Argument from Vagueness

Overview and Background

The Argument from Vagueness is a prominent argument in metaphysics, especially in debates about composition and the existence of ordinary objects. It is most closely associated with Ted Sider, who offers a detailed and influential version in his book Four-Dimensionalism (2001), though it draws on earlier ideas from David Lewis and others.

At its core, the argument attempts to show that commonsense ontology—which holds that there are ordinary objects like tables, chairs, mountains, and organisms with somewhat blurry boundaries—is unstable. According to the argument, if such objects existed as we ordinarily think, there would have to be vague facts about which things exist or about which collections of physical simples (indivisible, fundamental entities) compose a further object. But, the argument continues, there cannot be vague facts about existence or composition. Therefore, the commonsense picture of the world must be revised.

Proponents use this reasoning to motivate more radical ontologies, such as:

• Mereological nihilism: only simples exist; there are no composite objects.
• Mereological universalism: any collection of simples, no matter how scattered, composes a further object.

The argument has become a central point of reference in contemporary metaphysics and in the philosophy of vagueness.

Formal Structure of the Argument

Sider’s formulation aims to be formally rigorous. The main ideas can be captured as follows.

1. Setup: Vagueness and borderline cases

   Ordinary objects seem to have indeterminate boundaries. For example, consider slowly removing atoms from a table. At some point, we may reach a borderline case where it seems unclear whether there is still a table. Similarly, for any given region of space filled with particles, there may be a borderline case regarding whether those particles compose a table at all.

   This suggests:

   • There are borderline cases of composition: cases where it is vague whether some simples compose an object of a certain sort.

2. Premise: No metaphysical vagueness in existence

   The argument then asserts a key metaphysical thesis: facts about what exists cannot themselves be vague. While our language or knowledge may be vague, reality itself, at the level of what entities exist, is taken to be precise. On this view, there is no “in-between” state of an object’s existing and not existing.

   This leads to the claim that:

   • It cannot be an objective matter of metaphysical indeterminacy whether a certain object exists.

3. From precise existence to precise composition

   If existence is precise, then the relation “these simples compose that object” must also be precise. Either a given set of simples composes a further object, or it does not; there cannot be borderline cases in the composition relation itself.

   Combining this with the intuitive idea that there are borderline cases for everyday objects yields a tension:

   • Ordinary intuitions seem to demand vague composition.
   • The metaphysical principle disallows vague composition.

4. The squeeze: Rejecting the standard view of ordinary objects

   From this tension, the Argument from Vagueness concludes that the commonsense view—according to which there are many ordinary objects with fuzzy boundaries—cannot be maintained without postulating metaphysical vagueness in existence or composition.

   Since such metaphysical vagueness is taken to be impossible or deeply problematic, the argument pushes us toward more radical, but metaphysically sharp, views:

   • Nihilism: Only simples exist. No composite objects, such as tables, are part of fundamental reality.
   • Universalism: Any collection of simples—no matter how arbitrarily chosen—composes a larger object.

These alternatives avoid vague composition by making the rules of composition fully general and precise: in nihilism, composition never occurs; in universalism, it always does (given non-overlapping simples).

Philosophical Significance

The Argument from Vagueness is important for several reasons:

1. Metaphysics of Ordinary Objects

   It places significant pressure on commonsense realism about medium-sized dry goods (tables, chairs, people). Rather than simply asking whether such objects exist, the argument probes whether they can exist without introducing an unacceptable kind of vagueness.

2. Vagueness and Ontology

   Traditionally, discussions of vagueness focus on language (“bald,” “heap,” “tall,” etc.) and the sorites paradox. The Argument from Vagueness shifts the focus to ontological vagueness: indeterminacy in what there is, not just in how we talk. It thereby connects debates in the philosophy of language and logic with core metaphysical questions.

3. Methodological Lesson

   The argument exemplifies a methodology in metaphysics that reasons from structural constraints (e.g., “existence cannot be vague”) to conclusions about what the world must be like. It is often cited as a model of systematic, argument-driven metaphysics.

4. Motivation for Extremal Views

   Many find nihilism or universalism counterintuitive or revisionary. The Argument from Vagueness gives these positions a theoretical motivation beyond mere simplicity or elegance: they avoid a particular kind of vagueness that is argued to be untenable.

Criticisms and Responses

The Argument from Vagueness is widely discussed and highly contested. Critiques target almost every stage of the reasoning.

1. Challenging the ban on metaphysical vagueness

   One main line of response is to reject the premise that existence and composition cannot be vague. Some philosophers defend the possibility of ontic or metaphysical vagueness: reality itself may be indeterminate in certain respects. On this view, just as there can be borderline cases for predicates, there can be borderline objects whose existence is itself vague.

   Defenders of metaphysical vagueness argue that:

   • The idea of a world where some objects are “borderline existent” is no more incoherent than the idea of borderline bald people.
   • Formal tools (e.g., many-valued logics, supervaluationism) can be adapted to model ontic as well as linguistic indeterminacy.

   Proponents of the Argument from Vagueness often reply that such ontic vagueness conflicts with classical logic, obscures identity conditions, or undermines the clarity of metaphysical theorizing.

2. Reinterpreting vagueness as semantic or epistemic

   Another response insists that all vagueness is semantic (in our language) or epistemic (in our knowledge), not ontological. On this view, while it may be vague for us whether certain particles compose a table, there is in fact a precise truth of the matter that we simply do not or cannot know.

   From this perspective, one might:

   • Deny that there are any true borderline cases of composition at the metaphysical level.
   • Maintain that apparent vagueness in object boundaries is due solely to the indeterminacy of our concepts or our limited information.

   Proponents of the original argument tend to accept semantic vagueness but insist that the commonsense picture of ordinary objects as we understand it presupposes more than merely semantic indeterminacy.

3. Targeting the move to nihilism or universalism

   Some critics accept that composition cannot be vague but reject the conclusion that only nihilism or universalism remain. They seek intermediate, precise principles of composition—rules that determine exactly when simples compose objects without being vague, yet do not collapse into “never” or “always.”

   Examples might include:

   • Principles based on causal integration, spatiotemporal cohesion, or functional organization that are claimed to be sharp, even if difficult to state.
   • Highly detailed microphysical or structural conditions that allegedly avoid vagueness.

   Proponents of the Argument from Vagueness often respond that such intermediate principles, on scrutiny, either reintroduce vague cases or become indistinguishable from universalism in practice.

4. Questioning the link between sorites and composition

   Finally, some philosophers question whether the sorites-style reasoning about adding or subtracting particles actually shows that composition is vague, rather than showing, for example, that our ordinary terms (“table,” “person”) are vague. They argue that the Argument from Vagueness illegitimately transfers linguistic or conceptual indeterminacy into the domain of composition.

Debate over the Argument from Vagueness remains active. It is widely regarded as a central case study in how considerations about vagueness can have far‑reaching implications for what exists, illustrating deep connections between metaphysics, logic, and the philosophy of language.