gwern comments on Is Sunk Cost Fallacy a Fallacy? - Less Wrong
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That's like asking "If homeopathy worked and all the doctors were wrong, would they admit it?" You can't just flip a bit in the world setting Homeopathy_Works to TRUE and keep everything else the same. If homeopathy worked and yet doctors still didn't accept it, that would imply that doctors are very different than they are now, and that difference would manifest itself in lots of other ways than just doctors' opinion on homeopathy.
If funding the Apollo Project was a complete waste of money compared to the normal grant process, the world would be a different place, because that would require levels of incompetency on NASA's part so great that it would get noticed.
Or for another example: if psi was real, would James Randi believe it?
No; it's like asking "If homeopathy didn't work and all the homeopaths were wrong, would they admit it?" You can find plenty of critics of Big Science and/or government spending on prestige projects, just like you can find plenty of critics of homeopathy.
If homeopathy was a complete waste of money compared to normal medicine implying 'great' levels of incompetency on homeopaths, how would the world look different than it does?
Those people generally claim that Apollo was a waste of money period, not that Apollo was a waste of money compared to going to the moon via the normal grant process.