Here is a poll of philopher beliefs, but it does not directly ask about Kuhn's paradigm shift theory.
Speaking of crackpot ideas, Scott Aaronson's new book defends time travel:
Yes, the Grandfather Paradox has often been put forward as a “proof” that time travel into the past is logically impossible. But there are several loopholes in that “proof.” One of them is the possibility of resolving the paradox probabilistically or quantumly (as Deutsch proposed). Another loophole is that maybe Nature simply always finds a consistent deterministic evolution, no matter how unlikely it seemed a priori. (E.g., if you went back in time and tried to kill your grandfather, you’d always discover that the gun jammed, or you forgot to load it, or he recovered from the gunshot wound and went on to sire your parent, etc. etc.) So really the Grandfather Paradox should be seen as a central, obvious difficulty that any account of closed timelike curves needs to overcome.This is pretty wacky. I say that the Grandfather Paradox disproves time travel.
Your resolution of the paradox, in your first comment, is actually a good way to describe or visualize what happens in Deutsch’s resolution. (Indeed, since Deutsch avidly believes in the Many-Worlds Interpretation, he would regard it not just as a convenient way to visualize, but as a literal description of what happens in his proposal.)
However, one can also invent more complicated time-travel scenarios: for example, what happens if you flip a fair coin, and go back in time and kill your grandfather if and only if the coin lands heads? The beauty of Deutsch’s proposal is that it gives you an automatic way to compute a consistent story for any possible such scenario.
(Spoiler alert: in the above example, the solution is that you’re born with probability 2/3 and not born with probability 1/3. Or if you prefer, you’re born in 2 of 3 parallel universes, and not born in 1 of them.)
Here is a completely separate proof that we will never see time machines. If some future advanced civilization ever got time machines, then surely someone would decide that they are a really bad idea, and go back in time to kill the first inventor before he can create a time machine.
If you believe in Many-Worlds, then I suppose a time machine could take you to a parallel universe. But Many-Worlds is another crackpot idea with no scientific merit.
Frank Wilczek is promoting time crystals. These are not as crazy as time machines, as you cannot use them to violate logic and physics laws.