RoR: Forum

Referring to an example of Peikoff's on the validity of induction, Glenn wrote:

"[W]ithout some kind of causal explanation for the phenomenon of the sun rising in the morning, you can’t know that the generalization is true. So, Hume was right in the sense that just having seen the sun rise every morning for your whole life (simple enumeration) is not evidence for the fact that it will rise tomorrow morning. Unless you have a causal explanation (from Kepler, Newton, Einstein, whatever), you can’t “know” that the sun will rise tomorrow."

But in making an inductive inference, don't we assume as a qualification "all other things being equal." So wouldn't it be valid to infer that the sun will rise tomorrow, without knowing the causal relationship between the sun and the earth, so long as one included as a qualification "assuming no other significant astronomical changes"?

Even if one did know the physics behind the sun's behavior relative to the earth, one would still have to include that kind of qualification. So what does knowing the physics add to the validity of one's inference? The law of causality, which is based on the law of identity, simply says that the same thing must act the same way under the same conditions. Assuming the same kind of thing and the same conditions, is it not valid to infer the same action?

To be sure, just because all the swans one has seen so far have been white, one cannot infer that all future swans will be white, because whiteness is not a necessary property of swans in the same way that buoyancy (say) is a necessary property of ice cubes. But what would cause the sun not to rise tomorrow other than an unforeseen astronomical event? One can logically conceive of a black aquatic bird that is nevertheless a swan, since whiteness is not a necessary property of swans. One cannot logically conceive of the sun's not rising tomorrow, given the same astronomical conditions.

I have a feeling that I'm missing something, but I'm not sure what it is. :)

(Edited by William Dwyer on 2/25, 1:14pm)

Post 41

Friday, February 25, 2011 - 1:59pm

Bill,

But in making an inductive inference, don't we assume as a qualification "all other things being equal." So wouldn't it be valid to infer that the sun will rise tomorrow, without knowing the causal relationship between the sun and the earth, so long as one included as a qualification "assuming no other significant astronomical changes"?

I would say "no."

I would say that you have to know about the "permanence" of the dynamics between the earth and sun (the perpetual repetitiveness characteristic of a planetary orbit, as such). In astronomical terms, it's possible to conceive of an event repeated thousands of times, but not repeatable for thousands more times. Let's take a star, for example.

Let's say that the North Star was thought to be currently existing because we can see it -- and have seen it thousands of nights in a row . But let's say that, in reality, the North Star burned out several years ago (and is no longer really there). The reason that its light would still be in the sky would be because light travels, but the North Star may be dozens or hundreds of light-years away. In that case, we would still see the light in the sky, for several years, even though the star was gone.

On your view, generalizations might be made that mistakenly include invoking a current existence of the North Star (even though it is long gone). Alternatively, a generalization which takes into account how it is that light from stars gets here in the first place would NOT make the same mistake.

The difference stems from understanding mechanical limitations imposed from the fact that existence is just the spatio-temporal expression of identity. Things can't violate their nature; limitations prevent some generalizations from ever being able to be true (while, themselves, invoking other true, factual, or valid generalizations).

Ed

(Edited by Ed Thompson on 2/25, 2:00pm)

Post 42

Friday, February 25, 2011 - 2:36pm

Bill,
The idea as I understand it is: for someone who has no knowledge of astronomy or what the shape of the Earth is, or what the sun is, or "the dynamics between the earth and sun" as Ed called it, just seeing this ball of light rise in the morning and set in the evening would give no justification for believing that it will rise tomorrow, no matter how many times it has in the past. In this case their belief that the sun will rise in the morning is the same as the belief that all swans are white based on seeing only white swans.
Thanks,
Glenn

Post 43

Friday, February 25, 2011 - 3:42pm

Glenn,

What if they made up an explanation. Psychology is such that we are not very comfortable with the unexplained. For example, early man created Gods to explain natural phenomena. Where does that fit in this discussion?

Post 44

Friday, February 25, 2011 - 5:16pm

Hi Glenn,

I can see merit in a lot of what you say, but I don't think you've really addressed my point. Partly this is because I think you've skipped a few critical steps in your explanation. Let me try again.

Let's look at a caveman experiencing fire for the first time. He throws in a log into the fire, and it starts burning, eventually turning into ash. Maybe he throws in a second log, and sees the same result. He has enough knowledge already to know that wood does not normally convert into ash. So he recognizes that the fire is what's causing it. He's a caveman, so he knows nothing about chemistry and so doesn't understand in any deep way the cause and effect relationship. He just knows that there is a relationship. He knows that the fire is burning the wood.

Now how does he generalize that statement? How does he go from saying this specific fire burns this specific wood to fire in general burns wood in general? Your answer was that you recognize the cause and effect relationship and formulate it in conceptual terms. I don't know what that really means. The caveman does recognize the causal relationship, even if he doesn't understand it. As far as he might believe, this fire is a kind of creature that eats wood, or eats a part of the wood leaving the remains. He hasn't identified it as a chemical reaction. Nonetheless, he knows that the fire is what's causing the wood to become ash.

So how does he generalize this knowledge? Yes, he can jump to some abstract form immediately. Fire burns wood is one possibility for how he might do this. But it could also be "fire burns brown objects", or "fire burns solids", or "fire burns objects starting with the letter 'w' ". Recognizing a causal relationship is not the same thing as fully understanding it. And when you try to generalize, there is plenty of room for error. In these example generalizations about fire, we would say that he made a mistake in the process of generalizing. He incorrectly went from "some A is P" to "all A is P". If he thought fire burned solids, for instance, he made an error by thinking it was the solidity of the object that mattered, instead of the chemical composition.

So let's stop here. Is this a first-level generalization? Is it self-evident? I think it is supposed to be an example of a first-level generalization, but it is far from self-evident. And that makes me suspicious of the whole idea of self-evident, first-level generalizations.

What is self-evident? Well, let's just say that we can witness a causal interaction directly, and recognize the causal link. I'm not positive we can use the word self-evident, but we can clearly see that the fire is what's burning the wood so let's just take it as close enough. But identifying a cause and effect relationship is not the same as forming a generalization. We can see the fire is burning the wood, but going on to say that fire burns all wood is unjustified at that point. It does not follow directly from the identification of an instance of wood burning.

What can be generalized? We might generalize the idea that fire burns things. What things? We don't know yet...except this one piece of wood burned. We'd need to explore more to try to determine what the causal mechanism was, and then we could say more. So the self-evident part is not terribly useful. The mere identification of the fact that there is a causal relationship is not enough to formulate a generalization like all wood burns.

Also, we might find out that there is more than one kind of fire, so even generalizing to "fire burns stuff" might not be true. But there is a way in which it can be said to be true. If this were just an example of concept formation, then it works. The concept of fire is formulated, and the concept has referents. It's not a statement of fact, but a kind of categorization. We have a concept of fire, and part of the way we differentiate it from everything else is that it burns some objects. There's not a factual claim that "all A is P" except by definition.

While that works, it doesn't explain how to actually make generalized, factual statements. We can make concrete statements, like this fire burned this wood. And we can make conceptual categorizations, like we're going to define fire as this 'stuff' that burns other stuff. But we still need to be able to make a statement like "fire burns wood in general" that isn't true by definition. We still have to go back to the problem of induction!

Now maybe I misunderstood Harriman's book, but he seemed to be trying to build a structure of knowledge on a foundation of self-evident, first-level generalizations, which connects him to reality. If he can make some factual claims in the form of "all A is P", by declaring them self-evident, he has what looks like a possible path. He's got a bunch of concrete facts, some generalizations, and he can start working towards higher level generalizations. I don't think he explained the process in any real detail, but it sounds plausible anyway. But all of this rests on some initial self-evident, first-level generalizations. Some generalizations are needed to get started down that path. Having some be self-evident would solve that, but I don't really buy it.

You quoted Peikoff saying “… in the act of naming what he perceives, [the inducer] automatically drops the measurements of the perceived cause and effect and gains knowledge transcending the given concrete”.

But does that assume he uses the right names? If the caveman says that "fire burns solids", he'd be wrong (it doesn't burn all solids and can burn liquids too) while saying that is burned this particular solid would be right. And this isn't about knowledge being hierarchical and contextual. I agree that if he properly identified that it was certain materials, like wood, that burned, he'd be contextually correct and new information would just supplement his earlier knowledge. But that's doesn't negate the possibility of error. If he though the fire burned objects because of their solidity, instead of their chemical composition, he'd be wrong!

Now let's let the caveman continue his learning. At this point, he sees that fire is burning a log. He doesn't think that fire burns wood in general yet. He has no reason to. Fire could be based on something else. So he throws in a few other logs. They all burn too. He throws in a stone, and it doesn't burn. He throws in some water, and the fire diminishes, so it isn't burning either. Maybe he thinks that there's something special about the wood. He guesses it's the color, and throws in some dirt, but that doesn't seem to burn either. Finally, he thinks maybe it has something to do with the kind of object, like what it's made of. So he tries some moss and leaves. And they do burn. Great. Maybe he continues trying things, but now he has an reasonable hypothesis about why the fire burns the wood. He doesn't understand chemistry, but he can recognize that that things are made of different stuff.

Does he now have enough to make a more generalized statement? Can he say that fire burns wood in general now? If he does, he's make a couple of (not unreasonable) assumptions along the way. He's assuming that flammability is based on what something is made of. He's assuming that all wood is made up of either the same or similar enough material. None of this is self-evident! In fact, the second part is a generalized statement of it's own. To make the assumption that all wood is of the same kind of material, he'd need some causal explanation there. What would a caveman have at that point? Just the guess that since they grow the same way, look similar, and feel similar, they are made of the same kind of stuff. Not terribly scientific there!

The caveman doesn't now anything about chemistry or the chemical composition of wood to know why it's flammable, or what's really even going on when it burns. He just has enough information to formulate the hypothesis that fire burns based on the kinds of material, and that logs all seem to be made of the same material. Both statements have the possibility of being wrong (and not just contextually incomplete!). Both may be reasonable to conclude, but they are not automatically true.

Finally, going back to your swans and being white. You said we have no causal explanation for it, so we aren't justified in making that generalization. But what about wood being flammable? We don't (or at least didn't for a long time) have a causal explanation for why it must always be flammable. We know the chemical composition matters for fire, but we don't know that wood has to always have tat chemical composition. Has the world been irrational collecting fire wood for all of these millennium? Or is it reasonable to hypothesize that there's something about the nature of trees and their offspring that makes each one similar in composition, even if we don't know what exactly that is? I don't see any other way of making that generalization except through pure enumeration. You're welcome to try. But if that kind of answer is good enough for trees and fire wood, why isn't it good enough for swans? It's reasonable to conclude there's something about the kind of animal it is that allows for little variation from a norm. And given a huge sample set of all white swans, it might be reasonable to conclude that white is to swans as flammable is to trees. Both are a part of it's nature. If someone explained genetics to our ancestors, they might say "It appears that there's something in the genes of a swan that makes it white, just as there's something in the genes of a tree that makes it flammable". When new evidence arrived, like a black swan, they could just shrug their shoulders and say "Oops. Guess that's an attribute that varies".

Which brings up the question of how reliable does induction need to be? There's this idea that for it to be valid, it must only lead to true conclusions. If you end up with a false statement, you must not have applied it correctly. Some think that this is impossible, and therefore induction is not rational. Others try to show that it is always correct, we just have to alter what we mean by correct. It seems an third alternative is that induction can lead to false conclusions, but so what? When you find a contradiction, you'll realize your mistake and correct it. Which of these three models do you accept? Or is there an alternative?

Sorry for the long post. Hopefully it stirs your thinking. At this point, here are my major concerns:
1.) Is the idea of first-level generalizations even valid? Certainly we can experience causal interactions directly, but is the process of generalization ever self-evident?
2.) Are first-level generalizations necessary? It's a way of bridging the gap between concrete facts and generalized facts, but aren't their other, better approaches?
3.) How do we know wood in general is flammable? Is is logically flawed to make this statement throughout most of history? Or is it proper to speculate on causes of uniformity and assume that this tentative hypothesis justifies a general statement that all wood is flammable.
4.) What standard is needed for induction? Always leads to the truth when applied correctly? Or incomplete information can lead you to faulty generalizations, but you'll eventually spot your error?

Post 45

Sunday, February 27, 2011 - 9:18am

Hey, Joe.

Instead of addressing each of your concerns, let me summarize my understanding, at this time, of the Peikoff/Harriman view of induction and thereby try to answer some of your questions.

To stick with your example: suppose a primitive man observes, for the first time, a piece of wood burning. How can he generalize this situation? Well, the only way to infer future actions from past actions is by showing that the past actions were the effects of causes. Only a causal relationship can make a generalization true.

How does the primitive discover a particular causal relationship? He observes the flame causing the wood to burn. He perceives the cause-effect relationship between the fire and the burning of the wood. He doesn't need to know, at this point, why fire burns wood. He saw it with his own eyes. A hypothesis Peikoff makes (as he says, it's not original) is that as children we learn about causal connections from our experiences with our own personal efficacy. He goes into more detail about the distinction between personal efficacy and cause and effect in the external world, but the key first point is that we perceive particular causal relationships: we see the flame cause the wood to burn.

But at this point all we have is the perception of a causal connection linking particulars; this flame caused this piece of wood to burn. How do we get to a universally applicable truth - a generalization? We do it by using concepts. Suppose the primitive has the concept of "fire", which relates the particular fire he perceives to all fire, regardless of the measurements. Likewise with the concepts of "burning" and "wood". Then the proposition "fire burns wood" is a generalization, because we have conceptualized the perceived particular event and dropped the measurements of the causal relationship perceived. We are now saying that fire burns all wood.

To use Harriman's summary (p. 28): "When a first-level inducer identifies his concrete experience of cause and effect in terms of words, his perceptual grasp of the causal relationship becomes thereby a conceptual grasp of it, i.e., a generalization." [Emphasis added.] Note that a single instance of fire burning wood is all that's needed; it is both necessary and sufficient.

Now, it may be a fact that there are situations where wood doesn't burn. But, within the context of knowledge of the primitive, who hasn't seen wood that doesn't burn (otherwise he wouldn't make the generalization), it is true that all wood burns. He is contextually certain, given the extent of his current knowledge, that fire burns wood. He may be wrong, but he is entitled to be certain. This is the purpose of the preamble: "Within the context of the factors discovered so far, the following is the proper conclusion to draw." The reason that wood didn't burn in a particular situation must be due to additional factors and the original first-level generalization remains true.

The above is an example of a first-level generalization since it is directly perceived and involves only first-level concepts. It is "one derived directly from perceptual observation, without the need of any antecedent generalizations". [Harriman, p. 19.] It is self-evident because the perceptual is the self-evident.

Going back to the generalization "all swans are white"; there is no perception of a causal relationship between being white and being a swan. So, it isn't a first-level generalization. It may be a higher-level generalization that could be reduced, given the right facts, to a first-level generalization. But, without that reduction, the generalization "all swans are white" is an arbitrary proposition. It may be true (but it isn't), but you have no justification for believing it if your belief is based solely on the observation of white swans.

The model I accept (or, I should say, is consistent with my understanding of the Peikoff/Harriman view) is: If after further investigation you find that under certain circumstances your generalization leads to a false conclusion, then there must be an additional factor that changes the situation. But the existence of that additional factor doesn't change the truth of your original generalization. So, I see this as an alternative to the models you offered: first-level generalizations are self-evident, so must be true. Higher-level generalizations, if correctly reduced to first-level generalizations, are contextually true. They are true within your conceptual framework.

Thanks,
Glenn

Post 46

Sunday, February 27, 2011 - 12:24pm

Glenn,

Now, it may be a fact that there are situations where wood doesn't burn. But, within the context of knowledge of the primitive, who hasn't seen wood that doesn't burn (otherwise he wouldn't make the generalization), it is true that all wood burns. He is contextually certain, given the extent of his current knowledge, that fire burns wood. He may be wrong, but he is entitled to be certain. This is the purpose of the preamble: "Within the context of the factors discovered so far, the following is the proper conclusion to draw."

I am having trouble accepting this.

My trouble, I think, stems from what, after analyzing your words, appears to be a conceptual reliance that knowledge is "justified, true belief" (i.e., that knowledge is a belief). When you say he is entitled to certainty even though his thought may not correspond to reality, it runs dangerously close to a coherence theory of truth (rather than a correspondence theory).

Will you please address my concern?

Ed

Post 47

Sunday, February 27, 2011 - 2:14pm

Hi Glenn,

I appreciate the effort. I do believe that is what Peikoff/Harriman are saying. I just think that it's wrong.

The problem, of course, is that when you from a particular "this fire is burning this piece of wood", you generalized into something that could be considered true, that fire burns wood in general. And the rest of your post talks about contextual truth, like it does burn wood in general, but certain other factors (like how wet it is or if there is oxygen available) may modify that basic truth. But it is true in a context!

My problem is that you have the caveman generalize to something that we know is true, after gathering an enormous amount of data. You ignore the possibility of false generalizing by assuming he generalizes to something correct! But what if he generalized the same particular into something that we would disagree with it? What if he generalized to "fire burns all solid objects"?

Does fire burn all solid objects? No. If he made that generalization, he'd be wrong. And not just contextually wrong. He's not just wrong when other factors that were unknown change. He was wrong when the one thing he generalized about, the solidity of the object, was all that mattered. When he tries to burn a rock, it doesn't burn. When someone throws gasoline on the fire, it does burn. He generalized incorrectly. He went from a particular "this fire burns this solid object", to a generalization that was false "fire burns solid objects".

The issue is that when he generalizes, he isn't simply conceptualizing. He's not simply categorizing the information. He's making an inference about the causal relationship. If it were simply conceptualizing it, he might say "fire burns flammable stuff". He's created three related concepts. The fire, obviously, is one. The process of burning, which he has identified, is another. And the fact that this process affects some stuff is another. That's a simple conceptualization that doesn't smuggle in any assumptions. But if he said "Fire burns solid objects" or "Fire burns wood", he is. If he says "flammable stuff", he isn't making any assertion of why something is flammable. It could be because of its solidity. It could be because of it's chemical composition. It could be because the stuff has been cursed by a caveman priest. But if he says something else, he is making an assertion. He is doing more than just generalizing. He's claiming to recognize the basis of why something is flammable, and making a generalized statement based that. And since he's making a claim about the basis of why something is burning, he has the potential for error! The first-level causal connection he witnesses does not provide him with an explanation of the cause-effect interaction. He only sees that it exists, and what the cause is and what the effect is.

So this first-level generalization thing is not an automatic, self-evident process, which I think was a necessary part of the thesis of the book.

And I need to go further. If he did manage to figure out that it was the material of the object that mattered, he still needs justification for claiming that all wood, or even most wood, has that composition. Aside from the fact that we believe it to be true, how is this leap justified? This is really a second kind of generalization. Saying that wood is flammable is a generalization. And if you believe that generalizations can only be justified by a causal mechanism, then you must saying that wood is always composed of flammable material because of causal principle X. My claim is that this statement is not very different from "All swans are white", except that we don't know of any alternatives for the wood yet. But I don't believe there is any "causal principles X" that ensure that wood will be flammable, at least not one that was understood before the modern era!

Post 48

Sunday, February 27, 2011 - 5:56pm

A couple of quick comments:
Ed,
I'm only describing (maybe not very well) the contextual nature of certainty. Given my context of knowledge, I can be certain of my conclusion, but I could be wrong.

Joe,
The concept "solid object" is not a first-level concept, so the proposition "fire burns solid objects" isn't a first-level generalization.

I'll have more to say later.
Thanks,
Glenn

Post 49

Sunday, February 27, 2011 - 10:50pm

Glenn, I'll wait for your additional comments, but I don't think that's an answer. It doesn't matter what level concept the caveman uses. There is always the possibility that he's wrong because he's generalizing from one or some cases, to all cases. The only way you can say that he's definitely right is if he's simply categorizing data, meaning he's not making any kind of statement about the world. But "fire burns all wood" is definitely a statement about the world. There is definitely a possibility of error. We're using an example where you may feel certain that all wood burns (in the right context!), but that information isn't available to the caveman.

You're welcome to look for some way to save the theory of first-level generalizations, but I think it's a hopeless endeavor. If there's a possibility of error, which there always is, I think it's wrong to call it self-evident, as if it were automatic like perception.

Post 50

Sunday, February 27, 2011 - 11:17pm

I'm tempted to give a slight variation on the example. Say a child sees a table thrown into a fire and it burns. The child may than conclude that "fire burns all tables". But it clearly doesn't...it only burns those that are wood. Metal tables don't burn. This approach Objectivists take to try to claim that the child is correct within a context cannot be infinitely extended to make outright false statements true. There was nothing about the "tableness" of the table that caused it to burn. It was the wood. Wood burns, not tables. A child who used these first level concepts and the perceived causal connection would just be wrong, not just correct in a limited context. TABLE is a concept integrated by shape or function, not by material composition. Generalizing that all tables burn would be wrong because it has mis-identified the causal connection. Only when the child/caveman acquires enough information about fire to know that it depends on the kind of material can he make a proper, generalized statement. And he would still have to provide some justification for saying that all of something is made of an appropriate material (like all wood can burn).

Post 51

Monday, February 28, 2011 - 6:16am

Joe,

I think your counterexample (the proposition "fire burns tables") is a good one. It involves only first-level concepts and it represents the causal connection between fire and table that is perceived. So, why doesn't the child know that fire burns tables? He does! The fact that you know that metal tables don't burn is irrelevant to the knowledge the child has. He saw a table burn; he perceived it. Therefore, he says that tables burn. And they do. But this is not the same as the white swan generalization. There you only observe correlation; you don't see the color white being caused by being a swan.

You said: "This approach Objectivists take to try to claim that the child is correct within a context cannot be infinitely extended to make outright false statements true." I don't see your example as extending a context to make outright false statements. The child will find out later that metal tables don't burn, so then he'll modify his statement to reflect the new knowledge. The key statement in Peikoff/Harriman is:

A child learns, for example, that pushing a ball makes it roll. Later he discovers that this does not happen if the ball reaches a certain size or weight, or if it’s glued to the floor, or if it’s electrified in the presence of certain magnetic fields. None of this overthrows the initial first-level gen. On the contrary, the latter is necessary for anyone to be able to consider subsequent qualifications. You cannot reach, or validate, such a statement as “pushing moves a ball only under X conditions” until you have first grasped the elementary fact that “pushing moves a ball.” “A happens only under B” presupposes “A happens”, so no discovery of B is ever going to invalidate your initial observation.

This is from Peikoff's lectures on Induction, but it's basically the same as stated on p. 20 of Harriman.

Do you disagree with the general principle that new knowledge doesn't overthrow old knowledge when the context of the old knowledge is included? Or do you see the situation with first-level generalizations as not being an example of this principle?

Thanks,

Glenn

Post 52

Monday, February 28, 2011 - 9:18am

My last question to Joe in the previous post opens a whole can of worms. Kelley, in a review of OPAR, states that Peikoff hasn't integrated the contextual theory of knowledge with the correspondence theory of truth. Food for thought; nothing to do with the worms!

Post 53

Monday, February 28, 2011 - 11:48am

Glenn,

Ed,
I'm only describing (maybe not very well) the contextual nature of certainty. Given my context of knowledge, I can be certain of my conclusion, but I could be wrong.

Okay, but it seems you are talking about "psychological certainty" (the naive-realism kind of "seeing-is-believing certainty" we share with animals); rather than what I would refer to as true, human (philosophical) certainty -- which is either vague enough, or the context narrow enough, for it to never be falsifiable by later inputs of knowledge or perspective.

Ed

See:
Human Certainty: The only kind there is.

(Edited by Ed Thompson on 2/28, 11:49am)

Post 54

Monday, February 28, 2011 - 12:28pm

Ed,
I'm talking about the Objectivist concept of certainty, which must be contextual. See here for a nice discussion.
Thanks,
Glenn

Post 55

Monday, February 28, 2011 - 1:02pm

Glenn,

I have a seemingly different take on certainty (that it involves it being demonstrable that it's impossible to be wrong) and we may have to shelve the discussion as it seems it may actually be tangential. To elaborate, you can't ever be wrong about that of which you are certain.

Take Peikoff's example of type A bloods being compatible. Instead of wording it like he did in OPAR, he would need to word it differently, so that even a future discovery of the Rh factor couldn't possibly affect its truth/generalizability. A quick and dirty way to get to such certainty is to use relational statements only. The generalization that A is more compatible with A, than B is with A -- is veridical (not affected at all by other things, such as Rh factors).

Ed

Post 56

Monday, February 28, 2011 - 4:24pm

Glenn,

Do you disagree with the general principle that new knowledge doesn't overthrow old knowledge when the context of the old knowledge is included? Or do you see the situation with first-level generalizations as not being an example of this principle?

I'm not sure that I actually agree with it, at least not how it's being used. I do believe there is some validity to it, in that there are cases where new knowledge is not really overthrowing old knowledge. So I don't reject it. But I also don't think it applies to all cases. If it did, errors would be technically impossible.

It seems to me that the general principle must have bounds. I believe there is the possibility of error. And yet, this loose use of the principle seems to try to convert every case of error to be "true within a context". I know Objectivists hate to be wrong, but I never thought it was a basic premise of the philosophy!

Perhaps, as you mention, this is simply a lack of integration with the contextual theory and the correspondence theory.

Take the example of the child who rolls the ball. In many ways, that example is so obvious to us that we assume the child could not possibly mis-integrate the information. We see it rolling, and we assume that it is the shape of the object that matters. But what if we saw a child roll a ball, and then say "when I push on toys, they roll". The child then goes and takes a cube and tries to do the same thing, and it doesn't work. He would probably realize he had made an error. Now maybe some Objectivists would hear the child say that toys roll, and think "That's contextually true!". But I would hear it and say, the poor kid has incorrectly generalized. It isn't the fact that the ball is a toy that makes it roll. It is the shape of the object. And if I wanted, I could provide several other examples to the child to show him that it is indeed the shape. But the point was that the original generalization wasn't true in some contexts. It was false. All toys roll or all tables burn are clearly errors, and new knowledge does in fact invalidate them.

If we simply say that something is "true within the context of our knowledge", then error is impossible. We've just defined it away, and abandoned correspondence with reality. But is that what the contextual theory is all about? Isn't it about how each of our ideas is interconnected with the rest of our knowledge. That a statement is made within a context, and you need to be aware of that context. And that you can't rip the statement out of the appropriate context and still expect it to be true?

How about the idea that new knowledge does not necessarily invalidate previous knowledge. Is Newtonian physics wrong because of relativity, or correct within a context? I think it is correct within the context. But I see that as complete different from a statement that all tables burn when only some do. The Newtonian physics was correct in the recognition of certain relationships and factors. But saying that all tables burn has misidentified the source of the causal condition. It was not the table qua shape that mattered. It was the table qua material that mattered. The generalization is not just words thrown together. It is a statement about the causal connection. It is drawing a connection between tables and fire. And "tables" is a concept, which is a kind of mental categorization. The categorization is based on the shape or function of the referents. Connecting that concept to that causal interaction is a misunderstanding.

So I think there is a big difference between saying that all wood burns and all tables burn. All wood burns may have contexts in which it isn't true, such as when there is no oxygen or when the wood is soaked in water. But within the proper/normal context, the wood will burn. It applies to all wood, unless some outside factor changes. But the table example is just false. It just doesn't apply to some tables, no matter what context. It seems that you could still say that some knowledge is not invalidated by new facts, or radically different contexts. Within the appropriate context of reality, the statement is true. Within normal context, all wood does burn. But not all tables!

One interesting aside is that if the contextual theory can really excuse any false statement, then there would be absolutely nothing wrong with saying that all swans are white. If you ever found a black one, you could say that you weren't wrong but instead were just contextually right. And with that approach, it seems the whole need to justify a generalization through causal means would be unnecessary. Enumeration would be find. You could say that all swans are white because you've only seen white ones.

Presumably the point of trying to link generalization to causality is because the generalization must be justified in some way. To say that all A is P should be based on some underlying justification that supports the wide generalization. Without that justification, you are generalizing without reason. You'd be committing an error of reasoning. But look what happens when you treat the context theory as meaning that anything is true, if it is true within the context of your knowledge. Suddenly all swans are white, all tables do burn, and there is no such thing as a faulty generalization. I think these two ideas, that contextual knowledge omits error, and that generalizations must be justified, are incompatible. The former makes the latter unnecessary.

Going back to first level generalizations, you asked whether new knowledge can invalidate old knowledge there. I think in the case of error, it can. In the case you correctly generalized, new knowledge doesn't overthrow the previous knowledge but adds to it.

But now, I don't accept the validity of first-level generalizations. I could probably accept the idea that certain causal events are directly perceivable, and would therefore would act as a foundation of knowledge. But when the generalization happens, I don't see "first-level" generalizations as any different from any other. It seems both unnecessary, and incorrect.

If the reason causality is viewed as central to the process of generalization is because it provides the justification for it, then we can't just automatically generalize by naming what we see. The table burns does not automatically and correctly become all tables burn. The justification does not exist. Harriman tries to argue that somehow putting it into words does not need justification, because it automatically arrives at the truth. But only a perversion of contextual theory that dismisses any possibility of error could justify this, and that same theory would justify any approach! They are trying to make an exception for "first-level" generalizations so it doesn't need to be justified, and can therefore act as an equivalent to perception as an automatic and flawless process that become the foundation for further knowledge. I think that even these "first-level" generalizations need to be justified, and I think the attempt to treat them as automatic and flawless is wrong. I think they don't really justify that approach, and I think there are counterexamples.

Post 57

Tuesday, March 1, 2011 - 12:02am

Just a brief comment on certainty. Glenn wrote,

I'm only describing (maybe not very well) the contextual nature of certainty. Given my context of knowledge, I can be certain of my conclusion, but I could be wrong.

According to a Wikipedia entry, "Certainty can be defined as either (a) perfect knowledge that has total security from error, or (b) the mental state of being without doubt." I take it, Glenn, that you're referring not simply to psychological certainty (i.e., to the mental state of being without doubt), but to epistemological certainty. However, by the latter you do not, contrary to the Wikipedia entry, mean perfect knowledge that has total security from error. So you (and I suspect Objectivism) are not using epistemological certainty in its normally understood sense.

Objectivism also considers epistemological certainty as equivalent to knowledge, while simultaneously maintaining that one's knowledge could be mistaken. However, if I find myself mistaken about a conclusion that I had hitherto thought was true, I do not say that I knew it to be true, but now know that it's false. I say that I thought it was true, but now know that it's false. Granted, a claim to knowledge does prevent one from admitting the possibility of error, because if I thought I could be in error, I wouldn't claim knowledge in the first place. I'd simply say that I think that X is true, but that I could be wrong.

So I don't think that Objectivism's view of contextual certainty or contextual knowledge is correct. The discovery that not all type A bloods are compatible rendered false the conclusion that they are. It did not simply augment a previously true conclusion. Nor can one say that the compatibility conclusion constituted knowledge, albeit within an earlier context. One did not then know that all type A bloods are compatible, but now know that they are not. One thought, albeit with good reason, that they were compatible, but now know that they are not. One cannot know that two mutually exclusive propositions are both true. False conclusions, however rational, do not constitute knowledge.

Peikoff argues (in OPAR) that "since a later discovery rests hierarchically on earlier knowledge, it cannot contradict its own base." (P. 173) That's true, but it doesn't justify the claim that a false conclusion is "contextually" true or that it somehow constituted knowledge. Although the discovery of the Rh factor depended on previous knowledge, that doesn't mean that the previous conclusion that it falsified must therefore be thought of as true. Peikoff modifies that conclusion as follows: "Within the context of the circumstances so far known, A bloods are compatible." But here the conclusion isn't, "A-bloods are compatible"; it's "So far as I know, A bloods are compatible." Was that really the conclusion? Or was it "All A bloods are compatible"? He argues that the compatibility conclusion "represented real knowledge when it was first reached, and it still does so; in fact, like all properly formulated truths, this truth is immutable. Within the context initially specified, A bloods are and always will be compatible." (173)

Oh, come on! This is philosophical sleight of hand. The context initially specified was all type A bloods, and the conclusion was that all of them were compatible, which subsequent evidence showed to be false.

Post 58

Tuesday, March 1, 2011 - 12:36am

When I go on a longer sailing trip, depending upon where I am, my navigation may require a higher degree of confidence in some areas than others. I use estimates of the margin of error to apply to different navigational activities (e.g., plus or minus x percent of the listed offset by a current). What I'm talking about is not "feeling good" about my estimate but being able to shrink or expand my 'context' to maintain a level of safety.

When there is no danger anywhere near my current course, I won't add anything for a magin of error and just make a small point on the chart that uses the listed current. When I'm sailing in the vicinity of dangers (like submerged obstacles) I make a circle whose diameter represents the possible margin of error in measurement of current, and put the point marking my working position on the side of the circle farthest from the danger.

Estimating risk is a critical skill in life. We adjust our behavior based upon 'certainty' (whatever it is) of our estimates of risk. I'm not sure that this applies at all to the points you were making. But I noted how I adjust the boundary of my context to achieve 'certainty' that I can live with.

Post 59

Tuesday, March 1, 2011 - 10:01am