The philosophical problem of the relation of symbol to truth is far from solved, but there have been significant advances toward its solution. It is the common Christian understanding that God is Truth , and that all truths must ultimately find union in him. This is to say that all genuine truths must be compatible. The true conclusions of genuine science must be compatible with the true conclusions of genuine theology. Or, to bring this general statement to a more particular (...) level, the true conclusions of Biblical scholarship must be compatible with the true conclusions of the natural sciences. When this compatibility is lacking, and it so often is, we must assume that the conclusions of one field of truth-seeking or the other do not partake of the Truth which is God. And there is no guarantee that theology as a field of truth-seeking cannot err. Another characteristic of genuine truth is that it is not dependent upon any particular environment or milieu —either social, cultural, philosophical, or even theological. Unless we are to make the common but dangerous division of sacred and secular, of holy and profane, claim that these areas of human experience have nothing to do the one with the other, compartmentalise our thought, and ask, ‘What has Athens to do with Jerusalem?’, it must be concluded that there is no one specifically Christian milieu . Genuine truths must be true at all times, in all places, and for all men. But since we are not gods, we must hold these truths in what St Paul called earthen vessels , vessels shaped and moulded by our particular milieu. (shrink)
The strong weak truth table (sw) reducibility was suggested by Downey, Hirschfeldt, and LaForte as a measure of relative randomness, alternative to the Solovay reducibility. It also occurs naturally in proofs in classical computability theory as well as in the recent work of Soare, Nabutovsky, and Weinberger on applications of computability to differential geometry. We study the sw-degrees of c.e. reals and construct a c.e. real which has no random c.e. real (i.e., Ω number) sw-above it.
We show that for any computably enumerable set A and any equation image set L, if L is low and equation image, then there is a c.e. splitting equation image such that equation image. In Particular, if L is low and n-c.e., then equation image is n-c.e. and hence there is no low maximal n-c.e. degree.
Khutoretskii's Theorem states that the Rogers semilattice of any family of c.e. sets has either at most one or infinitely many elements. A lemma in the inductive step of the proof shows that no Rogers semilattice can be partitioned into a principal ideal and a principal filter. We show that such a partitioning is possible for some family of d.c.e. sets. In fact, we construct a family of c.e. sets which, when viewed as a family of d.c.e. sets, has (up (...) to equivalence) exactly two computable Friedberg numberings ¼ and ν, and ¼ reduces to any computable numbering not equivalent to ν. The question of whether the full statement of Khutoretskii's Theorem fails for families of d.c.e. sets remains open. (shrink)
E. C. Tolman's 'purposive behaviorism' is commonly interpreted as an attempt to operationalize a cognitivist theory of learning by the use of the 'Intervening Variable' (IV). Tolman would thus be a counterinstance to an otherwise reliable correlation of cognitivism with realism, and S-R behaviorism with operationalism. A study of Tolman's epistemological background, with a careful reading of his methodological writings, shows the common interpretation to be false. Tolman was a cognitivist and a realist. His 'IV' has been systematically misinterpreted by (...) both behaviorists and antibehaviorists. For this reason, Tolman's alliance with modern cognitivism and his influence on its development have been underestimated. (shrink)
Ursula Klein and E. C. Spary : Materials and expertise in early modern Europe: Between market and laboratory. Chicago: University of Chicago Press, 2010, 408pp, $50 HB Content Type Journal Article DOI 10.1007/s11016-010-9462-8 Authors Jonathan Simon, LEPS-LIRDHIST, Université Lyon 1, Université de Lyon, 69622 Villeurbanne cedex, France Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
We show that in the c.e. weak truth table degrees if b < c then there is an a which contains no hypersimple set and b < a < c. We also show that for every w < c in the c.e. wtt degrees such that w is hypersimple, there is a hypersimple a such that w < a < c. On the other hand, we know that there are intervals which contain no hypersimple set.