Philosophy of Identity: Essential and Accidental Properties

Endurantism holds that objects are three-dimensional entities that exist wholly at each moment of their existence. Perdurantism holds that objects are four-dimensional entities that exist as extended through time, with different temporal parts at different times. These are the two main competing theories about how objects persist through time. Perdurantism resolves the problem of persistence by treating objects as four-dimensional 'space-time worms' composed of temporal parts. When we say 'this car is blue,' we are referring to a temporal part of the car. When the car changes color, it's not the same object changing properties but rather different temporal parts having different properties. Endurantism resolves the problem by treating properties as temporally indexed—'the car is blue on Tuesday' and 'the car is red on Wednesday' are different properties, so there is no contradiction.

Temporal parts are philosophical concepts that address how objects maintain identity while changing over time; perdurantism holds that objects have temporal parts like spatial parts, making them four-dimensional entities where each moment is a distinct part, while endurantism claims objects are wholly present at each moment without temporal parts, instead explaining change through relational properties to time.

This section covers the fundamental debate about how objects persist through time. Lewis argues that if objects change intrinsic properties like form over time, these properties must be relations between objects and moments, not intrinsic properties. This contradicts our intuition that properties like form are intrinsic. There are three solutions: (1) attach 'at a certain moment' to the subject (perdurantism), (2) attach it to the property (properties are relative to moments), or (3) attach it to the copula (the act of possessing properties occurs at moments). The Bradley regress threatens the copula solution. The debate reflects a deeper methodological tension: descriptive adequacy versus explanatory economy. The stage view is a third option: unlike endurantism (objects persist without temporal parts) and perdurantism (objects are collections of temporal parts), the stage view holds that only temporal stages exist—no persisting objects. Ordinary names like 'Julie' refer to temporal stages at particular times, not to extended objects.

Two main positions exist regarding how the self exists through time: Endurantism holds that the self exists as each moment of its history, like a block of marble that goes through a river. Perdurantism views the self as a 4-dimensional entity made up of a series of spatial and temporal parts, like frames in a movie. The Ship of Theseus paradox illustrates identity over time - if you keep changing parts of a ship, at what point does it cease to be the same ship?

Endurantism holds that objects are three-dimensional entities that exist wholly at each moment, while perdurantism views objects as four-dimensional 'worms' consisting of temporal parts. A central challenge for endurantism is explaining how objects can have different intrinsic properties at different times (e.g., a mug being empty at one time and full at another). Lewis argues that endurantism faces two unsatisfactory solutions: reinterpreting properties as relations to times, or denying that objects have properties at past or future times. Lewis finds both solutions implausible and concludes that endurantism is 'hopeless' when confronted with the problem of temporary intrinsics. Lewis's critique reveals a fundamental disagreement about how to conceptualize time: Lewis asks endurantists to describe objects from a perspective outside of time, treating time as a four-dimensional block, while endurantists reject this approach because they take tense seriously.

Mereology is the study of parts and wholes in metaphysics. The central question is whether composite objects (objects with parts) actually exist, or if there are only simple substances without parts. Using a red pin as an example, we naturally perceive it as having metal, ink, and plastic parts, but the philosophical challenge is whether these parts exist in addition to the whole pin. If there are n simple parts, does that mean n+1 objects exist, or are there only n simple units? This seemingly abstract topic connects to fundamental issues in philosophy of mind, mathematics, and geometry.

Mereology studies how parts relate to wholes. Classical mereology accepts transitivity of parthood, unrestricted composition (any collection has a fusion), and uniqueness of composition. This leads to counterintuitive 'monstrous objects.' Neo-Aristotelian mereologists reject unrestricted composition, requiring unifying principles or forms for composition to occur. This debate reflects broader tensions between liberal and conservative approaches to metaphysical ontology.

All things are made up of smaller pieces: a zebra consists of head, tail, legs, and cells, which are made of nuclei, DNA, nucleotides, molecules, and atoms. Mereology studies how parts compose wholes. Reductionism seeks the smallest fundamental parts. Democritus proposed 'atoma' as indivisible particles, while Indian Buddhist traditions held atoms were pointlike and temporary. Grub argues quantum physics supports this view. The scientific atom, discovered in the early 19th century, was named for being fundamental but was later found to be composite. Grub distinguishes philosopher's atoms from scientist's atoms by calling indivisible quantum particles 'quantum abstract atoms.'

Merology is the philosophical theory studying the part-whole relationship. Merology Minimal establishes that the part relation is a partial order (reflexive, transitive, antisymmetric), but this is insufficient to characterize the part relation. To extend Merology Minimal, we add principles of composition (specifying when objects form wholes) or decomposition (specifying how wholes decompose). A merological sum is an aggregate of summands. There are two approaches to defining sum: taking composition as primitive (Fine's approach) or taking part as primitive (classical approach). Three classical sum definitions exist: Sum 1 (overlap condition), Sum 2 (containment and intersection condition), and Sum 3 (least upper bound condition). These definitions are not equivalent in general, as shown by counterexamples in mereological models.

This segment explores Abhidharma philosophy's sophisticated metaphysical analysis. The doctrine of two truths (conventional and ultimate) addresses apparent contradictions in Buddhist teachings. The lecture transitions to mereology (the study of parts and wholes), examining how multiple parts compose unified objects. Three positions exist: nihilism (no composition), moderate views, and universalism (always composition). Abhidharma holds ultimate reality consists of dharmas (dharma atoms) - mereological and temporal atoms that are not substances but properties. This atomistic view rejects the substance-attribute model. The segment concludes with Madhyamaka's critique: while accepting conventional analysis, Madhyamaka rejects Abhidharma's ultimate metaphysics, arguing dharmas lack inherent nature.

Philosopher Saul Kripke argued that our actual origin is the only possible origin. He divided origin into Alpha (our actual sperm and egg) and Beta (a hypothetical third party's sperm and egg). If we had been created from Beta, we would have a different origin. However, since a single person cannot exist in two different places simultaneously as two different individuals, it is impossible for us to have been created from Beta. Therefore, our actual origin is the only possible origin, making it a unique and essential characteristic.

There is a convergence between Kripke and Putnam's essentialist ideas and modern scientific strategies. Both involve abandoning superficial identification patterns (based on qualitative similarity) in favor of hidden structures that causally explain superficial properties. This pattern occurs not only in chemistry (where water is identified by molecular structure rather than superficial properties) but also in biology, where species concepts shift from morphological to relational approaches. The biological species concept, despite being anti-essentialist, can be shown to align with essentialist ideas by distinguishing between essential and accidental properties.

De dicto modality concerns necessity or contingency of propositions as wholes, while de re modality concerns necessity or contingency of properties of particular objects. Quine famously attacked de re modality as 'spooky Aristotelian essentialism,' arguing that ascribing necessity to objects rather than descriptions makes no sense. Kripke defends de re modality as legitimate metaphysics, arguing that things do have essential properties independent of how we describe them. This represents a return to metaphysics after the linguistic turn in philosophy, challenging the view that all modality is merely linguistic.

Kripke distinguishes necessity (metaphysics), analyticity (philosophy of language), and a prioricity (epistemology)—previously conflated. This opens room for a posteriori necessities (discoverable empirically) and synthetic necessities. Essential properties are those an object cannot lack without ceasing to be itself. The essentiality of origins suggests objects' origins are essential to their identity—a lectern made of wood couldn't have been made of ice. Kripke attacks the descriptional theory of names (Frege/Russell): (1) Descriptions might be mistaken—if Gödel stole Schmidt's theorem, calling him 'Gödel' is still true, (2) We often don't know enough about individuals for definite descriptions. Names fix reference through causal-historical chains, then take independent semantic lives. Unlike heat/mean molecular motion, pain cannot be identified with brain states because pain is picked out by an essential property (feeling pain)—you cannot separate pain from its experience. By 1970, analytic philosophy died because Kripke showed you cannot start with philosophy of language when investigating mind-world-language connections. Instead, people began with ontology and epistemology, focusing on phenomena themselves rather than terms describing them.

The concept of necessity has been central to philosophy since its origins, but was largely abandoned from Hume to the mid-20th century. Hume's empiricism challenged the idea of necessary connections between cause and effect, arguing that we only observe associations, not necessary connections. This skepticism extended to modal concepts generally. Kripke's work helped recover the importance of modal concepts by showing that there are multiple distinct types of necessity: logical necessity (incompatible with logical laws), epistemic necessity (incompatible with what we know), natural necessity (incompatible with natural laws), and metaphysical necessity (incompatible with the nature of things). This distinction allowed philosophers to recognize that different modal concepts serve different philosophical purposes. The distinction between necessary and contingent truths concerns the way things are in reality. A necessary truth is one that could not have been otherwise—it is true in all possible worlds. A contingent truth is one that could have been otherwise—it is true in the actual world but might have been false. This distinction is metaphysical, concerning the nature of reality itself, rather than epistemic (concerning our knowledge). Kripke argued that the traditional association between necessity and a priori knowledge, and contingency and a posteriori knowledge, is mistaken. He provided examples of necessary truths known a posteriori: (1) Identity statements like 'Hesperus is Phosphorus' (the evening star is the morning star), which are astronomical discoveries but express necessary identities. (2) Statements about the composition of substances, like 'water is H2O', which are empirical discoveries but express necessary truths about what water essentially is. He also provided examples of contingent truths known a priori: the definition of the meter as the length of a particular platinum bar in Paris. This is a contingent truth (the bar could have been a different length) but is known a priori (we don't need to measure the bar to know it's one meter long, since that's how we defined it). These examples show that necessity and contingency are independent of how we come to know truths. Kripke's 'Naming and Necessity' addresses fundamental questions about how names refer to objects. The descriptivist theory, associated with Frege and Russell, holds that the meaning of a name is given by a description or set of descriptions that the name satisfies. For example, 'Aristotle' might mean 'the philosopher who founded the Lyceum and was a student of Plato.' This theory explains how we can communicate about historical figures we've never met. However, Kripke argued this theory is inadequate because it cannot explain why certain descriptions are essential to a name's reference while others are merely accidental. His alternative was the theory of rigid designation: proper names refer to the same object in all possible worlds where that object exists, while definite descriptions are non-rigid designators that can refer to different objects in different possible worlds. Kripke's modal argument against descriptivism shows that if names meant descriptions, then statements about names would have modal implications that don't hold. For example, if 'Aristotle' meant 'the teacher of Alexander the Great,' then the statement 'Aristotle could have been someone other than the teacher of Alexander' would be contradictory. But this seems clearly true—we can easily imagine a world where Aristotle was not Alexander's teacher. Essentialism is the view that objects have essential properties (properties they must have to be what they are) and accidental properties (properties they happen to have but could lack). Essential properties are those that an object has in all possible worlds where it exists. This distinction was central to Aristotelian metaphysics but was largely abandoned in modern philosophy until Kripke's revival of essentialism. Kripke defended several essentialist theses: (1) The essentiality of origin: each person's origin (the specific sperm and egg from which they came) is essential to their identity—they could not have come from different parents. (2) The essentiality of material constitution: objects cannot be constituted by different matter and still be the same object. Following Frege and Russell, Kripke argued that existence is not a first-order property (a property that objects have) but a second-order property (a property of properties). When we say 'unicorns don't exist,' we are not saying that unicorns lack the property of existence; rather, we are saying that the property of being a unicorn is not exemplified by anything. This view treats existence as a logical operator (like a quantifier) rather than a predicate. Kripke argued that existence is a universal property (all existing things have it) but not a trivial one, because some things exist contingently while others exist necessarily.