Mark Chang wrote a comment this evening, but it is buried back on my Nov. 31 post in relation to the current U-Phil. Given all he has written on my attempt to “break through the breakthrough”, I thought to bring it up to the top. Chang ends off his comment with the sagacious, and entirely correct claim that so many people have missed:
“What Birnbaum actually did was use the SLP to prove the SLP – as simple as that!” (Mark Chang)
It is just too bad that readers of his (2013) book will not have been told this*! Mark: Can you issue a correction? I definitely think you should! If only you’d written to me, I could have pointed this out pre-pub.
That Birnbaum’s argument assumes what it claims to prove is just what I have been arguing all along. It is called a begging-the-question fallacy: An argument that boils down to:
A/therefore A
Such an argument is logically valid, and that is why formal validity does not mean much for getting conclusions accepted. Why? Well, even though such circular arguments are usually dressed up so that the premises do not so obviously repeat the conclusion, they are similarly fallacious: the truth of the premises already assumes the truth of the conclusion. If we are allowed to argue that way, you can argue anything you like! To not-A as well. That is not what the Great “Breakthrough” was supposed to be doing.
Chang’s comment (which is the same one he posted on Xi’an’s og here) also includes his other points, but fortunately, Jean Miller has recently gone through those in depth. In neither of my (generous) construals of Birnbaum do I claim his premises are inconsistent, by the way.
*But instead his readers are led to believe my criticism is flawed because of something about sufficiency having to do with a FAMILY of distributions (his caps on “family”, p. 138). This all came up as well in Xi”an’s og.
Chang, M. (2013) Paradoxes in Scientific Inference.
Error Statistics Philosophy 
This is not news. It was decided over forty years ago that Allan Birnbaum’s much hyped result contributed no more than a petitio principii detour. Durbin, if I’m recalling, spotted this early on.
Chang wrote:
“What Birnbaum did was to report the same result (TBB) when the two likelihoods were proportional (neither SP nor CP requires one to report the result this way!) – This is what SLP wants.”
I don’t think that Chang gets this right. Of course, as Birnbaum’s result is an equivalence, what SP and CP require is to report “what SLP wants”, so Chang’s sentence is not wrong as far as it is reporting facts. However, Birnbaum’s argument at least attempts to show that this is implied already by SP and CP and not just by the SLP itself; it doesn’t use the proportional likelihoods directly to decide what has to be reported. (I know we – i.e. Mayo and myself – disagree about whether Birnbaum really achieved to show this but certainly the problem – if there is one – is not as simple as what Chang suggests; and Mayo’s argument certainly delivers more than that.)