In metaphysics, ontology is the philosophical study of being. It investigates what types of entities exist, how they are grouped into categories, and how they are related to one another on the most fundamental level. Ontologists often try to determine what the categories or highest kinds are and how they form a system of categories that encompasses the classification of all entities. Commonly proposed categories include substances, properties, relations, states of affairs, and events. These categories are characterized by fundamental ontological concepts, including particularity and universality, abstractness and concreteness, or possibility and necessity. Of special interest is the concept of ontological dependence, which determines whether the entities of a category exist on the most fundamental level. Disagreements within ontology are often about whether entities belonging to a certain category exist and, if so, how they are related to other entities.
Willard Van Orman Quine was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century". He served as the Edgar Pierce Chair of Philosophy at Harvard University from 1956 to 1978.
A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. Propositions are also often characterized as being the kind of thing that declarative sentences denote. For instance the sentence "The sky is blue" denotes the proposition that the sky is blue. However, crucially, propositions are not themselves linguistic expressions. For instance, the English sentence "Snow is white" denotes the same proposition as the German sentence "Schnee ist weiß" even though the two sentences are not the same. Similarly, propositions can also be characterized as the objects of belief and other propositional attitudes. For instance if one believes that the sky is blue, what one believes is the proposition that the sky is blue. A proposition can also be thought of as a kind of idea: Collins Dictionary has a definition for proposition as "a statement or an idea that people can consider or discuss whether it is true."
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.
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.
Ruth Barcan Marcus was an American academic philosopher and logician best known for her work in modal and philosophical logic. She developed the first formal systems of quantified modal logic and in so doing introduced the schema or principle known as the Barcan formula. Marcus, who originally published as Ruth C. Barcan, was, as Don Garrett notes "one of the twentieth century's most important and influential philosopher-logicians". Timothy Williamson, in a 2008 celebration of Marcus' long career, states that many of her "main ideas are not just original, and clever, and beautiful, and fascinating, and influential, and way ahead of their time, but actually – I believe – true".
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.
Truthmaker theory is "the branch of metaphysics that explores the relationships between what is true and what exists". The basic intuition behind truthmaker theory is that truth depends on being. For example, a perceptual experience of a green tree may be said to be true because there actually is a green tree. But if there were no tree there, it would be false. So the experience by itself does not ensure its truth or falsehood, it depends on something else. Expressed more generally, truthmaker theory is the thesis that "the truth of truthbearers depends on the existence of truthmakers". A perceptual experience is the truthbearer in the example above. Various representational entities, like beliefs, thoughts or assertions can act as truthbearers. Truthmaker theorists are divided about what type of entity plays the role of truthmaker; popular candidates include states of affairs and tropes.
In analytic philosophy, actualism is the view that everything there is is actual. Another phrasing of the thesis is that the domain of unrestricted quantification ranges over all and only actual existents.
"Is Logic Empirical?" is the title of two articles that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide grounds for revising classical logic as a consistent logical rendering of reality. The replacement derives from the work of Garrett Birkhoff and John von Neumann on quantum logic. In their work, they showed that the outcomes of quantum measurements can be represented as binary propositions and that these quantum mechanical propositions can be combined in a similar way as propositions in classical logic. However, the algebraic properties of this structure are somewhat different from those of classical propositional logic in that the principle of distributivity fails.
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 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.
The analytic–synthetic distinction is a semantic distinction used primarily in philosophy to distinguish between propositions that are of two types: analytic propositions and synthetic propositions. Analytic propositions are true or not true solely by virtue of their meaning, whereas synthetic propositions' truth, if any, derives from how their meaning relates to the world.
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 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 and its dual possibly.
Meinong's jungle is the name given by Richard Routley (1980) to the repository of non-existent objects in the ontology of Alexius Meinong.
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.
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.
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.
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.
