As for the presentation of the argument in the new paper, Ellis says he has some misgivings that it will whip up unfounded fears about the safety of the LHC once again.
We will not discuss the details here, but a detailed presentation of the argument can be found in the entry on Frege's theorem and foundations of arithmetic as well as (Rosen 1993), which gives a clear and readable presentation of the main argument of (Wright 1983), which in turn is partially responsible for a revival of Fregean ideas along these lines.
In Cummins' forceful presentation of the argument, this independent calibration requirement is used to justify the conclusion that we should "dismiss philosophical intuition as epistemologically valueless" (1998, p. 125).
Given their acceptance of the principle of bivalence and their presentation of the argument as invoking a material conditional, they blocked the sorites by claiming some one conditional to be false (since not true) and that there comes a point in any sorites series where the relevant predicate ceases to apply and its negation does.
Second, let's abandon the idea, which reappears in many presentations of the Argument from the Unlearning Problem; that learners' hypotheses must be explicitly falsified in the data in order to be rejected.
Separability is, however, an explicit premise in all of Einstein's later presentations of the argument for the incompleteness of quantum mechanics, both in correspondence and in print (see Howard 1985 for a detailed list of references).
Still, the DBA depends upon the theory of preference and utility, and as Kaplan notes (Kaplan 1996), this does not emerge straightforwardly from standard presentations of the argument of the sort considered in section one, nor in the depragmatized versions, as observed in the previous section.
One may question whether the appropriate or intended sense of 'rational' is invoked in these cases in which it seems right to say that rational beliefs can come apart from betting quotients, but such objections just highlight the lack of clarity in most presentations of the argument over what sort of rationality is supposed to be at stake.
Some Stoic presentations of the argument recast it in a form which replaced all the conditionals, 'If A then B', with 'Not(A and not-B)' to stress that the conditional should not be thought of as being a strong one, but rather the weak Philonian conditional (the modern material conditional) according to which 'If A then B' was equivalent to 'Not(A and not-B)'.
These, at least, are mature presentations of the argument.
