Poincaré on the Foundation of Geometry in the Understanding

This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study of groups of operations. In place of the established view I offer a revised view, according to which Poincaré held that axioms in geometry are in fact assertions about invariants of groups. Groups, as forms of the understanding, are prior in conception to the objects of geometry and afford the proper definition of those objects, according to Poincaré. Poincaré’s view therefore contrasts sharply with Kant’s foundation of geometry in a unique form of sensibility. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them

Effect of Biocyclic Humus Soil on Yield and Quality Parameters of Processing Tomato (Lycopersicon esculentum Mill.)

A field experiment was conducted to evaluate the effects of biocyclic humus soil, a newly found apparently carbon stabilized form of organic matter with significantly different characteristics from common composts or other forms of organic matter (humus), on yield and quality of processing tomato. The experiment was laid out in a completely randomized design with three replications and three fertilization treatments (untreated, inorganic fertilizer and biocyclic humus soil). The highest fruit yield (116.8 t/ha) was obtained by using biocyclic humus soil. There were no treatment effects on fruit firmness (4.34-4.60 kg/cm2), total soluble solids (4.29-4.76 °Brix) and total acidity (0.25-0.31 g citric acid/100 g fruit) content of fruits. In conclusion, the tomato plants grown in biocyclic humus soil had 45% more yield than in conventional plots, and this big difference is probably related to the fact that the humus soil as a substrate provides an optimum environment for plant growth