This volume of essays utilizes Karl R. Popper's critical vision in the study of philosophy proper, logic, mathematics, science as method and theory, and finally to the study of society and history. The core position of the volume is that the progress of knowledge is a fragmented process.

The Critical Approach to Philosophy; 1: Rationality versus the Theory of Rationality; 2: Reflections on Karl Popper's Epistemology; 3: What Hume Might Have Said to Kant; 4: Strength, Confirmation, Compatibility; 5: A Question about Plato's Theory of Ideas; 6: Popper and Wittgenstein; 7: Confirmation, the Paradoxes, and Positivism; 8: Overlooked Aspects of Popper's Contributions to Philosophy, Logic, and Scientific Method; The Critical Approach to Logic and Mathematics; 9: The Elimination of Variables by Regular Combinators 1; 10: On Popper's Use of the Notion of Absolute Logical Probability; 11: Aristotle's Theory of Modal Syllogisms and its Interpretation; 12: Logical Terminology and Theory of Meaning; The Critical Approach to Science; 13: The Nature of Scientific Problems and Their Roots in Metaphysics; 14: On the Problem of Truth and Understanding in Science; 15: The Mach Principle; 16: Phenomenological Theories; 17: The Simple Laws of Science and History; 18: The Neurophysiological Basis of Experience; 19: Realism and Instrumentalism: Comments on the Logic of Factual Support; 20: Observation and the Quantum; 21: Popper on Irreversibility; 22: The Theory of Complex Phenomena; 23: The Agreement between Mathematics and Physical Phenomena; 24: On the Reality of Elementary Particles; The Critical Approach to Society and History; 25: Social Science and Moral Philosophy: A Critical Approach to the Value Problem in the Social Sciences; 26: Popper and the Critical Philosophy of History; 27: The Open Society and Its Enemies; 28: The Tradition of General Knowledge; 29: Philosophy of History Before Historicism