Hume's Inductive Fallacy (General Questions).

Basically, the inductive fallacy came up in conversation on Secondlife (at Philosophy House) where pretty much the majority of folks assumed it to be true right off the bat without giving much thought to it. The general form of my response was that giving all considerations to relationships between entities, these relationships always are invariant based on some properties shared by the given entities in question, and that it's from these relationships that one can make judgments as to how they apply to different sorts of entities (consider how gravity applies universally across all massive bodies even when consider relativistic effects regardless of their given composition or how molecular bonds behave the same regardless of composing atoms). In the end, it was getting late and I felt that me and the other person (minus the jeering yammerheads/sideline-snipers) just didn't come to any common ground on the issue (especially when I pointed out that the only real leg the inductive fallacy can stand on is if analysis and synthesis were really two separate functions where one could not give way to the other).

So I'm left with a couple questions in mind to this conversaton. First, is there any basis to the inductive fallacy if one considers all knowledge (even statements of truth) as generative? Second, is there any honest manner to argue against the inductive fallacy when the opposing speaker(s) is/are hostile to anything contrary to the assumed conventions?

Thanks in advance.

Post 1

Monday, October 20, 2008 - 2:21pm

Brede,

I don't know about all knowledge being "generative." But a good way to argue against the fallacy of induction is via the necessity associated with impossibilities.

For example, using induction with some rules of reality, anyone can use "reaffirmation through deduction" to verify the induction that all live elephants are bigger than all live fleas. The reason that this induction is a necessary truth is because it is associated with biophysical impossibilities.

It's not possible for a flea to be bigger than a certain size, due to how it externally respirates through holes in its legs, how it achieves internal respiration by diffusion instead of through blood vessel pipelines, and possibly also due to it having an exoskeleton. It's also not possible for an elephant to be smaller than a certain size, due to the minimum number of cells required for elephant organs (and the minimum size of cells, dictated by biophysics).

In between these these two limits of biophysics lies a range of size impossibility (where no flea or elephant could exist). Therefore, we get to generalize the statement to all elephants and all fleas -- even though we didn't examine them all beforehand.

Try it out or something similar, and let me know if it "works."

:-)

Ed

Post 2

Monday, October 20, 2008 - 3:34pm

Knowledge gained through induction is not absolutely certainly true, but one can have lots of reasons to accept such an idea and no reason to reject it, it can be extremely useful for solving problems and achieving goals.

I'm not sure exactly what the fallacy is here.

Post 3

Monday, October 20, 2008 - 3:43pm

Dean,

Is it possible then, that there's a flea that's bigger than an elephant?

How do you propose that that could be true/possible?

Ed

Post 4

Monday, October 20, 2008 - 7:03pm

Can you provide an example of something that can't possibly be false other than "A is A, I have consciousness, and something exists"? Or do you include "A flea is smaller than an elephant" in their definitions so that it is "A is A"?

Post 5

Monday, October 20, 2008 - 7:40pm

Dean,

Can you provide an example of something that can't possibly be false other than "A is A, I have consciousness, and something exists"?

I just did (with elephants and fleas).

Or do you include "A flea is smaller than an elephant" in their definitions so that it is "A is A"?

The size relationship of a flea or elephant is not included in the definition of flea or of elephant, but it is a necessary truth about the relation between fleas and elephants.

It doesn't have to be in a definition in order to be true by necessity.

Ed

Post 6

Tuesday, October 21, 2008 - 11:32am

Ed,

I know this is never going to happen, but just to appreciate the principle in your position a bit more, if you were to see something that resembled an elephant in every way except for size, and if this thing were found to be smaller than some flea, then you would have to conclude that it's not an elephant. Basically, You are "locking in" the traits needed to be a member of a category. Right?

Jordan

Post 7

Tuesday, October 21, 2008 - 11:40am

Bridget,

The better responses to the Problem of Induction are to accept that induction does indeed contain the problem posed, but argue that the problem is circumnavigable and not devastating, much akin to Dean's "lots of reasons" for accepting induction.

Jordan

Post 8

Tuesday, October 21, 2008 - 5:46pm

Jordan,

Ed,

I know this is never going to happen, but just to appreciate the principle in your position a bit more, if you were to see something that resembled an elephant in every way except for size, and if this thing were found to be smaller than some flea, then you would have to conclude that it's not an elephant.

If you know it'll never happen then why ask (when it's obviously arbitrary)? What can be gained from the postulation or the attempted defense of the arbitrary?

Basically, You are "locking in" the traits needed to be a member of a category. Right?

That's a primacy of consciousness stance, which is absurd. I don't get to "lock in" things, but physics and biophysics "get to" lock things in and out. There are some things -- and this shouldn't come as a surprise to you, Jordan, it really shouldn't -- there are some things that are physically impossible.

Ed

Post 9

Tuesday, October 21, 2008 - 8:29pm

"There are some things that are physically impossible." You make this claim using your knowledge of reality's physics, and your knowledge of reality's physics is not actually reality's physics, but information about reality's physics gained through induction using the scientific method. Generalizations can have flaws when you haven't examined all the cases... and there are an infinite number of cases in many generalizations. So some generalizations can never be absolutely certainly true.

Although reality has behaved some way in the past, it is not absolutely certain that it will continue to behave in such a way. Although you have perceived and are aware of a great deal of parts of reality, you have not perceived nor are you aware of everything. Hence there may soon be a flea bigger than an elephant, due to changes in how reality works, or there may be a flea bigger than an elephant in outer-space. Or maybe there are giant extremely-difficult-to-perceive fleas everywhere! (reminds me of Final Fantasy: The Spirits Within)

Post 10

Tuesday, October 21, 2008 - 9:35pm

Dean,

... Or maybe there are giant extremely-difficult-to-perceive fleas everywhere! (reminds me of Final Fantasy: The Spirits Within)

Well, it's fantasy ... I'll give you that.

Seriously though, asking me to answer to the arbitrary -- to some effused conjecture not based on any evidence anywhere -- is like asking a bird to peck off its feathers or wings, or like asking a shark to bite off its own tail. It's really not different from these in any meaningful way.

Like Peikoff says in OPAR:

[secular] Agnosticism is not simply the pleading of ignorance. It is the enshrinement of ignorance. It is the philosophic viewpoint that demands such pleading -- in regard to effusions that are disconnected from evidence. ...

The agnostic miscalculates. ... In struggling to elevate the arbitrary to a position of cognitive respect, he is attempting to equate the arbitrary with the logically supported. This is not merely an affirmation of ignorance; it is an epistemological egalitarianism intent on obliterating an essential distinction. Such an attitude is incomparably more destructive than any error committed by a man devoted to reason who takes definite stands on the basis of mistaken arguments.

A passion for the arbitrary does not derive from concern for logic. Its root is a feeling that has been given precedence over logic.

Post 11

Tuesday, October 21, 2008 - 10:45pm

Dean,

So some generalizations can never be absolutely certainly true.

Were you aware (when you typed it) of the absolute certainty to which that generalization appeals?

Ed

Post 12

Wednesday, October 22, 2008 - 5:52am

I found this so incomprehensible that I actually did some reading on Hume.

Thanks for the impetus.

I am surprised that DMG fell right into the Humean Pit of Uncertainty.

Is reality invariant? Can the laws of reality change? The question is meaningless, similar to "is mathematics green?" I saw comet Hale-Bopp come and go over a couple of months and I was in the path of a solar eclipse where it was about 60% of totality. Both were unusual. Less unusual, but still uncommon, are the failure of traffic lights at a major intersection. Of course things change. Of course we have new experiences, certainly if we live long enough or travel far enough.

But the laws of reality do not change.

Our perceptions change as our experiences change.

The real problem is figuring out how guys like Hume are taken seriously, not just in their own time, but for decades and centuries.

One of my longtime friends is a computerist. We met when he was a programmer. He manages projects now, still codes when he can. Pursuing knowledge, he went to a conference on semiotics, hoping to learn about how information is conceptualized and communicated. The one thing he took from that was that if you want to get ahead in that field, dress funny. Wierd hats, odd jewelry -- or for that matter, always wearing something orange -- is how you communicate your special status. In Chinese ideograms, the word for "king" (wang) is based on the picture of the king's hat.

David Hume housed himself in a special building called an "Ivory Tower" whose obvious majesty awed the gullible into accepting his special status.

To answer Bridget directly, I like David Kelleys' challenge: How do you drive your car? Do you drive on the assumption that reality -- as opposed to, say, a traffic light -- is likely to change or that past experience is not a predictor of the future?

Post 13

Wednesday, October 22, 2008 - 10:05am

Hi Ed,

I was asking just in order to nail down your principle. Crazy hypos are okay for that. In skeletal form, the question was just: if you identify something as an essential attribute for all members of a set, and if something new comes along which is just like the members of the set, except that it�s missing that essential attribute, then it isn�t a member of the set? But hey, your conversation with Dean is much more interesting, so don't worry bout my inquiry. I�ll leave you two to it.

Jordan

Post 14

Wednesday, October 22, 2008 - 5:28pm

I think the conversation is over. I differentiate extremely high confidence from absolute certainty. Ed equates them. Neither of us are budging.

MEM:

I am surprised that DMG fell right into the Humean Pit of Uncertainty... But the laws of reality do not change.

MEM, you are contradicting yourself! You cannot both be surprised and be God. (An all knowing being can not be surprised by gaining info, since everything is already known). (This response to MEM is meant to be comical.) (By know in this response I mean absolute certainty.)

And here's some metaphysics 101 for you: Axiom, Certainty. Ah, so there is a difference between absolute certainty (axiom certainty) and extremely high confidence (certainty). But don't believe me! Or Joe! Punks.

Post 15

Wednesday, October 22, 2008 - 7:48pm

Dean,

I think the conversation is over. I differentiate extremely high confidence from absolute certainty. Ed equates them. Neither of us are budging.

The conversation may be over, but not for the reason you adduce. You mischaracterize my position. I don't deal in absolute -- but contextually-absolute -- certainty. And contextually-absolute certainty is different from something that is merely extremely likely; or from someone who is merely highly or extremely confident.

Ed

(Edited by Ed Thompson on 10/22, 7:50pm)

Post 16

Friday, October 24, 2008 - 6:33am

Jordan and Dean,

Axioms are certainly certain, because of attempted denial. When you attempt to deny them, you get a contradiction (sometimes called "reaffirmation through denial"), and contradictions prove error.

Let me repeat that.

Contradictions don't just make it likely that you're in error, they prove it. Contradictions are a means to contextually-absolute certainty. Knowing that contradictions don't lead to degrees of certainty, but full-on certainty -- you can apply them to synthetic, empirical generalizations, too.

Ed

Post 17

Friday, October 24, 2008 - 7:24am

Here is an example of the process:

You have a pair of normal dice and say to yourself: "Hmmm. Let me see what kind of results I get when I roll them. I want to be able to generalize about the kinds of results I can get from rolling two normal dice. And, on top of that, I want to be able to be certain about the kinds of empirical results I can get from rolling two normal dice." You roll the dice 36 times and get the following frequency distribution:

Total	Number of combinations	Probability
2	1	2.78%
3	2	5.56%
4	3	8.33%
5	4	11.11%
6	5	13.89%
7	6	16.67%
8	5	13.89%
9	4	11.11%
10	3	8.33%
11	2	5.56%
12	1	2.78%
Total	36	100%

from:
http://wizardofodds.com/gambling/dice.html

You say to yourself: "Heyyyy, I was trying to roll a 13 but, in 36 consecutive rolls, I never got a single 13 roll! What the heck is going on here???"

You ask yourself: "Hmmm. Is there a way that, instead of just counting-up supposedly-disconnected instances of dice rolls with crude and brute enumeration -- is there a way that I could figure out what kind of dice rolls I'll get, at all times in the future; and be able to be certain?"

You think to yourself: "Hmmm, in order to do something like this, I'll need to understand the mechanics of dice rolling. And ... once I understand the mechanics ... I will be able to generalize to all dice rolls, everywhere, without the possibility of error!"

You begin to manipulate the dice in order to see what kind of limits there are to outcomes. You try out all of the 36 permutations. You find the limits of 2 and 12. You ask yourself if you can understand why you can only get the inclusive set of 2-12 from dice, and why it is that no other outcomes are possible.

When you understand why, you are in the position to veridically generalize. And the really important thing is that you can get to this veridical generalization without ever having to have experienced 36+ rolls of dice.

Ed

(Edited by Ed Thompson on 10/24, 7:27am)

Post 18

Friday, October 24, 2008 - 8:10am

And here is a disturbingly-generous account of rival views:

Ed says living elephants will always be bigger than living fleas -- citing biophysics as a restraint on the possibility that he is in error. However, I (Dean or Jordan) can fantasize an exception.

Let's say that a flea was being kept alive in microgravity in outer space by advanced aliens. The aliens were making sure that, even though the flea doesn't have a heart and blood vessels, that proper circulation would occur regardless of its body size. The microgravity would allow the flea's body to expand to, say, one-fifth of a centimeter -- so all we would need to do then is to find out how we can keep an elephant alive at less than a fifth of a centimeter!

Since the only force that could reduce the size of an elephant like that is a black hole, if we dropped an elephant into a black hole and measured its decrease in size and its life -- there might be a split-second where the elephant was less than one-fifth of a centimeter but still alive!

So, there it is! In order to fantasize an exception to Ed's general rule, all we have to do is arbitrarily postulate the existence of advanced aliens who are schooled in flea-hemodynamics, along with postulating that black holes are a directly-experiencable fact (rather than a theory explaining directly-observed facts), and postulate that a multi-cellular organism can get compressed down to less than a millionth of its natural size ... and still be alive for a split-second!

Hmf! We've blown Ed's so-called veridical generalization out of the water! And we didn't even need more than a couple of completely arbitrary postulates in order to do so! Hahahahahahaaaaaaaaaaaa!

:-)

Ed

(Edited by Ed Thompson on 10/24, 8:13am)

Post 19

Friday, October 24, 2008 - 1:49pm