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The titile essay of this collection suggests that Bertrand Russell's lifelong preoccupation: the disentanglement, with ever-increasing precision, of what is subjective or intellectualy cloudy from what is objective or capable of logical demonstration. The first five essays he calls 'entirely popular': they include two on the revolutionary changes in mathematics in the last hundred years, and one on the value of science in human culture. The last five, 'somewhat more technical', are concerned with particular problems of philosophy: the ultimate nature of matter, the connection between the sense-data and physics, the problem of casuality and different ways of knowing. In these one can see the Russell method in operation, intellectual analysis dissecting the problem to its bare bones.