Roderick Chisholm asked a question in 1967 about Adam and Noah (Chisholm 1967). Adam lived 930 years, Noah 950. Surely Adam could have lived a year longer, and Noah a year less: nothing in either man's essence hangs on a single year. Grant the concession once and a world opens in which Adam lives 931 and Noah 949. Grant it again from there, and again, and the two lifespans trade places entirely — a world in which the man who lives 950 years is Adam and the man who lives 930 is Noah, which is to say a world in which each is the other. Every step was innocent. The destination is not. Chisholm's Paradox is the ancestor of every later argument that possibility is *chained*: that what is possible depends on where the question is asked from, and that iterating small admissible variations carries one somewhere no single leap could have reached.

Hugh Chandler (1976) ran the structure on artifacts rather than patriarchs, and aimed it at exactly the machinery this book uses — his paper is titled "Plantinga and the Contingently Possible," and the modal apparatus of Plantinga (1974b) turns on the same transfer principle the present argument turns on. A bicycle assembled from a given set of parts could have been assembled with one part swapped; from *that* world, another swap is admissible; and the chain terminates in an assembly too distant from the original to have been possible for the original bicycle. Nathan Salmon developed the sharpest version on Kripke's table: the table made from a given hunk of wood H could have been made from the slightly different hunk H′, and a table made from H′ could have been made from H″ — which was not possible for the original table (N. Salmon 1981, 1989; the example descends from Kripke 1980). Salmon then drew the conclusion the others resisted. Metaphysical accessibility — the relation a world bears to those worlds that count as possible *relative to it* — is not transitive; so S4, the axiom licensing the collapse of a two-step modal chain into a single step, fails for the metaphysical operator, and the S5 transfer fails with it. Graeme Forbes answered by keeping the logic and locating the trouble in vagueness, first through degree-theoretic treatments and then through counterpart-theoretic ones (Forbes 1984, 1985). Lewis answered through the inconstancy of counterpart relations: on counterpart theory, no individual literally exists in more than one world, and its modal properties are read off the individuals elsewhere that most resemble it — and which resemblance relation is in play shifts with context (Lewis 1968, 1986). Timothy Williamson supplies the epistemicist option, on which such a series has a sharp cutoff that is unknowable rather than absent (Williamson 1994). Behind all of them stands Kripke's origin essentialism, the thesis that a thing could not have come from a wholly different origin and still be that thing (Kripke 1980). The dispute is sixty years old and has produced no settled verdict.

Brought to bear on the present argument, the objection targets the logic directly rather than the ontology, which makes it more dangerous than most of this section's entries. Necessary Possibility is established at [§2.1.10](<2.1.10 Necessary Possibility.md>): whatever is possible, its possibility is necessary (◇P → □◇P), with the bilateral companion that whatever is impossible, its impossibility is necessary (¬◇P → □¬◇P). It is packaged into S5 at [§2.1.4](<2.1.4 Modal Stability.md>); the move from the actuality of change to its necessary possibility at [§2.3](<2.3 Necessary Possibility of Change.md>) runs on it, and so does the Modal Identity of [§2.6.6](<2.6.6 Modal Identity.md>). If possibility is chained, the transfer is unsound, and no amount of care about T, S, and Φ — Temporality, Spatiality, and Physicality, the three structural Conditions — repairs it. The objector here concedes the framework, concedes possible-worlds semantics, concedes origin essentialism, and produces cases. That is the hardest kind of objection to answer, because there is nothing exotic to reject.

A clarification before the moves, and a distinction the replies turn on. The argument's ◇ 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](<2.1 The S5 Pipeline.md>)). And two readings of any modal claim about a particular thing have to be kept apart. A *de dicto* claim is about a proposition — "it is possible that some table was made from different wood." A *de re* claim is about a thing — "this table is such that it possibly was made from different wood." The first says something about what the range of possibilities contains; the second says something about what a particular object could have survived. Three forms of the objection press at three different resolutions: the chained-origin move as Chisholm and Chandler state it, Salmon's principled rejection of transitivity, and the counterpart-theoretic inconstancy version. Each reply below diagnoses the cases rather than denying them, which is the more demanding standard: the intuitions driving the series are genuine, and an account that merely contradicted them would have explained nothing.

*First.* The chained-origin move holds that the series of small variations is individually innocent and jointly unacceptable, so possibility must be relative to a starting point. Each link is possible relative to its predecessor; the endpoint is not possible relative to the origin; therefore what is possible varies with where the question is asked.

The reply begins by separating the two readings, because on one of them there is no case at all. Read *de dicto*, "a table made from slightly different wood" is among the least exotic possibilities ever entertained in philosophy: furniture workshops witness it by the thousand daily. Every such table is already among the ways Reality permits, and no act of carpentry puts it there — the carpenter never once consults the accessibility relation. The cases become cases only on the *de re* reading: could *this very table* have originated in H″ and still be *it*? That is a question about how much origin-swapping identity tolerates. It is a substantive and interesting question. It is not a question the transfer principle was ever answering, because the transfer ranges over the modal status of propositions and not over the persistence of a token individual across worlds. The distinction is the same one [§4.4.1](<4.4.1 Modal Realism.md>) draws against counterpart theory, running in the other direction: what the argument needs across worlds is instantiation of a structural role, never a numerically identical token recurring, and the chained-origin cases press exclusively on tokens.

*Second.* Salmon's version blocks that reply by refusing the relabeling. His ◇, he insists, is the metaphysician's own unrelativized operator and not a disguised accessibility relation; the cases show that operator to be non-transitive, and calling the variation "accessibility" redescribes the problem rather than answering it.

The reply takes the global question directly. Ask of the far link: is a table made from H″ among the ways Reality permits, or not? The question admits one answer. If yes, it was in W all along, and what varied along the chain was never membership but tolerable distance from a shifting anchor — a fact about the essentialist premise, not about the logic. If no, then no sequence of intermediate worlds puts it there, since traversing intermediates is not a way of enlarging the range. Either way, nothing has entered or left the domain.

The chain also cannot travel without paying. To move from H to H′ to H″, the argument must concede at every link that the intermediate origin is possible; that concession is what licenses the step. But a conceded possibility, run through the transfer, is a necessary possibility: each step certifies its own destination as a permanent member of the domain. Meanwhile no step removes anything, because unreachability is not eviction — that an origin cannot be reached from a given anchor is silent on whether it is in the range at all. So the chain deposits members and withdraws none. Pursued to its end, the argument has populated the global domain it set out to fragment, and the only thing still varying at the far link is the *de re* label: which of those necessarily possible tables counts as *this* one.

One further pressure, the difference-maker point of [§2.1.5](<2.1.5 The S5 Bottleneck.md>). If "possible at one world, impossible at another" states a fact about a single unrelativized operator, then something must make the difference between the two worlds. That something would have to concern what possibility itself answers to, and a fact of that kind is arrangement-independent and structural — which is precisely the cross-world stability the objection was contesting. The variation hypothesis consumes the resource it needs.

The candor the rest of this chapter keeps is owed here too. Salmon can plant on the disputed point and hold that the unrelativized operator simply is non-transitive, taking the cases as primitive data about it rather than as evidence to be diagnosed. Against a philosopher who does that, none of the above is a formal refutation, because its load-bearing premise is the fixed-domain reading he declines. What the reply secures is narrower and still worth having: the objection cannot be run without conceding, link by link, the very possibilities whose global standing is at issue, and the position it defends turns out to be a position about a relation between worlds rather than about the range those worlds jointly compose.

*Third.* The counterpart-theoretic version drops non-transitivity in favor of inconstancy. On Lewis's treatment, a *de re* modal claim about the table is made true by what happens to the table's counterparts — the objects in other worlds that resemble it most in whatever respects the conversation is weighting. Weight origin heavily and the H″-table is no counterpart of this table; weight function or appearance instead and it is. So "possibly made from H″" comes out true in one conversation and false in another, and any transfer principle stated over such claims inherits the instability.

The reply is that inconstancy of this kind is variation in representation, not variation in the domain. What shifts with context is which similarity respects a *de re* predication tracks — a fact about the semantics of counterpart talk. Nothing shifts in which worlds are among the ways Reality permits, and the whole plurality remains available to every context that draws on it. The inconstancy defense is also an awkward ally for the objector, since it concedes that the chained-origin data are produced by a context-sensitive representational device rather than discovered in the logic of possibility. A phenomenon that varies with conversational salience is not the sort of thing a modal axiom is answerable to.

A kindred move presses the vagueness directly rather than through counterpart semantics, and it is the most honest form of the objection. Each origin-swap is tolerable, the endpoints are not, and no step is the step at which identity lapses. That is a sorites — a chain of individually harmless steps whose endpoints differ in a way no single step seems to introduce, as in the grain-by-grain removal that turns a heap into a non-heap — run on essence rather than on heaps. Forbes proposes degrees of counterpart-hood; supervaluationism proposes that the claim be assessed on every admissible way of sharpening the vague predicate; Williamson's epistemicism proposes a sharp cutoff that no one is in a position to locate. The present account takes no stand among the three, and does not need to: sorites series do not show that the predicates involved are world-relative. They show that the predicates are *tolerant* — that they survive small changes in their subject matter. Treating tolerance as evidence against a modal transfer principle mislocates the finding, though it is an interesting mislocation, and one worth the sixty years it has occupied. What the counterexamples establish is that *de re* origin essentialism gradates. Reading them as a refutation of the transfer requires one additional step: letting ◇ mean "reachable from the world of evaluation." That is a legitimate operator with a genuinely non-S5 logic, and it is not the operator in which the conclusions of metaphysics are stated. When Salmon writes that the far origin was not possible for the table *originally*, that adverb is carrying the argument, and it is a word about starting points.

The status reading that makes this diagnosis available is fixed at [§1.2.6](<1.2.6 Statuses Together.md>) and [§2.1.7](<2.1.7 Two Readings.md>): the claim is not that a necessity operator scopes over a possibility operator by climbing an accessibility relation, but that whatever is possible has its possibility as a settled status. The Bottleneck at [§2.1.5](<2.1.5 The S5 Bottleneck.md>) marks the single point at which a rival can disagree. Lewis's concrete plurality, whose counterpart theory supplies the third move's machinery, is [§4.4.1](<4.4.1 Modal Realism.md>). Williamson's necessitism is [§4.4.6](<4.4.6 Necessitism.md>). Sider's structuralism is [§4.4.7](<4.4.7 Sider's Structuralism.md>). The modal-collapse worry is [§4.4.9](<4.4.9 Modal Collapse Objection.md>). Gasking's parody, which tests the argument's form rather than its logic, is [§4.4.10](<4.4.10 Gasking's Parody of the Ontological Argument.md>).

*What converges.* Each of the three forms turns on a relation between worlds rather than on the range the worlds compose. The chained-origin move is a case only on the *de re* reading, and the transfer never ranged over token identity. Salmon's principled version asks a global question that admits one answer either way, and cannot advance its chain without certifying, at every link, a permanent member of the domain it means to fragment. The counterpart-theoretic version relocates the variation into context-sensitive representation, where it is no longer the sort of fact a modal axiom answers to. Underneath all three is a sorites on essence, and tolerance is not world-relativity.

Chisholm's Adam and Noah do not trade places. What the series shows is that "same man" bears a great deal of counterfactual stretching without anyone being able to say where it snaps, which is a fact about the elasticity of identity under supposition and not a discovery about the range of ways Reality permits. The lifespans were always in that range. The question the chain makes vivid is only ever which of them we are still entitled to call Adam's.


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← [4.4.10 Gasking's Parody of the Ontological Argument](<4.4.10 Gasking's Parody of the Ontological Argument.md>) | [4.5 What the Rivals Carried](<4.5 What the Rivals Carried.md>) →
