Kripke structurally dismantles the metalinguistic view of identity by isolating the metaphysical relationship an object holds with itself. He critiques the assertion, exemplified by Rosser, that identity is merely a relation between names, deploying the conceptual device of “schmidentity.” This linguistic thought experiment stipulates a relation holding strictly between an object and itself, bypassing human nomenclature entirely. By proposing this hypothetical language construct, Kripke forces a confrontation with the logical inadequacy of reducing identity to human language. He demonstrates that identity statements containing bound variables operate independently of linguistic naming conventions, meaning that “identity should just be taken to be the relation between a thing and itself” (108). This methodological choice establishes the groundwork for his broader philosophical project: decoupling metaphysical truths from the specific quirks of human epistemology, thereby challenging the dominant descriptive theories of reference that blur the line between an object and the word used to describe it.

Building on this foundation, the text delineates a rigid boundary between metaphysical necessity and epistemic possibility through the assertion of origin and substance as essential properties. This discussion crosses between Essence and the Necessity of Origin and Identity Truths as Necessary A Posteriori. Responding to Sprigge’s arguments about essentialism, Kripke notes that while Queen Elizabeth II could have lived a completely different life or lacked royal blood, she could not have originated from different biological parents, such as the Trumans. Though Kripke does not explain the complete idea of “essence,” he uses the example of a unique sperm and egg combination to illustrate the point at which no reasonable person would argue that two people are the same. Similarly, while one might empirically discover the specific material of a wooden table, the proposal of a hypothetical ice duplicate “is not to imagine this table as made of wood or of ice, but rather it is to imagine another table” (114). These examples illustrate that an object’s material and biological origins are necessary truths about these objects, even though they are discovered a posteriori. Discovering what a table is made of remains an empirical process, but once discovered, its material composition operates as a necessary truth. By untangling what is a priori knowable from what is necessarily true, Kripke redefines how philosophy approaches the essence of particulars, rejecting the notion that counterfactual possibility allows for the fundamental alteration of an object’s core substance.

The theory of rigid designation then extends from proper names to natural kind terms, transforming scientific discoveries into necessary metaphysical truths. Kripke contests Kant’s framing of “gold is a yellow metal” as an analytic truth by distinguishing between initial surface marks and internal structure (39). He introduces the concept of a qualitatively identical epistemic situation in which gold looks yellow because of an atmospheric condition but is actually blue. Even if we discovered that gold is actually blue, we would not then assert that “gold” does not exist. Instead, we would change the definition of gold to be “a metal that is blue.” Furthermore, iron pyrites remains a counterfeit despite its visual similarities to gold because it lacks the necessary atomic structure. As such, the atomic structure of gold is a necessary truth and a condition of its identification. Even if gold appeared entirely different to how it appears in the real world, the hypothetical gold, given that it has the atomic number 79, would still be gold. This reasoning reframes natural kind terms as functioning identically to proper names: Their reference is fixed by contingent external effects, but their true essence is discovered empirically through scientific inquiry. Consequently, statements identifying water as H₂O or lightning as electrical discharge function as necessary a posteriori truths. This shift systematically dismantles the cluster concept theory of reference, proving that human definitions do not dictate reality.

This analytical framework culminates in a critique of the mind-body problem, utilizing a theological metaphor to expose logical inconsistencies within standard materialist accounts. Examining the type-type identity claim that pain equals C-fiber stimulation, Kripke argues that God could create molecular motion (heat) without sentient beings to feel it. Though heat was initially fixed as a reference by the sensation of feeling heat, molecular motion exists independently of that sensation. However, God could not create C-fiber stimulation and have it be pain without explicitly making creatures feel the stimulation as pain. Because both pain and C-fiber stimulation are rigid designators, their identity, if true, must be necessary. Yet the asymmetric requirement of conscious experience for pain demonstrates that C-fiber stimulation can exist without pain. Since pain is picked out directly by its immediate phenomenological quality rather than by a contingent intermediary sensation, the apparent contingency of their relationship cannot be explained away. This asymmetry uses the structural logic of rigid designation to challenge a dominant scientific paradigm, forcing a reevaluation of physicalist theories of consciousness by demonstrating that mental states lack the external contingencies of physical phenomena. In other words, pain cannot be only the physical state of C-fiber stimulation, just as the sensation of heat is not synonymous with the movement of molecules, which is actually heat, but is a consequence of the material reality.

Finally, the Addenda reinforce the necessity of the causal-historical chain by examining the ontological void inherent in myth and fiction. Early in Naming and Necessity, Kripke uses his insistence that unicorns cannot possibly exist as a “surprising” argument. In the Addenda, he clarifies that discovering a biological animal that resembles a unicorn does not prove the myth real because the “historical connection that shows that the myth is about these animals” is fundamentally absent (157). Unicorns are, by definition, mythological, so the rigid designator “unicorn” can only refer to a non-existent creature. Furthermore, reference shifts, such as “Madagascar” transforming from a region to an island, demonstrate how communal intention can occasionally override historical transmission. These clarifications emphasize that successful reference requires an unbroken historical tether to reality. Without a concrete initial baptism, a descriptive cluster remains fundamentally empty, incapable of picking out a unique species or individual across counterfactual realities.