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Substance theory posits that a core substance is the foundational element of reality and individual identity. Its metaphysical significance lies in understanding objects as entities with independent existence.

Four-dimensionalism argues that beings exist as temporal as well as spatial four-dimensional entities, with time being the fourth dimension. Metaphysically, it implies that identity is a matter of having distinct temporal parts at different times.

This concept revolves around the question of whether identical entities must have all their properties in common. Metaphysically, it examines the nuanced understanding of object individuation and the possible existence of indistinguishable yet distinct entities.

Nominalism and Realism are two opposing views concerning the existence of universals. Nominalism denies their existence, whereas Realism affirms it, giving rise to differing metaphysical implications regarding the nature of categories and the possibility of shared identity.

Essentialism is the view that certain categories have an underlying essence that defines their true nature. Metaphysically, it implies that objects have some property(ies) that are essential for their identity and existence.

Ego Theory asserts the existence of a persistent, immaterial self as the basis of identity, while Bundle Theory denies it, stating that our identity is just a bundle of perceptions and experiences. The metaphysical significance lies in contrasting notions of what constitutes self-identity.

This concept explores how an object or person maintains their identity despite changes over time. The metaphysical significance relates to understanding what conditions must be met for an entity to remain 'the same' even as it undergoes transformation.

The theory of relative identity contends that objects are identical relative to a particular concept or category but might not be absolutely identical. Metaphysically, it suggests that identity can be context-dependent and not intrinsic to objects.

This problem in metaphysics questions how two objects (e.g., a statue and the lump of clay it's made from) can occupy the same space at the same time. It explores issues of coinciding objects and which properties are essential for their identity.

Existentialism posits that existence precedes essence, meaning that individuals create their own identities through actions and choices rather than adhering to a predetermined essence. Metaphysically, it elevates personal choice and agency as fundamental to identity.

The theory of personal identity attempts to delineate what makes an individual the same person over time. It discusses the metaphysical significance of how continuity of consciousness and memories, physical body, or psychological characteristics contribute to the persistence of a person's identity.

Bundle theory suggests that an object consists merely of a collection of properties and does not possess a stable underlying existence. Metaphysically, it challenges the notion of a persistent identity of objects, asserting that no self-subsistent substance underlies those properties.

Leibniz's Law, or the Identity of Indiscernibles, states that if two entities share all the same properties, they are identical. In metaphysics, this principle is used to analyze the uniqueness and individuation of objects in the universe.

This principle states that if A is identical to B, and B is identical to C, then A must be identical to C. Metaphysically, it's a fundamental principle of the logic of identity, ensuring consistent identity relations across different scenarios.

This is a thought experiment that tests concepts of identity. It questions whether an object that has had all of its components replaced remains fundamentally the same object. Metaphysically, it highlights the problem of diachronic identity—that which persists over time.