This cluster questions the modal machinery the argument rides on: necessity, possibility, and possible worlds. If the semantics of possibility differed, the canonical lift might not follow. The reply begins with a distinction. The argument's operator ◇ means *real possibility*: membership in one fixed global domain W, the complete range of ways Reality permits (§[§1.2.1](<1.2.1 Possibility.md>), 2.1). A theory may instead model local reachability, epistemic openness, or world-relative accessibility. Those are legitimate relative modalities, but variation in them does not by itself vary membership in W. The engagements below ask whether a rival has offered a different account of real possibility or only a different relation inside or alongside the same global domain.

The objections of [§4.3](<4.3 Physics and Mind.md>) press whether the present account leaves something out: experience, intrinsic nature, mathematical applicability, mind itself. The objections of this section press the modal apparatus the argument runs on. If the modal logic is wrong (if necessity, possibility, and counterfactual reasoning do not behave as the argument assumes) then □(T∧S∧Φ) does not follow even if T, S, and Φ (Temporality, Spatiality, and Physicality, the three structural Conditions the book's argument derives, borne by Time, Space, and Substance) are exhaustive.

The space of moves is well-charted. Lewis (1986) develops concrete modal realism, on which possible worlds are concrete entities of the same kind as the actual world; the actual world is just the world we inhabit. Williamson (2013) develops necessitism, on which everything that exists exists necessarily and the only contingency is qualitative rather than ontological. Counterpart theory (Lewis 1968) replaces transworld identity with similarity relations and changes what "the same necessary being" can mean across worlds. The Barcan formulae (named for Ruth Barcan Marcus's 1946 derivations linking quantifiers and modal operators) press whether quantification and modality commute, with consequences for whether necessary existents must exist in every possible world. Stalnaker (1976) presses the moderate realist line, on which possible worlds are abstract maximal properties or ways the world could have been. Kripke (1980) gives the standard picture against which the alternatives press their cases. Plantinga (1974b) develops a robust modal realism for theological purposes. The literature is dense, technical, and inconclusive on most of the central questions.

The argument's strategy across the section is to distinguish three questions that modal theories often run together: the global domain of real possibility, the semantics used to represent it, and the ontology assigned to worlds or domains. The canonical proof depends on the first, not on Lewisian concreteness, transworld identity, Barcan formulae, or a particular local accessibility relation. Structural roles enter only where a candidate world or ground is offered as a realizer of genuine change. A thin abstract representation need not instantiate temporal succession, spatial extension, or causal persistence; a theory that offers it as physical reality, a ground of experience, or a complete change-realizer inherits the richer burden. The sections below therefore test each framework at the resolution it claims.


- [4.4.1 Modal Realism](<4.4.1 Modal Realism.md>)
- [4.4.2 Linguistic Ersatzism](<4.4.2 Linguistic Ersatzism.md>)
- [4.4.3 Combinatorialism](<4.4.3 Combinatorialism.md>)
- [4.4.4 Modal Fictionalism](<4.4.4 Modal Fictionalism.md>)
- [4.4.5 Modal Expressivism](<4.4.5 Modal Expressivism.md>)
- [4.4.6 Necessitism](<4.4.6 Necessitism.md>)
- [4.4.7 Sider's Structuralism](<4.4.7 Sider's Structuralism.md>)
- [4.4.8 Whiteheadian Process Metaphysics](<4.4.8 Whiteheadian Process Metaphysics.md>)
- [4.4.9 Modal Collapse Objection](<4.4.9 Modal Collapse Objection.md>)
- [4.4.10 Gasking's Parody of the Ontological Argument](<4.4.10 Gasking's Parody of the Ontological Argument.md>)
- [4.4.11 Chisholm’s Paradox: Chained Origins](<4.4.11 Chisholm’s Paradox Chained Origins.md>)


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← [4.3.12 Haecceitism](<4.3.12 Haecceitism.md>) | [4.4.1 Modal Realism](<4.4.1 Modal Realism.md>) →
