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Logical Consequence Logical consequence is arguably the central concept of logic. The primary aim of logic is to tell us what follows logically from what. In order to simplify matters we take the logical consequence relation to hold for sentences rather than for abstract propositions, facts, state of affairs, etc. Correspondingly, logical consequence is a relation between a given class of sentences and the sentences
Charles Hartshorne: Neoclassical Metaphysics Charles Hartshorne (1897-2000) was an intrepid defender of the claims of metaphysics in a century characterized by its anti-metaphysical genius. While many influential voices were explaining what speculative philosophy could not accomplish or even proclaiming an end to it, Hartshorne was trying to show what speculative philosophy could accomplish. Metaphysics, he said, has a future as well as a past. He
Plotinus (204—270 C.E.) Plotinus is considered to be the founder of Neoplatonism. Taking his lead from his reading of Plato, Plotinus developed a complex spiritual cosmology involving three foundational elements: the One, the Intelligence, and the Soul. It is from the productive unity of these three Beings that all existence emanates, according to Plotinus. The principal of emanation is not simply causal, but also contemplative.
Aquinas: Philosophical Theology In addition to his moral philosophy, Thomas Aquinas (1225-1274) is well-known for his theological writings. He is arguably the most eminent philosophical theologian ever to have lived. To this day, it is difficult to find someone whose work rivals Aquinas’ in breadth and influence. Although his work is not limited to illuminating Christian doctrine, virtually all of what he wrote is shaped by
Plato: Phaedo The Phaedo is one of the most widely read dialogues written by the ancient Greek philosopher Plato. It claims to recount the events and conversations that occurred on the day that Plato’s teacher, Socrates (469-399 B.C.E.), was put to death by the state of Athens. It is the final episode in the series of dialogues recounting Socrates’ trial and death. The earlier Euthyphro dialogue
Epsilon Calculi Epsilon Calculi are extended forms of the predicate calculus that incorporate epsilon terms. Epsilon terms are individual terms of the form ‘εxFx’, being defined for all predicates in the language. The epsilon term ‘εxFx’ denotes a chosen F, if there are any F’s, and has an arbitrary reference otherwise. Epsilon calculi were originally developed to study certain forms of arithmetic, and set theory;