In the world we live in, we almost always reason with incomplete information. Each day we we encounter statements whose truth or falsity cannot be decided on the basis of what we know. In the social and political arena we recognize that different observers have access to different information. We deal every day with the fact that the truth or falsity of statements about the future may be affected by what we choose to do.
This fact has very profound implications for many issues. It means that to judge the rationality of our decisions, we do not have to pretend that there is some supernatural observer who knows everything: it is enough to demamnd that the different observers report what they see honestly.
When this rule is followed we discover that when we and another person each have enough information to decide whether something is true or false , we always make the same decision.
Thus philosophers who attempted to ground ethics, mathematics, and science in the judgements of an all-knowing being were mistaken. We can live rationally without having to believe in a being who sees everything. We need only believe in the ethical principle that observers should communicate honestly what they see. If we stick to this, then the fact that there will always be questions that we cannot answer need not prevent us from comming to agreement about how to understand those aspects of our world which we share in common.
This means that intuitional, cosmological, or topos logic is the right logic to understanding the world we live in. It is the correct type of logic to use for economics, sociology and political science. It's a shame that politicians, economists, and socialogists haven't taken up this type of logic. Cosmology and social theory point us in the same direction. They are the two sciences that cannot be formulated sensibly unless built into their foundations the simple fact that all possible observers are inside the systems they study. Solitary
What the hell is "intuitional, cosmological, or topos logic"?
In answer to your question, Bayesian probability is a fine way to work with incomplete information. In the limiting case (ie, representing certainties with P=1 and impossibilities with P=0), the probability calculus gives exactly the same answers as ordinary logic. But with probability (where probability expresses your degree of certainty in a particular proposition), you are able to express incomplete information in the form of probabilities between 0 and 1 and to express ranges of possibilities sensibly, and the probability calculus allows you to work with these values in a meaningful way.
I tried before to work out a logical system which takes our incomplete knowledge into account. It got a little convoluted. The system I came up with, was pretty much based on troubleshooting systems. Being a tech, it was the logical system I was most familiar with. Part of getting input into the system, was recognizing our subjectivity. Another part was looking for opposing viewpoints.
While a workable system, it still relied on incomplete information. Meaning garbage in garbage out.
The Bayesian system is a good system I suppose. I am not that familiar with it. But, it seems to only give us a probability if something is true or not. I see it as a subset to my system, in that it can supply better inputs into it. But, just like my system, it requires good input to make it work correctly.
Bottom line, we use what we got, and hope to come up with a good answer. But, we can never assume our answer is complete. There will always be new information to apply to any question without an axiomatic answer. Even then, we have to question the axioms sometimes. So, the best we can ever realistically hope for, is an heuristic truth.
Mathematics starts with the simplest, most "incomplete" sets of axioms possible and then creates very large, very complete bodies of theory.
Where are you copy-pasting this from I wonder...
Quote from: "GurrenLagann"Where are you copy-pasting this from I wonder...
:butthead: :shock: :lol: Solitary
Information and logic isn't always necessary. Sometimes a man's just got to do what a man's got to do.
Quote from: "GurrenLagann"Where are you copy-pasting this from I wonder...
It's from Three Roads To Quantum Gravity by Lee Smolin.
Check it out on Google Books (//http://books.google.co.uk/books?id=1LFxtamIWskC&pg=PT32&lpg=PT32#v=onepage&q&f=false)
Inductive reasoning, Bayesian inference, empiricism, and fuzzy logic. And sometimes guesswork.
Quote from: "SGOS"Information and logic isn't always necessary. Sometimes a man's just got to do what a man's got to do.
That's why sometimes I wish I wore a kilt. :lol: Solitary
Quote from: "Solitary"Quote from: "SGOS"Information and logic isn't always necessary. Sometimes a man's just got to do what a man's got to do.
That's why sometimes I wish I wore a kilt. :lol: Solitary
At least you're copying and pasting from books now instead of articles you've seen on the internet.
You've really got to understand what it is that you are copying and pasting though, or you end up just posting garbage out of context like your opening post here.
Quote from: "Jason78"Quote from: "Solitary"Quote from: "SGOS"Information and logic isn't always necessary. Sometimes a man's just got to do what a man's got to do.
That's why sometimes I wish I wore a kilt. :lol: Solitary
At least you're copying and pasting from books now instead of articles you've seen on the internet.
You've really got to understand what it is that you are copying and pasting though, or you end up just posting garbage out of context like your opening post here.
I'm so glad you learned so much about me instead of the subject lul. :roll: Solitary
Quote from: "Atheon"Inductive reasoning, Bayesian inference, empiricism, and fuzzy logic. And sometimes guesswork.
And, unlike formal logic of any sort, the human brain is best at the latter two. Our brains aren't binary, they're analog. We see a billion gradations between "best" and "worst", so we can see where the most "highest score"s cross and place our decision marker there - even if none of the choices is close to 50% of "best".
My car thinks like that and it seems like it has a brain of its own. :shock: Weird. Solitary