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Your thoughts on Hume's case against induction?

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Betsy: “Then how do you establish that one form of argument is correct and another form of argument is incorrect? By referencing and appealing to WHAT?”

In the case of traditional formal logic, by appeal to the structure of the argument, and the various rules of inference.

How? [can inductive generalisations be justified] Please explain in detail.

As I said before, they’re justified by how well they predict outcomes. Take your original example of round things. If we observe that round things will roll at such and such a velocity under such and such conditions, and work up a theory, and future experiments bear this out, then we have justified our inductive generalisation. We can test for falsity by varying the conditions, using square things as a control, and so on.

E

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Fred: “What is the probability - or the basis for any doubt whatever - that the earth orbits the sun, that a cow can't jump over the moon, or that the WTC was not destroyed and is still standing? Just semantics?”

What I have in mind here is the use of ‘context’ as a polemical device, since it’s possible to posit several different contexts for the same subject. While context has a perfectly legitimate use, I think there’s a strong tendency among Objectivists to make of it a polemical device.

Fred: “Look, with the exception of knowledge which pertains to existence and our knowledge of it as such (axioms), all knowledge is contextual.”

I agree that knowledge is contextual, which is why I think it’s unhelpful to make ‘context’ into a type of philosophical principle, rather than a useful rule of thumb.

Fred: “The irony is that the position you are upholding claims to be empirical and yet you deny the most evident fact of human knowledge, that we are absolutely certain of a great deal and that our knowledge is continually growing by leaps and bounds.”

Now you’ve upped the ante from “contextual certainty” to “absolute certainty”. What’s the point? We’ve agreed that we possess a lot of knowledge, and that we can be confident about a good deal of it. And as you say, here we all are, so we can rule out luck or circumstance as a basis for knowledge. It just strikes me that the insistence on certainty, absolute or otherwise, protests too much.

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...Yes, but at what point do we know that all the facts are in? We know from history that our knowledge on all sorts of subjects changes, sometimes quite abruptly, and in a way that invalidates previous knowledge.

Actually what we know from history is that while knowledge changes, expands and/or becomes more precise, it is not invalidated. Knowledge is always subject to change. We learn more. But that doesn't necessarily invalidate what we previously knew. If some fact is discovered and properly verified to be true, we may learn more about it with future investigation. We might for example discover that it is only true in certain limited domains (for example Newton's Laws). But future knowledge doesn't contradict it. Einstein's theories for example do not contradict Newton. Which is why, despite the fact that we now know that Newton's Laws are inapplicable in a number of areas (such as sub-atomic particles), they are still applicable in others. And while future theories in physics may be needed to explain certain phenomena which Einstein's theories do not, they will not invalidate Einstein's theories. GPS satellites will not fall out of the sky if it is discovered that Einstein's theories cannot explain some strange new phenomena, anymore than buildings collapsed when it was discovered that Newton didn't explain some things.

When explorers discovered the Americas, some highly speculative theories (which as such could not be considered knowledge) were debunked but much of the knowledge remained valid and was simply expanded and got more precise with increasing exploration. Some of what Lewis and Clark may have said, based on flimsy evidence, was perhaps later invalidated but it was probably mostly a matter of much of it just being made more precise. Future explorers simply built on their work.

It cannot possibly be explained how civilization grew and how we got from oxcarts to spaceships without grasping that knowledge builds on knowledge, new knowledge in fact not invalidating previous knowledge but expanding it.

For more on this I suggest the section in OPAR where Peikoff discusses this issue and I would draw your attention in particular to his discussion of "blood types".

Once again, how many more facts do we need to get in to know for certain that the earth orbits the sun or that a cow can't jump over the moon? And actually, if you pause to think about it, we can fill shelves and shelves in libraries with comparable knowledge. Without that knowledge, how could we have gotten to the moon and back? Consider the magnitude of the knowledge, in many areas, that was required for such an undertaking. Certain knowledge, not mere guesswork. And if you need verification that it was certain, well, we did it, right? In fact, doing it added even more to our cornocopia of knowledge and certainty. Thus, off we went to Mars. And in future decades building on that knowledge, we may head even further out. Is this a picture of knowledge invalidating knowledge?

Once again I recommend the reading of this work by D.C. Stove which debunks the Hume/Popper view you are espousing:

http://www.geocities.com/ResearchTriangle/...per/popper.html

Fred Weiss

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Betsy: “Then how do you establish that one form of argument is correct and another form of argument is incorrect? By referencing and appealing to WHAT?”

In the case of traditional formal logic, by appeal to the structure of the argument, and the various rules of inference.

Yes, but where do those rules come from and why is one "structure" better than another? Why is a syllogism without an undistributed middle preferable to one with one? Why is reasoning that does not lead to a contradiction better than reasoning that does?

How? [can inductive generalisations be justified]  Please explain in detail.

As I said before, they’re justified by how well they predict outcomes. Take your original example of round things. If we observe that round things will roll at such and such a velocity under such and such conditions, and work up a theory, and future experiments bear this out, then we have justified our inductive generalisation. We can test for falsity by varying the conditions, using square things as a control, and so on.

Using the prediction of outcomes as your standard, you can only show that SOME round things have rolled but never that ALL round things roll. Since a generalization is always of the form "ALL [units of a concept] .... [are or do something]," you haven't really justified or proved anything about the generalization at all. The Humean approach leads nowhere.

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All that is true, and that’s what this thread is about.  As I say, I am talking about standard formal and informal logic, where the standard understanding is that different considerations apply.

But you still seem to be conflating "standard" logic and formal logic. The former pertains to a particular set of relations, and the latter pertains to systematizing those relations as formal symbolic rules. The concept of validity pertains not to the specific relations, but to the "formal" aspect, namely "follows the rules". This is why the claim that induction is "not valid" is false. In a formal system that includes inductive generalization, induction is T-preserving. Special conditions can be stipulated so that inductive inferences can be declared "invalid", but that is only because of those stipulations, and not the concept of validity itself. Induction is formally valid, but non-standard (which is a sociological construct).

DavidOdden: “Setting aside the fact that all mice aren't black, you cannot stipulate that statement ex nihilo -- it is not axiomatically true.”

I’m not claiming axiomatic status for the statement.

I realize that: but in a formal Objectivist logic, you have to. This is one of the major differences between what constitutes a valid formal proof in "standard" formal logic and Objectivist logic, that "standard" formal logic puts no conditions on what statements can be used in a derivation.

I guess we have a different view of deductive arguments. In my view, one of their major functions is to draw out or highlight the implications of the major premise. In that case, conflating validity and truth can lead one to assume that since the form of the argument is valid, the content is also true, when this is not necessarily the case. Counter-examples, such as my black mice one, highlight this aspect. Also, since the example cannot be faulted on form, this at least shows that a distinction between form and content can in fact be made.

Well, it can be faulted on form, though not in the system you are operating under where unsound arguments are allowed as "valid". But more importantly, this highlighting of the "implications" of the major premise is false, because your garden variety FOPL does not highlight the implications of any actual premises. The assertion "All mice are black" actually implies that there exist mice -- at least one. But the standard formalization of that statement does not have that implication. So what a formal deduction is, is a system for deriving new strings of symbols from existing strings of symbols, but these strings of symbols have no necessary relationship to premises in an argument.

But what I think deduction does give you is a tool for checking whether you have translated the premises correctly into predicate calculus. It's a pretty fallible tool, though. Also useless since the predicates themself end up being incorrectly treated as atoms.

Yes, but at what point do we know that all the facts are in? We know from history that our knowledge on all sorts of subjects changes, sometimes quite abruptly, and in a way that invalidates previous knowledge. (Of course, this is also an inductive argument, but its justification lies not in appeals to the past, nor to some supposed “nature” of the scientific enterprise, but rather in future outcomes.)

Facts are never "in": they simply "are". Fact refers to metaphysical state of affairs, and we have knowledge of some of these facts. I will henceforth substitute "evidence" which is what I believe you mean. The answer is, never. We are never omniscient, and omniscience is exactly what is required for all of the evidence to be in (known). I take issue with your assertion that new evidence invalidates old knowledge: it cannot (however, new evidence can invalidate a previous conclusion, and new evdence can show that a particular phrasing of your knowledge may be wrong). The main point is that certainty is not the same as "certainty without the metaphysical possibility of error". That is the standard that the skepto-nihilists demand for the concept "certainty", and the reason is that they wish to deny that there is knowledge (by degrading the concept of "knowledge" to "suspicion"). As you presumably know, if you adhere to that standard for certainty (sometimes known, quite confusingly, as epistemic certainty), you cannot be certain of anything at all, including deductive proofs.

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DavidOdden: “But you still seem to be conflating "standard" logic and formal logic. The former pertains to a particular set of relations, and the latter pertains to systematizing those relations as formal symbolic rules.”

Perhaps we’re talking past each other. By “standard” I mean generally accepted notions of logic. By ‘formal” I mean “classical” or “Aristotelian” logic, as well as the various types of modern logics. By informal logic, I mean “inductive” style arguments such as analogy and simple enumeration.

I have been referring to classical and inductive logics, rather than modern logics, which are not my forte. In regard to classical logic, there is a general or standard understanding that form and content are independent. That is, the formulation: “All As are Bs; all Bs are Cs; therefore all As are Cs’” is valid regardless of the truth of the actual values represented by A, B and C. The formulation can also be understood as valid independently of these values. I’m aware that Objectivism doesn’t agree with this separation between content and form, and that it places conditions on what statements can be used in a derivation.

DavidOdden: “But more importantly, this highlighting of the "implications" of the major premise is false, because your garden variety FOPL does not highlight the implications of any actual premises. The assertion "All mice are black" actually implies that there exist mice -- at least one.”

The syllogism as I expressed it details the relationship between propositions about mice, black things and blind things, and the conclusion spells out the implied relationship. But this relationship is a matter of form. Whether it exists in reality requires us to go beyond what is implied in the syllogism. One can test this by the assertion: “All mice are black”. If this implies the existence of mice, then “All unicorns are fierce” implies the existence of unicorns.

But what I think deduction does give you is a tool for checking whether you have translated the premises correctly into predicate calculus. It's a pretty fallible tool, though. Also useless since the predicates themself end up being incorrectly treated as atoms.

DavidOdden: “I take issue with your assertion that new evidence invalidates old knowledge: it cannot (however, new evidence can invalidate a previous conclusion, and new evdence can show that a particular phrasing of your knowledge may be wrong).”

This is taking us beyond the subject of induction. I agree that in many cases, new knowledge builds on old, but sometimes a sea-change occurs in human thought, where earlier knowledge is invalidated. The replacement of the Ptolemaic system of planetary motion is one such example.

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Fred: “Actually what we know from history is that while knowledge changes, expands and/or becomes more precise, it is not invalidated. Knowledge is always subject to change. We learn more. But that doesn't necessarily invalidate what we previously knew.

Perhaps invalidate is too strong a word, although some major past theories have since been debunked. On the other hand, if factual knowledge is understood as justified true belief, much that has previously passed as knowledge may not have qualified as knowledge anyway.

What I have in mind here is somewhat similar to what you say about the way that our understanding of Newton’s laws is modified in the light of Einstein’s theories. I heard something on the radio a while back to the effect that a physicist of the 18 century, who had absorbed Newton’s theories, would with some difficulty be able to converse with a modern physicists, whereas a pre-Newton physicist would be totally lost.

Maybe the speaker was over-stating the case, especially when one compares Newton’s laws with relativity, but I think there’s more than a grain of truth in what he said. It seems that periodically the human species undergoes major shifts in what I would call world-view, so that previous knowledge and ways of life are seen through quite a different lens.

This new perspective doesn’t necessarily invalidate old knowledge, but may well cast it in a new light, with the effect that the old knowledge becomes for us something different from what it was for our forebears.

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Betsy: “Yes, but where do those rules come from and why is one "structure" better than another? Why is a syllogism without an undistributed middle preferable to one with one? Why is reasoning that does not lead to a contradiction better than reasoning that does?”

The rules of logic are not like trains. They don’t “come from” anywhere. They are created for a particular purpose. Logic is about ensuring correct reasoning and consistency of belief. An argument consists of moving from one proposition to another, according to certain rules that connect the propositions.

A syllogism with a distributed middle is regarded as valid because it connects the terms of the major premise with those of the conclusion, as per my mice example, viz: mice, blackness; blackness, blindness; mice blindness. Where a term is undistributed, the connection fails. A contradiction indicates an inconsistency in the terms used, and is therefore to be avoided. And so on.

Betsy: “Using the prediction of outcomes as your standard, you can only show that SOME round things have rolled but never that ALL round things roll. Since a generalization is always of the form "ALL [units of a concept] .... [are or do something]," you haven't really justified or proved anything about the generalization at all.”

The generalisation in this case will take the form: under certain conditions, round things roll. That is sufficient as a generalisation, and takes into account context. Of course, it's only as good as the predicted outcome, but that's the way of science.

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...Perhaps invalidate is too strong a word, although some major past theories have since been debunked. On the other hand, if factual knowledge is understood as justified true belief, much that has previously passed as knowledge may not have qualified as knowledge anyway.

But if it was merely "justified true belief", i.e. they felt justified in believing it, then why shouldn't it be considered knowledge? That's actually what's wrong with regarding knowledge as equivalent to mere "justified true belief". What is needed for knowledge is proof, i.e. conclusive evidence. For over a 1,000 years people felt justified in believing in the Ptolemaic theory of the solar system. But the evidence for it not only was far from conclusive but there many indications of contrary evidence (of which Ptolemy himself was aware and tried to gloss over with his "epicycles").

Newton is entirely different. Not only was the evidence conclusive, repeatedly confirmed and re-confirmed in the 100+ years after him, but it continues to be right up to the present day - to such an extent that, as the "certainty singularists" will remind me, it is no longer necessary, i.e. it is absolutely certain, period, and no additional evidence is required to bolster that certainty. The difference now is that we know it doesn't apply in a number of physical domains. Our worldview is different now to the extent that we are now aware - to a considerable extent because of Newton - of physical phenomena of which Newton was entirely unaware (such as sub-atomic particles). But Newton was absolutely essential as a first step in that progression of knowledge. Before we could ever have begun to grasp some of these new phenomena it was necessary first to grasp the more basic phenomena - and that couldn't have been done without Newton.

So, once again, not only doesn't modern physics invalidate Newton, it rests on his shoulders. Just, presumably, as any future physics will rest on Einstein. I am sure that most modern physicists, as Stephen contends, will fully acknowledge this when they are in their laboratories even as they feel obliged to mouth the Popperian dogma of skeptical doubt when they philosophize about the epistemology underlying their work.

Fred Weiss

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Betsy: “Yes, but where do those rules come from and why is one "structure" better than another? Why is a syllogism without an undistributed middle preferable to one with one? Why is reasoning that does not lead to a contradiction better than reasoning that does?”

The rules of logic are not like trains. They don’t “come from” anywhere.

They don't come from reality?

Are they just made up arbitrarily for the hell of it? Are they based on fantasy?

They are created for a particular purpose. Logic is about ensuring correct reasoning
If your standard is subjective, correct reasoning is whatever you feel is correct. If your standard is social, it is what the majority believe is correct as shown in an opinion poll. "Correct reasoning" by what standard?

and consistency of belief.

Why is consistency of belief of any value?

An argument consists of moving from one proposition to another, according to certain rules that connect the propositions.
Is ANY method that connects propositions equally valid? Can I connect propositions based on the rule: "Two propositions can validly be connected if at least two words in the first proposition appear in the second proposition." If not, why not?

A syllogism with a distributed middle is regarded as valid because it connects the terms of the major premise with those of the conclusion, as per my mice example, viz: mice, blackness; blackness, blindness; mice blindness. Where a term is undistributed, the connection fails.

WHY is it "regarded as valid" and an undistributed middle is not?

A contradiction indicates an inconsistency in the terms used,
WHY?

and is therefore to be avoided.

WHY? What's so bad about inconsistency?

Betsy: “Using the prediction of outcomes as your standard, you can only show that SOME round things have rolled but never that ALL round things roll. Since a generalization is always of the form "ALL [units of a concept].... [are or do something]," you haven't really justified or proved anything about the generalization at all.”

The generalisation in this case will take the form: under certain conditions, round things roll. That is sufficient as a generalisation, and takes into account context. Of course, it's only as good as the predicted outcome, but that's the way of science.

In other words, all you are saying is "Under certain conditions SOME round things have rolled." Since a generalization is always of the form "ALL [units of a concept] .... [are or do something]," you haven't really justified or proved anything about the generalization at all.

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But if it was merely "justified true belief", i.e. they felt justified in believing it, then why shouldn't it be considered knowledge?

On re-reading, I realize this opening sentence doesn't make any sense and, if it means anything, actually suggests the opposite of what I intended to convey. So, if I could edit my post, I'd remove it.

Fred Weiss

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Fred: “That's actually what's wrong with regarding knowledge as equivalent to mere "justified true belief". What is needed for knowledge is proof, i.e. conclusive evidence.”

The theme of this thread has been this very point: what counts as justification for inductive-type knowledge? What counts as “proof” or “conclusive evidence”? If a long run of successful predictions is regarded as conclusive evidence, I won’t argue with that. Of course, it's more difficult to justify some knowledge in that way – historical, economic, psychological etc – but long-run successful prediction would be sufficient justification for especially scientific knowledge.

As for Newton and certainty, yes, we now understand his theories as being justified within certain parameters, and that modification has implications for generalisations we might make according to Newtonian physics. We need to stipulate the conditions under which the physics applies. Where previously Newton’s laws were regarded as universal, they are now seen as local, so any previous certainty on this point has been shown to be misguided.

E

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Betsy: “Are they [the rules of logic] just made up arbitrarily for the hell of it? Are they based on fantasy?”… "Correct reasoning" by what standard?”

As I mentioned before, the rules of logic are created to ensure correct reasoning and consistency of belief. Fantasy has nothing to do with it. The standard of validity is consistency between statements. This is of value because to hold inconsistent beliefs is to fall into contradiction, and non-contradiction in logic is a matter of necessity.

Betsy: “Can I connect propositions based on the rule: "Two propositions can validly be connected if at least two words in the first proposition appear in the second proposition."

Of course not. The terms in question must be what the proposition is about. The proposition “all mice are black” and the conclusion “all mice are blind” are about the terms mice, blackness and blindness, not about the term “are”, and they require a distributed middle that connects them.

Betsy: “WHY is it [a distributed middle] "regarded as valid" and an undistributed middle is not?”

The distributed middle is valid because it connects the terms of the major premise with those of the conclusion. The validity arises from consistency and coherence, which is demonstrated by the meanings of the terms and the way they are connected, as above.

Best: “In other words, all you are saying is "Under certain conditions SOME round things have rolled."

No. I’m saying that "under certain conditions, all round things of a certain type will roll”. The justification is borne out by what actually happens during subsequent experiments.

E

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"When on innumerable occasions we observe certain experiences succeeding others, we naturally feel under similar circumstances in the future like events or causes will be followed by like effects. ... only custom or habit may validly be said to serve as the foundation for this causal idea."17 There is no guarantee, no matter how accustomed we may have become to certain sequential events of the past that the sequence will necessarily repeat itself. He concluded that the "whole of our science assumes the regularity of nature - assumes the future will be like the past ..."

The essential error that Hume is making is his failure to grasp why sequential events of the past repeat themselves and what would prevent those events from recurring. The concept of causality and the interaction of entities is neglected by Hume's explanation. According to Hume, it is humans who assume the repetitive nature of actions; humans form customs for observed events. Clearly, it is not a custom or an an arbitrary assumption that the sun will rise tomorrow. Given the nature of the entities, there is no other action possible. Unless another external causal event were to intervene (the sun going nova, a massive meteor), the sun will always rise. Humans simple observe and form conceptual generalizations. The generalization can either explicitly state or implicitly assume causality as the factor that validates the regularity of events of nature.

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My goal in this dialog is to demonstrate, for the benefit of anyone capable of understanding, to what lengths opponents of causality and identity will go to avoid or evade dealing with reality, sense perception, and entities.

“Are they [the rules of logic] just made up arbitrarily for the hell of it? Are they based on fantasy?”… "Correct reasoning" by what standard?”

The rules of logic are the rules of reality. I asked Eddie, who advocates logic, where HIS logic comes from.

As I mentioned before, the rules of logic are created to ensure correct reasoning and consistency of belief. Fantasy has nothing to do with it. The standard of validity is consistency between statements. This is of value because to hold inconsistent beliefs is to fall into contradiction, and non-contradiction in logic is a matter of necessity.

Observe that Eddie uses terms like "correct" without acknowledging that correctness means correspondence with reality. The consistency which matters isn't consistency between statements, but consistency with observation of reality. Eddie also assumes that contradictions are wrong, but what makes them wrong is that they are proposed as descriptions of reality and contradictions can't exist in reality. He doesn't explain why "non-contradiction in logic is a matter of necessity." That would require citing reality.

“Can I connect propositions based on the rule: "Two propositions can validly be connected if at least two words in the first proposition appear in the second proposition."

The function of logic is to connect statements and propositions with reality rather than with each other, so I proposed a way of "connecting propositions" which has nothing to do with reality just to see what Eddie would say about it.

Of course not. The terms in question must be what the proposition is about. The proposition “all mice are black” and the conclusion “all mice are blind” are about the terms mice, blackness and blindness, not about the term “are”, and they require a distributed middle that connects them.

Eddie just restates that someone must follow the rules without explaining why. Also he claims the proposition is "about the terms mice, blackness and blindness" rather than real mice and their real characteristics.

“WHY is it [a distributed middle] "regarded as valid" and an undistributed middle is not?”

The Law of Distributed Middle is valid because it is required for a conclusion to agree with reality.

The distributed middle is valid because it connects the terms of the major premise with those of the conclusion. The validity arises from consistency and coherence, which is demonstrated by the meanings of the terms and the way they are connected, as above.

Eddie continues to write about "connecting terms" with "consistency and coherence"

without acknowledging that terms must be connected to, consistent with, and cohere with reality.

“In other words, all you are saying is "Under certain conditions SOME round things have rolled."

So far, Eddie has made inductive generalizations ["All round things roll."] without justifying his generalization by reference to the real properties of real things and how they cause the actions.

No. I’m saying that "under certain conditions, all round things of a certain type will roll”. The justification is borne out by what actually happens during subsequent experiments.

Eddie doesn't reference any fact of reality which justifies his claims about "all round things."

Let's see if Eddie ever deals with reality, sense perception, and entities.

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Fred: “That's actually what's wrong with regarding knowledge as equivalent to mere "justified true belief". What is needed for knowledge is proof, i.e. conclusive evidence.”

The theme of this thread has been this very point: what counts as justification for inductive-type knowledge? What counts as “proof” or “conclusive evidence”? If a long run of successful predictions is regarded as conclusive evidence, I won’t argue with that. Of course, it's more difficult to justify some knowledge in that way – historical, economic, psychological etc – but long-run successful prediction would be sufficient justification for especially scientific knowledge.

What you are asking for here is really a worked out theory of the philosophy of science. I can't provide you that I'm afraid. (Stephen might want to make some comments).

But I will say that successful prediction, even a long run of it, may not be enough. Depending on the complexity of the theory - certainly something like Newton's or Einstein's - would require I think successful prediction from a suitable variety of perspectives and under a wide variety of conditions. And there also needs to be no contrary evidence.

But, yes, evidence needs to be substantial.

Where previously Newton’s laws were regarded as universal, they are now seen as local, so any previous certainty on this point has been shown to be misguided.

That certainty was never justified in the first place. We can never know with certainty what will apply to anything and everything, now or in the future, under any and all conditions known or unknown. Such certainty would presuppose omniscience. I always gringe when I watch scientific programs on TV and they talk about some phenomenon or another challenging Einstein's theories. The latest example was an interesting program I saw regarding some of the initial puzzlement about gamma ray emissions from very distant starts. Eventually, I gather, with additional observations and some brilliant analysis, they figured out how it could be consistent with Einstein. But in my view, even if it had caused some questions, so what? As I said previously it won't make GPS satellites fall out of the sky if some new theory is required to explain some odd new phenomena, anymore than the other planets started doing pirouettes around Jupiter when it was discovered that Mercury's orbit wasn't consistent with Newton.

Or, so Columbus didn't discover the westward route to "the Indies" afterall. He "merely" discovered the Americas!

Fred Weiss

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Betsy: “Observe that Eddie uses terms like "correct" without acknowledging that correctness means correspondence with reality.”

In my understanding, this dialogue has been about the justification for arguments using formal (classical) logic and informal logic, and most recently, the status of the rules of logic. In the case of classical logic, no appeal to reality (the external world) is necessary to establish the validity of a deductive syllogism. On the other hand, one can establish the truth of the premises by appeal to reality, but this does not affect the status of the rules of logic.

Betsy claims that such rules are based on reality and can only be justified by appeal to reality, and in her most recent post highlights the fact that I am not appealing to the external world to justify such rules. She is quite entitled to point this out, but such an observation does not in itself constitute an argument.

And that highlights the value of understanding the rules of logic. A deductive argument is a series of internally consistent, connected statements, such that the conclusion necessarily follows from the premises. That is, if all As are Bs, and all Bs are Cs, it necessarily follows that all As are Cs. It’s not necessary to appeal to the external world to understand this syllogism; one simply uses one’s mind.

Betsy: “Eddie doesn't reference any fact of reality which justifies his claims about "all round things."

And this highlights the confusion that arises when inductive-style arguments are treated in the same manner as deductive ones. Inductive-style arguments do appeal to the external world, and my justification: “under certain conditions, all round things of a certain type will roll”, is indeed an appeal to reality, since “certain conditions”, “round things” and “rolling” all refer to real world phenomena.

E

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In my understanding, this dialogue has been about the justification for arguments using formal (classical) logic and informal logic, and most recently, the status of the rules of logic. In the case of classical logic, no appeal to reality (the external world) is necessary to establish the validity of a deductive syllogism.

This isnt quite right. Classical logic would be one example of a formal reasoning system, and it certainly be possible to create different reasoning systems by starting with different axioms and inference rules. None of this requires any direct reference to reality in the sense you mean. However, given that we have many possible systems, how do we describe which one we are going to use? Why are the rules of classical logic better than any other arbitrary set of rules, assuming that the system is consistent? Simply because classical logic is better suited to describing reality during our day to day experiences. Although classical logic can be thought of as 'just' being a set of rules describing valid inferences, the reason we choose to use THIS set of rules is precisely because of the nature of both reality and ourselves.

An analogy here would be geometry. There are several different systems of geometry, all internally consistent. If we take 'truth' to simply mean consistency, then all of these would be equally 'true', due to axiomatic independence. However in this context 'true' is being used to refer to a correspondence with reality. With this definition, it is perfectly possible to talk about one geometry being 'true' within a given context while another isnt, assuming that the first one is better suited to describing reality.

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But I will say that successful prediction, even a long run of it, may not be enough.

Yes, that is right. Experimental confirmation is a necessary but not sufficient condition. Eddie's "a long run of successful predictions" is a very poor standard, taken by itself. For instance, both special relativity and the Lorentz ether theory make the exact same experimental predictions, but they are completely different physical theories. Are they then both taken to be correct? Same with general relativity. There are several theories that live within the experimental error bounds of general relativity, and there is currently no way to distinguish them experimentally. Even so for quantum mechanics. There are a whole slew of quantum theories that share essentially the same mathematical formalism, and they too are currently indistinguishable by experiment.

Clearly any theory that contradicts experimental fact is no longer viable, but prediction alone is far from sufficient, Popperian/Kuhnian nonsense notwithstanding.

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Betsy: “Observe that Eddie uses terms like "correct" without acknowledging that correctness means correspondence with reality.”

In my understanding, this dialogue has been about the justification for arguments using formal (classical) logic and informal logic, and most recently, the status of the rules of logic.  In the case of classical logic, no appeal to reality (the external world) is necessary to establish the validity of a deductive syllogism.

That would be news to Aristotle who first identified the laws of classical, formal logic and established the validity of a deductive syllogism by appealing to "being qua being," i.e., things that ARE, i.e., reality.

On the other hand, one can establish the truth of the premises by appeal to reality, but this does not affect the status of the rules of logic.
Then what gives the rules of logic their status -- if not reality?

Betsy claims that such rules are based on reality and can only be justified by appeal to reality, and in her most recent post highlights the fact that I am not appealing to the external world to justify such rules. She is quite entitled to point this out, but such an observation does not in itself constitute an argument.

If appeals to reality do not justify the rules of logic, WHAT DOES??

And that highlights the value of understanding the rules of logic. A deductive argument is a series of internally consistent, connected statements, such that the conclusion necessarily follows from the premises. That is, if all As are Bs, and all Bs are Cs, it necessarily follows that all As are Cs. It’s not necessary to appeal to the external world to understand this syllogism; one simply uses one’s mind.
Without appealing to reality, WHAT IS the value of understanding the rules of logic? Is it just a neat little word game not based on and inapplicable to reality?

Betsy: “Eddie doesn't reference any fact of reality which justifies his claims about "all round things."

And this highlights the confusion that arises when inductive-style arguments are treated in the same manner as deductive ones. Inductive-style arguments do appeal to the external world, and my justification: “under certain conditions, all round things of a certain type will roll”, is indeed an appeal to reality, since “certain conditions”, “round things” and “rolling” all refer to real world phenomena.

But do they do so validly, truthfully, and usefully? If so, HOW and how do you PROVE it.

If inductive arguments don't refer to the real world validly, truthfully, and usefully, why bother with them?

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You can only formally deduct new knowledge from old knowledge once you've established that old knowledge's relationship to reality (ie. it is true).

There's not too much point in deducing something from false knowledge... what you get is false, although consistent with your previous knowledge.

Despite what symbolic logic tells you, if you don't keep in mind the full context of the knowledge as well, you're likely to make an error, or be unable to apply your deduced knowledge correctly.

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You can only formally deduct new knowledge from old knowledge once you've established that old knowledge's relationship to reality (ie. it is true).

There's not too much point in deducing something from false knowledge... what you get is false, although consistent with your previous knowledge.

Despite what symbolic logic tells you, if you don't keep in mind the full context of the knowledge as well, you're likely to make an error, or be unable to apply your deduced knowledge correctly.

What is "false knowledge?" If an idea is false, it is not knowledge. How can you define "knowledge" as that which doesn't correspond to reality?

It is possible to deduce a true premise from false premises: Dogs are men, men walk with 4 legs, therefore, dogs walk with 4 legs. The issue with the deductive syllogism is not the truth of the conclusion, but wether the conclusion follows from the premises.

This shows that you that in order to insure that your deductive process coressponds to reality, one must first establish the truth of one's premises by induction.

Paul

:D

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What is "false knowledge?"  If an idea is false, it is not knowledge.  How can you define "knowledge" as that which doesn't correspond to reality? 

It is possible to deduce a true premise from false premises: Dogs are men, men walk with 4 legs, therefore, dogs walk with 4 legs.  The issue with the deductive syllogism is not the truth of the conclusion, but wether the conclusion follows from the premises. 

This shows that you that in order to insure that your deductive process coressponds to reality, one must first establish the truth of one's premises by induction. 

Paul

:D

I agree my phrase "false knowledge" was improper.

But I'm not convinced by the second paragraph.

What you've deduced is "dogs [are men and] walk with 4 legs" which is incorrect. If dogs are men, it's not correct that they walk with 4 legs. If dogs aren't men, but are dogs, they its true that they walk with 4 legs. If they aren't men though, then the deduction was wrong.

If you keep in mind the meaning of the words (which symbolic logic usually doesn't), I'm not sure you can deduce something true from something false.

I'm not arguing with you about the importance of induction of making your deductive process correspond with reality.

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But I'm not convinced by the second paragraph.

What you've deduced is "dogs [are men and] walk with 4 legs" which is incorrect.  If dogs are men, it's not correct that they walk with 4 legs.  If dogs aren't men, but are dogs, they its true that they walk with 4 legs.  If they aren't men though, then the deduction was wrong.

I really like his example, so I have an uncontrollable urge to defend that deduction. It is a perfectly "valid" (and unsound) formal deduction:

Ax(Dog(x)->Man(x)) premise

Ax(Man(x)->4-LeggedWalk(x)) premise

----

Ax(Dog(x)->4-LeggedWalk(x)) Law of Transitivity

You can of course also deduce the false statement "Dogs are men and walk on 4 legs"; but you cannot deny that the statement "Dogs walk on 4 legs" is formally deduceable from those two false premises. This a very nice demonstration of why it is essential in doing formal logic that premises be true.

If you keep in mind the meaning of the words (which symbolic logic usually doesn't), I'm not sure you can deduce something true from something false.

The enterprise of trying to deduce anything would be pointless if you did keep in mind the meanings of words. When you know the meaning (referent) of "dog" and "man", you know that dogs usually walk on 4 legs and men usually walk on 2, so no deduction is needed -- you already know what you were trying to "deduce". However: if the "something true" is combined with "something false", then no matter what, you can always deduce the "something true" from the compound statement, by disentangling the true statement from the false one. Remember that symbolic logic has nothing at all to do with meanings of words: that is why they typically use P, Q and R, in order to divorce the enterprise from words and the suggestion of real-word referents.

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but you cannot deny that the statement "Dogs walk on 4 legs" is formally deducible from those two false premises.

It's been a little while since I looked at formal logic, and I'll grant that "dogs walk on 4 legs" is formally deducible. But in context, I still think it's wrong, although I'm willing to be shown otherwise. I don't think it's an incorrect deduction, but a false statement.

If I were to say something like "God doesn't exist" you would agree with me. But if I now say "God is what I call my television" and then say "God doesn't exist", you would disagree with me, assuming that my television exists. That's what this deduction seems to be doing.

"Dogs walk on 4 legs" is not true if dogs are men.

Suppose I use a classic syllogism and change it:

All dogs are mortal.

Socrates is a dog.

Therefore Socrates is mortal.

When I would then say "Socrates is mortal", what I would mean by Socrates is different from what most people would mean by Socrates. In fact, since there is nothing in reality that corresponds to this "Socrates", my conclusion is meaningless.

Remember that symbolic logic has nothing at all to do with meanings of words: that is why they typically use P, Q and R, in order to divorce the enterprise from words and the suggestion of real-word referents.

I understand that, and that's what I'm unsure about. Is there much use for this type of logic (outside of, say, math) if it divorces it from words and real-word referents? Isn't the conclusion therefore also divorced from reality?

It's true that if you kept in mind the meaning of dog you wouldn't have to deduce that dogs have 4 legs, so maybe that's something you don't need to deduce. If I say:

All humans are mortal.

I am a human.

Therefore I am mortal.

If I keep in mind the meanings of the words this deduction simply takes what I know about the concepts and deduces a new statement. That's what a deduction basically does, it takes what you already know, and draws a conclusion from it. When I keep in mind what humans are and what I am, then my conclusion is useful to me. Since I (meaning me, myself) am mortal, I shouldn't jump out my window without a parachute.

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