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potato comments on (Subjective Bayesianism vs. Frequentism) VS. Formalism - Less Wrong
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Ok, I am a Bayesian, i.e., I use bayesianism over frequentism, and find frequentest methods rather silly. And I am at least what I would call a finite frequentist, i.e., I think komolgorov models finite frequency.
I am not here to say that Bayesianism is on equal ground with Frequentism, at all. If Bayes's interpreted sentences can be empirically verified, and freqeuntist interpretations cannot be empirically verified, than this is to bayesianism's favor. It means it is the more useful theory. But it is not grounds to use "is" where we should use "models" instead. It is not because bayesains need to be put on equal footing with frequentists that I propose this terminology in place of the copula; it is because rationalists should be clear, specially in philosophy. So just to be clear, we should use "model" instead of "is" because it is what is really going on; the concepts of Hofstadterish formalism and model theory, are the best way to understand how probability theory ends up telling us how to distribute beliefs. The relation between subjective degree of belief, and probability theory, is clearly not identity, or the copula.
Subjective degrees of belief are a part of your cognition. Probability theory is a repeatable process consisting in shuffling squiggles on paper, or some other medium. These are not identical. Q.e.d.
We might call this the "paper projection fallacy". Where you project some pattern in squiggles on a piece of paper into your mind. Analogous to the "mind projection fallacy".