Inconsistent Mathematics Inconsistent mathematics is the study of commonplace mathematical objects, like sets, numbers, and functions, where some contradictions are allowed. Tools from formal logic are used to make sure any contradictions are contained and that the overall theories remain coherent. Inconsistent mathematics began as a response to the set theoretic and semantic paradoxes such as Russell’s Paradox and the Liar Paradox—the response being that

Theories of Explanation Within the philosophy of science there have been competing ideas about what an explanation is. Historically, explanation has been associated with causation: to explain an event or phenomenon is to identify its cause. But with the growth and development of philosophy of science in the 20th century, the concept of explanation began to receive more rigorous and specific analysis. Of particular concern

Gottfried Leibniz: Causation The views of Leibniz (1646-1716) on causation must stand as some of the more interesting in the history of philosophy, for he consistently denied that there is any genuine causal interaction between finite substances. And yet from another perspective, he sought to integrate both old and new causal taxonomies: On the one hand, Leibniz put forth a theory of causation that would accommodate

Free Will Most of us are certain that we have free will, though what exactly this amounts to is much less certain. According to David Hume, the question of the nature of free will is “the most contentious question of metaphysics.” If this is correct, then figuring out what free will is will be no small task indeed. Minimally, to say that an agent has

Juan Donoso Cortés (1809—1853) Juan Donoso Cortés, parliamentary statesman, diplomat, government minister, royal counselor, theologian, and political theorist, may not be well known among modern political philosophers. However, his ideas had an enormous influence in the spheres of politics and religion in the nineteenth and twentieth centuries. Donoso’s theories were uniquely influential in shaping the ideological trajectory that began with the reaction against the Enlightenment