Arguing from negative proof

[4gold]

Several arguments are given in this forum from the position of negative proof:

[center]"God does not exist, because there is no proof of his existence."

"Evolution must be true, because there is no other theory that explains the evidence."

"Dark matter must exist, because there is no other way to explain the universe."[/center]

And then there are logical inferences we all make from the absence of evidence, or else we couldn't have arguments, such as:

[center]"Mathematics is consistent, even though its consistency cannot be proven."

"The scientific method is reliable, even though its reliability cannot be proven."

"The laws of logic are rational, even though its rationality cannot be proven."

"The rules of morality are the same for you and me, even though the rules cannot be agreed upon."[/center]

My questions are:

How convinced should we be by arguments made by negative evidence?

Is there any way, other than Bayesian inference, to interpret the validity of arguments made by negative evidence?

[4gold]

Obviously all debates can only work if, by standard, you and your opponent can agree on at least three things. These agreements we call axioms, and unless we agree on three axioms, the debate isn't likely going anywhere.

Doesn't this present us with a dichotomy?

Unless we agree on presumptions based on negative evidence, we cannot debate each other. But if we present arguments with negative evidence, I believe you stated that it creates a false dichotomy, unless a true dichotomy exists.

Are the presumptions upon which we all argue creating a false dichotomy? Doesn't this violate the law of noncontradictions?

[ShadowRishi]

Obviously all debates can only work if, by standard, you and your opponent can agree on at least three things. These agreements we call axioms, and unless we agree on three axioms, the debate isn't likely going anywhere.

Doesn't this present us with a dichotomy?

Unless we agree on presumptions based on negative evidence, we cannot debate each other. But if we present arguments with negative evidence, I believe you stated that it creates a false dichotomy, unless a true dichotomy exists.

Are the presumptions upon which we all argue creating a false dichotomy? Doesn't this violate the law of noncontradictions?

I'm afraid you're going to have to re-phrase that. Examples would help, methinks.

[4gold]

I'm afraid you're going to have to re-phrase that. Examples would help, methinks.

For example, in order for ShadowRishi and 4gold to even discuss this matter, we have to both agree that the laws of logic are correct. Otherwise, there is no sense in arguing. However, there is no evidence that the laws of logic are correct. Thus, we have to start all of our debates from a premise of negative evidence.

But you said earlier that an argument from negative evidence produces a false dichotomy. So when you begin arguing from the laws of logic, aren't you contradicting yourself?

[Furrowed Brow]

there is no evidence that the laws of logic are correct. Thus, we have to start all of our debates from a premise of negative evidence.

Which logic are we talking about? There is more than one e.g. propositional, predicate, three valued logics of various flavours and fuzzy logic.

Propositional (Boolean) logic reduces to truth tables. The tables are the proof of consistency. The evidence of the correctness of this calculus is the computer you are sitting at reading this post. Predicate logic lacks a decsion procedure like truth tables, but since Goedel and Church we know the limits of standard predicate logic.

However this is still an interesting problem. There is an expectation that humans are not Turing machines, and they seem quite able to think predicate logic; but as yet there is no recognised means for mechanising predicate logic. Until we know how humans think this question remains undecided. However, if you search the internet you will find oddballs who think they might have solved the problem.

[4gold]

Which logic are we talking about? There is more than one e.g. propositional, predicate, three valued logics of various flavours and fuzzy logic.

I think you would be better able to answer that question than I would. I had never heard of those types of logic until you just brought them up. I just remember my philosophy professors talking about how we cannot have conversations unless we begin with the presumption that our laws of logic are correct, even though there is no way to prove this.

[Cathar1950]

Which logic are we talking about? There is more than one e.g. propositional, predicate, three valued logics of various flavours and fuzzy logic.

I think you would be better able to answer that question than I would. I had never heard of those types of logic until you just brought them up. I just remember my philosophy professors talking about how we cannot have conversations unless we begin with the presumption that our laws of logic are correct, even though there is no way to prove this.

I like to read C. Hartshorne as he deals with these kinds of logic systems.
A Newtonian view of the univese has its limits even if it works.
Likew Whitehead they have a more organic view of the universe and there concept of God is relational and social.

[Furrowed Brow]

Which logic are we talking about? There is more than one e.g. propositional, predicate, three valued logics of various flavours and fuzzy logic.

I think you would be better able to answer that question than I would. I had never heard of those types of logic until you just brought them up. I just remember my philosophy professors talking about how we cannot have conversations unless we begin with the presumption that our laws of logic are correct, even though there is no way to prove this.

Your Professor might have had a couple or three ideas in mind. He could have been thinking of Goedel. For any system as rich as standard arithmetic (Or Russell/Whitehead's system presented in the Principia Mathematica) there will be some true theorem that cannot be proved within that system. Or he might have been talking about the lack of a decision procedure for Predicate logic. A decision procedure being a means to test the validity or invalidity of all arguments within that system. Alternatively he might have been thinking of propositional theorems like the law of excluded middle. A theorem for which there has been some debate as to its applicability to fundamental reality, particularly when faced with the wave particle theory of quantum theory. Other rules are also debatable. For example, a school of philosophy dubbed intuitionism rejects reductio ad absurdum.

[Pi]

How convinced should we be by arguments made by negative evidence?

Without direct evidence the best that one can accomplish is 'a working hypothesis'. "Absence of proof is not proof of absence", however, absence of proof does not permit any logical conclusion.

[4gold]

Your Professor might have had a couple or three ideas in mind. He could have been thinking of Goedel. For any system as rich as standard arithmetic (Or Russell/Whitehead's system presented in the Principia Mathematica) there will be some true theorem that cannot be proved within that system. Or he might have been talking about the lack of a decision procedure for Predicate logic. A decision procedure being a means to test the validity or invalidity of all arguments within that system. Alternatively he might have been thinking of propositional theorems like the law of excluded middle. A theorem for which there has been some debate as to its applicability to fundamental reality, particularly when faced with the wave particle theory of quantum theory. Other rules are also debatable. For example, a school of philosophy dubbed intuitionism rejects reductio ad absurdum.

Essentially, any argument based on logic has to presume that logic gets us closer to the truth, even though there is no evidence that logic gets us closer to the truth -- am I reading you right?

[4gold]

Without direct evidence the best that one can accomplish is 'a working hypothesis'. "Absence of proof is not proof of absence", however, absence of proof does not permit any logical conclusion.

But even "logical conclusions" are not based on evidence, right? I mean, from what I understand, there is no evidence that the laws of logic get us closer to the truth. We just presume they do.