It’s years since this thread came up, but just my two cents on this suggestion.
Correct me if I’m significantly wrong, but I think your premise is that overwhelming evidence is first assembled in a good theoretician’s brain, is logically processed into a theory, and then the correct theory is presented and found correct by virtue of this process. The crucial process was that they had to accumulate enough pieces of evidence in accord with the theory to select it, since you believe information theory prohibits any other ways of going about this business.
The thing is, if we follow the line of argument that the number of pieces of information must correspond to the number of possible hypotheses, then surely you would need an infinite number of pieces of information because the number of possible hypotheses (possible statements about the universe) is infinite too.
If you argue that it is a finite number, surely you are suggesting that a gigantic number of hypotheses have been removed in pre-selection based on how relevant they appear. If pre-selection occurs, you must also be open to the possibility that the number of possible hypotheses is far less than an arbitrary 100,000,000 and even single-digits. I think the whole accumulated mountain of science actually exists such that you do not need to generate your entire theory from an infinite number of possibilities, but judge from between a grossly-reduced number, the reducing of the vast number of other possibilities having been done by the work of your predecessors.
So if it satisfies you more, there may have been a huge number of possible theories at the start of humankind, but the combined weight of human experience and endeavour has whittled them down in certain areas to numbers which can be distinguished between by great scientists. In other areas, such as the precise nature of consciousness, we are just as baffled as before!
The thing is, if we follow the line of argument that the number of pieces of information must correspond to the number of possible hypotheses, then surely you would need an infinite number of pieces of information because the number of possible hypotheses (possible statements about the universe) is infinite too.
See Bayesian probability, Occam’s razor, Kolmogorov complexity, Solomonoff induction. You only need to raise a certain hypothesis in probability above the alternatives, not exclude all other hypotheses with certainty.
It’s years since this thread came up, but just my two cents on this suggestion.
Correct me if I’m significantly wrong, but I think your premise is that overwhelming evidence is first assembled in a good theoretician’s brain, is logically processed into a theory, and then the correct theory is presented and found correct by virtue of this process. The crucial process was that they had to accumulate enough pieces of evidence in accord with the theory to select it, since you believe information theory prohibits any other ways of going about this business.
The thing is, if we follow the line of argument that the number of pieces of information must correspond to the number of possible hypotheses, then surely you would need an infinite number of pieces of information because the number of possible hypotheses (possible statements about the universe) is infinite too.
If you argue that it is a finite number, surely you are suggesting that a gigantic number of hypotheses have been removed in pre-selection based on how relevant they appear. If pre-selection occurs, you must also be open to the possibility that the number of possible hypotheses is far less than an arbitrary 100,000,000 and even single-digits. I think the whole accumulated mountain of science actually exists such that you do not need to generate your entire theory from an infinite number of possibilities, but judge from between a grossly-reduced number, the reducing of the vast number of other possibilities having been done by the work of your predecessors.
So if it satisfies you more, there may have been a huge number of possible theories at the start of humankind, but the combined weight of human experience and endeavour has whittled them down in certain areas to numbers which can be distinguished between by great scientists. In other areas, such as the precise nature of consciousness, we are just as baffled as before!
See Bayesian probability, Occam’s razor, Kolmogorov complexity, Solomonoff induction. You only need to raise a certain hypothesis in probability above the alternatives, not exclude all other hypotheses with certainty.