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Saul Aaron Kripke was an American analytic philosopher and logician. He was Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Princeton University. Kripke is considered one of the most important philosophers of the latter half of the 20th century. Since the 1960s, he has been a central figure in a number of fields related to mathematical and modal logic, philosophy of language and mathematics, metaphysics, epistemology, and recursion theory.
In grammar, the term particle has a traditional meaning, as a part of speech that cannot be inflected, and a modern meaning, as a function word (functor) associated with another word or phrase, in order to impart meaning. Although a particle may have an intrinsic meaning, and may fit into other grammatical categories, the fundamental idea of the particle is to add context to the sentence, expressing a mood or indicating a specific action.
Modal logic is a kind of logic used to represent statements about necessity and possibility. It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation. For instance, in epistemic modal logic, the formula can be used to represent the statement that is known. In deontic modal logic, that same formula can represent that is a moral obligation. Modal logic considers the inferences that modal statements give rise to. For instance, most epistemic logics treat the formula as a tautology, representing the principle that only true statements can count as knowledge.
Logical possibility refers to a logical proposition that cannot be disproved, using the axioms and rules of a given system of logic. The logical possibility of a proposition will depend upon the system of logic being considered, rather than on the violation of any single rule. Some systems of logic restrict inferences from inconsistent propositions or even allow for true contradictions. Other logical systems have more than two truth-values instead of a binary of such values. Some assume the system in question is classical propositional logic. Similarly, the criterion for logical possibility is often based on whether or not a proposition is contradictory and as such, is often thought of as the broadest type of possibility.
Organum is, in general, a plainchant melody with at least one added voice to enhance the harmony, developed in the Middle Ages. Depending on the mode and form of the chant, a supporting bass line may be sung on the same text, the melody may be followed in parallel motion, or a combination of both of these techniques may be employed. As no real independent second voice exists, this is a form of heterophony. In its earliest stages, organum involved two musical voices: a Gregorian chant melody, and the same melody transposed by a consonant interval, usually a perfect fifth or fourth. In these cases the composition often began and ended on a unison, the added voice keeping to the initial tone until the first part has reached a fifth or fourth, from where both voices proceeded in parallel harmony, with the reverse process at the end. Organum was originally improvised; while one singer performed a notated melody, another singer—singing "by ear"—provided the unnotated second melody. Over time, composers began to write added parts that were not just simple transpositions, thus creating true polyphony.
De Interpretatione or On Interpretation is the second text from Aristotle's Organon and is among the earliest surviving philosophical works in the Western tradition to deal with the relationship between language and logic in a comprehensive, explicit, and formal way. The work is usually known by its Latin title.
Fitch's paradox of knowability is one of the fundamental puzzles of epistemic logic. It provides a challenge to the knowability thesis, which states that every truth is, in principle, knowable. The paradox is that this assumption implies the omniscience principle, which asserts that every truth is known. Essentially, Fitch's paradox asserts that the existence of an unknown truth is unknowable. So if all truths were knowable, it would follow that all truths are in fact known.
The English modal auxiliary verbs are a subset of the English auxiliary verbs used mostly to express modality. They can be distinguished from other verbs by their defectiveness and by their neutralization.
A modal verb is a type of verb that contextually indicates a modality such as a likelihood, ability, permission, request, capacity, suggestion, order, obligation, necessity, possibility or advice. Modal verbs generally accompany the base (infinitive) form of another verb having semantic content. In English, the modal verbs commonly used are can, could, may, might, shall, should, will, would, ought to, used to and dare.
Modal realism is the view propounded by philosopher David Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours." It is based on four tenets: possible worlds exist, possible worlds are not different in kind from the actual world, possible worlds are irreducible entities, and the term actual in actual world is indexical, i.e. any subject can declare their world to be the actual one, much as they label the place they are "here" and the time they are "now".
In philosophy, potentiality and actuality are a pair of closely connected principles which Aristotle used to analyze motion, causality, ethics, and physiology in his Physics, Metaphysics, Nicomachean Ethics, and De Anima.
In linguistics and philosophy, modality refers to the ways language can express various relationships to reality or truth. For instance, a modal expression may convey that something is likely, desirable, or permissible. Quintessential modal expressions include modal auxiliaries such as "could", "should", or "must"; modal adverbs such as "possibly" or "necessarily"; and modal adjectives such as "conceivable" or "probable". However, modal components have been identified in the meanings of countless natural language expressions, including counterfactuals, propositional attitudes, evidentials, habituals, and generics.
Epistemic modality is a sub-type of linguistic modality that encompasses knowledge, belief, or credence in a proposition. Epistemic modality is exemplified by the English modals may, might, must. However, it occurs cross-linguistically, encoded in a wide variety of lexical items and grammatical structures. Epistemic modality has been studied from many perspectives within linguistics and philosophy. It is one of the most studied phenomena in formal semantics.
Studies that estimate and rank the most common words in English examine texts written in English. Perhaps the most comprehensive such analysis is one that was conducted against the Oxford English Corpus (OEC), a massive text corpus that is written in the English language.
Two-dimensionalism is an approach to semantics in analytic philosophy. It is a theory of how to determine the sense and reference of a word and the truth-value of a sentence. It is intended to resolve the puzzle: How is it possible to discover empirically that a necessary truth is true? Two-dimensionalism provides an analysis of the semantics of words and sentences that makes sense of this possibility. The theory was first developed by Robert Stalnaker, but it has been advocated by numerous philosophers since, including David Chalmers.
In linguistics, hortative modalities are verbal expressions used by the speaker to encourage or discourage an action. Different hortatives can be used to express greater or lesser intensity, or the speaker's attitude, for or against it.
Formal semantics is the study of grammatical meaning in natural languages using formal tools from logic, mathematics and theoretical computer science. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language. It provides accounts of what linguistic expressions mean and how their meanings are composed from the meanings of their parts. The enterprise of formal semantics can be thought of as that of reverse-engineering the semantic components of natural languages' grammars.
Logical consequence is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises? All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth.
Alexander Robert Pruss is a Canadian philosopher and mathematician. He is currently a professor of philosophy and the co-director of graduate studies in philosophy at Baylor University in Waco, Texas.
Extended modal realism is a metaphysical theory developed by Takashi Yagisawa. It concerns the question of what it means that something is possible or necessary. Modal realism is the view that besides the actual world, there are many possible worlds. They exist as alternate versions of the actual world we live in. It contrasts with actualism, which holds that there is only one world: the actual world. Extended modal realism is a special form of modal realism. It includes the controversial thesis that there are not just possible worlds but also impossible worlds. An impossible world is a world that contains a contradiction. Extended modal realism understands modality as a dimension similar to space and time. In this sense, a regular object, like a tree or a car, is not just extended in space and time but also across possible and impossible worlds: some parts of it exist in the actual world and other parts exist in non-actual worlds. There is only one universe encompassing everything that is real in the widest sense: the actual, the possible, and the impossible.
References
- ↑ Matthews, Peter (2003). The Concise Oxford Dictionary of Linguistics. Oxford: Oxford University Press.
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