Abstract
Scientific progress is achieved not only by continuous accumulation of knowledge but also by paradigm shifts. These shifts are often necessitated by anomalous findings that cannot be incorporated in accepted models. Two important methodological principles regulate this process and complement each other: Ockham's Razor as the principle of parsimony and Plato's Life Boat as the principle of the necessity to 'save the appearances' and thus incorporate conflicting phenomenological data into theories. We review empirical data which are in conflict with some presuppositions of accepted mainstream science: Clinical and experimental effects of prayer and healing intention, data from telepathy, psychokinesis experiments and precognition, and anecdotal reports of macro-psychokinesis. Taken together, the now well documented possibility of these events suggests that such phenomena are anomalies that challenge some widely held beliefs in mainstream science. On the other hand, scientists often fear that by accepting the reality of these phenomena they also have to subscribe to world-models invoking ontological dualism or idealism. We suggest accepting the phenomena as real, but without questionable ontologies commonly associated with them. We outline how this might work