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Modal Collapse
In modal logic, modal collapse is the condition in which every true statement is necessarily true, and vice versa; that is to say, there are no contingent truths, or to put it another way, that "everything exists necessarily". In the notation of modal logic, this can be written as \phi \leftrightarrow \Box \phi. In the context of philosophy, the term is commonly used in critiques of ontological arguments for the existence of God and the principle of divine simplicity. For example, Gödel's ontological proof contains \phi \rightarrow \Box \phi as a theorem, which combined with the axioms of system S5 leads to modal collapse. Since some regard divine freedom as essential to the nature of God, and modal collapse as negating the concept of free will, this then leads to the breakdown of Gödel's argument. References Collapse Collapse or its variants may refer to: Concepts * Collapse (structural) * Collapse (topology), a mathematical concept * Collapsing manifold * Coll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a ''possible world''. A formula's truth value at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Necessarily True
Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components (other than its logical constants). Thus, logical truths such as "if p, then p" can be considered tautologies. Logical truths are thought to be the simplest case of statements which are analytically true (or in other words, true by definition). All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence. Logical truths are generally considered to be ''necessarily true''. This is to say that they are such that no situation could arise in which they could fail to be true. The view that logical statements are necessarily true is sometimes treated as equivalent to saying that lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contingency (philosophy)
In philosophy and logic, contingency is the status of propositions that are neither true under every possible valuation (i.e. tautologies) nor false under every possible valuation (i.e. contradictions). A contingent proposition is neither necessarily true nor necessarily false. Overview Propositions that are contingent may be so because they contain logical connectives which, along with the truth value of any of its atomic parts, determine the truth value of the proposition. This is to say that the truth value of the proposition is ''contingent'' upon the truth values of the sentences which comprise it. Contingent propositions depend on the facts, whereas analytic propositions are true without regard to any facts about which they speak. Along with contingent propositions, there are at least three other classes of propositions, some of which overlap: * '' Tautological'' propositions, which ''must'' be true, no matter what the circumstances are or could be (example: "It is the cas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ontological Arguments For The Existence Of God
An ontological argument is a philosophical argument, made from an ontological basis, that is advanced in support of the existence of God. Such arguments tend to refer to the state of being or existing. More specifically, ontological arguments are commonly conceived ''a priori'' in regard to the organization of the universe, whereby, if such organizational structure is true, God must exist. The first ontological argument in Western Christian traditionSzatkowski, Miroslaw, ed. 2012. ''Ontological Proofs Today''. Ontos Verlag. "There are three main periods in the history of ontological arguments. The first was in 11th century, when St. Anselm of Canterbury came up with the first ontological argument" (p. 22). was proposed by Saint Anselm of Canterbury in his 1078 work, ''Proslogion'' (), in which he defines God as "a being than which no greater can be conceived," and argues that such being must exist in the mind, even in that of the person who denies the existence of God. Oppy, Gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divine Simplicity
In theology, the doctrine of divine simplicity says that God is simple (without parts). The general idea can be stated in this way: The being of God is identical to the "attributes" of God. Characteristics such as omnipresence, goodness, truth, eternity, etc., are identical to God's being, not qualities that make up that being as a collection, nor abstract entities inhering in God as in a substance; in other words, one can say that in God both essence and existence are one and the same. This is not to say that God is a simpleton or "simple" to understand. As Peter Weigel states, "Divine simplicity is central to the classical Western concept of God. Simplicity denies any physical or metaphysical composition in the divine being. This means God is the divine nature itself and has no accidents (properties that are not necessary) accruing to his nature. There are no real divisions or distinctions in this nature. Thus, the entirety of God is whatever is attributed to him. Divine si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel's Ontological Proof
Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development that goes back to Anselm of Canterbury (1033–1109). St. Anselm's ontological argument, in its most succinct form, is as follows: "God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist." A more elaborate version was given by Gottfried Leibniz (1646–1716); this is the version that Gödel studied and attempted to clarify with his ontological argument. Gödel left a fourteen-point outline of his philosophical beliefs in his papers. Points relevant to the ontological proof include :4. There are other worlds and rational beings of a different and higher kind. :5. The world in which we live is not the only one in which we shall live or have lived. :13. There is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
S5 (modal Logic)
In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book ''Symbolic Logic''. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas and tautologies, and inference apparatus with substitution and modus ponens, but extending the syntax with the modal operator ''necessarily'' \Box and its dual ''possibly'' \Diamond. The axioms of S5 The following makes use of the modal operators \Box ("necessarily") and \Diamond ("possibly"). S5 is characterized by the axioms: *K: \Box(A\to B)\to(\Box A\to\Box B); *T: \Box A \to A, and either: * 5: \Diamond A\to \Box\Diamond A; * or both of the following: :* 4: \Box A\to\Box\Box A, and :* B: A\to\Box\Diamond A. The (5) axiom restricts the accessibility relation R of the Kripke frame to be Euclidean, i.e. (wRv \land wRu) \implies vRu . Kripke semantics In terms of Kripke seman ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divine Freedom
Divine freedom is the concept that God has free will. One argument advanced against the concept of divine freedom is that it may contradict the principle of omnibenevolence, by limiting God's choices to only actions with perfectly good consequences. According to saint Augustine of Hippo, since evil is absence of being and of perfection Perfection is a state, variously, of completeness, flawlessness, or supreme excellence. The terminology, term is used to designate a range of diverse, if often kindred, concepts. These have historically been addressed in a number of discrete a ..., the fact that God is the Highest does not limit His perfection, being, or freedom. References See also * Absence of good * Argument from free will * Euthyphro dilemma * Modal collapse * Conceptions of God Religious philosophical concepts {{theology-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Will
Free will is the capacity of agents to choose between different possible courses of action unimpeded. Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgements which apply only to actions that are freely chosen. It is also connected with the concepts of advice, persuasion, deliberation, and prohibition. Traditionally, only actions that are freely willed are seen as deserving credit or blame. Whether free will exists, what it is and the implications of whether it exists or not are some of the longest running debates of philosophy and religion. Some conceive of free will as the right to act outside of external influences or wishes. Some conceive free will to be the capacity to make choices undetermined by past events. Determinism suggests that only one course of events is possible, which is inconsistent with a libertarian model of free will. Ancient Greek philosophy identified this issue, which remains a major focus o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a ''possible world''. A formula's truth value at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Logic
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic. An important issue for philosophical logic is the question of how to classify the great variety of non-classical logical systems, many of which are of rather recent origin. One form of classification often found in the literature is to distinguish between extended logics and deviant logics. Logic itself can be defined as the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theology
Theology is the systematic study of the nature of the divine and, more broadly, of religious belief. It is taught as an academic discipline, typically in universities and seminaries. It occupies itself with the unique content of analyzing the supernatural, but also deals with religious epistemology, asks and seeks to answer the question of revelation. Revelation pertains to the acceptance of God, gods, or deities, as not only transcendent or above the natural world, but also willing and able to interact with the natural world and, in particular, to reveal themselves to humankind. While theology has turned into a secular field , religious adherents still consider theology to be a discipline that helps them live and understand concepts such as life and love and that helps them lead lives of obedience to the deities they follow or worship. Theologians use various forms of analysis and argument ( experiential, philosophical, ethnographic, historical, and others) to help understa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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