Some Logical Aspects of the Fiducial Argument

摘要: SUMMARY The papers by Dempster and Williams in this issue are discussed. DR DEMPSTER'S paper is valuable that it sets up a clear model terms of which some aspects the fiducial argument can be However, question does not accurately represent situation contemplated Fisher connection. Although expressed himself several times as averse to certain formalist axiomatic versions process statistical inference, was because he had any fundamental objection formalization, but rather his recognition, (a) limitations formal processes (b) fact formalization inductive would exceedingly complex-much more complex than formalizations mathematical arguments. In system so far considered logicians (see, for example, Tarski, 1930) set consequences 6(S) S propositions an increasing function X, sense if S' includes S, then V(S') V(S). has many pointed out such property true inference. Another point miathematical logic one normally concerned with "derivability" proposition, "truth". Tarski (1933) showed notion "truth" could introduced into system, provided part hierarchy systems, each its notion, applying systems lower hierarchy. Any account probabilistic inference will require further "knowledge". proposition "p known" clearly have imply true", just derivable" implies true" (given axioms true). Again, sequence need contemplated, corresponding class p known changes time. Anyone familiar work now difficult problems semantics feel confident time we shall attain greater clarity on these matters, awareness difficulties already met connection truth meaning make anyone cautious expecting much progress "knowledge" near future. We therefore left less completely formalized situations supplemented judgements concerning their applicability given cases. Such model, applicable argument, which, indicated