I take the following as my definition of Truth:
The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real. --by Charles Sanders Peirce.
I considere the following to be a given.
There is no way to know the actual Truth of any relevant statement[1]. Everything we think or believe may be just a dream or simulation.
Truth is real and objective. There exists statements that describe things how they really are.
There are patterns in the world and they have predictive power. While the fact that the sun rose many thousand times during my life time and never missed a day might not predict that it will rise tomorrow by pure logic [2] I still assume it does because the whole thing is already challanging enough.
If Truth is the limit of investigation and we don’t know the Truth, i.e. we don’t reached that limit of an investigation, how can we achieve an estimate of the difference in distance between one of two believe systems and the Truth.
The development of science seems directed toward a limit. This might itself be considered an indication that the belief system of science is closer to the truth than say that of religion.
The belief system of science changes with the occurance of new facts, not invalidating previous beliefs but limiting their validity or making them more precise. E.g. Newtons laws of motion are a good approximation for the predictions or General Relativity for slow speed.
The belief system of science acknowledges clashes and conflicts and tries to improve the belief system in that area.
Other belief systems are Bullshit as described by Frankfurt in that they don’t seem to care about their distance to the Truth.
Since patterns have predictive power and belief systems with a low distance to the Truth describe these patterns well such believe systems have predictive power.
Bullshit on the other hand has no predictive power since by definition it disregards any relationship to the Truth.
The predictive power therefore seems to be inversely correlated to the distance of a believe system from the Truth.*
How may one evaluate the predictive power of a believe system of which all descriptions of predictive power are by definition unreliable statements?
In theory and for a small area of expertise one might perform experiments to test their predictive power.
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One may drop stones and measure the time they need to reach the ground depending on the height from which they are dropped.
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One may pray to a God and observe if this results in a change of affairs.
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One may take Homeopathic prescriptions and observe the change in healt status.
Experiments my give indication of predictive power but they never prove the presence of absence of predictive power. A person taking a certain medication and predict to feel better may or may not feel better when the medication is helpfull or without effect. Statistical independent repetion of experiments to avoid systematical errors may be used to improve the estimation of predictive power of a believe system.
This is only possible for a very limited part of any realistic believe system. Physicist only perform a miniscule part of the experimentsthe underpin the belief system of modern physics themselves. Modern experiments are so complex that hundreds of scientists work together to perform a single experiments. For these experiments no person exists that observed all parts of the experiment. Still we in general assume that we can trust these experiments. No assertion of predictive power