Bunge’s Mathematical Structuralism Is Not a Fiction

In this paper, I explore Bunge’s fictionism in philosophy of mathematics. After an overview of Bunge’s views, in particular his mathematical structuralism, I argue that the comparison between mathematical objects and fictions ultimately fails. I then sketch a different ontology for mathematics, based on Thomasson’s metaphysical work. I conclude that mathematics deserves its own ontology, and that, in the end, much work remains to be done to clarify the various forms of dependence that are involved in mathematical knowledge, in particular its dependence on mental/brain states and material objects

AN ELECTRON MICROSCOPE STUDY OF CULTURED RAT SPINAL CORD

Explants prepared from 17- to 18-day fetal rat spinal cord were allowed to mature in culture; such preparations have been shown to differentiate and myelinate in vitro (61) and to be capable of complex bioelectric activity (14–16). At 23, 35, or 76 days, the cultures were fixed (without removal from the coverslip) in buffered OsO4, embedded in Epon, sectioned, and stained for light and electron microscopy. These mature explants generally are composed of several strata of neurons with an overlying zone of neuropil. The remarkable cytological similarity between in vivo and in vitro nervous tissues is established by the following observations. Cells and processes in the central culture mass are generally closely packed together with little intervening space. Neurons exhibit well developed Nissl bodies, elaborate Golgi regions, and subsurface cisternae. Axosomatic and axodendritic synapses, including synaptic junctions between axons and dendritic spines, are present. Typical synaptic vesicles and increased membrane densities are seen at the terminals. Variations in synaptic fine structure (Type 1 and Type 2 synapses of Gray) are visible. Some characteristics of the cultured spinal cord resemble infrequently observed specializations of in vivo central nervous tissue. Neuronal somas may display minute synapse-bearing projections. Occasionally, synaptic vesicles are grouped in a crystal-like array. A variety of glial cells, many apparently at intermediate stages of differentiation, are found throughout the otherwise mature explant. There is ultrastructural evidence of extensive glycogen deposits in some glial processes and scattered glycogen particles in neuronal terminals. This is the first description of the ultrastructure of cultured spinal cord. Where possible, correlation is made between the ultrastructural data and the known physiological properties of these cultures

Parmenides reloaded

I argue for a four dimensional, non-dynamical view of space-time, where becoming is not an intrinsic property of reality. This view has many features in common with the Parmenidean conception of the universe. I discuss some recent objections to this position and I offer a comparison of the Parmenidean space-time with an interpretation of Heraclitus' thought that presents no major antagonism.Comment: 11 pages, accepted for publication in Foundations of Scienc

Inconsistent boundaries

Research on this paper was supported by a grant from the Marsden Fund, Royal Society of New Zealand.Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected (Varzi in Noûs 31:26–58, 1997). In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of empty parts, in delivering a balanced and bounded metaphysics of naive space.PostprintPeer reviewe

Parameterized optimized effective potential for atoms

The optimized effective potential equations for atoms have been solved by parameterizing the potential. The expansion is tailored to fulfill the known asymptotic behavior of the effective potential at both short and long distances. Both single configuration and multi configuration trial wave functions are implemented. Applications to several atomic systems are presented improving previous works. The results here obtained are very close to those calculated in either the Hartree-Fock and the multi configurational Hartree-Fock framework.Comment: 8 pages, 3 figure