Two Kinds of "Induction": Important similarities and trivial differences

[Dragonfly]

Not quite. Any a posteriori statement that logically implies the denial of an analytic statement is false.

Not necessarily. It can mean that the analytic statement is not applicable to the physical situation. If you measure angles on a spherelike object, you'll get a denial of Euclid's theorems. That doesn't invalidate Euclid nor the relations you find, it only means that Euclid's analytic statements are not suited to the occasion.

[BaalChatzaf]

Not quite. Any a posteriori statement that logically implies the denial of an analytic statement is false.

Not necessarily. It can mean that the analytic statement is not applicable to the physical situation. If you measure angles on a spherelike object, you'll get a denial of Euclid's theorems. That doesn't invalidate Euclid nor the relations you find, it only means that Euclid's analytic statements are not suited to the occasion.

Euclid's postulates are not tautologies (analytic true judgements). They are ... well.... postulates. Posits, assumptions, beginning statements to a theory. The initial setup of an intellectual board game. That is why both Euclidean and non-Euclidean geometries exists as consistent theories.

Ba'al Chatzaf

[tjohnson]

No. I said any statement that logically implies a contradiction is false.

I take these as equivalent; "self-contradictory" and "logically implies a contradiction".

[Dragonfly]

Euclid's postulates are not tautologies (analytic true judgements). They are ... well.... postulates. Posits, assumptions, beginning statements to a theory. The initial setup of an intellectual board game. That is why both Euclidean and non-Euclidean geometries exists as consistent theories.

I wasn't talking about his postulates, but about his theorems, like the theorem about the sum of the angles of a triangle.

[tjohnson]

Not necessarily. It can mean that the analytic statement is not applicable to the physical situation. If you measure angles on a spherelike object, you'll get a denial of Euclid's theorems. That doesn't invalidate Euclid nor the relations you find, it only means that Euclid's analytic statements are not suited to the occasion.

Ah... but the moment you apply the analytic statement to physical situation it is no longer analytic, it's now synthetic. Simply the same as mathematics vs applied mathematics.

[Ellen Stuttle]

Reason uses deduction and induction, it is the application of logic to facts, at least ultimately. Falsification of a theory--a theory must at least be falsifiable to be valid--is part of the scientific method. Flights of imagination are all alright as an aid to inquiry and understanding though they verify nothing.

What in the hell are you people talking about? If you aren't proposing to improve the scientific method what are you proposing?

Brant, if all you mean by "induction" is the formulation of generalized a posteriori beliefs about how reality works, we do form such beliefs (though I think it's preferable, because clearer, less likely to be misinterpreted, to call such beliefs by Popper's term, "conjectures"). If you mean by "induction" the validation of such beliefs, the conclusive demonstration of the truth of such beliefs, we can never conclusively demonstrate the truth of generalized a posterioris. But not only does "reason" not require our justifying such beliefs; it's unreasonable to claim that they can be justified.

The statement that a theory must be falsifiable to be valid (I'm assuming you mean by "valid," true) isn't demonstrable. We don't know that it couldn't happen that some unfalsifiable theory was true. But an unfalsifiable theory can't be tested; thus it isn't a scientific theory.

As to "what in the hell" we people are talking about? Which people? Some of us are attempting to elucidate how science works; we aren't getting anwhere with at least one of us, i.e., Michael. In his most recent reply to me (his post #386) he says:

The main issue is that induction exists and is a valid means of obtaining knowledge—scientific knowledge—and works in harmony with deduction.

The statement "induction exists" has already been addressed earlier in the thread. If the claim is that some people in fact believe that their inductive statements (generalized statements about how the world always works) have been validated, yes, some people do that. In this sense, "induction exists." If the claim is that induction exists as a valid method and that it's the method science actually uses, the claim is false. Michael has very far to go if he hopes to demonstrate its truth.

Ellen

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[Ellen Stuttle]

Michael, see my post above replying to Brant. That's about all I want to say regarding your latest to me (post #386). What you wrote is a good example of why I soon find any attempt to discuss substantive issues with you hair-tearingly irritating. You claim that I've "not understood [your] words or [i'm] mischaracterizing them by removing context." That I don't have any feeling of understanding more than a fraction of what you've been writing on these issues is true. I think that much of what you write isn't comprehensible, that it's rambling, undigested thought, even the intent of which is often unclear. If I remove context in replies by addressing only such points as seem to me partly comprehensible, it's because I have no idea how to address the rest of what you write short of replying with very long posts contrasting and comparing your word use in one sentence with that in another or others, detailing the unclarities. I have lots of experience on the basis of which to conjecture, however, that even if I went to the trouble of doing that, you wouldn't pause to reflect but would just come back with further confusions -- and further rhetoric, as for instance your paragraph asking if I "honestly think that [you] believe the world is flat." What out-of-left-field place did that come from? I've said nothing whatsoever indicating that I think you believe the world is flat.

I commented in the reply to Brant on your statement:

The main issue is that induction exists and is a valid means of obtaining knowledge—scientific knowledge—and works in harmony with deduction.

I'll repeat, changing only the last sentence:

The statement "induction exists" has already been addressed earlier in the thread. If the claim is that some people in fact believe that their inductive statements (generalized statements about how the world always works) have been validated, yes, some people do that. In this sense, "induction exists." If the claim is that induction exists as a valid method and that it's the method science actually uses, the claim is false. You have very far to go if you hope to demonstrate its truth.

Ellen

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[BaalChatzaf]

The statement "induction exists" has already been addressed earlier in the thread. If the claim is that some people in fact believe that their inductive statements (generalized statements about how the world always works) have been validated, yes, some people do that. In this sense, "induction exists." If the claim is that induction exists as a valid method and that it's the method science actually uses, the claim is false. Michael has very far to go if he hopes to demonstrate its truth.

Ellen

___

Hypothesis formulation exists. We all do it. In fact learning can be regarded as an exercise in hypothesis formulation. It comes in the form -- "Let's see if this works". Science is a sophisticated form of hypothesis formulation. Most of the time it is not in the form of enumeration of large numbers of examples. Maxwell's modification of the equation for magnetic induction by the addition of the dE/dt term was NOT motivated by gobs of evidence lying around in piles. It was motivated by a necessity for maintaining a conservation law, a purely mathematical consideration. Similarly, Einstein's postulate of relativity was motivated by an asymmetry in the theory of electromagnetic forces implicit in the Lorentz Force Law. Einstein's equivalence principle was not motivated by the necessity to explain a large number of particular facts. This process of hypothesis formulation was called Abduction by C.S.Peirce who first formulated this as the driving principle behind scientific theories. Yes, Abduction is based on facts, but it is motivated by a requirement for causes and or symmetry in physical laws. This is not the same thing as Bacon's Induction which is rarely done in physics.

Every so often you see Bacon's type of induction in the form of fitting curves to data. That is how Kepler got elliptical orbits for the planets. He had gobs of data from Tycho Brahe's observatory to figure out. It turns out that he could not get a proper fit using circular motions, so he resorted to ellipses and hit the jackpot. It was Newton who postulated a force with an inverse square law (acting at a distance) to -explain- Kepler's results. Likewise Boyle's Law was gotten originally from fitting curves to data, but it took the molecular hypothesis to -explain- boils law.

Theories do not leap out of heaps of fact as did Athena from the Brow of Zeus.

Ba'al Chatzaf

[Ellen Stuttle]

The statement "induction exists" has already been addressed earlier in the thread. If the claim is that some people in fact believe that their inductive statements (generalized statements about how the world always works) have been validated, yes, some people do that. In this sense, "induction exists." If the claim is that induction exists as a valid method and that it's the method science actually uses, the claim is false. Michael has very far to go if he hopes to demonstrate its truth.

Ellen

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Hypothesis formulation exists.

Yes, of course, hypothesis formulation exists. I said so, only using Popper's term "conjectures," in the previous post. If that's all that's meant, then no problem. But if the claim is that hypotheses can be conclusively validated -- and that is what I understand Michael to be claiming -- then he isn't talking science.

Ellen

PS: Adding a point I've made before: the verificationist attempt amounted to good ole induction by enumeration, since the idea is that we eventually get enough confirming instances to conclude that a hypothesis has been conclusively demonstrated as true.

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Edited October 12, 2007 by Ellen Stuttle

[BaalChatzaf]

PS: Adding a point I've made before: the verificationist attempt amounted to good ole induction by enumeration, since the idea is that we eventually get enough confirming instances to conclude that a hypothesis has been conclusively demonstrated as true.

___

Doomed to failure. Popper's battle was with the Verificationists of the Vienna Circle.

Ba'al Chatzaf

[John Dailey]

~ 'THE' ancients believed the earth was flat; 'THE' (I love how that word's used when referring to a group of people or a culture) ancients also believed the earth was round. Who will argue that? The ones who believed it was round were the intellectual aristocracy of the times. The rest were the predominant uneducated. Let's give this word 'THE' a break here. Talk about 'over-generalizing'!

Dragon:

~ You say...

But we never can be sure that we've reached the point where we can be absolutely [!] sure [aka: 'certain'?] that our theories are correct.

~ That's *your* 'theory' about knowledge-attainment, correct? Sounds a bit 'absolutistic' ("never"?) and, well, pretty 'certain' (or 'sure'), as stated. Would you care to re-phrase it, regarding its being...'correct'?

LLAP

J:D

[John Dailey]

~ Re this whole 'flat earth' idea, was it ever really a 'theory' (in the present-day sense we mean by that term; you know, beyond hypothesis via containing predictability)? Or was it merely 'common opinion' amongst the little-traveled uneducated? I say the latter, only.

~ 'Theory' is too noble a term to give the idea, as it is re turtles-standing-on-turtles. It was a practical viewpoint of living for those whose life-style vision was hemmed within their lives' horizon.

~ Same goes for Von Daniken's (not to mention Velikovsky's)... hypothetical (can we say 'conjecturally imaginative'?) ideas. 'Theories', these are not, any more than 'flat earth' or zodiac signs ever were.

LLAP

J:D

Edited October 12, 2007 by John Dailey

[John Dailey]

~ Can someone point me to finding where Sir Isaac Newton spelled out a 'theory' of gravity? I'm a bit perplexed on this. I thought he (as many pre-Einstein) had a real prob re this 'action-at-a-distance' situation (re 'explaining' it), and that what he said about gravity merely described how it worked...not why it worked as it did, in his mathematical elucidations.

LLAP

J:D

[John Dailey]

MSK:

~ You say...

All I am trying to do is show that the same standard that is used for criticizing induction works just as well against deduction...

~ Well, kudos for that, but, if you've been catching some of my posts on this subject (other than haranguing against all who make a point to ignore J.S.Mill while still arguing against induction's worth in science), I have been stressing 'applying the same standard' to the criticisms themselves. For my money, they all come under the 'stolen concept' category.

LLAP

J:D

[tjohnson]

Dragon:

~ You say...

But we never can be sure that we've reached the point where we can be absolutely [!] sure [aka: 'certain'?] that our theories are correct.

~ That's *your* 'theory' about knowledge-attainment, correct? Sounds a bit 'absolutistic' ("never"?) and, well, pretty 'certain' (or 'sure'), as stated. Would you care to re-phrase it, regarding its being...'correct'?

LLAP

J:D

What does 'correct' mean in this context? Given any arbitrary theory which predicts a certain outcome in an experiment you will invariably get different results. So how is one to know the theory is 'correct'?

[BaalChatzaf]

~ Can someone point me to finding where Sir Isaac Newton spelled out a 'theory' of gravity? I'm a bit perplexed on this. I thought he (as many pre-Einstein) had a real prob re this 'action-at-a-distance' situation (re 'explaining' it), and that what he said about gravity merely described how it worked...not why it worked as it did, in his mathematical elucidations.

LLAP

J:D

For Gravity (its causes) Newton famously said -- I feign no hypothesis. In short, Newton gave a law which describes the mutual gravitational force that bodies exert on each other, his famous inverse square law, but said not a word concerning the causes of gravitation.

Ba'al Chatzaf

[tjohnson]

~ Can someone point me to finding where Sir Isaac Newton spelled out a 'theory' of gravity? I'm a bit perplexed on this. I thought he (as many pre-Einstein) had a real prob re this 'action-at-a-distance' situation (re 'explaining' it), and that what he said about gravity merely described how it worked...not why it worked as it did, in his mathematical elucidations.

LLAP

J:D

WHY is the sky blue? Because it isn't green. Do you think we can ever answer why something happens? I think we must be satisfied to know how things work. Newton may have had a problem with 'action at a distance' but didn't have anything better to explain his empirical relationship, I guess.

[John Dailey]

Dragon:

~ You say (in post #388, replying to MSK)...

That is a perfect illustration of the fact that analytic statements give no information about reality, in contrast to synthetic statements, confirming the distinction between analytic and synthetic statements.

~ Question #1: Is your statement, itself, an analytic one or a synthetic one?

~ Question #2: Is the 'confirmation' you assert as being, an empirical ('synthetic') one, or a tautological ('analytic') one?

~ Question #3: Does the answer (whichever) to #2 DEPEND upon the answer to #1? (I think that's a real mind-bender, don't you agree?)

LLAP

J:D

Edited October 12, 2007 by John Dailey

[BaalChatzaf]

Dragon:

~ You say (in post #388, replying to MSK)...

That is a perfect illustration of the fact that analytic statements give no information about reality, in contrast to synthetic statements, confirming the distinction between analytic and synthetic statements.

~ Question #1: Is your statement, itself, an analytic one or a synthetic one?

~ Question #2: Is the 'confirmation' you assert as being, an empirical ('synthetic') one, or a tautological ('analytic') one?

LLAP

J:D

It is a statement in the metalanguage which deals with language that talks about the world Outside Us.

Ba'al Chatzaf

[Dragonfly]

~ You say...

But we never can be sure that we've reached the point where we can be absolutely [!] sure [aka: 'certain'?] that our theories are correct.

~ That's *your* 'theory' about knowledge-attainment, correct? Sounds a bit 'absolutistic' ("never"?) and, well, pretty 'certain' (or 'sure'), as stated. Would you care to re-phrase it, regarding its being...'correct'?

It's a question of simple logic. We may safely assume that we are not omniscient, agreed? That means that we never can be sure that a universally quantified statement about the world is correct, because when we would know definitely that it is correct, that would imply that we never could learn anything new with regard to such statements in the future, in other words, we would have to be omniscient, which is a contradiction with our assumption that we are not omniscient. The error in your (implied) argument is that the fact that we can never be sure that universally quantified statements (UQS) about the world are correct, somehow implies that we can't be sure of anything. That is a non sequitur, however. We can for example be sure that 2 + 2 = 4, as that is an analytic statement, which cannot be falsified by empirical evidence. Statement (1): There is no way that we can be sure that a UQS will never be falsified in the future. How could we falsify (1)? By giving a counterexample. But we can only give a counterexample if we are omniscient, in contradiction with our assumption. Therefore we can be sure that we cannot be sure about the truth of UQS's. That is no contradiction, as (1) is not a UQS. The usual scoffing of Objectivists at "you never can be sure of anything" is attacking a straw man. We never claimed that.

[tjohnson]

~ Question #1: Is your statement, itself, an analytic one or a synthetic one?

~ Question #2: Is the 'confirmation' you assert as being, an empirical ('synthetic') one, or a tautological ('analytic') one?

~ Question #3: Does the answer (whichever) to #2 DEPEND upon the answer to #1? (I think that's a real mind-bender, don't you agree?)

LLAP

J:D

1. It is of course a synthetic statement.

2. The answer would of course have to be construed as empirical

3.Yes, it does but not sure if it's a mind bender or not.

[John Dailey]

gs:

~ You say...

science is an excellent way [it has a 'way'?] of refining the structure of knowledge, which would of course include weeding out misconceptions, erroneous assumptions, etc.

~ Would you stress this point (this...'way'...) as thereby EXCLUDING anything hinting at 'induction', yet relying ONLY upon 'falsification' of imaginated conjecturalizing? --- I notice that you speak in terms of 'refining' and 'weeding out' (which fits Popper's single criterion), but, implicitly, other than Popperian 'imagining', nothing in terms of how to 'add to' scientific knowledge is mentioned...or even hinted at.

~ Interesting perspective on 'scientifically' acquired...knowledge. Wonder what Mill would say?

LLAP

J:D

Edited October 12, 2007 by John Dailey

[John Dailey]

JUST A "COMMENT':

~ Baal 'explaining' to Dragonfly what 'analytic' and 'synthetic' statements are really all about.

~ That post (#394) was a trip I'm sure Dragon appreciated it...NOT.

LLAP

J:D

Edited October 12, 2007 by John Dailey

[John Dailey]

Dragon:

~ You say...

The usefulness of the analytic-synthetic division has nothing to do with its age...

~ You say...

...it is so useful while it enables us to see clearly which statements tell us something about reality (as in physics) and which statements do not (as in abstract mathematics [is there any other kind?])

~ You say...

The so-called "contextual truth" is just a confusing weasel term to avoid admitting that all our knowledge about reality is tentative...

~ Would you clarify as to which of these statements of yours are analytic...and which not?

LLAP

J:D

[John Dailey]

Baal:

You say...

Any a posteriori statement that [i think you meant 'which', here] logically implies the denial of an analytic statement is false.

~ Would you say that *your* statement thereof is 'analytic', or...synthetic?

~ May (or 'Can') we...umm...ADD to this: "Any statement which logically implies the denial of a true...synthetic...statement is false." --- Or, more simply, refine all to "Any statement which logically implies the denial of a 'true' (of whichever division-type)...is false"?

~ I mean, is there really all that much of a need to have 2 types of 'truths' and 2 types of 'falseness'? I mean, REALLY?

LLAP

J:D