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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
Meaning and Context-Sensitivity Truth-conditional semantics explains meaning in terms of truth-conditions. The meaning of a sentence is given by the conditions that must obtain in order for the sentence to be true. The meaning of a word is given by its contribution to the truth-conditions of the sentences in which it occurs. What a speaker says by the utterance of a sentence depends on the
Predicative and Impredicative Definitions The distinction between predicative and impredicative definitions is today widely regarded as an important watershed in logic and the philosophy of mathematics. A definition is said to be impredicative if it generalizes over a totality to which the entity being defined belongs. Otherwise the definition is said to be predicative. In the examples below, (2) and (4) are impredicative. Let π be
Pacifism Pacifism is the theory that peaceful rather than violent or belligerent relations should govern human intercourse and that arbitration, surrender, or migration should be used to resolve disputes. Pacifism is as much an element of Western thinking as is the notion of Just War Theory, the argument that the state may legitimately or morally bear arms. While most people accept the necessity of war,
Gregory of Nyssa (c. 335—c. 395 C.E.) Gregory of Nyssa spent his life in Cappadocia, a region in central Asia Minor. He was the most philosophically adept of the three so-called Cappadocians, who included brother Basil the Great and friend Gregory of Nazianzus. Together, the Cappadocians are credited with defining Christian orthodoxy in the Eastern Roman Empire, as Augustine (354—430 C.E.) was to do in
Philosophy of Peace Peace is notoriously difficult to define, and this poses a special challenge for articulating any comprehensive philosophy of peace. Any discussion on what might constitute a comprehensive philosophy of peace invariably overlaps with wider questions of the meaning and purpose of human existence. The definitional problem is, paradoxically, a key to understanding what is involved in articulating a philosophy of peace. In