1) Nothing is ever proven in science. A proof is an operation of formal logic and is applicable mainly to mathematical truth only, which is basically simply consequence of axioms.
2) Science shows the validity of a theory by demonstrating it is a good model for a set of observations. It is not possible to literally prove any property of the reality. It is only possible to construct models of reality based on observations. The validity of these models is judged by their ability to make predictions.
3) Observation is any phenomenon which leaves some sort of relatively stable track of its existence. There can never be anything uncertain about an observation, only about the interpretation. There is a dependency between the repeatability of obsevations and reliability of the theory. That has historically been observed to be universally significant measure of the predictive power of the theory.
4) The mission of science is to model phenomenons. A model is a compact historically valid description of observations with significant demonstrations of predictive power (concerning then future). Scientific theory is the highest graduation point of this process. A theory is immediately invalid or at most only a limited approximation if it does not match some observation. (Though obviously this effect is sometimes just some fringe outlier. Never the less the exact interpretation of the sentence is still true, but it may often mean nothing more than the inability of the theory and experimenter to predict and observe the exact nature of chaotic thermal noise.)
5) Historically prevalent theories (like Newtons mechanics) have not been wrong, the word is not correct for the context, because they have only been appriximations which have later on been made more accurate by other theories (like Einsteins theory of relativity). Science does not assume theories to be exact models of the world, only good fits to the observations of their time with significant nonzero predictive power.
6) The purpose of peer review is to improve the reliability of generally accepted scientific models and increase the efficiency of progress by cutting out clearly invalid or highly unlikely meaningful material.
7) A phenomenon is not guilty of existence until shown otherwise.
Problem of induction
I'm of the opinion that this is nothing more than playing the game by the rules you have learned. If one day the rules no longer apply or you learn there are exceptions to the rules, you play by the new rules. Shouldn't this be trivial?
And as opposed to what? Not playing by those rules? Or playing by the rules someone else invented? Playing by random rules? Or not playing at all? Feel free, but expect anything.
I would say there is nothing wrong with the goal of logical positivism at all in its root. It was just taken too seriously. Too many saw the ultimate goal to be some sort of absolute mechanism for knowledge and nothing less would constitute to anything, but perhaps they failed to see the reason why such a road could only be approximated and approached never to be reached and perhaps to some extent the arbitrary nature of this endevour. The reason perhaps being finiteness of human experience. Perhaps the same fundamental principle which limits all courses of thought. Manifested by Gödel's incompleteness theorem and Turing's halting problem. We can't deal with absolutes or infinities. There is no finite self consistent doctrine and there can never be. After all, this was essentially proven. But why did they even expect such a thing? We can still approach infinitely even if we know we'll never reach it. We just need to decide to do so even if it is arbitrary and in some sense futile.
...and I still find it somewhat comforting that we also know that...
...any finite-state machine, if left completely to itself, will fall eventually into a perfectly periodic repetitive pattern. The duration of this repeating pattern cannot exceed the number of internal states of the machine...
Dualism, qualia and philosophical zombies - the hard problem of consciousness
1) The claim is that qualia cannot be reduced to anything physical.
2) That is the claim, now demonstrate it, because I don't feel it.
What is it like to be a bat? Nagel argued that even if we knew everything there was to know from a third-person, scientific perspective about a bat's sonar system, we still wouldn't know what it is like to be a bat.
I don't see how this would point towards dualism. To me it simply means we are not the bat. The causal chain of thinking about pain is not the same as feeling the pain. And obviously "we" cannot have the same causal chain without becoming the bat.
"If my mental processes are determined wholly by the motions of atoms in my brain, I have no reason to suppose that my beliefs are true ... and hence I have no reason for supposing my brain to be composed of atoms."
Perhaps so, but nature doesn't care and neither do I. And in some ways, neither do you. Because you have no reason to suppose or to do anything at all. You just do. We keep living, and we keep playing the game, in the end because that's what we are, that's what we do and in some sense that's what we must do.
Causal interaction requires that dualism must explain how consciousness interacts with physical reality. Well they certainly don't explain it, but when someone said quantum mechanics they grabbed their last straw. I'd like to see their faces if quantum mechanics turned out to be deterministic, but though I think that'll turn out to be the case, even if that's not, we know things about the nature of quantum mechanics which seems to make it irrelevant. The statistical nature of quantum mechanics seems completely devoid of something I'd call mind and we understand and have tested that nature very well.
Somehow the strongest argument for the existence of some unknown aspect (which I still don't really believe) of the mind in is my mind the following scenario.
Let's say a machine capable of copying humans is made, and it is used to make a copy of you. (It is in fact impossible to copy exact quantum states, but let's say they are not meaningful or just simply ignore it.)
1) At the same time the original is destroyed. What do you experience? How do you feel (if anything) after this process has taken place?
2) Both the original and the copy are kept. What do you experience? Which "you" do "you" experience?
What does the experiencing? The universe? Is there a well defined you?
1.1) You die and experience nothing. A new consciousness is born (with your memories) and the universe goes about its merry business never knowing any better. But, what is death anyway?
1.2) You observe as if you'd been transported. But then is it actually "you" who's experiencing it or is it the universe somehow? One thing to consider is that the wavefunction of that which is essentially you has nonlocal properties according to quantum mechanics. Your wavefunction actually covers the whole universe and though it has peak existence here and now it is as objectively as can be, true, that you simultaneously exist everywhere and in fact everytime as well. You will "feel" what happens on the other side of the universe. Even locally your atoms are continuously tunneling from place to place and time to time and have no unique objective existence. You already are an information state of the universe. So quantum mechanics which was supposed to be the saviour of dualism has basically already beamed you up.
2.1) You keep your old body and experience nothing out of the ordinary. The copy is just a new consciousness born, but the universe can't tell the difference and perhaps neither can the copy, for the copy's point of view he was just you transported.
2.2) As you now essentially exist identically in two places at once you experience some sort of odd synthesis and duality of experience (but how?), perhaps what was you was some weird mechanism of the universe and something really odd occurs ...or not! According to quantum mechanics when atoms interact they entangle their states to some extent depending on the strength of this interaction. However, all atoms continuously interact (if only extremely weakly) with all other atoms. And they have a history of interaction as long as the lifetime of the universe already. You are already entangled with yourself, your friends, your surrounding and the rest of the universe. You have no independent existence, you never had. It's all just a matter of degrees. Perhaps whatever we could ever do could only be described as an unusually quick fast change in our state of affairs.