EXISTENTIAL LOGICISM · TERMS AND NOTATION

Existential Logicism: Terms and Notation

The core labels, primitives, and distinctions behind the arguments, with the connected core vocabulary of Finite Mind, Finite God.

Matthew Tripp Zejda

I use these terms to follow the same questions from occurrence into knowing, grounding, time, mind, and moral life. A word can recur across those arguments without keeping exactly the same role. The definition and source named beside an entry tell you which meaning is in use.

This reference gives definitions and explanatory summaries, not replacements for the proofs. The argument links lead to the substantive pages; the source locators identify the formal definitions, conditions, and discussions behind each entry.

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All definitions remain visible. Use Find in page to search the full text, open either lookup panel, or browse the nine groups below. Entry titles provide permanent links to their definitions. In the alphabetical panel, a notation alias leads to the entry that explains its local role. Wide formulas scroll horizontally; focus a formula and use the arrow keys when needed.

Browse terms and aliases A–Z

Browse notation by symbol and role

A — minimal epistemic agent
B = E — ultimacy-as-totality
CanTok_A(S) — tokening capacity
D / Dep — dependence in a fixed mode
CDE — complete dependence explanation
E — FMFG totality
F — LEIR foundation set
F — DMF continuation function
F_L(S) — admitted successors
F_A — tokenable-state frame
Fin(S) — finite present condition
G — global negation of occurrence
G_M — God-concept token
I_A — EL interface structure
I(M) — FMFG experiential interface
J_A — inferential relations
Judg_A(t) — judgment output
M — finite mind
Moral(P) — moral content
N0 — absolute nonbeing content
N_abs — abstract-nothingness label
N_loc — local-absence label
Next_L(S) — unique successor
ObjMor(P) — strong moral objectivity
Occ(x) — occurrence
PD — purely dependent occurrence
PE — Primitive Experiential Profile
Pun_A(t) — sanction output
R — reality domain
Rep_h(r,q) — representation in a host
RepPast(r) — past-directed token
RepFuture(r) — future-directed token
S_n — present configuration
S_skeptic — skeptical content
S* — epistemic act-state
SG — self-grounded occurrence
Sys(S) — system
TI(S) — temporal integration
Tok_A(S) — actual token
U_A — input and update relations
V / V0 — proposed external view
Val(v) — valuer
VR(S) — value registration
WC(S) — world-coupling
World(w) — realization admissibility
WPPD(n) — present-only commitment
Z(A) — skeptical self-statement
γ(S) — comparison profile
Ξ_L — transition readout
σ — declared successor map
App_M(P,w) — moral applicability

EL core labels and pillars

The seven pillars develop different arguments. The source locations keep their own premises attached; a definition is not a substitute for the argument.

01Existential Logicism (EL)

Lookup: EL · Logic-Based Engine · Logic-Based Tool

I develop Existential Logicism as a connected account of existence, knowledge, time, mind, and morality. Its starting points are tested by asking whether an attempted denial relies on what it denies. The seven pillars then develop distinct arguments whose conclusions retain their own definitions and premises.

The Logic-Based Tool gives the continuous prose account. The Logic-Based Engine includes the formal arguments. Connecting the pillars does not make every later conclusion follow from the occurrence anchor alone.

Engine, Chapter 1, especially §§1.2–1.4; Tool, Chapter 1.Existential Logicism project

02Existential Logicism–Undeniability

Lookup: EL-undeniability · Undeniability · Denial test

A proposition is EL-undeniable when every meaningful attempt to deny it already presupposes its truth. The test concerns the conditions of the denial actually being made, not how confident a speaker feels or how familiar a belief has become.

A proposed anchor has to meet that test. Calling a claim undeniable is not a substitute for showing the relevant dependence. A later result may instead be a consequence of additional explicitly stated premises.

Engine, Formal Argument 1.4, Definition 1.1 and the EL–Undeniability Schema.Undeniable Facts · Formal argument

03Existential anchors

Lookup: Anchor · Foundational occurrence

The truths identified by the EL-undeniability test: abandoning them while attempting meaningful denial undermines the performance of that denial itself. They supply a starting point that ordinary contingent beliefs do not supply.

The occurrence of a doubt is such a starting point. Its occurrence does not establish that all the objects, theories, or explanations represented in the doubt are correct. I keep that minimum distinct from the additional support used in the later pillars.

Engine, Formal Argument 1.4; Formal Argument 2.5.Undeniable Facts · Formal argument

04Seven Pillars of Existential Logicism

Lookup: Seven Pillars · Pillars

The seven connected pillars are the Epistemic Refutation Paradox, Illusion of Nothingness, Logical Elimination of Infinite Regress, Persistent Present Determinism, Spectrum of Consciousness, Contingency Guillotine, and Deterministic Moral Forces.

Tripp’s Prison develops the account of finite access and shared knowledge within this architecture. The Elios Paradox belongs with the spectrum argument; Is–Ought Representation belongs with DMF. Their distinct names do not make them additional numbered pillars or interchangeable proofs.

Engine and Tool, Chapters 1–8; Engine, formal contents.Existential Logicism project

05Epistemic Refutation Paradox (ERP)

Lookup: ERP · Pillar 1

An actual global denial of occurrence supplies an occurrence in the very context it denies. If a claim says that nothing at all obtains, its performed token prevents that claim from being true of the context containing it.

The argument begins below a privileged “I,” self-awareness, or a particular theory of consciousness. An illusory or misclassified event can still occur. What is secured is occurrence, not the accuracy of the event’s represented content or a complete account of its carrier.

Engine, Formal Argument 2.5, Definitions 2.1–2.6 and Theorem 2.4.Epistemic Refutation Paradox · Formal argument

06Tripp’s Prison (TP)

Lookup: TP · Epistemic frame closure · Cross-Frame Structural Warrant · Blueprint–Carrier Boundary · Intersubjective blueprint

Every claim an epistemic agent actually considers is realized through its own access structure. The act of evaluating a representation is another frame-internal token; it is not a step outside every interface.

This is a constructive account of knowing. Recognized peers can compare genuinely independent access paths, make predictions, encounter shared resistance, and correct their descriptions. Cross-Frame Structural Warrant concerns the additional evidence needed for that shared blueprint. The Blueprint–Carrier Boundary distinguishes warranted structure from identifying its ultimate carrier. Agreement by itself supplies neither independence nor truth.

Engine, Formal Argument 2.11, Theorem 2.8 and Cross-Frame Structural Warrant; EG, Chapter 3.Tripp’s Prison

07Illusion of Nothingness (ION)

Lookup: ION · Pillar 2 · Inescapability of Existence · INE

I distinguish absence within a realized background, a null designation within a framework, and the absolute denial of every obtaining condition. The first two are coherent uses of “nothing”; they do not provide a state, source, recipient, or exhaustive alternative of absolute nonbeing.

The host of a description is not inserted into the candidate world it describes. ION’s wider exclusion uses its explicit realization and role principle: an exhaustive actuality cannot rely on operative conditions while denying every instance of their obtaining. ERP supplies the actual token; this further ontological argument has its own conditions.

Engine, Formal Argument 3.9, Definitions 3.2–3.6 and Theorem 3.4.Illusion of Nothingness

08Logical Elimination of Infinite Regress (LEIR)

Lookup: LEIR · Pillar 3 · Infinite regress

A complete dependence explanation cannot consist only of borrowed support with no nonborrowed foundation. For a declared nonempty target and dependence mode, every target must reach some obtaining foundation in finitely many dependence links, possibly zero.

The conclusion carries the complete-explanation requirement, the present realization condition, and the earlier exclusions it uses. It does not derive a particular physical mechanism merely by demanding explanation, require one identical foundation for every target, or reject every feedback process. A historical predecessor and an existential ground are different explanatory roles.

Engine, Formal Argument 4.11, Definition 4.5 and Theorem 4.4.Logical Elimination of Infinite Regress

09Persistent Present Determinism (PPD)

Lookup: PPD · Pillar 4 · Persistent Present

PPD joins two commitments: one complete present configuration obtains at a resolution, and its continuation is determined by the complete source and full law. Past events can have occurred and left consequences without remaining co-actual beside the present. Predictions and plans are present representations, not stored future regions.

The formal account states present-only ontology, finite realized content, a complete causally closed source, a faithful full law, contrastive source sufficiency, and actual continuation separately. The observation of one outcome does not establish all of them. Deliberation remains among the real processes through which a successor is produced.

Engine, Formal Argument 5.12, Theorem 5.4 and Remarks 5.9–5.10.Persistent Present Determinism · Formal argument

10Spectrum of Consciousness (SOC)

Lookup: SOC · Pillar 5 · Spectrum

The spectrum account investigates forms of world-coupling, system-relative value registration, and temporal integration across actual systems. Evidence establishes the relevant capacities, and declared comparison procedures organize their differences.

The Primitive Experiential Profile is a true-or-false eligibility condition. Richness is compared through a separate structural profile, not degrees of truth of that predicate. Profiles can be tied or incomparable. Neither a species label nor a coarse structural checklist supplies a universal consciousness score, a ranking of moral worth, or a sufficient-condition proof of private experience.

Engine, Formal Argument 6.5, Definitions 6.1–6.5, Remark 6.6 and Theorem 6.1.Spectrum of Consciousness and Elios · Formal argument

11Elios Paradox

Lookup: EP · Elios · Matched-evidence parity

A reflective agent cannot consistently accept a specified kind of evidence as warranting confidence in a human mind and reject relevantly matched evidence elsewhere solely because the system is nonhuman or artificial. The agent must apply the standard consistently, revise it consistently, or justify an independently supported relevant difference.

The theorem does not assume that every superficially similar system has matched evidence. ERP establishes that the agent’s skeptical token occurs; it does not by itself prove another system’s private experience. The paradox concerns evidential parity, not identical phenomenology.

Engine, Formal Argument 6.5, Definition 6.7 and Theorem 6.2.Spectrum of Consciousness and Elios · Formal argument

12Contingency Guillotine (CG)

Lookup: CG · Pillar 6 · Guillotine Test

On the constitutive account I defend, an applicable moral judgment receives its evaluative ordering and practical stakes through valuers. It cannot retain that same moral force while becoming independent of every such valuing relation. The formal comparison includes a nonempty valuer-free interpretation; it does not confuse that case with absolute nothingness.

Independence from one person’s approval is not independence from all valuers. Affected people may supply stakes an offender ignores. Descriptive truths can remain true when moral applicability fails. CG’s conclusion is distinct from the further causal account supplied by DMF and from the additional personhood premises used in FMFG.

Engine, Formal Argument 7.10, constitutive valuer premise, Definition 7.3 and Theorem 7.3.Contingency Guillotine · Formal argument

13Deterministic Moral Forces (DMF)

Lookup: DMF · Pillar 7 · Deterministic Morality · Internal ought · Is–Ought Representation

DMF places valuers, choices, judgments, and sanctions inside the causal account rather than treating the person being judged or the responder as a metaphysical exception. Its explanatory result inherits PPD’s full conditions. Its rejection of all-valuer-independent desert separately inherits CG’s constitutive argument.

Responsibility remains causal participation and answerability. Protection, restraint, repair, learning, and prevention must be assessed through declared values and evidence, not justified by causal attribution alone. My practical standard is to reduce suffering and support well-being, including the chooser. An internal ranking describes an agent’s valuations and beliefs; it does not guarantee compliance, accuracy, or ethical endorsement.

Engine, Formal Arguments 8.4 and 8.12; Theorems 8.4–8.5 and responsibility corollary.Deterministic Moral Forces · Formal argument · Is–Ought Representation

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EL primitives: occurrence, agents, and access

Occurrence, the capacity to represent, an actual token, its content, and the structure that realizes it are different things.

14Occurrence

Lookup: Occ(x) · Obtaining

An occurrence is a minimally individuable obtaining item, state, fact, event, process, or state-change. A dynamic event is one kind of occurrence, not the definition of all obtaining. I write $\operatorname{Occ}(x)$ when $x$ obtains in the context being considered.

The term does not require conscious experience or accurate interpretation. A dream, calculation, description, or mistaken classification can occur without every object it represents existing as depicted. The reality of an occurrence and an account of its kind remain distinct questions.

Engine, Definition 2.1; Definition 3.1; Notation and Symbol Guide, §2.Epistemic Refutation Paradox · Formal argument

15Reality

Lookup: R · Reality obtains

In the minimal occurrence vocabulary, reality is the totality of what obtains. Saying that reality obtains says that at least one occurrence obtains. The formal notation $\mathcal R$ marks the declared domain; it does not add an object outside reality that supplies reality.

This minimal designation is not a complete physical ontology or a proof that a particular state, theory, mind, or model exhausts actuality. A candidate interpretation and an obtaining reality also have different roles.

Engine, Definition 2.2; Definition 4.1; Notation and Symbol Guide, §2.Epistemic Refutation Paradox · Formal argument

16Epistemic interface

Lookup: I_A · Access structure · Epistemic cell · U_A · J_A

An epistemic interface is the structured way an agent is related to occurrences: how inputs are admitted, registered, transformed, and made available for judgment or inference. ERP requires no particular physical implementation of that structure.

For comparisons in Tripp’s Prison, the interface is $\mathcal I_A=\langle\mathcal F_A,U_A,J_A\rangle$ : the tokenable-state frame, input and update relations, and inferential relations. The frame is one component, not the whole interface. The actual embodiment and channels make an epistemic cell; this does not identify the ultimate carrier of all represented reality.

Engine, Definition 2.3; Definition 2.13, pp. 43–44.Tripp’s Prison

17Tokening

Lookup: Tok_A(S) · CanTok_A(S) · Epistemic agent · Minimal epistemic agent · Token

$\operatorname{Tok}_A(S)$ says that agent $A$ actually instantiates a substantive representational state $S$ . $\operatorname{CanTok}_A(S)$ instead records its capacity to do so. An actual token entails the capacity, but a tokenable state need not already have been performed.

A token is real as a token without its content automatically being true. The minimal epistemic agent is an actual token-capable system; reflective self-assessment and a particular experiential profile are further conditions, not assumptions built into every use of “agent.”

Engine, Definition 2.4; Definition 2.13; Notation and Symbol Guide, §4.Epistemic Refutation Paradox · Formal argument

18Global negation of occurrence

Lookup: G · Global denial · No occurrences

The schematic content $G:\ \forall x\,\neg\operatorname{Occ}(x)$ denies every occurrence. ERP asks whether that global denial can be true of the context in which it is actually tokened. The denial cannot exclude its own occurrence from the scope it claims to exhaust.

This result does not infer that every sentence is true because it is spoken. Nor does examining an empty candidate interpretation make that interpretation realized. The actual denial context and the candidate’s alleged obtaining are different questions.

Engine, Definition 2.5 and Theorem 2.4; Notation and Symbol Guide, §2.Epistemic Refutation Paradox · Formal argument

19Epistemic act

Lookup: Assertion · Doubt · Evaluation

An occurrence in which content is formed, entertained, doubted, denied, or asserted through an epistemic interface. The role can be realized in silent questioning, a spoken judgment, or an actual computational or displayed representation.

In Tripp’s Prison, evaluating a content is represented by a tokened state encoding an attitude toward that content. The performed evaluation remains within the agent’s frame. Capacity to evaluate is not an actual evaluation, and an actual evaluation is not automatically correct.

Engine, Definition 2.6; Definition 2.14.Tripp’s Prison

20Epistemic frame

Lookup: F_A · Tokenable states

The tokenable-state component of an agent’s interface: $\mathcal F_A=\{S\mid\operatorname{CanTok}_A(S)\}$ . Membership records what the agent can token, not which states it has actually tokened.

A frame can contain the capacity to represent an absent object, a mistaken hypothesis, or another agent. That does not place the referent inside the mind or certify its existence. Inputs, updates, and inferential relations belong to the fuller interface structure, not to this state-set notation alone.

Engine, Definition 2.13, pp. 43–44.Tripp’s Prison

21Epistemic act-state

Lookup: S* · Higher-order evaluation

For an evaluated content $S$ , an epistemic act-state $S^*$ encodes an attitude toward that content in the agent’s representational scheme. An actual evaluation includes $\operatorname{Tok}_A(S^*)$ , not merely membership of $S^*$ in the frame.

“I take this to be true,” “this is imagined,” and “this is doubtful” illustrate different attitudes. Their realizing states remain internal to the access structure even when they concern something beyond that access.

Engine, Definition 2.14 and Lemma 2.7.Tripp’s Prison

22Skeptical scenario

Lookup: S_skeptic · Skeptical hypothesis · Σ (skeptical-scenario label)

A frame-internal content $S_{\mathrm{skeptic}}$ that purports to undermine the reliability or reality of an agent’s other states. The agent must be able to take an attitude toward it; actual evaluation requires an actual tokened attitude.

A perfectly deceiving simulation, global illusion, or denial of correspondence can be examined in this way. The scenario may overturn an interpretation or a purported referent. If it is actually tokened, it cannot thereby annihilate the occurrence of its own token.

Engine, Definition 2.15 and Corollary 2.19.Tripp’s Prison

23Naïve External View

Lookup: Naive external view · V0 · V · View from nowhere

A proposed presentation $V$ that is supposed both to function in reasoning and to have no realizing representation in any epistemic frame. Tripp’s Prison excludes that combination: an operative presentation is realized through some frame.

The target is alleged frame-free access, not the possibility that represented things extend beyond one agent’s access. I do not use this result to identify realism itself with an error or to put every represented object inside the mind.

Engine, Definition 2.16, Lemma 2.9 and Theorem 2.10.Tripp’s Prison

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ION: absence, candidates, and representation

The host of a representation and the candidate it describes remain distinct. An ontological alternative needs more than a writable description.

24World / reality-candidate

Lookup: World · W (world label) · World(w) · Reality-candidate · Candidate interpretation

ION begins with a candidate interpretation $w=\langle D_w,I_w\rangle$ , consisting of a domain and an interpretation of its vocabulary. At this syntactic stage neither a nonempty domain nor a nonempty occurrence extension is imposed.

$\operatorname{World}(w)$ adds a realization requirement: the candidate is offered as exhaustive actuality, including the real conditions of its own obtaining. The token describing it remains in its host, not automatically in $D_w$ . Formal describability and realization-admissibility are therefore separate.

Engine, Definition 3.2, p. 72, and realization and role principle before Theorem 3.4.Illusion of Nothingness

25Local nothingness

Lookup: N_loc · Local absence · LocalNothing_w(R,P)

A local absence is relative to a specified property and region within a background that is itself posited to obtain. $\operatorname{LocalNothing}_w(R,P)$ records that background together with the absence of $P$ -items in $R$ .

An empty box is not an absence of every obtaining condition. Equally, an empty predicate extension does not by itself prove a real container. ION’s local-absence lemma explicitly assumes the realized background; it does not manufacture one from the notation.

Engine, Definition 3.3 and Lemma 3.1, pp. 73–74.Illusion of Nothingness

26Abstract nothingness

Lookup: N_abs · Null designation · AbstractNothing_T(N_T)

A designated null item within a specified formal or computational framework: zero, an empty set, a null marker, or another declared absence. The source writes this role as $\operatorname{AbstractNothing}_T(N_T)$ .

Actual use or implementation of that framework supplies an obtaining token or structure. A mathematical designation alone does not assert that all its denoted objects are physically instantiated. The argument concerns the actual host of the use, not an empty reality generated by the null symbol.

Engine, Definition 3.4 and Lemma 3.2, pp. 73–74.Illusion of Nothingness

27Absolute nothingness

Lookup: N0 · Absolute nonbeing · No null source · No null sink

Absolute nothingness denies every entity, state, relation, law, capacity, interface, source, recipient, and occurrence. The expression $\mathrm{N0}:\ \forall x\,\neg\operatorname{Occ}(x)$ is schematic content, not a name conferring existence on an empty thing.

Under ION’s realization and role principle, absolute nonbeing cannot perform the obtaining role of a state, source, recipient, or exhaustive alternative. Writing an empty domain does not supply that realization. Excluding absolute nonbeing does not establish that a particular identity, memory, or person persists unchanged.

Engine, Definition 3.5; Theorem 3.4 and Remarks 3.10–3.12.Illusion of Nothingness

28Representation

Lookup: Rep_A(X) · Rep_h(r,q) · Token and referent · Host-framework dependence

$\operatorname{Rep}_h(r,q)$ means that an actual token $r$ in host $h$ represents content $q$ . The token, its host, and its content have different places in the relation. An agent-specific description of representation must preserve those distinctions too.

The token can represent a candidate world, an absent event, a fiction, or a contradiction. Its occurrence establishes something about its host, not automatic truth or realization of its content. A further claim that the representation identifies a carrier or exhaustive actuality needs its own support.

Engine, Definition 3.6 and Lemma 3.3, p. 75; TP, Definition 2.13.Illusion of Nothingness

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LEIR: dependence and foundations

The dependence mode stays fixed throughout the account. Grounding is not temporal firstness, and self-grounding is not a reflexive dependence edge.

29Dependence relation

Lookup: D(x,y) · Dep(x,y) · Dependence mode

$\operatorname{Dep}(x,y)$ says that $x$ depends on $y$ in one declared explanatory mode. The source requires obtaining relata and an irreflexive primitive relation: $\forall x\,\neg\operatorname{Dep}(x,x)$ .

Causal dependence, existential grounding, and epistemic justification are possible modes, but I fix the mode throughout a derivation. A temporal predecessor does not automatically supply an existential ground, and a justification is not automatically a physical cause. Writing an arrow does not establish the mechanism it purports to represent.

Engine, Definition 4.2, pp. 102–103.Logical Elimination of Infinite Regress

30Dependence chain

Lookup: Regress chain · Pure borrowing · Feedback and grounding

A sequence of obtaining members connected by the declared dependence relation, with $\operatorname{Dep}(x_i,x_{i+1})$ at each relevant edge. An endless chain may revisit a member; a strict descending chain has distinct members.

Repeated traversal of a cycle does not add a nonborrowed foundation. Yet the source does not reject every grounded cycle or feedback process: the question is whether circular borrowing alone is offered as the entire grounding explanation. The representation of a chain also does not assert a completed physical history.

Engine, Definition 4.3 and Lemma 4.2.Logical Elimination of Infinite Regress

31Self-grounded occurrence

Lookup: SG(x) · Self-grounded · Nonborrowed foundation

An obtaining item with no further outgoing dependence in the specified mode. The source’s condition is

\operatorname{Occ}(f)\land\neg\exists y\,\operatorname{Dep}(f,y).

Self-grounding here is not self-dependence. A zero-step path may end at a foundation without asserting a reflexive dependence edge. The structural endpoint condition does not by itself identify the ground’s internal mechanism, laws, or unique physical nature. Calling a candidate self-grounded is not a substitute for supplying its explanatory account.

Engine, Definition 4.4, p. 103; Definition 4.5 and Corollary 4.6.Logical Elimination of Infinite Regress

32Purely dependent occurrence

Lookup: PD(x) · Pure dependence

Relative to the same fixed dependence relation, a purely dependent item obtains and depends on a further occurrence:

\operatorname{Occ}(x)\land\exists y\,\operatorname{Dep}(x,y).

This is a mode-relative structural classification. In the complete-grounding question, pure borrowing means that support is deferred throughout the proposed account without an independently grounded member or independently justified ground of the whole. The term does not make an item unreal merely because it depends on something.

Engine, Definition 4.4; Notation and Symbol Guide, §6.Logical Elimination of Infinite Regress

33Complete dependence explanation

Lookup: CDE · Foundation-reaching coverage · Foundation-reaching path · F (LEIR foundation set)

For a nonempty target $X\subseteq\mathcal R$ , the source requires a nonempty foundation set $F\subseteq\mathcal R$ . Each target has a finite path to some $f\in F$ , and each foundation obtains with no outgoing dependence in that mode.

The path may have zero edges when the target is itself a foundation. Every target must be covered; the condition does not require the same foundation for all targets or that every path in the whole graph be well-founded. The dependence relation must express the actual explanation claimed. This is the adequacy requirement LEIR adopts, not a proof that a particular mechanism has already been found.

Engine, Definition 4.5 and Theorem 4.4, pp. 105–108.Logical Elimination of Infinite Regress

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PPD: states, records, and continuation

Present-only ontology, finite realized content, and source-determined continuation have separate conditions in the formal account.

34Present state

Lookup: S_t · S_n · State(S) · State space · Fin(S) · Finite present state

$S_n$ denotes the complete structured configuration of obtaining items and relations at a declared resolution index. Completeness includes the relations, capacities, and realized values in the source, not just a list of constituents. Different descriptions of the same complete configuration are not different states.

The state $S_n$ , predicate $\operatorname{State}(S_n)$ , and state space $\mathcal S$ have different roles. Indexing configurations does not make them co-actual. The finite-present condition additionally concerns finite realized specification, not an observer’s ability to give the state a short name.

Engine, Definitions 5.2 and 5.5; Remark 5.6.Persistent Present Determinism · Formal argument

35PPD-reality

Lookup: R_PPD · WPPD(n) · Present-only ontology

The present-only commitment says that exactly one complete configuration obtains at the declared index and includes every currently obtaining item. The formal source writes this commitment as $\mathrm{WPPD}(n)$ .

This condition records present-only ontology. It does not yet assert finite content, continuing change, or a deterministic successor law. Those additional conditions belong to the complete PPD argument. Presentness also does not mean that only one observer’s description or experience exists.

Engine, Definition 5.3, pp. 131–132; Theorem 5.4.Persistent Present Determinism · Formal argument

36Past representation

Lookup: RepPast(r) · RepPast(S_t) · Memory and records

$\operatorname{RepPast}(r)$ describes an actual present token $r$ whose content concerns a non-present past. A memory, written record, trace, or model can carry such a claim.

The claim’s present realization is distinct from its accuracy. A false memory can be real as a present token. A past event can genuinely have occurred and produced current consequences without remaining another co-actual region. PPD’s present-only ontology is a stated premise; mediation alone is not used to derive it.

Engine, Definition 5.4, Lemma 5.1 and Chapter 5 §§5.3, 5.10.Persistent Present Determinism · Formal argument

37Future representation

Lookup: RepFuture(r) · RepFuture(S_t) · Prediction · Plan

$\operatorname{RepFuture}(r)$ describes an actual present token whose content concerns a future time. A prediction, plan, expectation, or simulation can perform that role without being a stored future region.

The represented event need not occur merely because a token anticipates it. Planning can nevertheless change successor conditions by acting within the present causal organization. That is a claim about the plan’s actual role, not a power to escape the same complete source and full law.

Engine, Definition 5.4; Chapter 5 and Remark 5.9.Persistent Present Determinism · Formal argument

38Law of evolution

Lookup: F (evolution rule) · F_L(S) · Next_L(S) · Successor map · Contrastive source sufficiency

A general successor specification has the form $F_L:\mathcal S\longrightarrow\mathcal P(\mathcal S)$ . It assigns the set of successors admitted by a law specification $L$ . A coarse model may list several because it omits relevant detail.

Under the complete source, faithful full law, closure, contrastive source sufficiency, and continuation premises, the admitted set has one member, $\operatorname{Next}_L(S)$ . On the continuing domain the update is $S_{\sigma(n)}=\operatorname{Next}_L(S_n)$ . The successor convention does not independently establish a smallest physical time unit. Selecting one realized path is not proof that the full rule was single-valued.

Engine, Definitions 5.7–5.8, contrastive source sufficiency, Lemma 5.3 and Theorem 5.4.Persistent Present Determinism · Formal argument

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SOC and Elios: systems, profiles, and evidence

The predicates identify structural features. Comparing their forms and evaluating experiential evidence require the source’s further distinctions.

39System

Lookup: System (A) · Sys(S)

In the spectrum argument, a system is a physically or informationally instantiated process with identifiable internal states and causal dynamics. The predicate is $\operatorname{Sys}(S)$ .

This definition alone does not assume that the system is conscious, alive, intelligent, or a representational epistemic agent. World-coupling, value registration, and temporal integration are further predicates. The letter $S$ here denotes a system; its type is not the PPD state space or a physical admission ratio.

Engine, Definition 6.1, p. 186; Notation and Symbol Guide, compatibility of meanings.Spectrum of Consciousness and Elios · Formal argument

40World-coupled

Lookup: WC(A) · WC(S) · World-coupling

A system is world-coupled when its internal transitions are causally sensitive to, and causally efficacious upon, states of an external environment. The notation is $\operatorname{WC}(S)$ .

Both directions matter: the system is affected by its environment and can affect that environment in turn. The predicate is not merely a claim that some representation correlates with something outside it. A particular application must establish the relevant coupling rather than infer it from a material or species label.

Engine, Definition 6.2 and Theorem 6.1.Spectrum of Consciousness and Elios · Formal argument

41Value-registered

Lookup: VR(A) · VR(S) · Value registration · Functional value

A system has internal variables marking better and worse conditions for itself, and its dynamics tend to preserve or promote states marked as better and avoid those marked as worse. The predicate is $\operatorname{VR}(S)$ .

This is system-relative functional value: damage and integrity, deprivation and satisfaction, error and success, or reward and penalty signals. It is not automatically a moral judgment or proof of felt reward. The source keeps this registration predicate distinct from CG’s valuer predicate and an agent’s actual valuational organization in DMF.

Engine, Definition 6.3; Notation and Symbol Guide, §§8–9.Spectrum of Consciousness and Elios · Formal argument

42Temporally integrative

Lookup: TI(A) · TI(S) · Temporal integration

A system’s present state encodes information about prior states in a way that nontrivially shapes its future dynamics. The predicate is $\operatorname{TI}(S)$ . Memory and learning illustrate the role: what has happened changes how the system proceeds.

The definition does not require an autobiographical narrative, every kind of anticipation, or a co-actual archive of former states. Its empirical application must identify the retained information and its current causal role.

Engine, Definition 6.4, p. 187.Spectrum of Consciousness and Elios · Formal argument

43Primitive Experiential Profile and phenomenal evidence

Lookup: PE(A) · PE(S) · Primitive Experiential Profile · Phenomenal evidence · Structural profile · gamma · γ

Primitive Experiential Profile. In the spectrum formalism, PE denotes the Boolean eligibility condition

\operatorname{PE}(S)\Longleftrightarrow\operatorname{Sys}(S)\land\operatorname{WC}(S)\land\operatorname{VR}(S)\land\operatorname{TI}(S).

Its truth is not a degree of consciousness. The separate comparison profile $\gamma(S)=\langle c(S),v(S),\tau(S)\rangle$ describes declared aspects of coupling, regulation, and temporal organization. Componentwise comparisons allow ties and incomparability; the application supplies what the descriptors measure or compare.

Phenomenal evidence. Evidence supplied by one’s own experienced case is different from the structural conjunction PE. The actual token minimum and mediated evidence concerning another system do not automatically establish its private phenomenology. I do not assign the abbreviation PE to first-person evidence in this formal vocabulary.

Engine, Definition 6.5, Remark 6.6, Theorems 6.1–6.2 and concluding scope, pp. 187–192.Spectrum of Consciousness and Elios · Formal argument

44Zombie hypothesis and Z(A)

Lookup: Zombie-like system · Z(A) · Philosophical zombie

A zombie hypothesis considers apparently mind-like behavior without experience. In the Elios argument, $\mathrm Z(A)$ is specifically a skeptical statement that a reflective agent can token about itself: “I might be a pure zombie with no experience at all.” It is not the theorem’s predicate certifying a system to lack experience.

The actual skeptical token occurs whether or not its content is true. Elios then tests the consistency of an agent’s evidential standard across relevantly matched cases. A functional valuer is not made valuer-free merely by being called a zombie.

Engine, Formal Argument 6.5, Theorem 6.2; Formal Argument 7.10, Remark 7.6.Spectrum of Consciousness and Elios · Formal argument

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CG: valuers and moral interpretation

Moral applicability, descriptive truth, and compliance are separate roles. All-valuer independence is a stronger target than independence from one person’s approval.

45Valuer

Lookup: V (valuer label) · Val(v) · Val_w(v) · Valuerhood

A subsystem with a nontrivial ordering over accessible states whose dynamics are systematically sensitive to that ordering. Other things being equal, it tends toward states ranked better for it and away from those ranked worse. The source writes $\operatorname{Val}(v)$ , or $\operatorname{Val}_w(v)$ in a declared circumstance.

Valuerhood is not simply reading a moral sentence. Nor does a moral judgment require the wrongdoer’s approval: affected persons or other relevant valuers may supply the stakes. System-relative value registration, a valuer, and a complete agent’s valuational organization remain related but different descriptions.

Engine, Definition 7.1 and constitutive valuer premise, pp. 214–215.Contingency Guillotine · Formal argument

46Moral proposition

Lookup: Moral(P) · Moral applicability · App_M(P,w) · Moral evaluation · Failed applicability

A proposition whose content purports to evaluate states or actions and to license, require, or forbid behavior in an action-guiding sense. $\operatorname{Moral}(P)$ is not merely a report that some group approves a practice.

The source distinguishes descriptive truth, moral applicability $\operatorname{App}_M(P,w)$ , and actual compliance. Its moral evaluation is T or F when the relevant application conditions are met, and U when applicability fails. U is not a third physical condition. Under the constitutive premise, relevant valuers supply the evaluative ordering and practical stakes.

Engine, Definition 7.2 and constitutive valuer premise, pp. 214–215.Contingency Guillotine · Formal argument

47Strongly objective moral proposition

Lookup: ObjMor(P) · Strong moral objectivity · All-valuer independence

The strong claim that the same action-guiding moral interpretation remains applicable and determinately evaluated throughout the declared comparison class, independently of whether any valuers or valuing relations exist. Its source notation is $\operatorname{ObjMor}(P)$ .

The comparison class includes a nonempty valuer-free test case. This is stronger than impartial assessment, independence from one offender’s disapproval, or a descriptive truth about suffering. Replacing moral evaluation with a conditional about what someone would prefer changes the claim being tested; it does not establish the original unrestricted independence.

Engine, Definition 7.3 and Theorem 7.3, pp. 216–218.Contingency Guillotine · Formal argument

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DMF: agency, judgment, and responsibility

The chooser and the person responding are both within the causal account. Explaining an output does not establish that it is accurate, humane, or justified.

48Deterministic world

Lookup: Deterministic history · F (DMF) · Transition readout · Xi_L · Ξ_L · Fatalism

DMF uses a represented sequence of complete states together with the single-valued continuation function established under PPD’s full premise set. At continuing indices, $S_{\sigma(t)}=F(S_t)$ . The representation orders states; it does not make all of them co-actual.

Where behavior within a transition is at issue, the model also supplies the transition readout $\Xi_L(S_t)$ . A unique endpoint does not reconstruct every intervening action. A local agent/environment description is deterministic only when it contains the causally relevant input for that readout. Determinism does not mean outcomes occur regardless of the agent’s actual efforts.

Engine, Definitions 8.1–8.2 and Remark 8.6, pp. 234–237.Deterministic Moral Forces · Formal argument

49Contra-causal free will

Lookup: CCFW · Contra-causal authorship · Free will · Caused agency

The targeted authorship claim gives an agent source-independent control over a different action while the identical complete source and full law are held fixed. Considering alternatives, revising a decision after learning, or acting without coercion does not by itself supply that control.

The causal account keeps the person’s deliberation, learning, inhibition, communication, and planning inside what produces action. Adding an unspecified random deviation does not independently give the person ownership of it. Rejecting contra-causal authorship is not a rejection of caused agency or every compatibilist use of “freedom.”

Engine, Definition 8.4, Lemma 8.1 and Remarks 8.6, 8.11–8.12; EG, Chapter 16.Deterministic Moral Forces · Formal argument

50Moral judgment

Lookup: Judg_A(t) · Judgment · Valuationally-relative ought · Expected consequences

A valuing agent’s output that presents a moral evaluation of conduct, a person, or a state of affairs. DMF represents judgment as part of the agent’s behavior, with its causes and possible consequences included in the declared causal account.

A judgment is not automatically true or humane because it was produced. Likewise, explaining its cause does not endorse it. Valuationally-relative ought concerns the agent’s perceived options and ranking of expected consequences; it neither guarantees a greatest option nor predicts that the agent will comply. My practical assessment retains the suffering, evidence, capacity, and alternatives of everyone affected, including the chooser.

Engine, Definition 8.7; Definitions 8.13–8.14 and Is–Ought Representation; concluding guidance in Formal Argument 8.4.Deterministic Moral Forces · Formal argument · Is–Ought Representation

51Punishment

Lookup: Pun_A(t) · Sanction · Responsibility as causal locus

An imposed sanction or adverse treatment by an agent or institution in response to conduct it classifies as an offense or violation. DMF represents that output and relation as $\operatorname{Pun}_A(t)$ , within the same causal world as the conduct being judged.

Possible roles include deterrence, incapacitation, rehabilitation, signaling, consolidation of power, and satisfaction of retributive desires. Their actual operation and effects require evidence. Causal inclusion does not prove that punishment works, that harm is justified, or that intervention is needed. Protection, answerability, restraint, and repair can be evaluated without an unconditional debt of suffering.

Engine, Definition 8.8, Lemma 8.3, Theorem 8.5 and responsibility corollary.Deterministic Moral Forces · Formal argument

52Stance-free moral property

Lookup: Stance-free desert · Stance-independent morality

Applicable moral force independent of all constitutive valuers and their valuing relations, in the strong CG sense. Independence from a particular offender’s approval or evaluation by a stable shared standard is not enough to establish this property.

DMF’s causal sufficiency result and CG’s exclusion of this moral property are separate arguments. Joined under their premises, they exclude the specified source-independent authorship and all-valuer-independent retributive debt. They do not make empirical consequences arbitrary or erase the need to justify a response under an explicit practical standard.

Engine, Definition 8.10 and Theorem 8.5; Definition 7.3.Deterministic Moral Forces · Formal argument

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FMFG core commitments and collapse vocabulary

These entries retain their Finite Mind, Finite God meanings. The finite-interface argument, personhood argument, and totality claims are connected without becoming interchangeable.

53Finite Mind, Finite God (FMFG)

Lookup: FMFG

I develop FMFG by following God-claims through finite interfaces, interpretation, fairness, preference, personhood, and ultimacy. The opening formal section sets out a capstone schema whose fuller development is distributed through the later arguments.

Mediation alone does not show that the referent of every concept has the same limits as the mind tokening it. The personhood branch uses the preference-and-standpoint argument. The totality branch tests the stated ultimacy conditions. Their combination, rather than finite word length alone, drives the challenge to the classical God/no-God framing.

FMFG, §1.7 and its proof sketches; Chapters 2, 6–8; §11.8.1.Finite Mind, Finite God: the book

54Finite mind

Lookup: M · Finite epistemic subject

In FMFG a mind is an epistemic subject capable of entertaining concepts, forming doxastic attitudes, and making inferences. Its interface has bounded information capacity: at one time it cannot represent arbitrarily many independent distinctions with unbounded precision.

No particular material implementation is assumed in this definition. This limitation concerns the subject’s representational capacity. It is not, by itself, a proof that every represented object is small or finite, or that no reliable knowledge can extend beyond immediate sensation.

FMFG, Definition 1.3 and §11.8.1.Finite Mind Constraint

55Experiential interface

Lookup: I(M) · Presentational interface

FMFG writes $\mathcal I(M)$ for the internal presentational states through which something is available to a mind $M$ for judgment. A concept is tokened when a state in that interface functions as the mind’s presentation of it.

The interface may involve perception, memory, inference, imagination, and affect; it is not an unmediated possession of the represented source. This FMFG use retains its own definition. EL’s more explicit comparison tuple distinguishes a frame from its update and inferential relations; the similar letter does not erase those local definitions.

FMFG, Definition 1.3 and §11.8.1; EL Engine, Definition 2.13.Human Interface Thesis

56God-concept tokening

Lookup: G_M · God-concept · Tokening God

$G_M$ denotes a God-concept entertained by a finite mind. It functions for that mind through some state $s\in\mathcal I(M)$ that presents its content. The token and an alleged divine referent are not the same thing.

This locates the claim within an epistemic interface. It neither proves nor disproves the referent merely by locating the token. A testimony, revelation, or ultimacy claim must still be examined for what it asserts and what supports it. The later collapse arguments require their additional conditions.

FMFG, Theorem 1.1, Definition 1.3 and Chapter 2; §11.8.1.Finite Mind Constraint

57God/no-God frame

Lookup: God/no-God · The Bad Frame

The familiar staging of the religious question as a binary choice between theism and atheism, treated as rival answers to an already well-formed object-level question.

FMFG first asks what “God” names in that question: a finite agent, an alleged unlimited ultimate, or totality under a particular interpretation. The binary label does not settle the concept’s stability, its evidence, or its consequences. Questioning the frame is not simply substituting one answer inside it.

FMFG, §§1.2–1.6 and §11.8.1.The Bad Frame

58Collapse proof

Lookup: Collapse schema · Ultimacy collapse

A proof pattern examining whether a contested category survives the conditions attached to its meaningful use. In FMFG, certain God-readings cannot retain all their original commitments together: they move toward a finite agent or toward totality with a changed status for literal personhood.

The precise source conditions do the work. Tokening a finite representation is not a proof that its referent is finitely sized, and a claim that everything falls within a ground’s scope is not automatically numerical identity between that ground and everything. I keep the opening grounding-scope schema distinct from the later identity-with-totality argument.

FMFG, §1.7, especially Lemma 1.5 and Remark 1.6; Chapter 7 formal derivation; §11.8.1.The Bad Frame

59Existential ground

Lookup: Existential ground (FMFG) · EG · Ground

FMFG usage. The nonoptional fact of existence, the shared floor of whatever obtains, which remains when an object-level God-claim fails to name a stable kind of thing. Believers and nonbelievers are not divided into those who possess reality and those who lack it.

Connected EG usage. In Existential Ground I develop the broader integrated coherence structure: undeniable anchors, eliminated pseudo-alternatives, and the positive constraints that follow with their premises. That later integrated use is not substituted for FMFG’s introductory definition. Neither use names an extra object behind reality.

FMFG, §11.8.1 and Chapter 10; EG, §2.1 and Appendix B.Existential ground in FMFG

60Finite Mind Constraint

Lookup: FMC · Finite interface constraint

Any concept entertained by a finite mind is available through a token in its experiential interface. A God-concept cannot function for that mind as an epistemic grasp that bypasses all internal presentation.

The constraint concerns access, not automatic falsity. Human Interface Thesis develops how public revelation and authority claims pass through cognitive, linguistic, social, and interpretive channels. A reliable claim can be mediated; alleging an ultimate source does not remove the need to evaluate its finite presentation.

FMFG, Theorem 1.1 and proof sketch; Chapter 2; §11.8.1.Finite Mind Constraint

61Finite God Trap

Lookup: Preference-finitude · Preference structure · Personhood predicates · Finite God Collapse

The source tests a conjunction: ultimacy-as-totality, $B=E$ , together with literal nontrivial personhood. Personhood imports preference structure; the preference-finitude argument treats the bearer of an internal evaluative ordering as a proper standpoint rather than exhaustive totality as such.

That standpoint step must remain visible. On that account, retaining literal personhood yields a finite bearer; retaining ultimacy-as-totality requires changing the status of the personal predicates, for example through analogy or metaphor. Finitude here is not an insult about power, intelligence, size, or lifespan. CG’s valuer argument is connected but does not supply the entire personhood proof on its own.

FMFG, Chapter 7, Definitions 7.1–7.2 and Preference-finitude / Finite God Trap results; §11.8.5.Finite God Collapse: Preference and Personhood

62Totality

Lookup: E · Exhaustive reality · Ultimacy-as-totality

The maximal domain of all that obtains. In FMFG’s Chapter 7, $E$ denotes total existence and ultimacy-as-totality is explicitly the identity $B=E$ . That is a particular stated use of ultimacy, not an automatic consequence of the word “ground.”

A subject can belong wholly to reality without being the whole of reality. A ground can also be claimed to have everything within its grounding scope without numerical identity having been demonstrated. The source’s personhood and nondual arguments examine those claims through their actual additional premises.

FMFG, §11.8.1; Chapter 7 frame and Definition 7.2; Chapter 8.Finite God Collapse: Preference and Personhood

63Ultimacy

Lookup: Ultimate · Unlimited ultimacy · Grounding scope

A claim about what is final or decisive in meaning, value, standing, or explanation. FMFG distinguishes agentive-personal readings from ultimacy-totality readings; the latter cannot posit an ontologically independent remainder outside the scope they claim to exhaust.

Grounding scope, numerical identity with totality, and ordinary personal agency are different commitments. The word “ultimate” does not make their conjunction coherent by itself. The particular argument must say which commitments are being tested and retain the conditions required for its result.

FMFG, Definitions 1.4 and 7.2; Lemma 1.5 and Remark 1.6; §11.8.1.Nondual Collapse

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Sources and related references

I keep each definition attached to its source formulation. The numbered locators in this reference are book locations, not claims that an article link opens a particular PDF page. A narrower definition in a formal argument governs that use.

Engine. Matthew Tripp Zejda, Existential Logicism: A Logic-Based Engine for Navigating Reality. Chapters 1–8 and their ten formal sections; Notation and Symbol Guide, printed pp. 291–301. Open the Engine publication page.

Tool. Matthew Tripp Zejda, Existential Logicism: A Logic-Based Tool for Navigating Reality. The continuous prose account of the same connected questions. Open the Tool publication page.

FMFG. Matthew Zejda, Finite Mind, Finite God. Chapter 1 and its opening derivation, the Human Interface Thesis, the preference/personhood argument in Chapter 7, and Chapter 11, Terminology, Notation, and Conventions. Open the FMFG publication page.

EG. Matthew Tripp Zejda, Existential Ground: The Undeniable Foundation Beneath Reality, Time, God, and Life. The connected account is distinguished from the earlier source formulations rather than silently substituted for them. Open the EG publication page.

A source’s local symbols are not a universal notation imposed on every project. In particular, epistemic interfaces, state spaces, evaluative predicates, and physical quantities must retain their declared types and roles.

A

B

C

D

E

F

G

H

I

J

L

M

N

O

P

R

S

Symbols

T

U

V

W

X

Z

EL core labels and pillars

EL primitives: occurrence, agents, and access

ION: absence, candidates, and representation

LEIR: dependence and foundations

PPD: states, records, and continuation

SOC and Elios: systems, profiles, and evidence

CG: valuers and moral interpretation

DMF: agency, judgment, and responsibility

FMFG core commitments and collapse vocabulary

Sources and related references