The Problem of Induction and The Axiom of Order

Daniel:
>"No number of repeated observations can establish a universal law with any certainty or probability, and it is illogical to demand otherwise".

Nathan:
>Take out the word "any" and I'll agree, if by "probability" you mean computed probability.

Done!

"No number of repeated observations can establish a universal law with certainty or probability, and it is illogical to demand otherwise".

And of course, the non-computational sense of "probability" or "probable" is the colloquial one, which refers to our vague conjectures based on past experience - like "the new Star Wars movie will be crap, in all probability" or " it will probably rain at Easter, it always does". Such formulations are entirely innocuous to my point, as sure enough, the Star Wars movie *was* crap, and it *didn't* rain at Easter, neither of which we would dream of using as examples *for* or *against* the method of induction, or for or against any universal laws, and neither of which conflict in the slightest with Popper's alternative proposal. I myself use these and other words - "likely", "surely" etc - all the time in this hypothetical sense.

So, with that clear, do you still consider I am "completely misrepresenting" what you are saying? To the contrary, it looks to me as if we almost completely agree.

Nathan
>In short, if you affirm that humans can acquire useful knowledge of reality via induction, even without explicit falsificatory procedures, then we agree. If you deny that, then we disagree.

We disagree.

- Daniel

Nathan:
>But Daniel, you STILL have not answered the question, What is the 'logical justification' for logic and deduction?

I do not know why you STILL keep asking this question, seeing I have answered it a few posts back.

But I will recap:

Deductive logic can be shown to be deductively justified.

Induction cannot be deductively justified.

If you think that deduction cannot be deductively justified, or we should reject it because *it can be*, you are welcome to jettison logic. What you would be left with I cannot say.

Now you are welcome to accept a belief - such as induction - that lacks logical justification. Lots of people do. What happens then is they find *justifications elsewhere* - in tradition, in superstition, in what the government says, in their internal feelings or states, in "the way it has always been done". This I believe leads to irrationalism, or an unwillingness to accept reasoned argument. But that's just my opinion.

Nathan, in reading some of your other posts on various subjects, and during the course of this debate, I have been struck by how close you come to a Popperian position.

Recall that Popper says that *induction* does not really exist; that it is a kind of "optical illusion", that it only *appears* that we rely on induction.

Perhaps I might compare Popper's alternative with the traditional picture of the inductive method. You might find it resembles your own more than you suspect.

Jeff wrote:

Perhaps I missed it but, could you deductively demonstrate the/a deductive justification for deductive logic -- without circularity, of course?

Wasn't this part of Gödel's point - that no system can be proven by appeal to that system?

 

Nathan,

As I understand him, Gödel argues that a system cannot be both complete and consistent. It must be either complete, or consistent, or neither.

It's my understanding that traditional deductive logic is consistent but incomplete; it rests on propositions (axioms, as non-Objectivists would call them) that escape (logical) proof.

Perhaps it would help for me to mention that I disagree with Daniel (and Popper) when they argue that induction is not inductively valid. In my view, induction has worked quite well in the past, so inductively, I can say it'll work quite well in the future.

It's important to keep in mind that propositions derived inductively have always stemmed from striving toward forming some set of consistent observations. If a set of observations is found to be inconsistent, then it is falsified and not a valid induction.

See, that's what I think falsification does: it helps us keep our inductions more honest. Falsification complements induction.

Hi Nathaniel,

I'd ask you to think about precisely WHAT you must assume about the universe and about consciousness to make that so.

It's no secret that induction depends on the uniformity (regularity, order, etc.) of nature. But like most of us have been saying, such uniformity is not logically justifiable; nature is not necessarily uniform. 

As I say, [falsification is] inherent in the very nature of induction, conscious or unconscious. Don't you think?

I find it better to consider falsification as a complement to induction. Induction deals with building a theory up; falsification, shooting it down. In my view, they are (at least in part) flipsides to the same coin, as some Objectivists like to say.

•   A: 'If 100 X ARE black then all X are likely black'

• 'If an X is NOT black then A is false'?