nucleation

CLAIM-038: A communicative object is a context-indexed system of empirical constraints over a cover of contexts, and these need not extend to one globally realizable interpretation

3 min read

Properties16
StatusActive
Version3
Rolethesis
Warrantinterpretive
Tagscontextuality, philosophy-of-language
Linepragmatic-transport
Workswhat-survives-translation
AnswersQUESTION-332 — Is the communicative object a presheaf over contexts?
Rests onCLAIM-042 — The levels at which communicative observables exist organize observables, not objects: a communicative object is identified jointly by constraints from observables at several levels, which, where those observables share one state space, is the intersection of the regions they pick out
GroundsLIT-016 — The sheaf-theoretic structure of non-locality and contextuality, THEORY-012 — An empirical model is Kochen–Specker-noncontextual exactly when its context distributions glue to one global distribution, and since signed global sections always exist for no-signalling models, negative probability does not mark contextuality, THEORY-171 — When the causal constraints on events depend on context, deterministic assignments that are causal in each context can fail to glue into one causal assignment, so causal structure is itself a source of contextuality, LIT-843 — Combining contextuality and causality: a game semantics approach
SupportsCLAIM-105 — In documented reconstruction chains, steps that keep most local judgements commonly change their global compatibility: translation preserves local meanings while changing the global structure of meaning
Argued byARG-010 — Causality paradoxes in relativity show that locally consistent descriptions can lack a global realization, so local interpretations need not be fragments of one global interpretation
ComplementsCLAIM-043 — Equal entropy does not entail equal relational structure, and a collection of local entropies need not characterize global compatibility, CLAIM-131 — A compatible family of sections of the event sheaf always glues, so where a communicative object lacks a global realization the obstruction lies in its supports or distributions, not in the event sheaf
UsesTERM-042 — communicative object, as a context-indexed system of empirical constraints over a cover
Cited as “complements” byCLAIM-247 — The bearer of communicative identity reversed, from an operational object defined on observed responses to a kind that can outrun observation, and no turn argues the change; both stances stand in the record
Rendered intodocs/arguments-by-conclusion.md

Graph View

The claim

A78: “we no longer need to postulate a global semantic object and then ask how translations represent it. We can begin with local observational data and investigate whether a global object exists.” The intersection of regions (CLAIM-042) “presupposes a single ambient state space”; the sheaf approach starts from local sections (TERM-002). “Local interpretations need not be fragments of a single globally realizable interpretation. … It also distinguishes the theory from merely saying that meanings are fuzzy, ambiguous, or context-dependent. The incompatibility is a precise property of the system of local constraints.” The example is CASE-035.

Manuscript §3: “The key ontological shift is that an empirical model can remain well-defined even without a global hidden meaning state.”

Version 2 states the object in TERM-042’s terms. A compatible family of the local sections A78 starts from always glues (CLAIM-131). What need not extend to a global interpretation are the supports or distributions the data impose on those sections.

Where the sources came from

U29: “I think the nucleation record has some useful sheaf contextuality resources we could connect to.” A78: “I couldn’t reopen its live index in this pass, so I verified these papers against their primary publication records rather than claiming to have rechecked every Nucleation annotation.” It named Abramsky and Brandenburger 2011, Abramsky et al. 2015, Abramsky, Barbosa and Mansfield 2017, Dzhafarov and Kujala 2013, and Gogioso and Pinzani 2021. The record held the first (LIT-016, with the gluing criterion read in THEORY-012), the second (LIT-278), the contextual fraction (LIT-265, unread), Abramsky’s cohomology paper (LIT-277), and Ganter and Wille (CLAIM-119). None of these readings was consulted. The manuscript cites Abramsky and Brandenburger only.

What it does not say

That pragmatic judgements are contextual (CLAIM-009). It says the theory does not presuppose that they are not.

A further kind of non-gluing

When causal constraints depend on context, deterministic data that is causal in every context can still fail to glue (THEORY-171; LIT-808, LIT-800). Here the obstruction comes from the structure of the contexts themselves, not from probabilities. That is another way local interpretations need not be fragments of one global one.

Prior art, with a different emphasis

Abramsky and Sadrzadeh 2014 (LIT-841) apply presheaves and gluing to discourse meaning. That is prior art for this claim’s vocabulary. In their account, though, the discourse meaning is the global section, and a failure to glue rejects the reading. It does not leave an object without a global interpretation.

Language data are not compatible families

  • Compatibility. In Wang et al. (LIT-842) the language data are signalling, so they are not compatible families. Version 1’s compatibility premise would have needed Contextuality-by-Default, or a sheaf corrected for signalling. Version 2, in TERM-042’s terms, does not ask the data to agree on overlaps, so signalling data are communicative objects too. Which criterion of global extension then separates contextuality from direct context effects, as the defeat condition requires, is CLAIM-037’s question.
  • More non-gluing. Abramsky, Barbosa and Searle (LIT-843) give a second, independent instance of the non-gluing noted above, from incomparable causal pasts (Example 7.2). They also give an example of a gluing that is not unique (Example 7.3).

Physical support offered and declined

The owner twice offered physics as evidence for this claim: closed timelike curves at U46, and simultaneity at U47. Both were declined (ARG-010, undercut by CLAIM-144 and CLAIM-141). The claim does not need them. Its evidence is LIT-016 and CASE-035.

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