The Problem of Induction and The Axiom of Order

Jordan:
>Like I said, the alternative to "existence exists" is "nothing exists," which is contradictory, and contradictions cannot exist. Therefore, existence must always exist.

The criticism of this is, of course, that the term used in this formulation is so broad that it is completely innocuous. It doesn't tell you anything you didn't know already. So its boldness, or informative content, is close to nil, and all you can really do with it is have boring verbal debates about "what do you mean by 'existence'...?"

- Daniel

Post 21

Tuesday, May 31, 2005 - 7:06pm

Hi Nathan,

But what makes "nothing exists" contradictory?

That's like asking why "married bachelor" is contradictory. Just as you can't find a married bachelor, neither can you find nothing existing. Or: The logical opposite of existence is non-existence, and the verbal equivalent to non-existence is "nothing." "Existence" and "nothing" are mutually exclusive and jointly exhaustive. This is what makes "nothing exists" contradictory.

Like Daniel and I are trying to explain, humans manage to get by even if they subscribe to orders that don't exist.

Daniel,

I wrote the following in an Objectivist google group on May 22, 2004. It speaks to your comment, so I thought I'd share.

Objectivist axioms...often tell you what to avoid. For instance...

1. The primary axiom -- existence exists -- tells us to stay away from Descartes "cogito ergo sum" because that puts consciousness epistemologically before existence.

2. Placing 'identity' before 'existence' will also consign us to a rationalist outlook. Or in my view, it will show us where Aristotle went wrong, as it seems that he viewed essence as ontologically prior to existence.

3. And treating identity as an axiom allows us to avoid Sartre's idea that essence ontologically follows existence. (I think Objectivism treats existence and identity as ontologically equal.)

[Perhaps one day] you might find the axioms to be a positive guide to knowledge (i.e., they might tell you where to go conceptually), but in the least, they'll act as a negative guide (i.e., they'll tell you where to avoid.).

G'night,Jordan

Post 22

Tuesday, May 31, 2005 - 8:22pm

Daniel said:

The problem that bothers us is that induction is deductively unjustified as a source of truth.

You do not use deduction to justify truth. You use it to confirm similar examples of already inductively justified truth.

Truisms are inductive. To assume you must somehow get justification through deduction is a misunderstanding of a posteriori and a priori -- and leads to such silly statements as "there is no logical justification for induction."

Induction is "proved" by the validity of its generalizations. In other words, do they hold up to reality? And the only way to prove that is through ... induction.

Post 23

Tuesday, May 31, 2005 - 8:49pm

Jordan:

Hi Nathan,
But what makes "nothing exists" contradictory?
That's like asking why "married bachelor" is contradictory. Just as you can't find a married bachelor, neither can you find nothing existing. Or: The logical opposite of existence is non-existence, and the verbal equivalent to non-existence is "nothing." "Existence" and "nothing" are mutually exclusive and jointly exhaustive. This is what makes "nothing exists" contradictory.

I don't think I wish to quarrel along these lines, as others have done so ad nauseum.

What I WOULD like to say in conclusion is that nothing we can say LOGICALLY demonstrates the NECESSITY of existents having existed for all time and continuing to do so for eternity.

That's what started this line of thought. The fact that axiomatization was necessary is our clue. That's all I have to say on that for now.

Nathan Hawking

Post 24

Tuesday, May 31, 2005 - 9:13pm

David:

Daniel said:

The problem that bothers us is that induction is deductively unjustified as a source of truth.
You do not use deduction to justify truth. You use it to confirm similar examples of already inductively justified truth.

David, the nature of induction is that conclusions or beliefs solely based upon it cannot ever be fully "justified."

If the conclusion can be logically justified, it is no longer simple induction.

To assume you must somehow get justification through deduction is a misunderstanding of a posteriori and a priori -- and leads to such silly statements as "there is no logical justification for induction."

Linz's rant notwithstanding, "there is no logical justification for induction" is true in some senses and untrue in others.

It is true insofar as a particular belief which is (solely) inductively acquired.
It is false insofar as the relative efficacy and legitimacy of induction itself, as I believe my original post demonstrates.

Induction is "proved" by the validity of its generalizations. In other words, do they hold up to reality? And the only way to prove that is through ... induction.

I would not use the word "proved." That has connotations of certitude and conclusiveness. Induction, by its nature, cannot deliver that.

I prefer the word "corroborate" for inductive thinking: ": to support with evidence or authority : make more certain."

Notice the DEGREES implied in "support" and "more."

http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=corroborate

Nathan Hawking

Post 25

Tuesday, May 31, 2005 - 9:52pm

David:
>Induction is "proved" by the validity of its generalizations...And the only way to prove that is through ... induction.

David, could you show how the reasoning you've used above is not a logical fallacy of the following type:

http://datanation.com/fallacies/begging.htm

Do you realise such an argument could equally be employed to "prove" that, say, God created the Universe. Would you accept such a proof?

Or, if you accept question-begging reasoning *is* a logical fallacy, why do you think it a good idea to base your argument on it?

Is that the reason for your quotes around "proved" - you sense that you really haven't proved it at all?

- Daniel

(Edited by Daniel Barnes
on 5/31, 9:54pm)

Post 26

Wednesday, June 1, 2005 - 12:10am

Daniel:

David:
>Induction is "proved" by the validity of its generalizations...And the only way to prove that is through ... induction.

David, could you show how the reasoning you've used above is not a logical fallacy of the following type:

http://datanation.com/fallacies/begging.htm

Do you realise such an argument could equally be employed to "prove" that, say, God created the Universe. Would you accept such a proof?

Or, if you accept question-begging reasoning *is* a logical fallacy, why do you think it a good idea to base your argument on it?

Is that the reason for your quotes around "proved" - you sense that you really haven't proved it at all?

I suggested to David that "corroborated" is a better word than "proved."

As I've pointed out, there is one interesting sense in which induction corroborates induction which is not question-begging:

There is CONSIDERABLE order in the universe, and induction depends upon order for its efficacy.
Using induction itself, we can examine the pattern of success of induction, and we find that it is enormously successful at enabling us to discern reality.

There's nothing fallacious about, until we start reaching for terms like "proof" and "certitude" in the strong senses of those words.

Nathan Hawking

Post 27

Wednesday, June 1, 2005 - 8:12am

Hi Nathan:

What I WOULD like to say in conclusion is that nothing we can say LOGICALLY demonstrates the NECESSITY of existents having existed for all time and continuing to do so for eternity.

I wouldn't necessarily include "time" as a necessary attribute for existence, but that's fairly irrelevant here. I simply disagree with you. As "married bachelors" necessarily cannot withstand logic (although Quine would disagree with me), neither can "nothing exists." The difference is that we can deny that bachelors exist, whilst we cannot deny that existence exists.

But this is tangential to the purpose of this thread. I'm happy to let it go.

Carry on,
Jordan

Post 28

Wednesday, June 1, 2005 - 8:39am

OK. Forgive my contribution to this discussion because all the Popper that I have read consists of two classic papers/lectures available on the internet and Rafe Champion's interpretation of Popper's work.

When Popper attacks induction, this is what I understand him as doing/saying.

1) All observation is laden with theory, so the idea that induction creates theories and is a process apart from observation is misguided because we usually make inferences from observations automatically.
2) To the degree that induction is the method that makes universal generalizations from particular instances, it begs the question and will always be open to skepticism.
3) To mitigate the problems with and limitations of universal generalizations, they should be framed in such a way that they can be tested and shown to be false. This will facilitate good science.

Whatever the limitations of such a criticism, I think that most of the inner logic is sound, and that any good thinker should be familiar with the importance of testability (or what Popper calls "falsifiability") as an integral part of the scientific process.

Note: Edited to clarify point1.

(Edited by Abolaji Ogunshola on 6/01, 10:51am)

Post 29

Wednesday, June 1, 2005 - 11:54am

Abolaji wrote:

OK. Forgive my contribution to this discussion because all the Popper that I have read consists of two classic papers/lectures available on the internet and Rafe Champion's interpretation of Popper's work.

When Popper attacks induction, this is what I understand him as doing/saying.

No forgiveness required. Expertise in the history of philosophy is not a requirement for contributing to a thread.

1) All observation is laden with theory, so the idea that induction creates theories and is a process apart from observation is misguided because we usually make inferences from observations automatically.

That's a very good point, and one worth stressing, I think.

We're not just talking about that induction which leads to science or major intellectual beliefs. As Laj notes, ALL observation entails automatic inferences--and this occurs even unconsciously. Drawing inductive inferences is inherent in the nature of intelligence itself.

That's why I deem the Axiom of Order an epistemological axiom as well as a metaphysical one--intelligence cannot even get off the ground with some automatic assumption of order. It is pervasive. We cannot even open our eyes and see without using it at some level.

2) To the degree that induction is the method that makes universal generalizations from particular instances, it begs the question and will always be open to skepticism.

I would agree with this using "skepticism" in the weak sense, that absolute certitude about inductive beliefs is inattainable, but not in the strong or extreme sense of Skepticism, that induction or inductive beliefs offer NO degree of certainty.

3) To mitigate the problems with and limitations of universal generalizations, they should be framed in such a way that they can be tested and shown to be false. This will facilitate good science.

Whatever the limitations of such a criticism, I think that most of the inner logic is sound, and that any good thinker should be familiar with the importance of testability (or what Popper calls "falsifiability") as an integral part of the scientific process.

I concur, especially for scientific contexts. This is a healthy mental posture for GENERAL, even everyday, use of induction, too.

For example, we might have lifelong knowledge of the nature of a friend who finds himself accused of theft. We believe our friend to have been completely honest theretofore. But concluding from that experience that "he didn't do it," or "he's incapable of theft" is to turn an inductive conclusion into an absolute.

At best, we can say "Based upon my experience, he probably didn't do it." That's the appropriate mental inclination toward inductively-derived beliefs--we must be willing to abandon them upon their genuine falsification.

Nathan Hawking

Post 30

Wednesday, June 1, 2005 - 11:57am

Nathan:
>I suggested to David that "corroborated" is a better word than "proved."

Very Popperian of you!

>As I've pointed out, there is one interesting sense in which induction corroborates induction which is not question-begging:

I assume your example below refers to your axiomatic approach? (which does not help David's case. Never mind)

While I think your earlier solution is not a bad stab at it, it does not work IMHO. I will have to break it down a bit to show this, so will do so a bit later today.

- Daniel

Post 31

Thursday, June 2, 2005 - 2:46am

Jordan writes:
>1. The primary axiom -- existence�exists -- tells us to stay away from Descartes "cogito ergo sum" because that puts consciousness epistemologically before existence.

As you know, the Popperian schema is similar to Objectivism in this respect.

>3. And treating identity as an axiom allows us to avoid Sartre's idea that essence ontologically follows existence. (I think Objectivism treats existence and identity as ontologically equal.)

Yes, the Law of Identity insists on this. However, despite the importance she placed on it, even Rand herself forgets the Law now and again. For example - somewhat embarrassingly - when outlining the steps in her theory of concept formation:

1. Cognition and Measurement (ITOE)

"...The (implicit) concept "existent" undergoes three stages of development in man's mind. The first stage is a child's awareness of objects, of things - which represents the (implicit) concept "entity." The second and closely allied stage is the awareness of specific, particular things which he can recognize and distinguish from the rest of his perceptual field-which represents the (implicit) concept "identity."...

Now, it seems this first implicit conceptual stage "entity" in the theory is a blunder, as it is prior to "identity", and cannot exist - nor could the child's awareness of it. As Importance of Philosophy.com points out in its article on the LOI: "...An entity without an identity cannot exist because it would be nothing."

So I tend to think you must be correct overall, despite faux pas like this in Rand's theory.

>[Perhaps one day] you might find the axioms to be a positive guide to knowledge (i.e., they might tell you where to go conceptually), but in the least, they'll act as a negative guide (i.e., they'll tell you where to avoid.)

This is probably good advice.

- Daniel

�

Post 32

Thursday, June 2, 2005 - 8:09am

Thanks for writing back, Daniel,

You've made an interesting point about Rand's theory of concept-formation that I hadn't noticed before. I wonder what other Objectivists would have to say about it.

-Jordan

Post 33

Thursday, June 2, 2005 - 9:05am

Guys, the proof that induction is a valid process is the very fact that you are alive at this moment. It was through induction that you made the generalizations that got you through every moment of living.

"Moving vehicles can kill me because I'm a soft living tissue."

"Food is good for me and necessary for my survival."

"Work is good for my soul."

"Crop rotation makes for better vegetables."

Etc.

The "proof" or corroboration of induction is in its success and our introspecting on it to verify the method -- and checking the final generalization against reality through further induction.

Since induction is the method for understanding reality and forming generalizations, you cannot then ask, "How can we 'deductively' prove the validity of induction?" As I think Nathan noted, you have to use the method to prove the validity of the method.

Post 34

Thursday, June 2, 2005 - 10:16am

David,

Lots of folks have survived (and continue to survive) using induction, even though their inductively derived views were flawed. It is a mistake to automatically attribute a good outcome to inductive efficacy.

Jordan

Post 35

Thursday, June 2, 2005 - 11:29am

Jordan,

They survive because of good inductions, not because of their bad ones. They survive in spite of their bad ones. They are alive only to the extent to which they are rational.

Post 36

Thursday, June 2, 2005 - 12:25pm

Hi David,

They survive because of good inductions, not because of their bad ones. They survive in spite of their bad ones. They are alive only to the extent to which they are rational.

Then I wonder if you think people are dead to the extent to which they are irrational. :-)

That aside, you seem to measure whether an induction is good by how well it keeps people alive. So if inducing that the world is flat does a better job of keeping me alive than would inducing that the world is round, then I should keep with the induction that the world is flat? To be sure, I can imagine (not necessarily induce) that if I were a sailor from a long time ago, inducing that the world is flat would do a better job of keeping me alive because I'd stay close to shore for fear of falling off the world's edge. And staying closer to shore makes it easier for other sailors to spot me or makes it easier for me to swim ashore in case my boat sinks. A more realistic example would be that one Wright brother's untimely demise. Had he just stuck with the induction that human airflight was impossible (because we were too damn heavy), he never would've gotten his plane off the ground, and crashed, and died.

-Jordan

(Edited by Jordan on 6/02, 12:27pm)

Post 37

Thursday, June 2, 2005 - 1:48pm

Hi David,
>As I think Nathan noted, you have to use the method to prove the validity of the method.

Perhaps I could tackle this in another way, and maybe reply to Nathan at the same time. Nathan actually noted that we have *two* methods of learning about reality. One is *empirical* - that is, by observation and experiment - and one is *argumentative*; that is by logic and reasoning.

The beauty of this arrangement is that one can be used to *criticise* the other. The flaws the assumptions behind someone's reasoning might become evident by experience. Likewise, logic can also reveal underlying patterns behind inconsistent phenomena in reality.

Now for a long time *the method* of empirical science has been assumed to be *inductive* - that is, we move from observations to theories, from the particular to the general. The criticism of this from a logical point of view began with Hume, and it has become evident that induction is weak in a number of respects. For example, if induction is the way to find universal laws, it must in itself be able to be formulated as a universal law. Yet problems abound, starting with: *how many* observations does it actually take to formulate such a law? 20,000? 200? 2? And worse yet, it seems the history of science shows a habit of formulating universal laws based on any number of observations between 0 (Einstein's theory of relativity,which was formed theoretically) and any number you'd care to think of. Further, there is the infinite regress once one appeals to a universal law of induction which can only be confirmed once that principle is established. Further to that, there is another apparent logical error that theory follows observation - yet how do we decide what to observe?

Now despite all these very good logical criticisms, scientists have stuck with their belief in the inductive method, not because they have solved these issues satisfactorily, but mostly because they couldn't think of a better one. Even Hume himself, having impeccably demonstrated that induction was illogical, *remained an inductionist himself*, concluding, somewhat gloomily, that all if mankind had to believe in induction, and belief in induction was irrational, *mankind was irrational*.

Now it is this *second* conclusion that Hume was wrong in. Because what if it could be shown that our belief in induction was actually a kind of "optical illusion" - that in reality, our empirical method was something else entirely,something that had few if any of the logical problems entailed by induction? This empirical method, Popper proposed, was *falsification* - the idea that while we cannot logically find via inductive inferences definitive confirmations, we can find, via the modus tollens, definitive *refutations*. No number of white swans observed will finally confirm a theory that "all swans are white", a single black swan will refute it.

So the answer is - and this is the simplest reply to Nathan's idea too: *why bother* with trying to justify the inductive method of empiricism in the first place, when we now have a logically sound alternative?

- Daniel

(Edited by Daniel Barnes
on 6/02, 1:52pm)

Post 38

Thursday, June 2, 2005 - 2:13pm

In response to Daniel (and Popper) -- how do we know what to theorize about if we have nothing to observe? In my view, observation comes first. Also, how does science progress if all it can do is falsify some rather than verify any of an infinite (or at least really big) number of theories? Popper didn't do a good job of answering this for me.

Guys, I'm off for awhile. Maybe see you next week. Enjoy without me.

Jordan

Post 39

Thursday, June 2, 2005 - 2:32pm