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So you have belief in Bayes, logic and evidence (empiricism). I give you that at least that you mark it as belief. However it is not justified - by its own admission. Bayes claims you can never possess the Truth - you just converge to some pragmatical result, which by itself also does not provide for the truth. Quine correctly called it as undetermination of scientific theory. It is impossible to converge to anything under strict empiricism and Bayesianism, each empirical evidence opens untold myriads of new "truths".
Sure, which is what I described as "willful ignorance before". Which is absolutely hilarious - at the same time people like this can utter some very stern and ultimate statements such as "I have belief in Bayes, logic and empiricism" but at the same time refuse any discussion. It is hilariously exactly in line of Quines two dogmas of empricism that are presuppositional and cannot be verified neither by Bayesianism nor by Empiricism. Moreover, this ideology does not even provide for any possibility of a thing such as the "Truth" that they are so proud of declaring. It is insane.
Just to flesh it out, Bayesian theorem requires presuppositions to generate likelihood. From the top of my head, radical skeptics such as Hume or Descartes or even physicists created concepts like Carthesian Demon or Bolzman brains, which completely skew the likelihood function. No amount of empirical data can shift the posterior - you are completely relying on your arbitrary presuppositions. In that sense how are you more justified? That is why Hume and Quinne are so devastating, they completely ended secular/emprical metaphysis and why philosophers moved over to stuff like phenomenology. It is interesting how the same zombie ideas about explanatory power of empiricism pop up again and again without realization of how bankrupt the whole thing is when it comes to paradigmatical thinking and grounding ones worldview in philosophical basics: metaphysics, epistemology and ethics.
I used it as an ANALOGY of somebody taking things for granted from another paradigm for which he has not the same foundation. But I can use another analogy - imagine Newtonian who who denies Einstein Theory of relativity but he borrows that vocabulary to describe black holes. And who thinks it is absolutely normal, just citing things that "everybody knows" etc. That was my analogy.
I find Godel's proof interesting because it actually tackles the topic of existence of abstract entities, so that discussion is not turned into if Newton or Einstein is "true" empirically.
I have observational and intuitive evidence for this that I can't share with you in words. My belief is justified, I just can't give you an essay on why. I could give you parable and metaphors, or ask you to think about certain things, but I can't put it entirely down in words, if that makes sense. How does your framework deal with this? It seems like it demands a verbal justification and rejects other justifications.
1 - .99999999.... does not bother me. I also belief, justifiably, we can't do better for empirical beliefs. But again, I can't give you a verbal essay as to why. I could guide you there, but I can't take you all the way there. It's observational, intuitive, and logical, not verbal. My beliefs ultimately rest on these things more or less, whereas it seems yours rest on the verbal, if that makes sense.
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