The term ``neurophilosophy'' is often used either implicitly or explicitly for characterizing the investigation of philosophical theories in relation to neuroscientific hypotheses. The exact methodological principles and systematic rules for a linkage between philosophical theories and neuroscientific hypothesis, however, remain to be clarified. The present contribution focuses on these principles, as well as on the relation between ontology and epistemology and the characterization of hypothesis in neurophilosophy. Principles of transdisciplinary methodology include the `principle of asymmetry', the `principle of bi-directionality' and the `principle of transdisciplinary circularity'. The `principle of asymmetry' points to an asymmetric relationship between logical and natural conditions. The `principle of bi-directionality' claims for the necessity of bi-directional linkage between natural and logical conditions. The `principle of transdisciplinary circularity' describes systematic rules for mutual comparison and cross-conditional exchange between philosophical theory and neuroscientific hypotheses. The relation between ontology and epistemology no longer is determined by ontological presuppositions i.e. ``ontological primacy''. Instead, there is correspondence between different `epistemological capacities' and different kinds of ontology which consecutively results in ``epistemic primacy'' and ``ontological pluralism''. The present contribution concludes by rejecting some so-called `standard-arguments' including the `argument of circularity', the `argument of categorical fallacy', the `argument of validity' and the `argument of necessity'.