Consider the following.

Suppose you have a bag of marbles. The bag may contain only marbles colored white or it may not. You do not know. What is the probability that the bag contains only white marbles. You don't know, so lets say the probability the bag only contains white marbles is X.

Suppose you draw a marble from the bag and it is white. The result of this draw doesn't tell you the probability of X, but you do learn something from it. You learn the probability of X is closer to 1 than you previously thought. Why? Because each time you draw a marble and find it to be white, you decrease the number of ways a non white marble could be in the bag.

For example, suppose the bag has 3 marbles in it. W stands for a white marble. B stands for a non-white(black) marble. If 3 marbles are in the bag the possible starting conditions are:
WWW (3 white marbles)
WWB (2 white marbles and black marble)
WBB (1 white marbles and 2 black marbles)
BBB (3 black marbles)

Before we start drawing marbles the probability that all the marbles are white is .25. Now suppose we draw a white marble. Now only two marbles are left in the bag and we've eliminated one possible initial starting condition. The remaining possible starting conditions are:
WWW
WWB
WBB.

We now know that the probability all the marbles are white is .33. Suppose we draw another white marble. The remaining possible starting conditions are:
WWW
WWB

We now know that the probability all the marbles are white is .5. Do you see what is going on here? Every time you observe a white marble while never observing a non-white marble confidence in the proposition that all the marbles are white increases.

It is essentially this thinking that we use to determine what is a fact or at least likely to be true of reality and what isn't.

Unfortunately, at no point does proof that all the marbles are white materialize until all marbles are out. However, I agree that we do use sloppy thinking like that all the time. It isn't a "fact of reality" that you're discovering, you're engaging in a useful heuristic (congratulations, you're describing what we already knew about the limitations of our minds and assumptions). Now, someone will be along to tell you a story about swans shortly.

-Our brains didn't evolve to seek truth.

Only if you know how many marbles are in the bag, of course. If you don't know that, then you have no means of determining the probability at all, and are just talking out your ass if you begin to assign probabilities to the colors of the marbles based on what you've already drawn.

And, of course, if you can discount the existence of other variables too. For example, if you have a bag filled with marbles that were randomly dropped into a bag by a machine, but what you don't know is that, after the bag was filled a person came by and covered the top layer of the bag with exclusively white marbles, then you'd just be sitting there, drawing white marbles over and over and making assertions of probability, gleefully unaware of the complicating variable that's influencing what's going on.

Oh, and the potential color the marbles could be also plays a roll. I mean, if you're doing this with a bag of randomly selected marbles, and you know that there were only two kinds of marbles in the initial pool, then the probability of them all being white is higher than if the initial pool contained three types of marbles.

See how confounding variables make short work of simplistic assertions of probability based on prior observation? Every marble you find is a white marble, right up until you find your first non-white marble.

(January 6, 2015 at 9:02 pm)Rhythm Wrote: Unfortunately, at no point does proof that all the marbles are white materialize until all marbles are out. However, I agree that we do use sloppy thinking like that all the time. It isn't a "fact of reality" that you're discovering, you're engaging in a useful heuristic (congratulations, you're describing what we already knew about the limitations of our minds and assumptions).

-because our brains didn't evolve to seek truth.

In the example in the OP there are two propositions:
Proposition A) All the marbles are white.
Proposition B) Not all the marbles are white.

Only one proposition can be true. Each time you draw a marble and find it to be white, while never drawing a marble and finding it to be black.....each time you do that the probability that proposition A is true becomes more likely.

Is the speed of light in a vacuum really a constant? We don't know for absolute certainty. We consider it to be a fact because we have made many many observations and each one adds to our confidence in the veracity of proposition that the speed of light in a vacuum is constant.

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(January 6, 2015 at 9:07 pm)Esquilax Wrote: Only if you know how many marbles are in the bag, of course. If you don't know that, then you have no means of determining the probability at all, and are just talking out your ass if you begin to assign probabilities to the colors of the marbles based on what you've already drawn.

The example I used in the OP works for any bag of marbles containing N number of marbles. The probability that all the marbles are white always moves closer to 1 with each draw of a white marble while never drawing a black one. You can work this out for yourself with 4 marbles or 5...or 10,000 marbles.

Suppose you have 3 colors of marbles. White, red, and blue. You can consider red and blue to be non-white marbles(or black). It really doesn't matter how many different colors the bag could contain. The bag either contains all white marbles or it does not.

(January 6, 2015 at 9:08 pm)Heywood Wrote: In the example in the OP there are two propositions:
Proposition A) All the marbles are white.
Proposition B) Not all the marbles are white.

Only one proposition can be true.

Correct. But you won't know which until you've drawn every marble. Probability is, itself, a heuristic. Not proof. That we engage in this sort of thinking and then feel confident that we have "proof enough" is, again, indicative of nothing more or less than the limitations of our mind and what our minds evolved to do.

Quote:Each time you draw a marble and find it to be white, while never drawing a marble and finding it to be black.....each time you do that the probability that proposition A is true becomes more likely.

Until you draw a non-white one. At which point your 99% probability drops to 0, even though nothing about the bag or the marbles has changed.

(January 6, 2015 at 9:08 pm)Heywood Wrote: The example I used in the OP works for any bag of marbles containing N number of marbles. The probability that all the marbles are white always moves closer to 1 with each draw of a white marble while never drawing a black one. You can work this out for yourself with 4 marbles or 5...or 10,000 marbles.

Unless the bag is constantly being refilled without your knowledge, or contains black marbles that have been coated externally with white paint, or has a secret compartment sown in containing a black marble, or an insane person is drawing the marbles and reporting them all as white, even if they aren't...

Confounding variables. They exist even if you don't consider them. That's rather the danger of them.

Yes, there is very little that can be known for absolute certain. Life is a matter of probabilities. That's why a preliminary study of say 20 people is not considered very reliable and anecdotal evidence even less so. Large sample sizes are necessary to learn much of anything. And yes, no matter how large the sample, that Black Swan might still be out there.

Just to note though with regard to your marble example. It's highly optomistic. The world is a great deal messier than that. Chances are that you'd have no way of knowing even that all of the marbles had to be either black or white. There's a world of color possibilities out there.

I think woody has discovered falsifiability.

(January 6, 2015 at 9:19 pm)Jenny A Wrote: Just to note though with regard to your marble example. It's highly optomistic. The world is a great deal messier than that. Chances are that you'd have no way of knowing even that all of the marbles had to be either black or white. There's a world of color possibilities out there.

The bag will contain marbles of the same color or it will not. The truthfulness of the proposition that the bag contains only marbles of the same color is not impacted by the number of color possibilities.

But you ability to claim knowledge is, understand? Just as explained before, the probability changes even though the color of the marbles does not. Because we're actually talking about two separate things here. The status of the marbles in the bag, and the status of our knowledge about the marbles in the bag.

also, I was going to suggest you read some Karl Popper.
http://en.wikipedia.org/wiki/Karl_Popper

You -are- describing one of the ways that human beings arrive at "facts", (whether those facts are true or false)- but there are other ways with greater degrees of provisional assurance. Your example, for example (the speed of light), wasn't arrived at solely through the process you are describing.