence is conclusive. Given contextual knowledge, we cannot base any conclusion on the potential of a conflict in the future.

[Eiuol]

So when researchers just collect data without yet attempting to make causal hypotheses, they are not doing science? Or when they analyze their data to find patterns (like noting the peculiar fact that, of every raven they observed, it was black--though still invoking no notion of a cause) they are not doing science? I'd disagree, but then, this might just be a semantic difference.

Data collection is obviously a part of science, but that does not mean when someone collects data it is science or even is valid science. The existence of a submarines could not prove the hypothesis that all ravens are black unless you can confirm some causal relationship. To validate a hypothesis requires a causal relationship (that is, if two things are involved). The number of submarines observed will have no bearing on a hypothesis until you can confirm some sort of causal relationship. Nor would there even be a point of researching the two in relation to each other until you know some characteristic of submarines was also present in ravens.

[Jake_Ellison]

It doesn't! But philosophically, one does not need to see all Ps to conclude that all P are Q.

If all the Ps seen are Q, then the evidence is conclusive.

What method did you use to determine that?

Given contextual knowledge, we cannot base any conclusion on the potential of a conflict in the future.

What's an example of someone basing a conclusion on the potential of a conflict in the future? I browsed through the thread and I don't recall anyone mentioning future events.

Also, your first and second sentences are not contextual knowledge. I assume you meant to have a connection between your fisrt two sentences, and the third, but I don't see how your third statement about contextual knowledge is related to your first two, which are a context-free claim.

Edited October 22, 2009 by Jake_Ellison