Metaphysical realism in the context of "Mathematical entity"

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⭐ Core Definition: Metaphysical realism

Philosophical realism—usually not treated as a position of its own but as a stance towards other subject matters—is the view that a certain kind of thing (ranging widely from abstract objects like numbers to moral statements to the physical world itself) has mind-independent existence, i.e. that it exists even in the absence of any mind perceiving it or that its existence is not just a mere appearance in the eye of the beholder. This includes a number of positions within epistemology and metaphysics which express that a given thing instead exists independently of knowledge, thought, or understanding. This can apply to items such as the physical world, the past and future, other minds, and the self, though may also apply less directly to things such as universals, mathematical truths, moral truths, and thought itself. However, realism may also include various positions which instead reject metaphysical treatments of reality altogether.

Realism can also be a view about the properties of reality in general, holding that reality exists independent of the mind, as opposed to non-realist views (like some forms of skepticism and solipsism) which question the certainty of anything beyond one's own mind. Philosophers who profess realism often claim that truth consists in a correspondence between cognitive representations and reality.

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Metaphysical realism in the context of Mathematical object

A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol, and therefore can be involved in formulas. Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex; for example, theorems, proofs, and even formal theories are considered as mathematical objects in proof theory.

In philosophy of mathematics, the concept of "mathematical objects" touches on topics of existence, identity, and the nature of reality. In metaphysics, objects are often considered entities that possess properties and can stand in various relations to one another. Philosophers debate whether mathematical objects have an independent existence outside of human thought (realism), or if their existence is dependent on mental constructs or language (idealism and nominalism). Objects can range from the concrete: such as physical objects usually studied in applied mathematics, to the abstract, studied in pure mathematics. What constitutes an "object" is foundational to many areas of philosophy, from ontology (the study of being) to epistemology (the study of knowledge). In mathematics, objects are often seen as entities that exist independently of the physical world, raising questions about their ontological status. There are varying schools of thought which offer different perspectives on the matter, and many famous mathematicians and philosophers each have differing opinions on which is more correct.

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Metaphysical realism in the context of Perspectivism

Early forms of perspectivism have been identified in the philosophies of Protagoras, Michel de Montaigne, and Gottfried Leibniz. However, its first major statement is considered to be Friedrich Nietzsche's development of the concept in the 19th century, influenced by Gustav Teichmüller's use of the term some years prior. For Nietzsche, perspectivism takes the form of a realist antimetaphysics while rejecting both the correspondence theory of truth and the notion that the truth-value of a belief always constitutes its ultimate worth-value. The perspectival conception of objectivity used by Nietzsche sees the deficiencies of each perspective as remediable by an asymptotic study of the differences between them. This stands in contrast to Platonic notions in which objective truth is seen to reside in a wholly non-perspectival domain.

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Metaphysical realism in the context of Speculative realism

Speculative realism is a movement in contemporary Continental-inspired philosophy (also known as post-Continental philosophy) that defines itself loosely in its stance of metaphysical realism against its interpretation of the dominant forms of post-Kantian philosophy (or what it terms "correlationism").

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