FINITE MIND, FINITE GOD · TERMS AND NOTATION

Finite Mind, Finite God: Terms and Notation

The vocabulary of finite knowing, revelation, fairness, ultimacy, and institutional authority, together with the logic and notation used to examine it.

Matthew Tripp Zejda

I use these terms to follow a claim from the mind that receives it to the meaning and authority it is asked to carry. A revelation has a route of transmission. A requirement has conditions of access and capacity. A statement about ultimacy has to retain a coherent target.

This reference gives definitions and explanatory summaries. The source locators identify the book’s relevant passages; the argument links lead to the fuller explanations. Established logical vocabulary is distinguished from the specialized meanings I give terms within Finite Mind, Finite God.

Find a term Find notation Sources and reading

All definitions remain visible. Use Find in page, open either lookup panel, or browse the seven groups. Entry titles link directly to their definitions. A formula wider than the screen can be scrolled horizontally; focus its panel and use the arrow keys when needed.

Browse terms and aliases A–Z

Browse symbols and their source meanings

𝓘_A, T_A, ↝_A, ⊢_A
FMFG token-states, update, and local inference

δ and φ
Public doctrinal claim and propositional content

𝓕_(e,δ), h ∘ k ∘ d ∘ s ∘ ℓ ∘ c
Six-stage revelation filter; composition reads right to left

τ: 𝓛 → 𝓐
Chapter 5: lived experience to transmissible artifacts

τ: L → A
Appendix: public language to an anchor domain

F(R_i) and ⋂
Shared functions across the declared religious systems

P: personhood family
Personal agency predicates, not Chapter 9 inclusion

x ≻_B y
A subject’s strict preference among alternatives

E and B = E
Chapter 7 totality and the identity condition

L(x), B ≠ E
Limitation as nonidentity with totality

P: 𝓐 → {0,1}
Chapter 9 agent-inclusion predicate

σ(a), d: Σ* → {0,1}
Public records and a decision procedure

m: Σ* → M
Proxy metric and its output space

κ ∈ Σ*
A compliance marker within the record language

J_0 … J_n
An authority sequence ending at a nonappealable source

(R,S,E)
Rewards, sanctions, and enforcement; E is not totality here

∀
Universal quantification over the declared domain

∃
Existential quantification over the declared domain

¬
Classical negation

∧
Conjunction

∨
Inclusive disjunction

→
Material conditional, distinguished from a map arrow

↔
Biconditional

□
Necessity under the declared modal semantics

◇
Possibility under the declared modal semantics

⊨
Semantic consequence

⊢
Formal derivability; distinguish the indexed local relation

⊥
Contradiction in a proof system

∈, ∉
Set membership and nonmembership

∅
Empty set, not absolute nonbeing or the empty string

⊆
Subset inclusion, allowing equality

{x ∈ A | φ(x)}
Set-builder notation within a stated domain

⟨a,b⟩ and (a,b)
Ordered pair notation

f: A → B
Function, domain, and codomain

f[A]
Range or image of the function on A

Σ
Alphabet

ε
Empty string

Σ*
All finite strings over the alphabet

Revelation, filtering, and interpretation

I begin with the finite interface in which a claim becomes available, then follow the transmission and interpretation through which it acquires public authority.

64Epistemic interface

FMFG term or specialized use

Lookup: I_A · 𝓘_A · T_A · ↝_A · ⊢_A · Token-states · Interface structure

An agent’s organized access to content: the token-states it can host, the ways those states can update, and the inferential relations through which it evaluates them. In Chapter 2 I write

\mathcal I_A:=(T_A,\leadsto_A,\vdash_A).

Here $T_A$ is a nonempty set of token-states, $\leadsto_A$ is an update relation, and $\vdash_A$ is the agent’s local inferential relation. A report, memory, doubt, or interpretation has to become available within that structure to matter to the agent. The tuple specifies an epistemic role, not a particular physical implementation. Its local inference relation is not, merely by being written with a turnstile, a guarantee of correct reasoning.

FMFG, Definition 2.1, p. 26.Human Interface Thesis

65Public doctrinal claim

FMFG term or specialized use

Lookup: δ · Doctrine · Binding religious claim

A proposition presented within a community as a guide to belief or action and as carrying normative authority. I use $\delta$ for such a claim when it is grounded in an alleged revelation, scripture, or religious authority.

The label describes the claim’s public role. It does not establish that the proposition is true, that its claimed source is genuine, or that its authority is justified. Those are the matters the interface and transmission analysis examines.

FMFG, Definition 2.2, p. 27.Human Interface Thesis

66Testimony

Standard term in FMFG use

Lookup: Report · Testimonial evidence

An act or artifact through which a source presents a proposition $\varphi$ as true to a recipient, who treats that presentation as evidence for it. Speech, a written report, and an institution’s account of a revelation can all occupy this role.

Testimony distinguishes the recipient’s access to a report from access to the reported event itself. Human mediation does not automatically make testimony false. It identifies the route by which the claim reaches the recipient and the warrant that route must supply.

FMFG, Definition 2.3, p. 27; §2.4.Human Interface Thesis

67Transmission chain

FMFG term or specialized use

Lookup: Transmission · Oral transmission · Testimonial chain

A finite sequence of agents and artifacts connecting an originating event or report to the token through which a claim reaches a particular recipient. Memory, speech, copying, translation, and institutional teaching can form different links in that sequence.

The final recipient encounters the transmitted content through an interface. Naming a divine or nonhuman origin does not remove the subsequent transmission conditions. Multiple repetitions of a report also need not be independent routes back to its source.

FMFG, Definition 2.4, p. 27; §§2.4–2.7.Human Interface Thesis

68Human Interface Thesis

FMFG term or specialized use

Lookup: HIT · Human-interface bound · No revelation bypass

Every public doctrinal claim available to a human epistemic agent is received and evaluated through human-interface conditions. What is asserted as revelation reaches public religious life through tokening, language, testimony, transmission, and interpretation.

The Finite Mind Constraint concerns meaningful access in general. The Human Interface Thesis applies that boundary to public religious authority. It does not infer that a reported revelation is false simply because it is mediated. It rules out treating mediation as absent when assessing the authority humans can claim from the report.

FMFG, Definition 2.5, p. 27; Theorem 2.11 and Corollary 2.12, pp. 30–31.Human Interface Thesis

69Revelation Filter

FMFG term or specialized use

Lookup: Revelation filtering · 𝓕_(e,δ) · Canon selection · Interpretive uptake

The combined transformations through which an alleged revelation becomes a publicly received doctrinal claim. I distinguish cognitive tokening, linguistic encoding, social transmission, documentary stabilization, canon selection, and interpretive uptake.

\mathcal F_{(e,\delta)}:=h\circ k\circ d\circ s\circ\ell\circ c.

Composition is read from right to left: $c$ tokens the event, $\ell$ encodes it in language, $s$ transmits it socially, $d$ stabilizes a document, $k$ selects a canon, and $h$ supplies interpretive uptake. These are roles in the account, not a claim that every tradition follows an identical historical sequence. The filter identifies conditions to investigate; it is not an automatic falsity operator.

FMFG, Definition 2.6, p. 28; §2.3.Human Interface Thesis

70Steelman hermeneutic

FMFG term or specialized use

Lookup: Smartest Reading · Steelmanning · Interpretive charity

The interpretive policy of examining a tradition in its strongest coherent form while remaining answerable to its own commitments. In the formal account, that means coherence, preservation of the intended ultimacy claim, qualification of anthropomorphic language, moral intelligibility under the tradition’s justice commitments, and recognition of finite human mediation.

I am granting the strongest reading, not granting its truth. A reading still has to bear the implications of what it says. Charity is not permission to replace a tradition with an unrelated view that happens to be easier to defend.

FMFG, Definition 6.1, p. 94; §6.2.Smartest Reading

71Silence of new revelation

FMFG term or specialized use

Lookup: Closed revelation · Silence pressure

The pressure created when a tradition claims that decisive public revelation is complete, yet its inherited record remains subject to transmission and interpretive dispute. I ask what role the absence of a fresh, publicly decisive correction plays in preserving the authority of that record.

This is the book’s diagnostic of closed-revelation claims. It is not a census of all religious experiences, and it does not say that nobody reports new revelation. The relevant question is whether a claimed update can publicly resolve the authority problem without passing through the same interface conditions.

FMFG, §2.8, p. 24; §11.8.2, p. 174.Human Interface Thesis

72Apophatic move

Standard vocabulary in FMFG use

Lookup: Apophasis · Apophatic theology · Negative theology · Limit language

A shift from straightforward positive descriptions of ultimacy toward negation, limit language, or carefully qualified analogy. Instead of treating the ultimate as a larger instance of an ordinary agent, the interpretation limits what its predicates can literally assert.

In my account, this is a response to the finite structure carried by ordinary person-language. It can be a genuine discipline of meaning. It becomes an ineffability shield only when positive authority is retained while the grounds for evaluating it are withdrawn.

FMFG, Definition 6.2, p. 94; §§6.3–6.6.Smartest Reading

73Apophatic convergence

FMFG term or specialized use

Lookup: Apophatic Convergence Theorem · Negative-theology convergence

The conditional result of applying the steelman hermeneutic to a strong ultimacy claim under the book’s predicate-finitude constraint. Ordinary literal agent-predicates cannot simply remain unchanged while their finite conditions of application are denied. A coherent interpretation must qualify them toward an apophatic register.

The formal theorem distinguishes that discipline from an alternative response: keeping the positive commitments while using ineffability to block their evaluation. I am tracing the consequences of the stated commitments, not predicting that all religions will historically become one doctrine.

FMFG, Theorem 6.7, pp. 97–98; Corollary 6.8, p. 99.Smartest Reading

74Ineffability shield

FMFG term or specialized use

Lookup: Ineffability · Evaluability blockade

The combination of two moves: a claim continues to carry positive practical or authority commitments, while an appeal to ineffability blocks examination of what those commitments mean or what supports them. The claim is made consequential and then insulated from the scrutiny that consequence requires.

Saying that language has limits is not enough to count as a shield. The defining tension is retaining determinate authority while refusing the conditions under which that authority could be assessed.

FMFG, Definition 6.3, p. 95; §6.6.Smartest Reading

Back to the reference opening

Fairness and salvation

Access, capacity, belief, and public profession are different conditions. The fairness argument depends on keeping them distinct.

75Belief gate

FMFG term or specialized use

Lookup: Assent gate · Belief-gated salvation

A soteriological requirement that makes holding or assenting to specified propositions a condition of salvation, liberation, or decisive standing. The gate concerns belief itself, not merely hearing the proposition or publicly repeating it.

That distinction matters when accountability depends on a response an agent cannot produce at will. A profession may satisfy an institution’s observable rule without establishing the inward belief the rule claims to measure.

FMFG, Definition 4.4, p. 59; §§4.1–4.3.Salvation Paradox

76Soteriological criterion

FMFG term or specialized use

Lookup: Soteriology · Salvation condition · Criterion C

A condition that a religious system treats as necessary, sufficient, or both for salvation or its corresponding ultimate success. Soteriology is the account of how that standing is attained, lost, or judged.

The criterion need not be propositional belief. It may concern conduct, orientation, practice, or another requirement. I keep the kind of condition explicit so that an argument about belief gates is not silently extended to every possible account of salvation.

FMFG, Definitions 4.2–4.3, p. 59.Salvation Paradox

77Fairness Clause

FMFG term or specialized use

Lookup: FC · Fairness condition · Access and capacity

The conjunction of access-sensitive and capacity-sensitive accountability. A system satisfies the clause when it makes culpability responsive both to whether an agent could realistically encounter and understand the relevant content and to whether the agent could meet the required response.

In Chapter 3 I identify this structure in the traditions’ own accountability commitments. Their particular exceptions need not be identical. The shared constraint is that a demand cannot be assessed fairly as though the agent possessed access or ability that the agent actually lacked.

FMFG, Definition 3.7, p. 42; Theorem 3.13, pp. 44–45.Fairness Clause

78Access Condition

FMFG term or specialized use

Lookup: Epistemic access · Genuine access · Ignorance exception

The rule that lack of relevant epistemic access must affect culpability. The underlying access is a realistic opportunity to encounter and understand the content, not simply contact with words that remain unintelligible or unavailable as a live claim.

Chapter 3 distinguishes the agent’s epistemic access from the system’s Access Condition: the latter is the requirement to excuse or reduce culpability where the former is lacking. Encounter, understanding, and eventual conviction are still different. Giving someone the message does not, by itself, establish belief.

FMFG, Definitions 3.1 and 3.4, p. 41; Lemma 4.9, p. 60.Fairness Clause

79Capacity Condition

FMFG term or specialized use

Lookup: Normative capacity · Ability to respond

The rule that responsibility must be adjusted to the agent’s actual ability to meet the requirement. The relevant normative capacity includes the competence and opportunity needed to understand and respond under the circumstances.

The source distinguishes that capacity from the Capacity Condition imposed on a system’s judgments. A demand does not supply the ability to comply. Nor does the ability to repeat a formula establish the ability to sincerely believe it. Access and capacity have to be assessed separately, even though they interact.

FMFG, Definitions 3.2 and 3.5, p. 41; §3.1.Fairness Clause

80At-will test

FMFG term or specialized use

Lookup: At will · Direct doxastic voluntarism · Doxastic involuntarism

A test of direct doxastic voluntarism: can the agent sincerely adopt a belief simply by deciding to believe it, without a change in what makes the proposition convincing? Saying the words or imagining that the proposition is true does not pass the test.

The test does not deny indirect influence through inquiry, attention, habits, or changed circumstances. It distinguishes that causal influence from an immediate voluntary switch. In the salvation argument, the distinction matters when a system treats nonbelief itself as a blameworthy refusal.

FMFG, §4.3.1, pp. 50–51; Definition 4.5, p. 59; Lemma 4.8, p. 60.Salvation Paradox

81Salvation Paradox

FMFG term or specialized use

Lookup: SP · Nonculpable nonbelief · Unreached and unconvinced

The instability of combining a strict belief gate, excusal for nonculpable ignorance, and fair accountability under finite conditions. Reaching a person with the content does not establish that the person can sincerely accept it. A reached but nonculpably unconvinced person can therefore face the same relevant limitation as an unreached person.

The formal result requires revision in at least one direction: extend excusal to nonculpable nonbelief, deepen the criterion so it tracks culpable orientation rather than bare assent, or abandon the fairness constraint. The apparent advantage of remaining ignorant exposes the problem with an exposure-sensitive gate; it is not advice to avoid learning. Mere disagreement does not establish that a particular person’s nonbelief is nonculpable.

FMFG, §§4.5–4.7, pp. 53–57; Definition 4.7 and Theorem 4.11, pp. 60–62.Salvation Paradox

Back to the reference opening

Translation layers and drift

A representation can preserve insight without becoming the reality it represents. These terms distinguish the map, its transmission, and the patterns being explained.

82Translation layer

FMFG term or specialized use

Lookup: τ · tau · L → A · Experience to artifacts · Language to anchors · Religions as translation layers

A culturally stabilized way of carrying lived reality into a portable human form: texts, practices, institutions, and interpretive rules through which a community navigates its world. The layer is a representation, not the reality it addresses.

Chapter 5, Definition 5.4:

\tau:\mathcal L\longrightarrow\mathcal A.

Here $\mathcal L$ is lived, tokenable experience for finite agents; $\mathcal A$ is the domain of transmissible artifacts. The map goes from experience into its public forms.

The terminology appendix, §§11.6 and 11.8.4:

\tau:L\longrightarrow A.

In this appendix usage, $L$ is a public language and $A$ is an anchor domain supplying meaning and reference. I keep these two source contexts distinct: their domains and codomains differ, so the shared letter $\tau$ does not make them one interchangeable mapping. The formal translation-layer argument in Chapter 5 uses the first typing.

FMFG, Definition 5.4, p. 77; §§11.6 and 11.8.4, pp. 171 and 176.Religion as Translation

83Map–territory gap

Standard distinction in FMFG use

Lookup: Map-territory gap · Map and territory · Representation gap

The difference between a finite representation and the reality it represents. A map selects, compresses, classifies, and carries priorities. Even a useful map is not identical to its territory.

I use this distinction to prevent a tradition’s symbolic system from certifying itself as ultimate reality. The gap does not entail deception or universal error. It means that the representation remains partial and open to correction, and that a claim of exhaustive identity requires more than the map’s usefulness.

FMFG, Definition 5.3, p. 77; §5.2.Religion as Translation

84Translation drift

FMFG term or specialized use

Lookup: Semantic drift · Interpretive drift

Changes in meaning and emphasis introduced as a tradition is transmitted, translated, selected, interpreted, and institutionally maintained. The content that reaches a later community can differ from what earlier participants intended or understood.

Drift is not limited to mistranslating a word. A stable wording can acquire a different practical meaning through a changed interpretive setting. The term identifies a transmission process to investigate; it does not establish that every change is a deterioration or that a particular claim is false.

FMFG, §§2.6–2.7 and Chapter 5; §11.8.4, pp. 176–177.Religion as Translation

85Doctrinal divergence

FMFG term or specialized use

Lookup: Doctrinal conflict · Religious divergence

A conflict among a family of religious systems in which central commitments cannot jointly hold in the same sense. Definition 5.5 concerns disagreement about such matters as ultimacy, salvation or liberation, the afterlife, or normative authority, not merely differences in wording.

Different transmission histories and local constraints help explain how the branching arises. Identifying the conflict does not yet determine which claim fails, and it does not imply that all the systems lack genuine insight. The interpretation must first establish that the commitments really are incompatible.

FMFG, Definition 5.5, p. 77; Lemma 5.9, pp. 78–79.Religion as Translation

86Existential convergence

FMFG term or specialized use

Lookup: Shared existential functions · F(R_i) · Functional convergence

A recurring overlap in existential motifs or functions despite doctrinal disagreement. Traditions can address suffering, mortality, moral formation, or meaning while giving incompatible accounts of ultimacy.

The formal model assigns a set of functions $F(R_i)$ to each religious system and asks whether a nontrivial overlap remains:

\bigcap_i F(R_i)\ne\varnothing.

This is convergence in the declared functions, not identity of doctrines. Chapter 5 combines it with divergence, cultural contingency, and interface constraints in an explicitly abductive translation-layer argument. The commonality does not make every tradition true or turn the explanatory comparison into a proof by logic alone.

FMFG, Definition 5.7, p. 78; Theorem 5.11, pp. 80–81.Religion as Translation

Back to the reference opening

Personhood, preference, and finitude

The argument concerns the structure carried by a personal attribution and its compatibility with a specified ultimacy claim. Finitude here must be read in its stated sense.

87Personhood predicates

FMFG term or specialized use

Lookup: P: personhood family · Personal agency predicates

Predicates whose ordinary use presents a subject as an agent with a standpoint: intending, choosing, approving, commanding, responding, or caring in a directed way. Definition 7.1 groups the relevant willing, affective, responsive, relational, and narrative roles.

The argument asks what structure those roles carry when they are attributed literally to ultimacy. A contrastive preference is not the same as an empty honorific. The reference shorthand $P$ for personhood predicates must also be distinguished from the Chapter 9 predicate $P(a)$ for an agent’s inclusion or standing.

FMFG, Definition 7.1, pp. 113–114; §7.2.2.Preference and Personhood

88Anthropomorphic predication

FMFG term or specialized use

Lookup: Anthropomorphism · Univocal predication · Analogical predication

Attributing humanlike psychological or agentive characteristics to the ultimate: treating it as a being that wants, commands, approves, resents, or changes its response as a person does.

My concern is the structure carried by the attribution, not whether the speaker imagines a human-shaped body. A literal, univocal attribution retains the ordinary predicate’s criteria. An analogical or negative use must say what those criteria become rather than quietly switching meanings when a difficulty appears.

FMFG, §§7.2–7.6; Definitions 6.4 and 7.1, pp. 95 and 113–114.Preference and Personhood

89Preference structure

FMFG term or specialized use

Lookup: Pref · x ≻_B y · Strict preference · Preference–Finitude Result

A nontrivial ranking of alternatives by a subject. Chapter 7 writes $x\succ_B y$ when $B$ prefers $x$ to $y$ , with at least one such strict comparison among the alternatives.

The definition identifies the ranking; the subsequent argument concerns what makes it attributable to that subject. My preference–finitude reasoning treats a genuine contrastive preference as operating from a determinate standpoint rather than an unrestricted identity with everything that obtains. That connection is part of the argument, not something proved merely by writing an ordering symbol.

FMFG, Definition 7.2, p. 114; Theorem 7.3, pp. 115–116.Preference and Personhood

90Ultimacy-as-totality

FMFG term or specialized use

Lookup: E: totality · B = E · Totality identity

The use of “ultimate” in which the proposed referent is identical with totality, not a further individual alongside it. In Chapter 7, $E$ names totality and the specified identity is $B=E$ .

That is stronger than saying that something grounds or explains everything. Grounding scope does not by itself establish identity with the totality grounded. When I examine the incompatibility between personal preference and totality, the relevant identity condition must therefore remain explicit. The book’s use of $E$ here also differs from the enforcement rule $E$ in the threat-architecture tuple.

FMFG, Definition 7.2, p. 114; Chapter 8; compare the identity condition in the personhood argument.Preference and Personhood

91Limitation

FMFG term or specialized use

Lookup: L(x) · B ≠ E · Finitude as non-totality · Partial standpoint

Nonidentity with totality in the sense used by the personhood argument. The reference shorthand $L(x)$ records that $x$ is not the all-inclusive whole. Chapter 7 states the corresponding condition for its subject as $B\ne E$ .

This is finitude as a partial standpoint or non-totality, not a numerical claim that every set being discussed has finitely many members. It must not be confused with the finite information-processing capacity of a mind or the size of a representation. A finite representation alone does not establish the finitude of its referent.

FMFG, §7.2.3, p. 102; Definition 7.2, p. 114.Preference and Personhood

92Predicate finitude

FMFG term or specialized use

Lookup: Finite predication · Predicate-use domain

The constraint that ordinary finite-agent predicates carry criteria of use, comparison, and application. Applied in the same literal sense to an alleged ultimate, they bring that structure with them rather than becoming unlimited merely because their subject is called God.

Definition 6.4 concerns predicates whose meaning is anchored in a practice and a domain of application. The resulting pressure toward apophatic qualification is not the claim that every grammatical positive sentence makes its referent a finite object. The relevant predicate, its sense, and the ultimacy claim have to be specified together.

FMFG, Definition 6.4, p. 95; Lemma 6.5, p. 96; Theorem 6.7, pp. 97–98.Smartest Reading

Back to the reference opening

Nondual ultimacy and practice

These are the alternative roles that ultimacy, religious language, and practice can play once a separate personal ruler is no longer assumed.

93Nondual ultimacy

FMFG term or specialized use

Lookup: Nondual Ultimate · Nonseparable ultimacy · Nonobjectual ground

An ultimacy model that does not position the ultimate as a separate personal subject standing over against the world. Definition 8.1 allows identity with totality or a nonobjectual ground, rather than a privileged individual among other individuals.

Those formulations have different commitments; “nondual” does not make them identical. The chapter follows how nonseparability changes the ordinary God/no-God dispute and what remains of practical or devotional language. Naming this model does not establish that a particular tradition’s full account is true.

FMFG, Definition 8.1, p. 127; Theorem 8.8, pp. 130–131.Nondual Collapse

94Reciprocity Principle

FMFG term or specialized use

Lookup: Reciprocal approach · Nonexclusive approach

The principle, within the nondual account examined in Chapter 8, that sincere approaches to the ultimate are not restricted to one exclusive creedal route. Different finite orientations can stand in a relation of approach or response without making one historically situated formula the sole condition of access.

This connects to the fairness concern about access across differing human circumstances. It is not an assertion that every practice is equally effective, every doctrine is compatible, or every claimed response is independently verified.

FMFG, Definition 8.2, p. 127; §8.3.Nondual Collapse

95Practice Primacy

FMFG term or specialized use

Lookup: Practice-first orientation · Transformative criterion

An orientation in which the decisive criteria of religious or spiritual success are practical and transformative rather than belief in a separable personal deity. What happens in disciplined living and transformation has priority over a bare declaration of assent.

This does not remove thought, teaching, or propositions from practice. It changes their role and the criterion by which success is judged. In Chapter 8, I use it to distinguish a practice-centered framework from an exclusive belief gate and from institutions that substitute compliance for transformation.

FMFG, Definition 8.3, p. 127; §8.4.Nondual Collapse

96Skillful means

Standard tradition term in FMFG use

Lookup: Upaya · Upāya · Instrumental teaching

The use of teachings, doctrines, or practices as instruments adapted to the learner and directed toward transformation. In Definition 8.4, at least some teachings may function in this way without claiming to be final, literal, exclusive descriptions of ultimate reality.

The term retains the Buddhist reference of upaya while naming the role being examined here. Instrumental usefulness is not the same thing as literal metaphysical truth, but neither does it make truth irrelevant or license treating every doctrine as merely a convenient fiction.

FMFG, Definition 8.4, p. 128; §11.8.6, p. 179.Nondual Collapse

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Institutions, proxies, and control

I distinguish the claimed standing from the public records used to judge it. The formal vocabulary describes an institutional mechanism, not a presumption of bad intentions.

97Unobservable predicate

FMFG term or specialized use

Lookup: Unobservable inclusion · P(a) · Public-record undecidability

A predicate that cannot be decided from the specified public records alone. Chapter 9 considers agents $a\in\mathcal A$ , observable records $\sigma(a)\in\Sigma^*$ , and an inclusion predicate $P:\mathcal A\to\{0,1\}$ .

Relative to those records, $P$ is unobservable when there is no public-record procedure $d$ that returns $P(a)$ correctly for every agent. The scope is relative to the declared record system, not an assertion of unknowability by every possible means. Claims such as being saved or in grace illustrate the target role; the example’s name alone does not prove the formal condition.

FMFG, Definition 9.1, p. 145.Control Overlays

98Observable predicate

FMFG term or specialized use

Lookup: Publicly decidable predicate · d(σ(a)) = P(a) · Observable record

A predicate whose value is publicly decidable from the declared records. Chapter 9 gives the condition as the existence of a procedure

d:\Sigma^*\longrightarrow\{0,1\},

such that $d(\sigma(a))=P(a)$ for every agent $a\in\mathcal A$ . The procedure takes the public record as input and returns the correct value of the predicate.

Attendance or a recorded utterance may be publicly checkable while the inward standing they are taken to indicate is not. Public evidence of a marker does not, by itself, establish a procedure that decides the deeper claim without error.

FMFG, Definition 9.1, p. 145.Control Overlays

99Proxy metric

FMFG term or specialized use

Lookup: m · m(σ(a)) · Proxy measure · M: metric codomain

A function of publicly observable records used in institutional decisions that purport to track an unobservable predicate:

m:\Sigma^*\longrightarrow M.

The codomain $M$ is a set of metric outputs, typically ordered or graded. It is not the finite mind denoted by $M$ in Chapter 1. An institution can use a score, classification, or ranking as a proxy without having established that the output is equivalent to the target standing.

The metric is the mapping. A particular record or compliance marker fed to it is a different object.

FMFG, Definition 9.2, p. 145.Control Overlays

100Compliance marker

FMFG term or specialized use

Lookup: κ · kappa · Membership marker · Conformity marker

A publicly observable token or pattern treated by an institution as presumptive evidence of inclusion or a sufficiently favorable proxy value. Chapter 9 writes $\kappa\in\Sigma^*$ for the marker.

A confession, ritual action, visible object, or affiliation can serve this role. The marker is not the proxy function itself and is not automatically the standing it is taken to indicate. Its evidential and institutional roles need to be distinguished, especially where public conformity can occur without the inward belief being claimed.

FMFG, Definition 9.3, pp. 145–146.Control Overlays

101Authority stacking

FMFG term or specialized use

Lookup: J_0 … J_n · Nonappealable authority · Interpretive gatekeeping

A sequence of justificatory authorities in which the legitimacy of a lower level is referred upward and the final level is treated as nonappealable within the system. The formal sequence is $(J_0,\ldots,J_n)$ , with each authority drawn from the system’s available justificatory sources.

The defining feature is where contestation is stopped, not how many books, officials, or traditions are cited. Authority stacking stabilizes decisions about the proxies by declaring which interpretation binds. It does not, merely by ending an appeal, establish the truth of the ultimate claim.

FMFG, Definition 9.4, p. 146; Lemma 9.8, pp. 148–149.Control Overlays

102Threat architecture

FMFG term or specialized use

Lookup: (R,S,E) · Rewards and sanctions · E: enforcement

The arrangement of promised rewards, threatened sanctions, and the rule that makes them consequential for compliance. Chapter 9 models it as $(R,S,E)$ : rewards $R$ , sanctions $S$ , and an enforcement rule $E$ that connects observable records to those outcomes or intermediate statuses.

The consequences can be social, reputational, material, psychological, or otherworldly. The term therefore includes inducements as well as punishments. This $E$ is an enforcement rule, not the $E$ used for totality in Chapter 7.

FMFG, Definition 9.5, p. 146; Lemma 9.9, pp. 149–150.Control Overlays

103Control overlay

FMFG term or specialized use

Lookup: CO · Control Overlay Theorem · Proxy governance · Map disguised as territory

An interpretive-normative system that combines an ultimacy claim, an unobservable inclusion predicate, governance through proxy metrics and compliance markers, authority protection, and enforcement through a threat architecture. All five belong to Definition 9.6.

The mechanism arises when finite institutional procedures are made to govern supposedly decisive standing. The Control Overlay Theorem follows that structure under its coordination and conflict conditions; it does not infer the whole mechanism from the mere existence of a rule or institution. A translation layer can carry genuine insight while an overlay elevates its proxies into ultimate categories. The diagnosis concerns function, not a requirement that the participants be insincere or malicious.

FMFG, Definition 9.6, pp. 146–147; Theorem 9.10 and Corollary 9.11, pp. 150–151; Remark 9.12.Control Overlays

104Primacy test

Website diagnostic

Lookup: Operational primacy · Transformation or compliance

My practical diagnostic for asking what a tradition actually places first: lived transformation and practice, or conformity to institutionally enforced proxies. Look at what is rewarded, what is sanctioned, and what happens when the claimed purpose and the compliance requirements come apart.

Here the name identifies a website diagnostic used with the control-overlay analysis, not a separately numbered theorem in the book. It asks which criterion governs the practice of the institution. It does not make the observer’s impression of one incident sufficient to settle that question.

Website reference usage, entry 104; compare FMFG, §§9.9–9.10, pp. 143–144, and Chapter 9’s formal account.Control Overlays

Back to the reference opening

Formal logic, mathematics, and semantics

These are established reference terms, not new FMFG theorems. They explain the notation used in the arguments and the distinctions needed to read it accurately.

105Proposition

Standard reference term

Lookup: Truth-apt content · p · q · φ

A truth-apt content: something that can be asserted as true or denied as false. The proposition is distinguished from a particular sentence-token used to express it.

In the formal sections, letters such as $p$ , $q$ , and $\varphi$ stand for propositions or formulas as the context specifies. The occurrence of a token expressing a proposition does not establish that proposition’s truth.

FMFG, §11.3, p. 168; established usage in the formal arguments.

106Propositional logic

Standard reference term

Lookup: Truth-functional logic · TFL

A logic that works with whole propositions or sentence letters and combines them with truth-functional connectives. It can examine the pattern of an argument without analyzing the internal subject-predicate structure of every sentence.

For example, $p\land q$ combines two contents by conjunction. First-order logic adds further expressive structure, including predicates and quantification over individuals.

FMFG, §11.4.1, p. 169; standard truth-functional logic.

107Predicate

Standard reference term

Lookup: P(x) · Property attribution

An expression with one or more argument places. Applying it to appropriate terms, or binding its variables, can form a truth-evaluable sentence. In $P(a)$ , the predicate is applied to the object named by $a$ .

A predicate’s meaning must be stated locally. A personhood predicate in Chapter 7 and an inclusion predicate in Chapter 9 are not the same property because the same letter can represent both.

FMFG, Chapters 7 and 9; standard first-order usage.

108First-order logic

Standard reference term

Lookup: Predicate logic · FOL · Quantificational logic

A formal language and logic that combines predicates, terms, variables, connectives, and quantifiers over the individuals in a domain. It can express the internal structure that propositional logic leaves within an unanalyzed sentence letter.

“First-order” specifies what the quantifiers range over. It does not mean that every model is a model of physical objects, or that a formula’s chosen domain exhausts reality.

FMFG, §11.4.2, p. 169; standard predicate logic.

109Quantifier

Standard reference term

Lookup: Quantification · Bound variable

An operator that binds a variable and specifies a condition on objects in its domain. The universal quantifier says that a formula holds of every object; the existential quantifier says that it holds of at least one.

Both the domain and the scope of the quantifier matter. A claim about every agent in one specified class is not automatically a claim about every possible kind of agent.

FMFG, §11.4.2, p. 169.

110Universal quantifier

Standard reference term

Lookup: ∀ · For all

The operator $\forall$ , read “for every.” The formula $\forall x\,\varphi(x)$ says that $\varphi$ holds for each object in the stated domain.

The domain supplies the reach of the claim. In Chapter 9’s public-decidability condition, correctness for every agent is stronger than success on a selected group of examples.

FMFG, §11.4.2, p. 169; Definition 9.1, p. 145.

111Existential quantifier

Standard reference term

Lookup: ∃ · There exists · At least one

The operator $\exists$ , read “there exists.” The formula $\exists x\,\varphi(x)$ says that at least one object in the stated domain satisfies $\varphi$ .

It does not say that there is exactly one. What the objects are and what counts as satisfying the predicate depend on the interpretation. A witness in a mathematical model is not automatically a physical realization.

FMFG, §11.4.2, p. 169.

112Negation

Standard reference term

Lookup: ¬ · Not

The connective $\neg$ , read “not.” In classical two-valued logic, $\neg p$ is true exactly when $p$ is false.

Negating a proposition is not the same as denying that a token of it occurs. Someone can express a false claim, and the expression can still be a real event.

FMFG, §11.4.1, p. 169.

113Conjunction

Standard reference term

Lookup: ∧ · And

The connective $\land$ , read “and.” The formula $p\land q$ is true exactly when both $p$ and $q$ are true.

A conjunctive requirement needs every component. Treating one condition of the Fairness Clause or one feature of the control-overlay definition as the whole would lose that structure.

FMFG, §11.4.1, p. 169.

114Disjunction

Standard reference term

Lookup: ∨ · Inclusive or

The connective $\lor$ , read as inclusive “or.” The formula $p\lor q$ is true when at least one disjunct is true, including the case in which both are true.

An exclusive choice needs an additional exclusion. The ordinary word “or” does not settle that choice of formal interpretation by itself.

FMFG, §11.4.1, p. 169.

115Material conditional

Standard reference term

Lookup: → · If then · Material implication

The truth-functional connective $\to$ . The formula $p\to q$ is false only when $p$ is true and $q$ is false.

This connective is not, by itself, a causal relation or a proof that the antecedent occurs. Its truth conditions explain the formal “if…then”; they do not remove the need to justify an argument’s premises.

FMFG, §11.4.1, p. 169.

116Biconditional

Standard reference term

Lookup: ↔ · Iff · If and only if

The connective $\leftrightarrow$ , read “if and only if.” In classical two-valued logic, $p\leftrightarrow q$ is true when the two propositions have the same truth value. It can be expressed as $(p\to q)\land(q\to p)$ .

A biconditional states both directions. Establishing only one implication does not establish the biconditional.

FMFG, §11.4.1, p. 169.

117Modal logic

Standard reference term

Lookup: Modal semantics

A family of logics that adds operators for modes such as necessity and possibility. The interpretation specifies which alternatives are relevant when a modal claim is evaluated.

Different accessibility conditions yield different modal systems. Using modal notation does not itself select a physical theory or establish that the represented alternatives are realized worlds.

Standard modal semantics; see forall x: Calgary, Chapter 44.

118Necessity operator

Standard reference term

Lookup: □ · Box · Necessarily

The operator $\Box$ , read “necessarily.” In relational possible-world semantics, $\Box p$ holds at a world when $p$ holds at every world accessible from it under the declared relation.

The relevant accessibility relation is part of the model. “Necessary” is not a synonym for strongly believed or repeatedly observed.

Standard modal semantics; forall x: Calgary, Chapter 44.

119Possibility operator

Standard reference term

Lookup: ◇ · Diamond · Possibly

The operator $\Diamond$ , read “possibly.” In relational possible-world semantics, $\Diamond p$ holds at a world when $p$ holds at at least one world accessible from it.

This is possibility under the model’s stated semantics. It should not be exchanged without argument for imaginability, probability, or actual physical realization.

Standard modal semantics; forall x: Calgary, Chapter 44.

120Possible world

Standard reference term

Lookup: World in modal semantics · Accessible world

An evaluation point in possible-world semantics, used to represent an alternative relative to which formulas can be assessed. A model supplies the worlds, their accessibility relations, and the interpretation of claims at them.

The semantic device does not itself settle what possible worlds are metaphysically. Calling an evaluation point a world does not make it another physically existing universe.

Standard modal semantics; forall x: Calgary, Chapter 44.

121Model (in logic)

Standard reference term

Lookup: Logical model · Model of a theory · Countermodel

An interpreted mathematical structure in which formulas can be evaluated. For a first-order language, it supplies a domain and interpretations of the nonlogical vocabulary. A model of a theory satisfies that theory’s sentences.

A countermodel to an inference makes its premises true and its conclusion false. Logical modeling is not by itself an empirical demonstration that the structure has been physically realized.

Standard first-order semantics; see forall x: Calgary, Chapters 30–31.

122Domain (of a model)

Standard reference term

Lookup: Quantifier domain · Domain of discourse

The collection of objects over which a model’s variables and quantifiers range. A formula about all objects is assessed relative to this declared domain.

The domain need not be the set of everything that exists. It can be a specified collection of agents, numbers, records, or other objects appropriate to the interpretation. This use of “domain” differs from the input set of a particular function.

Standard first-order semantics; forall x: Calgary, Chapter 23, §23.5.

123Interpretation function

Standard reference term

Lookup: Interpretation · Nonlogical vocabulary

The assignment of meanings to a formal language’s nonlogical symbols within a model. It assigns objects to constants, suitable functions to function symbols, and suitable relations to predicates.

The symbol and its assigned interpretation are different. Writing $P$ in two chapters need not mean that the two occurrences denote the same predicate; the source context specifies the assignment.

Standard first-order semantics; forall x: Calgary, Chapters 30–31.

124Validity

Standard reference term

Lookup: Deductive validity · Valid formula

An argument is deductively valid when, in the stated semantics, there is no case with true premises and a false conclusion. Validity concerns the consequence relation, not the actual truth of every premise.

For a formula, “valid” means true in all interpretations under consideration. A valid argument can begin from false premises. To call the argument sound requires more.

Standard consequence vocabulary; forall x: Calgary, Chapter 2.

125Soundness

Standard reference term

Lookup: Sound argument · Sound proof system

A sound argument is valid and has true premises. This is stronger than validity alone.

A sound proof system is a different, related notion: its derivations preserve semantic consequence, so what is derivable is entailed under the specified interpretation. Neither use makes a source premise true merely because it is printed in a formal argument.

Standard usage; forall x: Calgary, Chapters 2 and 22.

126Semantic entailment

Standard reference term

Lookup: ⊨ · Models · Entailment · Double turnstile

The relation written $\Gamma\models\varphi$ : every interpretation satisfying all premises in $\Gamma$ also satisfies $\varphi$ . For a single premise, $\psi\models\varphi$ expresses the corresponding consequence.

The double turnstile concerns truth across interpretations. It is not the single turnstile for a derivation under proof rules. Connecting the two requires a soundness or completeness result for the particular system.

FMFG, §11.4.3, pp. 169–170; standard semantic consequence.

127Syntactic derivability

Standard reference term

Lookup: ⊢ · Provability · Single turnstile · Derivation

The relation written $\Gamma\vdash\varphi$ : a proof using the specified rules derives $\varphi$ from assumptions in $\Gamma$ . The rules and assumptions belong to the statement of derivability.

The single turnstile identifies a proof relation, not a truth assignment. Chapter 2 also uses the indexed symbol $\vdash_A$ for an agent’s local inferential relation; that epistemic role should not silently acquire the metatheoretic guarantees of a sound formal calculus.

FMFG, §11.4.3, p. 169; Definition 2.1, p. 26; forall x: Calgary, Chapter 20.

128Consistency

Standard reference term

Lookup: Syntactic consistency · Inconsistency · ⊥

For the classical proof systems at issue here, a set of assumptions is consistent when it does not derive a contradiction. Inconsistency can be witnessed by a derivation of $\bot$ , or of a proposition together with its negation under the applicable rules.

Syntactic consistency and the existence of a satisfying model are distinct definitions. Their equivalence requires the relevant soundness and completeness connection; it is not obtained by exchanging the words “proof” and “model.”

Standard proof-theoretic usage; forall x: Calgary, Chapters 20 and 22.

129Contradiction

Standard reference term

Lookup: p ∧ ¬p · Incompatible commitments

A clash that cannot be true together in the relevant sense. In classical propositional logic, $p\land\neg p$ is the basic form: a proposition and its negation are asserted together.

Identifying a contradiction requires stable meanings and a shared scope. Two sentences about different times, domains, or senses of a word are not shown contradictory merely because their wording appears opposed.

FMFG, §§11.4.1–11.4.3, p. 169; standard classical usage.

130Reductio ad absurdum

Standard reference term

Lookup: Proof by contradiction · Reductio

A proof by contradiction: an assumption is shown to lead, together with the retained premises, to an inconsistency. The applicable inference rule then discharges that assumption and licenses the appropriate conclusion.

In classical reasoning, assuming the negation of a target and deriving a contradiction can establish the target. The contradiction tests the combined assumptions; identifying which commitment to reject requires keeping the premises and proof rule explicit.

Standard method; FMFG’s formal derivations; see Book of Proof, Chapter 6.

131Axiom

Standard reference term

Lookup: Starting assumption · Postulate

A statement adopted as a starting point within a formal system, rather than derived there from earlier statements. Calling something an axiom describes its role in that system.

It does not exempt an intended application from explaining why that starting point is appropriate. A conclusion drawn from axioms remains answerable to those assumptions and to the interpretation in which it is being used.

Standard formal vocabulary; used throughout the source derivations.

132Theorem

Standard reference term

Lookup: Proved result

A result established by proof from the adopted axioms, assumptions, definitions, and earlier results under the stated inference rules. Its scope includes the premises on which the proof depends.

A theorem title is not a substitute for its argument. Where a result is conditional, the condition remains part of what is established rather than disappearing when the result is cited.

FMFG, §11.3, p. 168, and the chapter derivations; standard proof vocabulary.

133Lemma

Standard reference term

Lookup: Supporting result

A proved result used to support another result. Its role is usually to isolate a step so that the later argument can invoke it without repeating the proof.

A lemma is not a guess or a weaker standard of evidence. Its use still carries its assumptions and scope into the theorem that depends on it.

Standard proof vocabulary; FMFG’s chapter derivations.

134Corollary

Standard reference term

Lookup: Immediate consequence

A result that follows from an established theorem with little additional reasoning. The name indicates its place in the argument, not freedom from the theorem’s conditions.

A corollary can make a practical or conceptual consequence explicit while remaining dependent on the precise result from which it follows.

Standard proof vocabulary; FMFG’s chapter derivations.

135Set

Standard reference term

Lookup: Collection

A mathematical collection of distinct elements considered together. Membership, not the order in which elements are listed, determines the set.

I use sets to specify such things as token-states, agents, alternatives, and records. Representing a collection mathematically does not by itself establish what exists physically or how that collection is realized.

FMFG, §11.5, p. 170; standard set notation.

136Element

Standard reference term

Lookup: ∈ · Membership · ∉

A member of a set. The expression $x\in A$ means that $x$ is an element of $A$ ; $x\notin A$ denies that membership.

Membership is not subset inclusion. An object can be a member of a set without every member of that object, when the object is itself a set, belonging to the larger set.

FMFG, §11.5, p. 170.

137Empty set

Standard reference term

Lookup: ∅ · Empty collection

The set with no elements, written $\varnothing$ . It remains a mathematical object within the formal account.

The empty set is not absolute nonbeing. Likewise, a language with no strings is different from a language containing the empty string. In the convergence condition, a nonempty intersection states that the declared collections share at least one element.

FMFG, Definition 5.7, p. 78; standard set usage.

138Subset

Standard reference term

Lookup: ⊆ · Subset inclusion

The relation $A\subseteq B$ means that every element of $A$ is also an element of $B$ . It permits equality: a set is a subset of itself.

A proper-subset claim additionally requires that the sets differ. Neither subset notation nor membership notation should be silently substituted for an identity or grounding claim.

Standard set notation; see Book of Proof, §1.3.

139Set-builder notation

Standard reference term

Lookup: {x · φ(x)} · Set comprehension

A way of specifying a set through a membership condition. The expression $\{x\in A\mid\varphi(x)\}$ collects exactly those members of the declared domain $A$ that satisfy $\varphi$ .

A shorter form, $\{x\mid\varphi(x)\}$ , relies on the domain being understood. The notation does not itself license an unrestricted collection in every set theory.

Standard set notation; FMFG’s formal domains; see Book of Proof, §1.1.

140Ordered pair

Standard reference term

Lookup: ⟨a,b⟩ · (a,b) · Ordered tuple

A two-place mathematical construction, written $\langle a,b\rangle$ or $(a,b)$ , in which position matters. In general, exchanging the first and second components produces a different pair.

Ordered pairs let us represent directed relations and input-output assignments. An ordinary two-element set does not record which element has which role.

Standard mathematical notation; see Book of Proof, §1.2.

141Relation

Standard reference term

Lookup: Binary relation · Relational structure

A mathematical specification of which ordered tuples stand in a given connection. A binary relation between $A$ and $B$ can be represented as a subset of $A\times B$ .

Its interpretation determines the connection: update, preference, accessibility, and dependence are different relations. Writing the same arrow shape does not make them the same. A general relation need not assign exactly one output to each input.

FMFG, Definitions 2.1 and 7.2; standard relation notation.

142Function

Standard reference term

Lookup: f: A → B · Mapping

A mapping that assigns exactly one output in its codomain to each input in its domain. In $f:A\to B$ , $A$ is the domain and $B$ the codomain.

Different inputs may have the same output, and some codomain elements may never occur as outputs. Translation maps, proxy metrics, and decision procedures occupy different functional roles even when written in the same general form.

FMFG, §11.5, p. 170; Definitions 5.4, 9.1, and 9.2.

143Domain (of a function)

Standard reference term

Lookup: Input domain · Function domain

The declared input set of a function. If $f:A\to B$ , the function assigns an output to every member of $A$ .

A function’s domain must be identified before its notation can be interpreted. For example, the two source uses of the translation map specify different input domains, despite both using the letter $\tau$ .

FMFG, §11.5, p. 170; Definition 5.4 and §11.6.

144Codomain

Standard reference term

Lookup: Output space · Target set

The designated output set of a function. In $f:A\to B$ , the codomain is $B$ . Every output belongs to it, but not every element of it has to be reached.

Chapter 9’s $M$ is the codomain of a proxy metric. It names a space of metric values in that definition, not the finite mind denoted by the same letter elsewhere.

FMFG, §11.5, p. 170; Definition 9.2, p. 145.

145Range / image

Standard reference term

Lookup: Range · Image · f[A] · f(A)

The set of outputs that a function actually takes on over its domain:

f[A]=\{f(x)\mid x\in A\}.

The range is contained in the codomain and need not equal it. “Actual outputs” here refers to outputs of the mathematical mapping, not a claim that every input-output pair has been physically performed.

Standard function notation; see Book of Proof, §§12.1 and 12.6.

146Alphabet

Standard reference term

Lookup: Σ · Sigma · Symbol alphabet

The set of symbols from which strings are formed. In the formal-language convention used by this reference, $\Sigma$ is a finite alphabet.

Chapter 9 applies the symbol-set idea to publicly observable signals and records. The alphabet specifies the available symbols; it does not bound every string to the same length or make the set of all finite strings finite.

FMFG, §§11.5–11.6, pp. 170–171; Definition 9.1, p. 145; reference convention.

147String

Standard reference term

Lookup: Word over an alphabet · ε · Empty string · σ(a)

A finite ordered sequence of symbols from an alphabet. Repetition and order matter. The empty string, often written $\varepsilon$ , has length zero.

A string’s existence as a record is distinct from whether the claim it expresses is true. In the institutional model, the observable record $\sigma(a)$ is a string-like public trace, not the inward standing that the institution seeks to infer.

FMFG, §11.5, p. 170; Definition 9.1, p. 145; standard finite-string convention.

148Kleene star

Standard reference term

Lookup: Σ* · Kleene closure · All finite strings

The construction $\Sigma^*$ collects all finite strings over $\Sigma$ , including the empty string. It places no fixed upper bound on string length; each member is nevertheless finite.

The empty string is an element of this collection, not the empty set. In Chapter 9, $\Sigma^*$ supplies the record domain used by public decision procedures and proxy metrics. This mathematical domain is not a claim that all such records are simultaneously physically instantiated.

FMFG, §11.5, p. 170; Definitions 9.1–9.3, p. 145; standard formal-language convention.

149Type–token distinction

Standard reference term

Lookup: Type-token distinction · Token and type · Token and referent · God-concept tokening

The distinction between a repeatable kind and a particular occurrence of it. A word-type can have many printed, spoken, or thought tokens. Two inscriptions can therefore be tokens of the same type without being the same event.

A token is also distinct from its referent and from the truth of its content. FMFG’s God-concept tokening locates the concept within a finite interface; it does not, simply by locating the concept, identify or measure whatever the concept purports to refer to.

FMFG, Definition 1.3, p. 13; Definition 2.1, p. 26; §§11.3 and 11.8.2.

Back to the reference opening

Sources and reading

I use the chapter definitions and their surrounding arguments as the authority for FMFG’s specialized meanings. The terminology appendix supplies the book’s reference conventions. Where those source contexts use the same symbol differently, both meanings are identified in the relevant entry.

Finite Mind, Finite God

Matthew Zejda, Finite Mind, Finite God (2026). Chapter and definition numbers here refer to the edition with “Terminology, Notation, and Conventions” as Chapter 11, printed pages 167–180. Page numbers are the book’s printed labels, not a PDF viewer’s page count.

Chapters 1–2 establish tokening and the public interface; Chapters 3–4 develop access, capacity, and salvation; Chapters 5–6 develop translation and interpretation; Chapters 7–8 distinguish personhood, totality, and nondual alternatives; Chapter 9 supplies the proxy and control vocabulary. The definitions here are explanatory paraphrases, not a transcription of the complete proofs.

Open the FMFG publication page

Logic and semantics

The standard reference entries retain their ordinary logical roles. For further explanations, I refer to forall x: Calgary, by P. D. Magnus, Tim Button, Robert Trueman, and Richard Zach, with contributions by J. Robert Loftis and Aaron Thomas-Bolduc. Its treatment of proof and semantics is a reference for the logical vocabulary, not an endorsement of my philosophical conclusions.

Sets, functions, and proof vocabulary

Richard Hammack, Book of Proof, third edition. Chapters 1, 4, 6, 11, and 12 provide the connected treatment of sets, theorem terminology, contradiction proofs, relations, and functions. FMFG’s own finite-string conventions and record notation are given in §11.5 and Chapter 9.

Open Book of Proof and its chapter contents

The connected EL reference

The Existential Logicism terms-and-notation page supplies the occurrence, frame, grounding, consciousness, and moral vocabulary used by the underlying framework. Those entries retain their own source contexts. A shared name is a reason to compare definitions, not permission to merge them.

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Revelation, filtering, and interpretation

Fairness and salvation

Translation layers and drift

Personhood, preference, and finitude

Nondual ultimacy and practice

Institutions, proxies, and control

Formal logic, mathematics, and semantics

Sources and reading

Finite Mind, Finite God

Logic and semantics

Sets, functions, and proof vocabulary

The connected EL reference