You CAN Change Your Axioms

[fnord_too]

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I can't believe that I have to bump this. It is one of my most important posts as far as I am concerned. It is pretty much the reason for my silly questions. Where is everybody?

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Ok, here's a reply for you.

First, you say this is second nature to WC scientists. I think you may mean mathematicians, since scientists do not have axioms. Maybe you mean scientists who are trying to find a mathematical model of something, in which case you are talking about the trial and error process of theorizing.

If you are talking about mathematics, this is obvious and deos not deserve a lot of discusstion.

I worry somewhat about statements like:
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If in your heart that conclusion feels like it must be true, all you have to do to remain consistent, is appropriately alter you initial premise or axiom. Of course by doing that you may wind up having to alter OTHER conclusions that stemmed from the original, but now altered premise.

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If you know something is true, say because you observed it, but your previous theories would not allow for it, then, yes, something is amiss and you shoud work on theories that are consistent with what is observed (and if you are dealing with general physical phenomena, i.e. not something like "Jane married Bobby? I didn't even think they knew each other"), then you should make novel predictions based on your new theories and develop experiments to see if these predictions hold. If on the other hand you 'know' something, but it violates theories (say "I KNOW that if I have two objects with identical drag to mass ratio's the heavier object will fall faster"), well, you get the idea.

You appear to jump to conclusions at times. The best example I can think of is in "Poker, Gaming, and Life" where you state your belief that there is some physical link between Hawking's life span with Lou Gherig's disease and his intelligence. I believe you said something like "There has to be a relation and scientists should be looking for a link between the two." (Obviously I don't have the book with me but I think that was the general idea.) I'm not saying there is not a link, but to assume one, to "know in your heart" that one exists is really taking a leap; I can think of several other factors for consideration in that particular case that have nothing to do with his intelligence beyond the fact that it has made him somewhat famous and productive even in his physically disabled state.

[Mr. Curious]

How does one weigh the value of changing the axiom versus the value of proving themselves right?

[coheedandcambria]

Humans are animals. We might be the smartest animal, but we cannot disassociate ourselves completely.

[BigDukeSix]

Unless David, you are the only conscious being in existence (which also makes you god, nice sideline.....) Then whatever you believe is true. You can alter the premise or the conclusion whenever you like.

Ridiculous?

seems so until you try and prove otherwise.

[imported_adhoc]

I know I said I would stop reading this forum after James Woods proved Hitler wasn't evil, but I failed and feel driven to comment on this thread. No scientist worthy of the name will "alter his axioms" (as you put it) to fit a conclusion he has already arrived at. That is the precise opposite of the scientific method, and anyone who does that is not only emphatically not a scientist but intellectually dishonest. Working from a conclusion (ie generalities) to an artificial set of axioms (ie particulars) pre-engineered to suit a desired conclusion (in this case explicitly qualified by a literally irrational emotional prejudice - "If in your heart that conclusion feels like it must be true") reverses the process of rational inquiry.

The scientific method proceeds from assumptions of ignorance by empirical necessity. It is a framework for the testing of hypotheses which is designed to place the bias of an observer outside the scope of the investigation. The changing of hypotheses which results from this process is not the alteration of axioms, it is the alteration of conclusions. Axioms may be altered when they no longer explain a body of conclusions that have been derived from empirical observation and corroborated, in a substantial way, by broader theory. They cannot be altered to fit individual bias or what one feels "in your heart to be true."

[Quaalude]

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Just wanted to point out that the unacceptability of coming to a conclusion that can't be reached from your initial premises (while its negation can) does not mean that you have to abandon that conclusion. If in your heart that conclusion feels like it must be true, all you have to do to remain consistent, is appropriately alter you initial premise or axiom. Of course by doing that you may wind up having to alter OTHER conclusions that stemmed from the original, but now altered premise. But if the conclusion that forced this alteration is especially clearcut or important to your values, you have no choice.

This whole procedure is second nature to world class scientists but takes some getting used to by your average Joe.

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This sounds similar to what artificial intelligence researchers call "nonmonotonic reasoning," except that nonmonotonic reasoning has nothing to do with feelings or values, and everything to do with withdrawing previous conclusions based on new information. And I don't think the average Joe is all that unfamiliar with it, as it is really just common sense reasoning.

There are numerous books on the subject, and of course, all hail the wiki.

-Travas

[Darryl_P]

I agree 100% with the OP but I can't figure out why it wasn't self-evident up until now? Or if it was, then why the need to create a thread about it?

Even an average Joe can relate to a belief system, even if the word "axiom" sets off certain fuzziness in his brain. I don't think the average Joe disagrees with the idea that one's belief system can change over the course of one's life and that in itself doesn't imply that the person ever had any weaknesses in the area of logic.

As an example look at Einstein. It's widely known that he was an atheist in his youth and believed in God in later years, yet his results didn't get exposed to any meaningful questioning based on this fact alone.

[benkahuna]

Yeah, I was thinking the same thing. Anti-scientific. You take evidence and form conclusions, not the other way around.

Obviously, you'll get nowhere if you refuse to ever change your intial assumptions (in any area in life), but denying other observations because you're really into some particular conclusion is not rational at all. I think this approach is how faith-based beliefs can persist in the face of strong evidence against the veracity of that belief. Could help people stay happy and sane, of course, which obviously would make it a very positive thing in some cases.

The more I think about it, the more dangerous Sklansky's idea seems to me. More than anything, I hope I'm interpreting his statement wrong.

[benkahuna]

David, in what situations do you see world class scientists following their intuition so strongly without producing worse results? Are you just talking about scientists believing in a Supreme Being or avoiding sociobiological conclusions?

I get the sense you have some specific ethic in mind here, but that you're not stating it explicitly.

[David Sklansky]

You guys got me all wrong. I'm talking about when experimental evidence doesn't fit the model. So the model has to change.