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Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the fundamental categories of human understanding. Some philosophers, including Aristotle, designate metaphysics as first philosophy to suggest that it is more fundamental than other forms of philosophical inquiry.
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. From the 1960s until his death, he was a central figure in a number of fields related to mathematical and modal logic, philosophy of language and mathematics, metaphysics, epistemology, and recursion theory.
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.
Arthur Norman Prior, usually cited as A. N. Prior, was a New Zealand–born logician and philosopher. Prior (1957) founded tense logic, now also known as temporal logic, and made important contributions to intensional logic, particularly in Prior (1971).
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 modal logics treat the formula as a 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.
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.
David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton University from 1970 until his death. He is closely associated with Australia, whose philosophical community he visited almost annually for more than 30 years.
In philosophy, metaphysical necessity, sometimes called broad logical necessity, is one of many different kinds of necessity, which sits between logical necessity and nomological necessity, in the sense that logical necessity entails metaphysical necessity, but not vice versa, and metaphysical necessity entails physical necessity, but not vice versa. A proposition is said to be necessary if it could not have failed to be the case. Nomological necessity is necessity according to the laws of physics and logical necessity is necessity according to the laws of logic, while metaphysical necessities are necessary in the sense that the world could not possibly have been otherwise. What facts are metaphysically necessary, and on what basis we might view certain facts as metaphysically but not logically necessary are subjects of substantial discussion in contemporary philosophy.
A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their metaphysical status has been a subject of controversy in philosophy, with modal realists such as David Lewis arguing that they are literally existing alternate realities, and others such as Robert Stalnaker arguing that they are not.
Subjunctive possibility is a form of modality studied in modal logic. Subjunctive possibilities are the sorts of possibilities considered when conceiving counterfactual situations; subjunctive modalities are modalities that bear on whether a statement might have been or could be true—such as might, could, must, possibly, necessarily, contingently, essentially, accidentally, and so on. Subjunctive possibilities include logical possibility, metaphysical possibility, nomological possibility, and temporal possibility.
In philosophy and modal logic, epistemic possibility relates a statement under consideration to the current state of our knowledge about the actual world: a statement is said to be:
Timothy Williamson is a British philosopher whose main research interests are in philosophical logic, philosophy of language, epistemology and metaphysics. He is the former Wykeham Professor of Logic at the University of Oxford, and a fellow of New College, Oxford.
A fallacy of necessity is a fallacy in the logic of a syllogism whereby a degree of unwarranted necessity is placed in the conclusion.
In philosophical logic, the concept of an impossible world is used to model certain phenomena that cannot be adequately handled using ordinary possible worlds. An impossible world, , is the same sort of thing as a possible world , except that it is in some sense "impossible." Depending on the context, this may mean that some contradictions, statements of the form are true at , or that the normal laws of logic, metaphysics, and mathematics, fail to hold at , or both. Impossible worlds are controversial objects in philosophy, logic, and semantics. They have been around since the advent of possible world semantics for modal logic, as well as world based semantics for non-classical logics, but have yet to find the ubiquitous acceptance, that their possible counterparts have found in all walks of 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 between what is contingent and what is necessary has been challenged since antiquity.
Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines. According to a common characterisation, philosophical logic is the part of the philosophy of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But other theorists draw the distinction between the philosophy of logic and philosophical logic differently or not at all. Metalogic is closely related to the philosophy of logic as the discipline investigating the properties of formal logical systems, like consistency and completeness.
Najm al-Dīn 'Alī ibn 'Umar al-Qazwīnī al-Kātibī was a Persian Islamic philosopher and logician of the Shafi`i school. He was a student of Athīr al-Dīn al-Abharī. His most important works are a treatise on logic, Al-Risala al-Shamsiyya, and one on metaphysics and the natural sciences, Hikmat al-'Ain. Further, he helped to establish the Maragha observatory along with Nasir al-Din al-Tusi and several other astronomers.
James Garson is an American philosopher and logician. He has made significant contributions in the study of modal logic and formal semantics. He is author of Modal Logic for Philosophers and What Logics Mean by Cambridge University Press. Garson is Professor of Philosophy at the University of Houston and has taught at the University of Pennsylvania, the University of Notre Dame, the University of Illinois at Chicago, and Rice University.
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.
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
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