An operation on inferential rules, called H-operation, is used to minimize the axiom basis for classical logic.

We attempt to define the classical propositional logic by use of appropriate derivability conditions called Cn-definitions. The conditions characterize basic properties of propositional connectives.

The sentential calculiR, under discussion, are axiomatizable and implication is among their primitive terms. The modus ponens and the rule of substitution are their primitive rules. ByS r is denoted the set of sentences obtained from the formulae of the calculusR by substituting sentences of a given language for all variables. The variablesx, y, z ... represent the elements of the setS r , the variablesX, Y, Z ... represent the subsets ofS R . The formulacxy designates an implication withx (...) as its antecedent andy as its consequent,cxy is always an element ofS R δ(X) means, thatX is closed with respect to the modus ponens rule.A R designates the class of allS R -substitutions of the axioms of the sentential calculusR. (shrink)

We argue that Yarkoni's proposed solutions to the generalizability crisis are half-measures because he does not recognize that the crisis arises from investigators' underappreciation of the roles of theory in experimental research. Rather than embracing qualitative analysis, the research community should make an effort to develop better theories and work toward consistently incorporating theoretical results into experimental practice.

Most discussions of the reproducibility crisis focus on its epistemic aspect: the fact that the scientific community fails to follow some norms of scientific investigation, which leads to high rates of irreproducibility via a high rate of false positive findings. The purpose of this paper is to argue that there is a heretofore underappreciated and understudied dimension to the reproducibility crisis in experimental psychology and neuroscience that may prove to be at least as important as the epistemic dimension. This is (...) the communication dimension. The link between communication and reproducibility is immediate: independent investigators would not be able to recreate an experiment whose design or implementation were inadequately described. I exploit evidence of a replicability and reproducibility crisis in computational science, as well as research into quality of reporting to support the claim that a widespread failure to adhere to reporting standards, especially the norm of descriptive completeness, is an important contributing factor in the current reproducibility crisis in experimental psychology and neuroscience. (shrink)