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Post 0

Tuesday, May 31 - 7:00pm

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A Solution to the Raven Paradox

ADOP Warning: The contents of this post address arguments which, to many, strongly resemble "angels dancing on pinheads" (ADOP) issues. (Double meaning intended.) Those who see such things as tiresome or uninteresting need read no further.

Jordan:

Heya Nathan,

True. But how does observing a green baloon make "all ravens are black" more likely, do you suppose?

To claim that observing a green balloon makes "all ravens are black" more likely is like what I was suggesting in my "severely limited universe" aid to the problem of induction (in the other thread).

I know. OK, OK, you nagged me until I came up with an apparent solution or two. LOL

The Raven Paradox

The problem, as stated here, http://en.wikipedia.org/wiki/Raven_paradox,
goes like this:

'The statement "all ravens are black" is logically equivalent to the statement "all non-black-things are non-ravens". If we observe a red apple, that is consistent with that statement. A red apple is a non-black-thing, and when we examine it, we observe that it is a non-raven. So by the principle of induction, observing a red apple should increase our belief that all ravens are black!'

Honest. Philosophers actually argue about such things.

This problem entails the following hidden assumptions:

Identity of entities: that one raven is distinct from another, that black is distinct from other colors.
Identity of classes: that the class of ravens is distinct from the class of all things non-raven.
That negation in deductive reasoning says something about the reasoning of induction.

On 1 and 2

Based upon identification alone, we can observe two independent classes of things and properly ask: Why would there be any necessary logical relationship between two independent classes of entities, ravens and non-ravens?

Suppose the entire class of non-raven things did not exist: Would that have any bearing on our inductive thinking* about whether all ravens were really black? No.

We would still observe* that every raven we'd seen was black, and hypothesize that all ravens are probably black.

(*Of course, as a member of the class of nonexistent non-ravens, thought and observation would be problematic. LOL Maybe a raven can be the observer.)

On 3

Applying DEDUCTIVE logical negation to an inductive statement is a violation of the inductive paradigm. Induction does not usually reason from what's NOT to what IS.

Applying an Axiom of Order

Induction is the reasoning from a limited number of observations to a belief that the perceived order applies in all cases, that the perceived order has an objective basis in fact.

If we accept the proposed Axiom of Order, we can see that induction is 'justified' on the basis of that axiom. In other words, we usually use inductive reasoning to infer things from ORDER, not its absence.

In the raven paradox:

Is the color of ravens an objective form of order? Yes.

Are the colors of "all non-black-things" an objective form of order? No.

Observing five red apples says absolutely nothing about the apparent order of raven coloration and the validity of an "all ravens are black" hypothesis.

Nathan Hawking

(Edited by Nathan Hawking on 5/31, 8:18pm)

(Edited by Nathan Hawking on 6/01, 6:27pm)

Post 1

Friday, June 3 - 11:59am

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Love the warning label. Reminds me of my very own Purr Alerts.

Here it comes again...... *purr alert*

Alerta de ronco de gato

Eu te amo, Michael querido

purrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

Post 2

Friday, June 3 - 4:09pm

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I've long thought this paradox carries no weight. Why? Imagine a Venn diagram of one circle inside another, with the inner one symbolizing black ravens and outer one symbolizing all black things. The complement of black ravens includes not only non-black non-ravens, but also black non-ravens. Therefore, using Hempel's type of argument, observing a non-black anything, e.g. a red apple, should increase the belief that all black things are black. Whoop-de-do!

Post 3

Friday, June 3 - 7:45pm

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Merlin:

I've long thought this paradox carries no weight. Why? Imagine a Venn diagram of one circle inside another, with the inner one symbolizing black ravens and outer one symbolizing all black things.

Sure. Venn diagrams would be the visual counterpart of my class argument.

Something like:

( Black things (Black ravens))

The complement of black ravens includes not only non-black non-ravens, but also black non-ravens.

The class of everything would be, I think:

((NonBlackNonRavens) (BlackRavens) (BlackNonRavens) (NonBlackRavens?))

Therefore, using Hempel's type of argument, observing a non-black anything, e.g. a red apple, should increase the belief that all black things are black. Whoop-de-do!

If my diagram is right, at first glance his arguments might seem to suggest that. I can see why that felt right.

But looking closer, I think Hempel would probably argue that ONLY A SINGLE CLASS can be further corroborated by seeing a non-class entity. The argument is against induction, which deals with a single class of like observations. That would seem to exclude using two classes, i.e., BlackRavens, and BlackNonravens.

If we admitted two classes we could also argue that belief in an unlimited number of putative classes would be simultaneously corroborated by seeing anything not in those classes. Like so:

((NonBlackNonRedNonGreenNonWhateverNonRavens) (BlackRavens) (RedRavens) (GreenRavens) (WhateverRavens) (BlackNonravens) (RedNonRavens) (GreenNonravens) ...)

I'm guessing that a logical (but even more undesirable) consequence of multiple classes is that seeing ANYTHING X corroborates belief in EVERY imaginable class Not X. In other words, seeing a red apple simultaneously corroborates all claims about all classes not involving red apples--or something quite like that. But I'm not sure.

Nathan Hawking

(Edited by Nathan Hawking on 6/04, 1:10am)

Post 4

Tuesday, November 1 - 10:22pm

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     I wish to add one thing here that I've seen NOWHERE in any discussions...or books...on deduction and/or induction:

     That is, what *I* see as an inherent relationship directly between them.

     To wit:

     Without induction, deduction has no 'meaning.'

     Deduction, when used, has an expectation of the next 'use' of it staying consistently the same as the last use.

     Such an expectation is an induction, no? (induction DOES imply expectation, now, doesn't it?)

     In short: any 'validity' to deduction...logically...requires acceptance of the 'validity' of induction's use, at least on THAT subject/process.

LLAP
J:D

P.S: That it is us humans doing such, rather than our discussing observations re 'all swans' or 'all ravens' or 'all purple cows' being empirically 'confirmed' re a universal (ergo its contrapositive [or modus whateverens]), I see (Kant's view of our 'not allowing definitions to change' nwst), as really irrelevent.

Now, I'll get back to my DOOM 3 game. (That end-boss is worse than Kant!)

(Edited by John Dailey on 11/01, 10:43pm)

Post 5

Tuesday, November 1 - 10:29pm

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John,

This is a post from one of those who is no longer with us. He used to posit that Rand's axiomatic concepts of existence, consciousness and identity, with causality thrown in for good measure were woefully incomplete without his own, one and only, never before identified, now completely simplified for us mortals through his profound insights:

Axiom of Order.

Actually, he was floating this idea to lay the philosophical foundation for intelligent design.

Didn't work around here.

Michael

Post 6

Tuesday, November 1 - 10:48pm

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Mike,
I'm aware of this.

Ntl, I thought the subject (The Song, not The Singer), or at least it's associated sub-subjects, worth...resurrecting.

LLAP
J:D

P.S: "Revenge Of The Sith" is out on DVD now ! (ok, it's not relevent...but I'm a SW fan.)

(Edited by John Dailey on 11/01, 10:49pm)

(Edited by John Dailey on 11/01, 10:53pm)

Post 7

Wednesday, November 2 - 12:18am

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Dailey makes a good point (deduction requires induction). Hawking was stuck on an error -- that our conceptual classification need be metaphysical, rather than merely epistemological.

All that is needed for conceptual discernment -- is that all cases (ravens) seen be black. Once a non-black raven is seen -- THEN our conceptual common denominator must change, to match the complex actuality of which we've been made aware.

In this sense, the PROPER definition of anything, is that which successfully distinguishes something from other known things at the time (and that is all that is needed). Against a background of "all other things" -- definitions will successfully differentiate the epistemological class in question. At the level of the toddler, definitions are broad. At the level of the post-graduate, definitions are narrowed (BECAUSE of awareness of fine detail).

The Raven Paradox is a category mistake (humans don't "know" in that way). Knowledge is successful distinguishment (and it is not anything other than that). As long as we successfully distinguish (discern, differentiate) -- we are using knowledge, in its only meaningful sense.

See my article on the veridicality of conceptual discernment (from my profile page) -- for more details.

Ed

Post 8

Wednesday, November 2 - 7:05am

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The idea that deduction depends on induction isn't new. Philosophers bring it up all the time, particularly those with an empirical bent. The big difference between induction and deduction is that the former extends knowledge from the known to the unknown, while the latter deals only with rearranging the known. The more rationalist philosophers reject that deduction depends on induction because is it really unknown what the sum will be the next time I add 7 and 5?

Jordan

Post 9

Wednesday, November 2 - 7:18am

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False dichotomy alert.

Deduction and induction are two different mental processes, not a hierarchy of the same mental process.

Deduction, technically speaking, does not depend on the process of induction. It depends on the products of induction. It depends on integrations made from sensory input, which is at first automatic (percepts), then integrations carried out by induction.

I am not sure that there even can be one without the other.

Michael

Post 10

Thursday, November 3 - 11:13pm

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Jordan:
Uh...your point is...you agree, or, you don't? Or...? I'm not clear on this (though, I AM inducing something.)

Mike:
I argued nothing about 'dichotomy'; and, I'm unclear on the use/need of deduction for using induction. And, though I made no 'technical' distinction re the process vs the products of induction, I'm glad that we agree that induction is necessary for 'expectations' of deduction to be considered...worth paying attention to.

LLAP
J:D

(Edited by John Dailey on 11/03, 11:21pm)

Post 11

Friday, November 4 - 6:04am

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John,

On this we agree. Induction is necessary first in order to create the perceptual and conceptual material that deduction uses (and you can only include "perceptual" if you extend "induction" to mean integrating percepts, which I see as very similar, except it is automatic).

Michael

Post 12

Friday, November 4 - 8:43am

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John,

My first point was just that your point wasn't new. My second point served just to add some light to this issue by highlighting some of the common claims.

That said, tentatively, I disagree with you. I agree that there's expectation with deduction -- that I expect a deductive syllogism to yield a true conclusion, and that if you and I deduce the same, I expect the same conclusion to follow. Perhaps we have to learn this expectation. Perhaps initially, we're uncertain whether 5 and 7 together will always sum to 12, and that we become convinced of this truth just after adding them together enough times. Developing this expectation as such would indeed would be an inductive process, and indeed, if induction were the only way to learn deduction (which I don't doubt), then without induction, "deduction" would lack meaning.

But a deductive truth doesn't depend on whether we inductively learn it, i.e., on our inductive expectations about said truth. In my view, "If Socrates is a man, and if all men are mortal, then Socrates is moral" is always true, even if no one is aware or convinced that it's always true. Deduction works regardless of whether people learn that it does. Thus, the deduction doesn't depend on induction, at least not in the way that I think you were suggesting.

Jordan

Post 13

Friday, November 4 - 8:54pm

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Michael:
     Put that way (which is not usually *my* wont), clearly we agree, to an acceptable point, whatever our quibbles. Without the 'material' for a process/method to be used on, what meaning re the worth of the process, hmm?

Jordan:
     On the one hand, you state that you...tentatively...disagree with me (and, thereby, all the other philosophers [whom I must've overlooked in my readings] whom you say 'bring it up all the time'); but, you don't actually clarify where regarding specifically what premise-point I (as they?) made you get off my train at. Indeed, the rest of your 1st-paragraph response implies virtually total agreement. You do argue in the 2nd paragraph an opposing perspective, but...I'll cover that below. --- Re the other philosophers who 'bring it up all the time,' I'd be interested in the arguments (which I've not yet run across) the disagreers (tentative or definite) have given; specifically, WHICH disagreers have (cogently, whether 'deductively' or 'inductively') logically argued exactly what against my main point?

     Re what you call 'a deductive truth' as being "...always true, even if no one is aware or convinced that it's always true", I can only ask: "By what ('logical'?) means is this determinable...by you?" And I must add: if no one is aware of such, such may be a 'fact,' but...a 'truth'? A 'deduction' (ie: 'deduced')? I think not.

     Further: "Deduction works regardless of whether people learn that it does." Apart from the fact that some person has to be using it (hence 'learned' it, and is thence 'aware' of its useability) for it to 'work', much less be used...by what ('logical'?) means is this determinable...by you?

     Lastly: "Thus..." does not follow without 'logical' answers to my above question...in both places.

     In short, re your opposing argument [!] (or rather, 'point'), are you using induction, deduction, both, or neither?  If either, (and/or both), then which...where? O-t-o-h, if neither...        :)

LLAP
J:D

(Edited by John Dailey on 11/04, 9:17pm)

(Edited by John Dailey on 11/04, 9:21pm)

(Edited by John Dailey on 11/04, 9:25pm)

(Edited by John Dailey on 11/04, 11:20pm)

Post 14

Saturday, November 5 - 7:21am

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Hi John,

I'm glad my first big paragraph of post 12 is in virtual total agreement with you. It captures the idea that learning deduction is inductive, which just means that comprehension of deduction depends on induction. I should've added, "so what?" because it really seems like a side issue. Accordingly, although I know philosophers who like to link deduction to induction, I can't think of any who specifically disagree that comprehending deduction depends on induction. Anyway, my second big paragraph went on to point out the that the logic of deduction (i.e., deduction itself) doesn't depend on induction because deductive truths are always true, even if we aren't aware that they are.

How do we know deductive truths are always true? On the one hand, this question is along the lines of questions like "how do we know the world doesn't disappear when we close our eyes?" or "how do we know Paris exists if we've never been there." On the other hand (and ignoring the first hand :-)), we know deductive truths are always true because they are just rearrangement of axioms, which are inescapably always true, even if we don't know it. "All cats are animals; Felix is a cat; therefore Felix is an animal," is just another way of saying "A cat is a cat."

And yes, I think true propositions are true even if we don't know they are true or are unaware of them. For example, I don't know how old George W. Bush is. But "George is [insert his actual age here]" still has a truth value, even though I don't know what it is. How do I know he has an age? The same way I know that Felix is a cat. It's an inescapable truth.

Jordan

Post 15

Sunday, November 6 - 12:28pm

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Hello again, Jordan:

     I'm glad that you're glad that (shades of R.D Laing's Knots!) we agree about your 1st paragraph, although, *I* wasn't talking about merely 'learning' deduction, but further, 'using' it; methoughts that that was also what you meant. If the latter false, then, my mistake (and you misunderstood my original argument, and later agreement with you), and, therefore, we really don't agree (sigh). I notice that you have no comment re my arguments about using deduction as requiring induction.

     Re other philosophers 'comprehending', I don't know how that is relevent to my original argument. I asked about your comment that 'other philosophers bring it up all the time.' --- Still waiting.

     Re your "...second big paragraph...", you did "...point out..." your belief/assertion, but, you didn't show (inductively or deductively) it's validity (ergo, my original argument's falsity.) Indeed, you never answered my final questions in my last post re which you used to determine the 'truth' of your own final assertions...that you (as in your just previous post, merely...) pointed out.

     Re the rest of your post, you have interesting questions...though, why rhetorically put, while not answering mine, I can only...induce; especially since you have nothing to comment re my distinction re 'truth' and 'fact.'

     To rephrase the latter point: I do not consider 'truth' and 'fact' as synonomous. 'Truth' is a characteristic of propositions; 'fact' is a characteristic of the universe. Truths have no existence apart from a proposition referring to a discovered fact. Facts can exist without propositions about them, hence, can exist without a 'truth' referring to them (all 'truths' refer to facts; that's the dif.) --- A guess that aliens inhabit Alpha Centauri is not a 'truth' until the 'fact' is discovered. The two terms are not synonomous in my meaning of the terms. One can debate this, true (!?), but, you made clear that you ignored my already clarified distinction, here re-clarified. May I ask, since I consider such to merely pointlessly prolong a debate (unless one debates for the pure sake of it), why?

LLAP
J:D

Post 16

Sunday, November 6 - 6:36pm

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Hey John,

I feel like I'm responding directly to your questions/points, so please clarify your questions/posts if again you think I don't answer them in this post. Incidentally, I don't think you answered how your idea is relevant, even though you think I misconstrued your argument.

And about your argument... I don't see how it equates to "deduction requires the use of induction." To me it still looks like you meant that deduction requires learning induction. I'd appreciate it if you would restate your argument, then offer an example. Without that, I'll venture to say that we don't use induction when deducing. The logic of the two, like MSK said, is categorically different and independent from each other. Or: Observing again and again and again that deduction provides certain conclusions is unnecessary for us to use deduction. (More on this two paragraphs down.)

I asked about your comment that 'other philosophers bring it up all the time.' --- Still waiting.

Other philosophers bring up all the time that deduction "depends" on induction, which is what I said. Whether they discuss that connection like you do, I can't say because I'm no longer clear on what you're trying to say. But you're welcome to google some empiricists to verify that they often discuss, in some way, deduction's "dependence" on induction.

Re your "...second big paragraph...", you did "...point out..." your belief/assertion, but, you didn't show (inductively or deductively) it's validity (ergo, my original argument's falsity.)

Sure I did, at least in Objectivist standards. I said deduction is like axioms. Just as axioms are "true" regardless of whethey they are known, so too is deduction "true" regardless of whether it is known. Do you think we need induction for axioms to be "true"?

Last, I agree that truth and fact aren't synonyms, and I agree that truth is a property of propositions. But the following doesn't work for me:

Truths have no existence apart from a proposition referring to a discovered fact.

"There's life on Alpha C" is a proposition. It is basic logic that that proposition is either true or false, do you agree? Whether we can determine its truth-value is irrelevant to its having one. Your assertion that propositions can't be true until facts of propositions are discovered is unsubstantiated and contrary to basic logic. But I'd rather not carry on this digression. Start a new thread if you really want to discuss truth and fact. I'm not terribly interested.

Instead, I'd rather you just clarify your position. Restate your argument, then demonstrate your argument through examples.

Jordan

Post 17

Monday, November 7 - 12:03am

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Jordan:

Start a new thread if you really want to discuss truth and fact. I'm not terribly interested.

Re this secondary territory ('truth'/'fact') *you* irrelevently initiated to my original argument (which never mentioned either of the terms), and *I* time-wastedly offered to explicate *my* view on, guess what? At this point...neither am I. --- BUT, also at this point, I must ask...Why did *you* bring them up? They were important then...until I responded? Ergo, they're not important now? Hmmmm....like I originally said, I'm inducing something.
.

Instead, I'd rather you just clarify your position. Restate your argument, then demonstrate your argument through examples.

Oh, you would, would you?

Ok.

Read Post #4. --- And then, *your* response, which clearly shows NO confusion (then, anyway) about *my* argument. Hopefully, your re-reading your response may clarify some things, making redundant your requirement that I 'Restate' my argument. Re-reading things does help, believe it or not.

Uh-h-h, re 'examples', why do I need (plural) them, when, like a single 'white crow', all you need to do is provide *1* counter-example? --- How about you give me that simple, little, single, lonely, isolated...*1*...counter-example?

Any new...'rathers'?

J-D

P.S: I'd 'rather' you respond relevently to ALL my un-answered questions before I spend more time on any new 'rather' you may randomly think up to post. --- You'll get 'answers' from me, but, only of the same relevent/irrelevent type that I get from you (until I get tired of irrelevency). So far, for all your ostensible 'challenge', you've argued nothing relevent against my original argument; you've merely innuended (ie: hinted a 'logical' argument) against it. --- Ball's in your court, Kemo Sabe; watch the net...(not to mention, my response).

(Edited by John Dailey on 11/07, 12:35am)

Post 18

Monday, November 7 - 6:52am

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John,

Why did *you* bring them up?

I didn't bring up "fact." You did. In post 12 I just said deduction doesn't depend on induction, which is just another way of saying deductive truth doesn't depend on inductive truth, which is just another way of saying, deduction holds, even if induction doesn't. We shouldn't have to muddle through "truth" and "fact" to understand this point.

I already re-read your "argument" several times. I asked for examples -- and of course you could've offered just one -- because your argument is incoherent, if it's about use rather than comprehension. I can't give a counter-example without having a theory or example to counter. Just explain why "A is B; B is C; Thus A is C" uses induction.

Until then, John, you have failed to restate your argument, to provide even one example of your argument, to clarify which questions I haven't answered, and you've ignored my comments that at least attempt to refute what appears to be your argument. I haven't the time for this. Someone else is welcome to chime in here and clarify John's idea. Until then, I'm out.

Respectfully,
Jordan

Post 19

Tuesday, November 8 - 12:48am

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Jordan:

     Now, *my* argument is "incoherent" (though so many other philosophers supposedly have brought it up all the time.)

     You demand that I give relevent responses to your comments, questions, and demands, while you chronically ignore mine; I make clear "you first" and you therefore decide "Ok, I'm outta here."

     As you wish.

     Clearly, any further discussion betwixt us...on any thing...would end up just as time-wastingly pointless. Let's both keep that in mind, ok?

J-D

(Edited by John Dailey on 11/08, 12:54am)