They agreed that it should not keep itself pure: a philosophy that confined itself to logical truths, seeing itself as a kind of mathematics of language, had sealed itself inside a futile, circular system of self-reference.
There Russell argued that the whole of mathematics could be derived from a few simple axioms that made no use of specifically mathematical notions, such as number and square root, but were rather confined to purely logical notions, such as proposition and class.
The only exception would be when the philosophical aspect of the discipline in question is confined to epistemological and logical matters and remains quite distinct from the substantive inquiries in which that discipline engages.
Finally, a term can be introduced by a stipulative definition into a ground language whose logical resources are confined, say, to classical conjunction and disjunction.
Will it be able to step outside the confines of logical impasses and find answers to them?
In many modern logical systems, definitions are said to be confined to the metalanguage only, and not to appear in the object language at all.
The background of logical empiricism described so far has been confined to the academic world, but events outside that domain shaped the movement as well.
Given these results and the likely oligogenic nature of maize grain carotenoid traits, it was logical to confine pathway-level prediction efforts to genes within the biochemical pathway.
The important question being raised by this objection is whether the logical or probabilistic support relations are themselves justifiers; or are the justifiers confined to the entities over which the support relations are to hold?
Therefore, logical models are basically asynchronous, meaning that the state transitions are not confined to specific times and may occur at any time when inputs/conditions are ready/satisfied.
