---
slug: infinitism
name: Infinitism
one_liner: "The third escape from the epistemic regress trilemma: accept the regress. A belief is justified by an infinite, non-repeating chain of distinct reasons — no foundational stopping point (contra foundationalism) and no loop back (contra coherentism), so justification is never completed but is the standing availability of a further reason at every challenged step."
type: prime
schema_version: 2
status: density_v2_draft
categories: [structural, epistemology, philosophical]
origin_domain: epistemology
alternate_origin_domains: [logic, metaphysics, philosophy_of_science]
aliases: [accept_the_regress, infinite_chain_of_reasons, endless_justification, regress_embracing_justification, turtles_all_the_way_down_as_stance]
related: []
solution_archetypes: []
review_flags:
- "OPERATOR-DERIVED (op-14 lattice/symmetry completion) — the CLEAN k-1-of-k completion of the epistemic-regress-response family: the corpus already holds the problem (`infinite_regress`) plus two of the three canonical responses (`foundationalism` = STOP, `coherentism` = LOOP); infinitism is the third and absent cell (CONTINUE / accept the regress). Independently surfaced by op-11 (analogy completion) as the coherentism-analog. Discovered 2026-07-04. STRONG hold (verified absent from corpus; established named position — Peter Klein; Aristotle's rejected third horn). STATUS: HOLD pending owner keep/cut."
- "Created 2026-07-04; STUB ONLY (frontmatter + Core Idea + Notes). SI/SF/similarity are PROPOSER ESTIMATES pending triangulation. Body sections (Structural Signature onward) NOT written."
- "Curate-as-triad note: recommend curating the regress-response triad TOGETHER — `infinite_regress` (problem) → {`foundationalism`, `coherentism`, `infinitism`} (the three exhaustive responses: STOP / LOOP / CONTINUE) — and drawing sibling edges among the three responses at incorporation."
- "Phase-C action: re-similarity-check vs `infinite_regress` (the problem this responds to), `foundationalism`, and `coherentism` (the sibling responses); confirm it is the genuine third response (accept-the-regress) and not a restatement of `infinite_regress` or a mere negation of foundationalism; draw sibling edges within the {foundationalism, coherentism, infinitism} response-set and a response-to-problem edge from `infinite_regress`; write a v1 draft and sync the one_liner across v1/v2 per CLAUDE.md before merge."
substrate_independence:
  composite_substrate_independence: 4
  domain_breadth: 4
  structural_abstraction: 4
  transfer_evidence: 3
  reasoning: 'The bare structure — treating an unbounded, non-repeating dependency chain as a legitimate grounding rather than demanding either a terminating foundation or a self-supporting loop — is substrate-neutral. It is the "CONTINUE" option in any grounding/dependency problem whose trilemma is STOP / LOOP / CONTINUE: justification chains in epistemology (the home case), causal chains (accept an infinite causal history rather than a first cause or a causal loop), definitional/semantic regress (accept unbounded definitional depth rather than primitives or circular definition), and meta-justification (reasons for reasons for reasons). domain_breadth scores 4 because the escapes are genuinely unlike siblings but they all share the same abstract regress-and-its-three-exits scaffold, keeping them a family rather than fully independent instances. structural_abstraction is 4 because the core is a pure claim about the legitimacy of an infinite non-repeating dependency chain, requiring no epistemic substance to state, though the canonical framing and defense live in justification-theoretic vocabulary. transfer_evidence is 3: the position is named and defended chiefly within epistemology (Klein), with the cross-domain "accept the regress" stance more often invoked informally (turtles-all-the-way-down) than developed as a rigorous named option, so evidence is real but thinner than the home case.'
similarity_to_nearest_existing_prime:
  slug: infinite_regress
  similarity: 0.6
structural_framed:
  label: structural
  aggregate: 0.44
  criteria: {vocab_travels: 0.6, evaluative_weight: 0.35, institutional_origin: 0.15, human_practice_bound: 0.3, import_vs_recognize: 0.5}
  rationale: 'Reads structural-to-mixed. The canonical statement uses epistemology vocabulary (justification, reasons, belief), which keeps vocab_travels and import_vs_recognize off the floor, but the load-bearing structure — accepting an unbounded, non-repeating dependency chain as a legitimate ground instead of demanding a foundation (STOP) or a loop (LOOP) — is recognized rather than imported and travels to any grounding/dependency problem (causal chains, definitional regress, meta-justification). The frame residue is the justificatory/normative cast of "reasons" and "warrant" (holding evaluative_weight and human_practice_bound above the floor), but the third-horn-of-a-trilemma shape underneath is substrate-neutral. Comparable framing to its sibling responses `foundationalism` and `coherentism`; slightly higher aggregate than a pure structural prime because the response is most naturally defended within a human epistemic practice.'
phase_b_passes_completed: []
---
# Infinitism

## Core Idea

Infinitism is the third response to the epistemic regress problem — the Agrippa (Münchhausen) trilemma — and the one that *accepts the regress* rather than escaping it. The problem: a belief is justified only if supported by a reason, which must itself be justified by a further reason, and so on. This chain can only do one of three things — it can STOP at a reason that needs no further support, it can LOOP back on itself, or it can CONTINUE without end. Those three exits are exhaustive, and the corpus already names the first two: `foundationalism` takes the chain to STOP at self-justifying foundations, and `coherentism` lets it LOOP into a self-supporting web. Infinitism is the remaining horn: it holds that a belief is justified by an *infinite, non-repeating chain of distinct reasons*, each supported by a further reason, with no foundational stopping point (contra foundationalism) and no return to an earlier link (contra coherentism).

The load-bearing move is a reconception of what justification *is*. For foundationalism justification bottoms out; for coherentism it closes into a network; for infinitism it is never "completed" at all. Justification becomes a standing property — the *availability of a further appropriate reason at every point where the chain is challenged* — rather than a finished structure that terminates or closes. The infinity is not a defect to be paid down but the correct shape of the answer: to demand that the chain end or loop is, on this view, to smuggle back exactly the arbitrariness (STOP) or circularity (LOOP) that motivated the trilemma in the first place. The distinctive commitment is that an unbounded non-repeating dependency chain can *legitimately* ground a belief — that "no foundation and no loop" is a coherent stance, not a failure state.

Read structurally, the same third-horn shape recurs in any grounding or dependency problem whose escapes are STOP / LOOP / CONTINUE. In *causal chains*, infinitism is the analog stance that accepts an infinite causal history rather than positing a first cause (STOP) or a causal loop (LOOP). In *definitional and semantic regress*, it is accepting unbounded definitional depth rather than terminating primitives or circular definitions. In *meta-justification*, it is granting reasons-for-reasons-for-reasons all the way up rather than a self-warranting rule or a mutually-supporting pair. Across these the shared abstract form is a regress with exactly three exits, and infinitism is always the one that says the third exit — keep going, non-repeating, without end — is itself a legitimate resolution. "Turtles all the way down," taken not as a joke but as a considered position, is this stance.

## Notes

**Provenance.** Produced by operator 14 (lattice / symmetry completion) as the clean k-1-of-k completion of the epistemic-regress-response family. The corpus already holds the *problem* — `infinite_regress` — together with two of the three canonical *responses*: `foundationalism` (STOP: terminate the chain at self-justifying foundations) and `coherentism` (LOOP: let the chain close into a mutually-supporting web). The trilemma has exactly three escapes — STOP, LOOP, CONTINUE — so the family has a single missing cell: the CONTINUE / accept-the-regress response. That cell is infinitism. It was independently surfaced by operator 11 (analogy completion) as the coherentism-analog. Discovered 2026-07-04. Established named position: Peter Klein's infinitism; Aristotle's explicitly-rejected third horn of the regress. Verified absent from the corpus. Manifest: STRONG hold — the cleanest lattice completion op-14 found (a textbook k-1-of-k gap where the corpus already has the problem plus two of three responses).

**For owner evaluation (keep/cut).** The case FOR is strong on *structural completeness*: infinitism completes a canonical, closed, exhaustive three-member family (the trilemma's three exits) where the corpus already carries the problem and two of the three responses — leaving the set visibly one-short. It is a *standard named position* (Klein), not a proposer coinage, and it is the third-horn shape that recurs beyond epistemology (causal, definitional, meta-justificatory regress). The case AGAINST: infinitism is the *least philosophically defended* of the three responses — a substantial camp regards it as a non-starter (an actual infinity of distinct reasons is psychologically unavailable and arguably viciously regressive). The proposer's recommendation is that *structural completeness argues for inclusion regardless of philosophical popularity*: the encyclopedia catalogs the response, not the consensus verdict on it, and an exhaustive family with one cell silently missing is a worse map than one that names all three and flags the third as contested. Sharp keep/cut question: *does the corpus want the complete regress-response triad (even the disfavored horn), or only the two responses that most epistemologists endorse?*

**At incorporation.** Re-run similarity against `infinite_regress` (the problem this responds to — screen hard to confirm infinitism is the *response*, not a restatement of the problem), `foundationalism`, and `coherentism` (the sibling responses; confirm infinitism is not merely the negation of foundationalism but a positive stance). If kept: curate the triad *together* — draw a response-to-problem relation from `infinite_regress` and sibling edges among `{foundationalism, coherentism, infinitism}` so the three exits are linked as a closed set (STOP / LOOP / CONTINUE), with a note that the set is exhaustive. Add a missing-edge flag recording the trilemma structure explicitly. Write a v1 draft and sync the one_liner across v1 and v2 per CLAUDE.md before merge.
