Generalizing a result of Todorčević, we prove the existence of directed sets D, E such that D ≱ [MATHEMATICAL SCRIPT CAPITAL P]κλ and E ≱ [MATHEMATICAL SCRIPT CAPITAL P]κλ but D × E ≥ [MATHEMATICAL SCRIPT CAPITAL P]κλ in the Tukey ordering. As an application, we show that the tree property for directed sets introduced by Hinnion is not preserved under products.
Fundamental limitations constraining the application of emergence to formulations of conscious mental states are explored within the paradigm of classical science. This paradigm includes standard interpretations of functionalism, computationalism and complex systems theories of mind -- theories which are ultimately justified by an appeal to emergentist principles. We define a distinction between extrinsic and intrinsic accounts of emergent conscious states, and examine the prospects for both. Extrinsic accounts are subject to relativities with respect to external observers that must be resolved (...) if the ontological character of conscious states is to be preserved. While this can, in some cases, be accomplished by imposing an appropriate invariance, no such strategy exists in the case of relativity with respect to boundary without absurd consequences. If, on the other hand, conscious states require intrinsic definition, a specification of the system boundary must be explicitly available if the conscious ontology is to be uniquely specified. Even minimal information requirements make this incompatible with locality constraints. We investigate what progress can be made in overcoming these obstacles by relaxing various assumptions. (shrink)
Cultures are constituted by binary oppositions: the absolute and the relative; the perfect and the imperfect; the stable and the unstable. Many of the world’s cultures have looked to revealed religion to discover the absolute: that which transcends the human, the intellect, and space and time. By positing a God who is omniscient and omnipotent, they conceive of an eternal and absolute that continues to exist in an immutable state.In such cultures new perspectives for reinterpreting the past are continually propounded. (...) This allows history to be rewritten and re-rewritten. History simply becomes a method for becoming conscious of the past.By contrast, many East Asian cultures have not developed such a concept of revealed religion. For them, history itself constitutes an absolute, something on which one can rely. History in East Asia is endowed with a normative function, a source of authority that does not permit easy rewriting. (shrink)
All surviving jawed vertebrate representatives achieve diversity in immunoglobulin‐based B and T cell receptors for antigen recognition through recombinatorial rearrangement of V(D)J segments. However, the extant jawless vertebrates, lampreys and hagfish, instead generate three types of variable lymphocyte receptors (VLRs) through a template‐mediated combinatorial assembly of different leucine‐rich repeat (LRR) sequences. The clonally diverse VLRB receptors are expressed by B‐like lymphocytes, while the VLRA and VLRC receptors are expressed by lymphocyte lineages that resemble αβ and γδ T lymphocytes, respectively. These (...) findings suggest that three basic types of lymphocytes, one B‐like and two T‐like, are an essential feature of vertebrate adaptive immunity. Around 500 million years ago, a common ancestor of jawed and jawless vertebrates evolved a genetic program for the development of prototypic lymphoid cells as a foundation for an adaptive immune system. This acquisition preceded the convergent evolution of alternative types of clonally diverse receptors for antigens in all vertebrates, as reviewed in this article. (shrink)