RoR: Forum

Hello Joseph Rowlands,

I read your article on Certainty and liked it. But I have some questions on your comments on the use of probability especially Bayesian probability. I would like to know your views on plausible reasoning i.e, reasoning under insufficient knowledge. For example if you have to pick one hypothesis among several, where the available knowledge does not conclusively point to any one hypothesis, how would you proceed?

Anbu

Post 1

Monday, January 14, 2008 - 7:13pm

Hi Anbu,

Before Joe answers your question, could you give us an example of the kind of thing you're talking about -- in which "you have to pick one hypothesis among several, where the available knowledge does not conclusively point to any one hypothesis"?

Thanks.

- Bill

Post 2

Monday, January 14, 2008 - 8:19pm

Joe,

Another great piece put into words understandable to folks from all different backgrounds. Good job. I do have a refinement for one part of it, however ...

Similarly if the data contradicts the conclusion, you'd have a serious reason to doubt it.

But often, when data contradict the conclusion, we have knowledge (not any kind of mere reason to believe or mere reason to doubt).

For an example, whenever a universal statement is made (whether positive or negative), then any "contradictory particular" rules them out 100%. For instance, if you have a notion that a pair of dice will never come up "doubles" and somebody rolls a "doubles" -- you are not partly wrong, but all the way.

And this (being 100% wrong) is something which can be 100% known. That dice can come up doubles, is beyond the shadow of any doubt (to any observer who's seen it do so before).

;-)

Ed

(Edited by Ed Thompson on 1/14, 8:22pm)

Post 3

Monday, January 14, 2008 - 8:53pm

Joe

I agree with you, certainty is a confusing term to a lot of people, and your article goes a long way to clearing some of the confusion. However, it seems to me that there are some things of which man can be 100% certain. They are:

Ethical Certainty

1. No man has the right to initiate physical and/or mental force against another. Retaliation is permitted only against those who are initiating physical and/or mental force against you.

Metaphysical Certainty.

1. Man is a being of volitional consciousness.

2. Man�s innate right is to have the right to his own life.

3. Reality is that which exists.

Epistemological Certainty.

1. Reason is man�s only absolute.

When you consider the concept of certainty in this manner, then you stop those who would argue in favor of uncertainty in their tracks. They can argue that all of the rest of our knowledge represents a degree of certainty, and at any given time newly discovered evidence can alter the nature of mans� knowledge. But they can�t argue that there is no possibility of man possessing at least some knowledge that is 100% certain.

Post 4

Tuesday, January 15, 2008 - 10:24am

Hi Bill,

I am currently working towards my doctoral degree in Satellite communications and in my work I extensively work with Bayesian Probability theory . I could give you several examples from my work but let me try my hand on a generic and much abused example of coin toss.

Let's say I take two coins and toss them. Let us assume that you know nothing about the fairness of the coins. The outcome could be one of (HH HT TH TT) with H=Heads and T=Tails. If I ask you to list them in the order of plausibility you would say that any order is good since you don't have sufficient knowledge to choose one over the other. Granted that if you could measure all the initial conditions of the tossing process, the wind velocity, etc, and if you had a powerful computer you could tell the outcome with certainty. But let's assume you don't have the time to do all that. So any ordering of the outcomes list is OK for you.

Now if I tell you before tossing that one coin is "slightly" biased towards Tails and the other "slightly" towards Heads your knowledge about the process improves to the point where you would now say that one of (HT TH) is more likelier than HH or TT.

If I give you an additional information that it is the first coin that is biased towards tails you would now list the outcomes in the order of plausibility as (TH HH TT HT) with the second and third entries interchangeable. Though you don't have complete knowledge to pick any one with certainty you could certainly indicate which one is more plausible than the other. Now if my life depended on the outcome I would "certainly" go with TH.

Now probability theory is the mathematical way of ordering these outcomes by assigning numbers to them corresponding to your belief in their plausibility and manipulating them in a consistent way. It is just a way to code your degree of belief on the plausibility of an hypothesis. I don't see any difficulty in saying 80 to 20 I prefer one hypothesis over another. The numbers simply indicate my level of ignorance. If I say 50/50 it only implies that I am completely ignorant about the two hypotheses.

Anbu

Post 5

Tuesday, January 15, 2008 - 11:19am

Anbu,

Bayesian theory is the theory of updated probabilities (based on system contingencies). It's merit is limited. For instance, it has no specific merit with probabilities of 1.0 and 0.0 -- which is most-often the case in philosophy; and even sometimes the case in science. Easy examples would be that there's a probability of 1.0 that I exist, and a probability of 0.0 that I don't; that the probability of a chemical compound of helium sulfide is 0.0; and the probability that Canada is north of Mexico is 1.0, etc.

For some background, I wrote a short blurb on this point here.

Ed

Post 6

Wednesday, January 16, 2008 - 5:42am