In analytic philosophy, anti-realism is the position that the truth of a statement rests on its demonstrability through internal logic mechanisms, such as the context principle or intuitionistic logic, in direct opposition to the realist notion that the truth of a statement rests on its correspondence to an external, independent reality. In anti-realism, this external reality is hypothetical and is not assumed.
Existence is the state of having being or reality in contrast to nonexistence and nonbeing. Existence is often contrasted with essence: the essence of an entity is its essential features or qualities, which can be understood even if one does not know whether the entity exists.
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all men are mortal", in first-order logic one can have expressions in the form "for all x, if x is a man, then x is mortal"; where "for all x" is a quantifier, x is a variable, and "... is a man" and "... is mortal" are predicates. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.
Substance theory, or substance–attribute theory, is an ontological theory positing that objects are constituted each by a substance and properties borne by the substance but distinct from it. In this role, a substance can be referred to as a substratum or a thing-in-itself. Substances are particulars that are ontologically independent: they are able to exist all by themselves. Another defining feature often attributed to substances is their ability to undergo changes. Changes involve something existing before, during and after the change. They can be described in terms of a persisting substance gaining or losing properties. Attributes or properties, on the other hand, are entities that can be exemplified by substances. Properties characterize their bearers; they express what their bearer is like.
In metaphysics, identity is the relation each thing bears only to itself. The notion of identity gives rise to many philosophical problems, including the identity of indiscernibles, and questions about change and personal identity over time. It is important to distinguish between qualitative identity and numerical identity. For example, consider two children with identical bicycles engaged in a race while their mother is watching. The two children have the same bicycle in one sense and the same mother in another sense. This article is mainly concerned with numerical identity, which is the stricter notion.
In mathematics, equality is a relationship between two quantities or, more generally, two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. Equality between A and B is written A = B, and pronounced "A equals B". In this equality, A and B are the members of the equality and are distinguished by calling them left-hand side or left member, and right-hand side or right member. Two objects that are not equal are said to be distinct.
In classical theistic and monotheistic theology, the doctrine of divine simplicity says that God is simple . God exists as one unified entity, with no distinct attributes; God's existence is identical to God's essence.
In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality, which is concerned with whether the internal definitions of objects are the same.
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.
In philosophy, supervenience refers to a relation between sets of properties or sets of facts. X is said to supervene on Y if and only if some difference in Y is necessary for any difference in X to be possible.
Mereology is the philosophical study of part-whole relationships, also called parthood relationships. As a branch of metaphysics, mereology examines the connections between parts and their wholes, exploring how components interact within a system. This theory has roots in ancient philosophy, with significant contributions from Plato, Aristotle, and later, medieval and Renaissance thinkers like Thomas Aquinas and John Duns Scotus. Mereology gained formal recognition in the 20th century through the pioneering works of Polish logician Stanisław Leśniewski, who introduced it as part of a comprehensive framework for logic and mathematics, and coined the word "mereology". The field has since evolved to encompass a variety of applications in ontology, natural language semantics, and the cognitive sciences, influencing our understanding of structures ranging from linguistic constructs to biological systems.
In logic and philosophy, a property is a characteristic of an object; a red object is said to have the property of redness. The property may be considered a form of object in its own right, able to possess other properties. A property, however, differs from individual objects in that it may be instantiated, and often in more than one object. It differs from the logical/mathematical concept of class by not having any concept of extensionality, and from the philosophical concept of class in that a property is considered to be distinct from the objects which possess it. Understanding how different individual entities can in some sense have some of the same properties is the basis of the problem of universals.
Begriffsschrift is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book.
A free logic is a logic with fewer existential presuppositions than classical logic. Free logics may allow for terms that do not denote any object. Free logics may also allow models that have an empty domain. A free logic with the latter property is an inclusive logic.
In philosophical logic, the masked-man fallacy is committed when one makes an illicit use of Leibniz's law in an argument. Leibniz's law states that if A and B are the same object, then A and B are indiscernible. By modus tollens, this means that if one object has a certain property, while another object does not have the same property, the two objects cannot be identical. The fallacy is "epistemic" because it posits an immediate identity between a subject's knowledge of an object with the object itself, failing to recognize that Leibniz's Law is not capable of accounting for intensional contexts.
In philosophy, specifically in the area of metaphysics, counterpart theory is an alternative to standard (Kripkean) possible-worlds semantics for interpreting quantified modal logic. Counterpart theory still presupposes possible worlds, but differs in certain important respects from the Kripkean view. The form of the theory most commonly cited was developed by David Lewis, first in a paper and later in his book On the Plurality of Worlds.
Haecceitism is a philosophical concept that stems from the field of metaphysics, particularly dealing with the nature of individuality and identity. The term "haecceity" itself comes from the Latin word "haecceitas," which means "thisness." This concept was originally developed in the medieval scholastic philosophy and is often associated with the philosopher Duns Scotus.
In modal logic, the necessity of identity is the thesis that for every object x and object y, if x and y are the same object, it is necessary that x and y are the same object. The thesis is best known for its association with Saul Kripke, who published it in 1971, although it was first derived by the logician Ruth Barcan Marcus in 1947, and later, in simplified form, by W. V. O. Quine in 1953.
In philosophy, similarity or resemblance is a relation between objects that constitutes how much these objects are alike. Similarity comes in degrees: e.g. oranges are more similar to apples than to the moon. It is traditionally seen as an internal relation and analyzed in terms of shared properties: two things are similar because they have a property in common. The more properties they share, the more similar they are. They resemble each other exactly if they share all their properties. So an orange is similar to the moon because they both share the property of being round, but it is even more similar to an apple because additionally, they both share various other properties, like the property of being a fruit. On a formal level, similarity is usually considered to be a relation that is reflexive (everything resembles itself), symmetric (if a is similar to b then b is similar to a) and non-transitive (a need not resemble c despite a resembling b and b resembling c). Similarity comes in two forms: respective similarity, which is relative to one respect or feature, and overall similarity, which expresses the degree of resemblance between two objects all things considered. There is no general consensus whether similarity is an objective, mind-independent feature of reality, and, if so, whether it is a fundamental feature or reducible to other features. Resemblance is central to human cognition since it provides the basis for the categorization of entities into kinds and for various other cognitive processes like analogical reasoning. Similarity has played a central role in various philosophical theories, e.g. as a solution to the problem of universals through resemblance nominalism or in the analysis of counterfactuals in terms of similarity between possible worlds.
This is a glossary of mereology. Mereology is the philosophical study of part-whole relationships, also called parthood relationships.
