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The second phase, called metaphysical, is in some cases merely a depersonalized theology: the observable processes of nature are assumed to arise from impersonal powers, occult qualities, vital forces, or entelechies(internal perfecting principles). In other instances, the realm of observable facts is considered as an imperfect copy or imitation of eternal ideas, as in Plato’s metaphysics of pure forms. Again, Comte charged that no genuine explanations result; questions concerning ultimate reality, first causes, or absolute beginnings are thus declared to be absolutely unanswerable. The metaphysical quest can lead only to the conclusion expressed by the German biologist and physiologist Emil du Bois-Reymond: “Ignoramus et ignorabimus” (Latin: “We are and shall be ignorant”). It is a deception through verbal devices and the fruitless rendering of concepts as real things.

The sort of fruitfulness that it lacks can be achieved only in the third phase, the scientific, or “positive,” phase—hence the title of Comte’s magnum opus: Cours de philosophie positive (1830–42)—because it claims to be concerned only with positive facts. The task of the sciences, and of knowledge in general, is to study the facts and regularities of nature and society and to formulate the regularities as (descriptive) laws; explanations of phenomena can consist in no more than the subsuming of special cases under general laws. Humankind reached full maturity of thought only after abandoning the pseudoexplanations of the theological and metaphysical phases and substituting an unrestricted adherence to scientific method.

In his three stages Comte combined what he considered to be an account of the historical order of development with a logical analysis of the leveled structure of the sciences. By arranging the six basic and pure sciences one upon the other in a pyramid, Comte prepared the way for logical positivism to “reduce” each level to the one below it. He placed at the fundamental level the science that does not presuppose any other sciences—viz., mathematics—and then ordered the levels above it in such a way that each science depends upon, and makes use of, the sciences below it on the scale: thus, arithmetic and the theory of numbers are declared to be presuppositions for geometry and mechanicsastronomyphysicschemistrybiology (including physiology), and sociology. Each higher-level science, in turn, adds to the knowledge content of the science or sciences on the levels below, thus enriching this content by successive specialization. Psychology, which was not founded as a formal discipline until the late 19th century, was not included in Comte’s system of the sciences. Anticipating some ideas of 20th-century behaviourism and physicalism, Comte assumed that psychology, such as it was in his day, should become a branch of biology (especially of brain neurophysiology), on the one hand, and of sociology, on the other. As the “father” of sociology, Comte maintained that the social sciences should proceed from observations to general laws, very much as (in his view) physics and chemistry do. He was skeptical of introspection in psychology, being convinced that in attending to one’s own mental states, these states would be irretrievably altered and distorted. In thus insisting on the necessity of objective observation, he was close to the basic principle of the methodology of 20th-century behaviourism.