Your thoughts on Hume's case against induction?

[Fred Weiss]

Yes; I think that's the essence of Fred's objection to certainty as a singular state. The emotional and the epistemological integrate at the point of founding that feeling of confidence in rational analysis of the facts. And unfortunately, it is perfectly correct to use the term in both ways. Referring to the emotion with a word such as "confidence" may help keep the concepts separate.

Gee, I hope not. Then I'd be falling into Gordon's distinction of "feeling" certain vs. "epistemic" certainty (which we all concluded I thought was an "anti-concept").

Just to clarify for the benefit of those who are unfamiliar with these hpo debates, it is possible for people to *feel* certain about many things, including the irrational. So obviously merely feeling certain doesn't constitute any basis for rational certainty. Rational certainty must be arrived at by reason supported by conclusive evidence, with no contrary evidence. So, whatever feelings may accompanying it, the rational basis for the certainty is not a feeling.

The question is whether a degree of evidence can be achieved sufficient for such certainty, but where additional supporting evidence can add even more weight to that certainty, making it in effect "even more certain".

I haven't been ignoring the arguments of all you "singularists", I'm just still thinking about it.

Incidentally, in relation to the discussion of rationalism, I'll pass along a "secret" to all of you on how to ward off that mode of thinking. I won't be convinced about this issue until I can thoroughly *concretize* it in my mind, i.e. reduce it to actual examples in reality. The reason for my delay is that, given the limited amount of time I've had to devote to this issue, the only examples I can come up with so far support the "singularist" argument. But I want to keep trying to come up with a counter example(s) - in effect, "See, here's an example of justifiable certainty, but where adding more evidence makes it even more certain". Something like, "It was certain that Saddam Hussein had WMD and he constituted a danger to us in that regard." Then we discover some actual caches of the stuff and some of the people involved in the program admit that he was planning to use them. Now we can be "even more certain of it". Notice, if it were true that the former was sufficient for the certainty and justified the invasion, then mentioning the discovery of actual caches of the stuff shouldn't matter and would be entirely superfluous. But I doubt anyone would fail to mention it if such evidence existed. If it doesn't add to the certainty, why mention it?

Fred Weiss

[Eddie]

Beaster: “The key here is to recognize that induction is not deduction. This means you don't state it in the form of a syllogism, and don't even think of it as deduction.”

Sure, induction is not formal logic, but inductive arguments do contain premises and conclusions, otherwise you couldn’t run a line of argument. Here’s one. Premise: I have observed the sun to rise for the last 50 years; conclusion: therefore, it will rise tomorrow.

Betsy: “Things act in accordance with their natures. Things with the same natures act the same.”

Betsy, you are just repeating my own words back to me. I queried how we can justify principles such as “like things act alike” and “nature is uniform” without appealing to those principles. You then promptly appeal to the very same principles. “Things act in accordance with their natures”, “things with the same natures act the same”, “like things act alike” and “nature is uniform” all express the same principle in different words.

One of the problems with reducing an inductive generalisation to an identity statement is that the latter tells us no more than what we already know. An inductive argument regarding cows’ jumping ability could run thus: 1) Some observed cows have limited jumping ability; 2) This is the case because of the nature of cows; 3) Therefore, all cows have limited jumping ability.

Thus, the conclusion (3) takes us beyond premise (1); we have extrapolated from “some observed cows” to “all cows”. But note that the identity statement (2) is also a premise of the argument. Reducing an inductive conclusion to an identity statement merely folds the conclusion back into the premise.

This procedure highlights the question-begging nature of the enterprise, viz: cows can’t jump over the moon because, well, cows can’t jump over the moon.

E

[y_feldblum]

Eddie, "Premise: I have observed the sun to rise for the last 50 years; conclusion: it will rise tomorrow" is not an inductive argument, except as all philosophy but Ayn Rand's would have it. Induction is tied to concept-formation; it is not merely perceptual, or memorization by rote.

[DavidOdden]

Eddie, "Premise: I have observed the sun to rise for the last 50 years; conclusion: it will rise tomorrow" is not an inductive argument, except as all philosophy but Ayn Rand's would have it.  Induction is tied to concept-formation; it is not merely perceptual, or memorization by rote.

I don't follow this. Are you saying that Rand redefines the concept of induction so that it is different from previous definitions? Induction certainly is indeed tied to concept formation, but the correct horse-cart relation is that concepts are formed inductively -- generalization to a universal statement from specific instances. Inductive generalization is what makes concept formation more than mere memorization.

[y_feldblum]

David Odden,

The process of forming and applying concepts contains the essential pattern of two fundamental methods of cognition: induction and deduction.

The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction.  The process of subsuming new instances under a known concept is, in essence, a process of deduction.

[iTOE, 36.]

The Ayn Rand Lexicon, ed. Harry Binswanger

Rand would laugh at the argument by induction which Eddie cited, because it has nothing to do with concepts. Like the argument, "I have seen a million white swans and not one black one; therefore all swans are white and none black," that argument is concrete-bound, neither conceptual nor induction.

Moreover, one does not generalize to "universal statements" but to concepts, which are mental states, and from which one may formulate universal statements.

I believe you may have the hierarchical order of concept and induction upside down. Concepts are things of a certain nature, which consciousnes of a certain type may form, by a certain method, and apply, by a certain method. The former method is known as induction (though in other contexts other floating abstraction processes are known by the same name). Concepts are the primary, whereas induction is hierarchically based on concepts.

Rand recognizes that what others have called induction is so absurdly silly it's worthy of no name but "silly". She also noted that it's very similar to the correct method by which conceptual consciousness functions, and realized that people in general used examples of "silly" to mean the proper method of induction, which nobody had yet fleshed out and which nobody knew how it really worked. It is not she that is redefining; she gave the correct name to the method people wanted to name but had no idea what it looked like. Before her, none of the definitions for induction made any sense - and for the people who thought some "formal" definitions did, the world stopped making sense.

[DavidOdden]

Rand would laugh at the argument by induction which Eddie cited, because it has nothing to do with concepts. Like the argument, "I have seen a million white swans and not one black one; therefore all swans are white and none black," that argument is concrete-bound, neither conceptual nor induction.

Moreover, one does not generalize to "universal statements" but to concepts, which are mental states, and from which one may formulate universal statements.

The quote you provide shows Rand's recognition that concepts are formed by induction, but you seem to be implying something different, that induction is only valid for forming concepts, and not for any other purpos. Since you reject Eddie's example saying that it has nothing to do with concepts, I have to conclude that you do not think that a mental integration of two or more units sharing common characteristics, measurement omitted, is therefore a concept: it might be a concept, or it might not be. If that's what you're claiming, that's a point worth pursuing independently. I will assume that you are not claiming that. In which case, a concept is being formed, one pertaining to the actions of a specific entity. The measurement being omitted is "on which day does the sun rise". The conclusion "the sun will rise tomorrow" is thus a valid concept formed on the basis of numerous concrete observations (the number varies, according to latitude).

Universal statements are mental states. There is no difference between a universal statement and a concept -- the referents are exactly the same.

Concepts are the primary, whereas induction is hierarchically based on concepts.

More specifically, induction is the name applied to a particular aspect of concept formation, focusing on measurement omission.

Rand recognizes that what others have called induction is so absurdly silly it's worthy of no name but "silly".

Would you give me a quote that shows this? I'm not familiar with any such statement that she made.

[Betsy]

Rational certainty must be arrived at by reason supported by conclusive evidence, with no contrary evidence. So, whatever feelings may accompanying it, the rational basis for the certainty is not a feeling.

I regard that as necessary, but NOT sufficient. Until you have identified the causal characteristic(s) of the entit(ies) involved which reduce an inductive generalization to an identity, you may know THAT a certain thing always happens, but you don't know WHY it happens and HAS TO happen.

The question is whether a degree of evidence can be achieved sufficient for such certainty, but where additional supporting evidence can add even more weight to that certainty, making it in effect "even more certain".

If you can reduce your generalization to an identity, it is sufficient for certainty regardless of the quantity of the evidence.

But I want to keep trying to come up with a counter example(s) - in effect, "See, here's an example of justifiable certainty, but where adding more evidence makes it even more certain". Something like, "It was certain that Saddam Hussein had WMD and he constituted a danger to us in that regard." 

The issue for me is did we have evidence which reduced the proposition "Saddam had WMD just before we invaded" to an identity. We know he had WMD previously because we saw them. We know he had them because he used them. To use them he had to have them. Therefore, he had them because he had them. As to whether he had them just before we invaded, we don't have enough evidence to reduce it to an identity. He could have hidden them, sent them to Syria, or destroyed them. We can't reduce it to an identity without evidence as to what actually happened to the WMD he previously had.

Then we discover some actual caches of the stuff and some of the people involved in the program admit that he was planning to use them.

Then we know he had them because he had them -- right THERE.

Now we can be "even more certain of it".

I would say that NOW we can be certain, but not previously. What we had previously was only a high degree of probability.

Notice, if it were true that the former was sufficient for the certainty

But it wasn't.

and justified the invasion,

What justified the invasion was the high probability that he had WMD.

then mentioning the discovery of actual caches of the stuff shouldn't matter and would be entirely superfluous.

The reason it is not superfluous is that the discovery converts the epistemological status of the claim from a high probability to a certainty.

[Betsy]

Betsy: “Things act in accordance with their natures. Things with the same natures act the same.”

Betsy, you are just repeating my own words back to me. I queried how we can justify principles such as “like things act alike” and “nature is uniform” without appealing to those principles.

LOOK AT REALITY and you will see that they do. That's where the idea comes from in the first place.

When you see many examples of HOW causality reduces to identity, then you realize, logically, that it must be that way. Otherwise, you wind up with a contradiction.

If you think contradictions can exist in reality, show me where. If you don't think there is such a thing as reality, then there is nothing to talk about, is there?

[Betsy]

One of the problems with reducing an inductive generalisation to an identity statement is that the latter tells us no more than what we already know.

Oh yes it does! It shows us -- in reality -- what it IS about the subject of our generalization that makes the generalization true. For instance, it shows what it is about cows than limits their jumping ability.

An inductive argument regarding cows’ jumping ability could run thus: 1) Some observed cows have limited jumping ability; 2) This is the case because of the nature of cows; 3) Therefore, all cows have limited jumping ability.

That wasn't the argument presented at all. Here is the actual argument:

The only way cows can jump is by using their leg muscles. The leg muscles of cows are such that they allow the cows to jump to heights of a couple of feet at most. The moon is tens of thousands of miles away from any cow. A couple of feet is less than tens of thousands of miles. Therefore, a cow's jump, which is to a height lower than the moon, is to a height lower than the moon.

Observe that he is discussing ALL cows. He is discussing the NATURE of cows -- how they jump, the physiological characteristics of a cow jumping, etc. He is showing why what makes it a unit of the concept "cow" -- having a certain physiology -- is the SAME thing that accounts for its jumping ability.

He is showing much more than the fact that some cows haven't been observed jumping over the moon. He is showing what it is about all cows that limits their jumping to a certain height.

[y_feldblum]

DavidOdden,

Induction is the name of a method of concept-formation (along with being the name of plenty of other things, most of which make no sense). With Rand's concept of concept, we recognize that there is only one proper method of forming one, and this method is called induction.

Induction refers to other things as well, such as the sun example; but that would not be a method of concept-formation taking Rand's concept of concept. Induction is also used in mathematics (to test whether a statement about k is true for all positive integers k, one tests whether it holds when one substitutes 0 for k, and then when one substitutes (k + 1) for k).

Under Rand's epistemology, when one forms a concept, one omits all measurements. There is no one measurement to omit.

Moreover, if one forgets for a minute that the sun ever rose on any specific day, how does one conclude that the sun will rise tomorrow? That is not logical, in addition to it not being induction (taken to be the proper method of forming concepts).

A is not non-A, and strings of words written or said are not mental states. The referents of statement and of concept are not the same.

What I quoted is all that The Ayn Rand Lexicon has on induction. All it said was, concept-formation is inductive. From that perspective, the assertion that induction refers only to some particular part of concept-formation is ludicrous. Rand did not use the term often, except to note that her theory of concept-formation is what others meant but couldn't name or define when they used the term.

Rand didn't use my words re "so absurdly silly ..." - and I don't have a quote for the idea - but I suppose her sentiments can be found just about every three pages in ITOE.

But most troubling is that you seem to think this:

P: X did Y yesterday;

P: X did Y today;

C: therefore X does Y every day;

C: therefore X will do Y tomorrow

is a valid inductive argument. Other people would call it induction - Rand wouldn't - but either way it's not valid. The argument which purports to be induction is actually a bastardized and absurd form of deduction, where the first conclusion does not follow from the premises.

[DPW]

Under Rand's epistemology, when one forms a concept, one omits all measurements.  There is no one measurement to omit.

I might comment on your post further later, but I wanted to note that this is wrong. With some exceptions, one does not omit all measurements when forming a concept. One omits all particular measurements within a range.

[y_feldblum]

Don, true. Example, one omits the measurement "ten feet", though one may retain the requirement, "of usable size, ie, five to fifteen feet."

[DavidOdden]

Induction refers to other things as well, such as the sun example; but that would not be a method of concept-formation taking Rand's concept of concept.

Why do you say this not an example of concrete formation? I asked this before, and I'll ask it again.

Under Rand's epistemology, when one forms a concept, one omits all measurements.  There is no one measurement to omit.

That's not true. There is clearly a concept "quadruped": it is defined as "animal with 4 legs". That is a measurement, and it cannot be omitted. You omit other non-essential measurements (such as weight, length, body temperature, having fur, etc.), but not all measurements. The concept "insect" must include a measurement of leg count.

A is not non-A, and strings of words written or said are not mental states.  The referents of statement and of concept are not the same.

Statements are not required to be spoken or written. I disagree with your characterisation of statement, but I see no point in arguing with you on that. The important point is that induction is the recognition 'this is the defining characteristic of all units identified by this concept', which is a universal statement.

What I quoted is all that The Ayn Rand Lexicon has on induction.  All it said was, concept-formation is inductive.  From that perspective, the assertion that induction refers only to some particular part of concept-formation is ludicrous.

ITOE discusses concept formation in a fair amount of detail. Starting on p. 9, as part of the process of concept formation, two or more units must be isolated, i.e. abstracted from reality. The process is not induction (Rand does not identify it as induction). A similarity between the units must be recognised, and this recognition is also not induction. There is more to say about concept formation: but I hope this is enough that you can see that concept formation is not identical to induction (leaving out the unrelated uses as in "induction coil" or "mathematical induction" as irrelevant). The only way you can deny that induction is a part of concept formation is to argue that it playts no role in concept formation (which you wuold not argue), or that it is the entirety of concept formation, and I've shown you why you cannot do that.

Rand did not use the term often, except to note that her theory of concept-formation is what others meant but couldn't name or define when they used the term.

Rand didn't use my words re "so absurdly silly ..." - and I don't have a quote for the idea - but I suppose her sentiments can be found just about every three pages in ITOE.

I'd like you to simply find any place in Rand's writings where she denigrates induction and derides others for having a bad version of induction. I looked at all instances of "induction" on the CD and cannot find anything at all to support your view, so I'd like you to tell me exactly what I missed. Something she says in FTNI p. 30 and repeats in the foreword to ITOE, speaking of the failings of post-Renaissance philosophy is relevant, in terms of her negative opinion of others:

They were unable to offer a solution to the 'problem of universals,' that is: to define the nature and source of abstractions, to determine the relationship of concepts to perceptual data—and to prove the validity of scientific induction

This is not an attack on others' versions of induction -- it is an attack on their failure to come to grips with induction.

But most troubling is that you seem to think this:

P: X did Y yesterday;

P: X did Y today;

C: therefore X does Y every day;

C: therefore X will do Y tomorrow

is a valid inductive argument.  Other people would call it induction - Rand wouldn't -but either way it's not valid. The argument which purports to be induction is actually a bastardized and absurd form of deduction, where the first conclusion does not follow from the premises.

I'm curious to know how you came to "know" that I think the above is a valid argument? I'm especially curious because I do not, so I'd like to know about the extra knowledge that you've got that I don't have.

Just to make clear why this cannot be valid, a valid conclusion requires integration of all of a person's knowledge: the person will have knowledge which prevents inductive generalization from just these two instances. I will tell you what that knowledge is, if you tell me what X and Y refer to, also "yesterday" (I can compute "today" if you tell me that value). I may need the exact day if, for example, X is "The sun" and Y is "rose in Tromsø".

[y_feldblum]

David Odden, the sun example, which I now recall is not yours but Eddie's, is not concept-formation because it does not deal with essential attributes. Concept-formation involves coming to understand the fundamental nature of a class of things. The sun example does not do this. No fundamental nature is being analyzed, no essential attributes are being abstracted from. All that happens is one leaps from "many times" to "all". Concept-formation is detailed quite well in ITOE and in OPAR; I needn't go into it here. The sun example, though, does not fit the pattern there identified. (I apologize for attributing that example to you.)

If a table has "a flat surface" by its definition (ie, incorporated into the concept), why cannot quadrupeds have "a leg and a leg and a leg and a leg"?

Ayn Rand had little to say about induction, other than that it was valid and other philosophers ought to have identified that fact long ago. But I don't recall her going into much detail about specifically what it is; she just didn't use that word. I can't lay claim to knowing, by her extensive writings on the word, whether it means the entire method of forming concepts or only part of it; all I can say is, from the two paragraphs I saw in Lexicon, that concept-formation is inductive, that is, its method is induction. But those paragraphs tell me the answer to the question, "how do I form concepts?": "by induction."

Ayn Rand denigrates what is not induction, or such is my recollection. But I simply don't feel like scouring her works to find a reference for that recollection. It'd be a lot of work and I've got plenty to do right now. But neither did I say that Rand denigrates it using specific terms. But you can try "definition by non-essentials," which is akin.

I recall Ayn Rand attacking some concept termed induction, but not induction.

[Eddie]

y Feldblum: “Like the argument, "I have seen a million white swans and not one black one; therefore all swans are white and none black," that argument is concrete-bound, neither conceptual nor induction.”

An inductive argument is one that derives a general principle from specific examples. In this and my sun example, the inductive premise – eg “nature is uniform” -- has been assumed. I guess I should have filled in the gaps. The above argument then becomes: I have seen a million white swans and not one black one; nature is uniform; therefore all swans are white and none black. The conclusion follows from the premise, via the inductive principle.

E

[Eddie]

Betsy: “LOOK AT REALITY and you will see that they do. That's where the idea comes from in the first place.”

Staying with our cow example, assume I decide to investigate the jumping ability of cows, as a means to ascertain whether they could jump over the moon. I choose only cows; I don’t include Little Jack Horner – except perhaps as a control. In that case, if my choice of cows is not to be arbitrary, it must be based on some justification. Nor can it be based on previous observations of cows without entering an infinite regress.

My choice of cows must then be based on some principle. Principles such as “like things act alike”, “things act according to their natures” or similar, would seem to fit the bill. And these are inductive principles. Of course, observing reality, in this case the behaviour of cows, does lead to more knowledge, and can confirm the inductive principle, but it doesn’t establish it because our investigations are already predicated on the very same principle.

Betsy: “Observe that he is discussing ALL cows. He is discussing the NATURE of cows -- how they jump, the physiological characteristics of a cow jumping, etc.”

My argument was: 1) Some observed cows have limited jumping ability; 2) This is the case because of the nature of cows; 3) Therefore, all cows have limited jumping ability. Bearster’s ideas about cows must surely be based on the observation of specific cows, since he cannot observe all cows.

These observations are then generalised across all cows in the requisite inductive manner. This generalisation from some cows to all cows requires a connecting principle. It makes no difference how one expresses this principle, as long as it provides a connection between the specific and the general. But if we wish to forestall an infinite regress, this principle cannot be derived from the observation of the cows.

In that case, my argument above accurately encapsulates Bearster’s procedure of investigating cows. His observations may certainly provide us with lots of useful information about cows. But they do not establish a logical basis for induction.

E

[y_feldblum]

Eddie, that may in fact be termed induction, but it is not what Rand termed induction and it has nothing to do with concept formation. I advise you to read Introduction to Objectivist Epistemology for a discussion of what is concept formation and induction.

Induction as you have it is not valid. Induction as Rand has it is.

I would like to note, in addition, that you have drastically misused the premise, "nature is uniform." It doesn't mean anything like you take it to mean, as I have observed you take it.

[Betsy]

My argument was: 1) Some observed cows have limited jumping ability; 2) This is the case because of the nature of cows; 3) Therefore, all cows have limited jumping ability. Bearster’s ideas about cows must surely be based on the observation of specific cows, since he cannot observe all cows.

These observations are then generalised across all cows in the requisite inductive manner.

That's wrong. Induction in neither enumeration of concretes nor a leap of faith from the observation of some concretes to conclusions about ALL concretes. Nor does inductive certainty require omniscience -- i.e., the observation of ALL cows.

Induction is the search for causes. If you find the cause with one observation of one cow, you can stop. If you have to observe more cows to see how they move and jump before you find the cause, you observe more. If you have to dissect cows, or animals similar to cows, to find the cause, that's what you need to do.

Since the Aristotelian/Objectivist view of causes is so different from that of David Hume, that is probably what we need to discuss first. Until you understand our view of causality, we're not going anywhere with induction.

[DavidOdden]

David Odden, the sun example, which I now recall is not yours but Eddie's, is not concept-formation because it does not deal with essential attributes.  Concept-formation involves coming to understand the fundamental nature of a class of things.

That would be true of we were forming the concept "the sun", but in this case the concept refers to actions of the sun (which presupposes the concept "sun"). So daily rising is an essential attribute. The class of things we're speaking of is solar risings. (Also, I hope you understand that I'm assuming a limited knowledge context, one which hasn't been valid for quite a long time -- the sun never rises, and it doesn't even do that thing every day).

[Eddie]

y Feldblum: “Eddie, that may in fact be termed induction, but it is not what Rand termed induction and it has nothing to do with concept formation. I advise you to read Introduction to Objectivist Epistemology for a discussion of what is concept formation and induction.”

I read the book some time ago, although I don’t remember that Rand said a lot about induction, apart from some passing comments to the professors in the appendix.

y Feldblum: “I would like to note, in addition, that you have drastically misused the premise, "nature is uniform." It doesn't mean anything like you take it to mean, as I have observed you take it.”

I’m not sure what you mean by this. Perhaps you could expand.

E

[Eddie]

Betsy: “Since the Aristotelian/Objectivist view of causes is so different from that of David Hume, that is probably what we need to discuss first. Until you understand our view of causality, we're not going anywhere with induction.”

The standard modern view of causation is something like “a relationship between two events or states of affairs, such that the first brings about the second". A simple example would be the billiard ball one, where one ball strikes another and causes it to move in a certain direction at a certain velocity.

As I understand it, Aristotelian causation concerns the nature of objects and how objects act in accordance with their nature, roughly “identity in action”. However, the early modern scientists found this understanding to be a barrier to their work, which involved the measurement of relationships – “forces” – between objects (‘events’) rather than within objects.

But regardless of whether one takes causation to refer to the relationship between objects, or some internal nature, I can’t see how this solves the problem that Hume identified, the logical problem of induction, especially since Hume includes our notions about causation as part of the problem.

E

[Betsy]

Betsy: “Since the Aristotelian/Objectivist view of causes is so different from that of David Hume, that is probably what we need to discuss first. Until you understand our view of causality, we're not going anywhere with induction.”

The standard modern view of causation is something like “a relationship between two events or states of affairs, such that the first brings about the second". A simple example would be the billiard ball one, where one ball strikes another and causes it to move in a certain direction at a certain velocity.

As I understand it, Aristotelian causation concerns the nature of objects and how objects act in accordance with their nature, roughly “identity in action”.

That's pretty close.

However, the early modern scientists found this understanding to be a barrier to their work, which involved the measurement of relationships – “forces” – between objects (‘events’) rather than within objects.

I don't see why that should be so. It is the nature of the objects which account for the relationships between objects including the forces between them. I relate differently to men than to women and I relate differently to people than I do to billiard balls.

But regardless of whether one takes causation to refer to the relationship between objects, or some internal nature, I can’t see how this solves the problem that Hume identified, the logical problem of induction, especially since Hume includes our notions about causation as part of the problem.

My view of induction -- there is no "Objectivist" theory of induction -- is that causation, as Objectivists construe it, is the key to solving the Problem of Induction.

First off, Hume's "billiard ball" model doesn't even account for the actions of billiard balls, let alone all of causality. The Objectivist view, on the other hand, explains what things are by investigating and discovering what things are resulting in conclusions that are as certain as "A is A."

[y_feldblum]

Eddie, Ayn Rand said little about induction; whether she had other terms for it or she did not formalize the concept, I don't know.

But whatever "X yesterday, X today; then X everday; then X tomorrow" is, it is not valid. And that is exactly the pattern of the sun example and the swans example.

The way you used the prhase "nature is uniform" - ie, which concept you were referring to - does not resemble in the slightest the way Betsy used it. "Nature is uniform" means things act predictably, ie, according to their nature; not that once you've seen one or one million, you've seen them all.

[DavidOdden]

But whatever "X yesterday, X today; then X everday; then X tomorrow" is, it is not valid.  And that is exactly the pattern of the sun example and the swans example.

We know that these two conclusion (daily sun rising, swan color) are actually, factually false so given knowledge of the relevant facts, deriving those conclusions is of course invalid. But knowledge -- thus conclusions -- are contextual. If you are speaking of the knowledge context where we know the concretes than invalidate the conclusion, then there is no question that your assessment is correct. But not everybody has that knowledge: so for such a person, are you claiming that the conclusion is still invalid? (And if so, why?)

[y_feldblum]

Why should it be valid? My argument is the rejection of a positive.