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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" (and likewise if something does not exist, it cannot exist). 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 Free will is generally understood as the capacity or ability of people to (a) choice, choose between different possible courses of Action (philosophy), action, (b) exer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Modal Logic
Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality, causation. For instance, in epistemic modal logic, the well-formed_formula, formula \Box P can be used to represent the statement that P is known. In deontic modal logic, that same formula can represent that P is a moral obligation. Modal logic considers the inferences that modal statements give rise to. For instance, most epistemic modal logics treat the formula \Box P \rightarrow P as a Tautology_(logic), tautology, representing the principle that only true statements can count as knowledge. However, this formula is not a tautology in deontic modal logic, since what ought to be true can be false. Modal logics are formal systems that include unary operation, unary operators such as \Diamond and \Box, representing possibility and necessi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 log ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Contingency (philosophy)
In logic, contingency is the feature of a statement making it neither necessary nor impossible. Contingency is a fundamental concept of modal logic. Modal logic concerns the manner, or ''mode'', in which statements are true. Contingency is one of three basic modes alongside necessity and possibility. In modal logic, a contingent statement stands in the modal realm between what is necessary and what is impossible, never crossing into the territory of either status. Contingent and necessary statements form the complete set of possible statements. While this definition is widely accepted, the precise distinction (or lack thereof) between what is contingent and what is necessary has been challenged since antiquity. Contingency and modal possibility In logic, a thing is considered to be possible when it is true in at least one possible world. This means there is a way to imagine a world in which a statement is true and in which its truth does not contradict any other truth in that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Ontological Arguments For The Existence Of God
Ontology is the philosophical study of being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of reality and every entity within it. To articulate the basic structure of being, ontology examines the commonalities among all things and investigates their classification into basic types, such as the categories of particulars and universals. Particulars are unique, non-repeatable entities, such as the person Socrates, whereas universals are general, repeatable entities, like the color ''green''. Another distinction exists between concrete objects existing in space and time, such as a tree, and abstract objects existing outside space and time, like the number 7. Systems of categories aim to provide a comprehensive inventory of reality by employing categories such as substance, property, relation, state of affairs, and event. Ontologists disagree regarding ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Divine Simplicity
In classical theistic and monotheistic theology, the doctrine of divine simplicity says that God is simple (without parts). God exists as one unified entity, with no distinct attributes; God's existence is identical to God's essence. Overview The being of God is identical to the "attributes" of God. Characteristics such as omnipresence, goodness, truth and eternity are identical to God's being, not qualities that make up that being as a collection or abstract entities inherent to God as in a substance; in God, essence and existence are the same. Simplicity denies any physical or metaphysical composition in the divine being. God is the divine nature itself, with no accidents (unnecessary properties) accruing to his nature. There are no real divisions or distinctions of this nature; the entirety of God is whatever is attributed to him. God does not ''have'' goodness, but ''is'' goodness; God does not existence, but ''is'' existence. According to Thomas Aquinas, God is God's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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. The argument uses modal logic, which deals with statements about what is ''necessarily'' true or ''possibly'' true. From the axioms that a property can only be positive if not-having-it is not positive, and that properties implied by a positive property must all also be themselves positive, it concludes that (s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 , thereby conflating necessity with possi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Divine Freedom
Divinity (from Latin ) refers to the quality, presence, or nature of that which is divine—a term that, before the rise of monotheism, evoked a broad and dynamic field of sacred power. In the ancient world, divinity was not limited to a single deity or abstract ideal but was recognized in multiple forms: as a radiant attribute possessed by gods, as a vital force pervading nature, and even as a quality glimpsed in extraordinary humans, laws, or acts. The Latin and its Greek counterparts (, ) conveyed something both immanent and awe-inspiring: a presence that could be felt in thunder, justice, ecstasy, fate, or beauty. Among the Greeks and Romans, divinity was not confined to a rigid theological system. Gods, heroes, and even emperors might be described as partaking in divinity, just as natural forces or virtue could be seen as expressions of divine essence. Philosophers such as Plato and the Stoics used the term to refer to the soul of the cosmos or the rational order of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Free Will
Free will is generally understood as the capacity or ability of people to (a) choice, choose between different possible courses of Action (philosophy), action, (b) exercise control over their actions in a way that is necessary for moral responsibility, or (c) be the ultimate source or originator of their actions. There are different theories as to its nature, and these aspects are often emphasized differently depending on philosophical tradition, with debates focusing on whether and how such freedom can coexist with determinism, divine foreknowledge, and other constraints. Free will is closely linked to the concepts of moral responsibility, praise, culpability, and other judgements which apply only to actions that are freely chosen. It is also connected with the concepts of Advice (opinion), advice, persuasion, deliberation, and Prohibitionism, prohibition. Traditionally, only actions that are freely Will (philosophy), willed are seen as deserving credit or blame. Whether free ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Modal Logic
Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality, causation. For instance, in epistemic modal logic, the well-formed_formula, formula \Box P can be used to represent the statement that P is known. In deontic modal logic, that same formula can represent that P is a moral obligation. Modal logic considers the inferences that modal statements give rise to. For instance, most epistemic modal logics treat the formula \Box P \rightarrow P as a Tautology_(logic), tautology, representing the principle that only true statements can count as knowledge. However, this formula is not a tautology in deontic modal logic, since what ought to be true can be false. Modal logics are formal systems that include unary operation, unary operators such as \Diamond and \Box, representing possibility and necessi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Theology
Theology is the study of religious belief from a Religion, religious perspective, with a focus on the nature of divinity. It is taught as an Discipline (academia), 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 deity, deities, as not only transcendent or above the natural world, but also willing and able to interact with the natural world and to reveal themselves to humankind. Theologians use various forms of analysis and argument (Spirituality, experiential, philosophy, philosophical, ethnography, ethnographic, history, historical, and others) to help understanding, understand, explanation, explain, test, critique, defend or promote any myriad of List of religious topics, religious topics. As in philosophy of ethics and case law, arguments ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
