• README ⤓ .txt 2026-07-17T121634.146 000000000000808
  Logics individuated by restricting or dropping cut—the transitivity of the consequence relation. The move is the youngest in the division and the most counterintuitive: transitivity looks less like a structural convenience than like what consequence is for, and a logic without it seems to lose the right to chain arguments at all.
• Inconsistent Mathematics ⤓ .md 2026-07-16T001414.000 000000000036608
  Robert K. Meyer's relevant arithmetic R# (1976) and his conjecture that it proves its own non-triviality; Ross Brady's non-triviality proof for naive set theory (1971, 1989); Chris Mortensen's Inconsistent Mathematics (1995), which named the programme; Graham Priest, "Inconsistent models of arithmetic" (1997); Zach Weber's Paradoxes and Inconsistent Mathematics (2021) for the current state.
• Noncontractive Logic ⤓ .md 2026-07-15T233755.000 000000000033576
  Elia Zardini, "Truth without contra(di)ction" (Review of Symbolic Logic, 2011); Greg Restall's earlier observation that contraction drives Curry ("How to be Really Contraction Free", 1993); Petersen (2000) on naive comprehension without contraction; Mares and Paoli (2014) for the general substructural framing. The counterpart to the nontransitive answer: same problem, different structural rule.
• Strict-Tolerant Logic ⤓ .md 2026-07-15T233755.000 000000000035520
  Pablo Cobreros, Paul Égré, David Ripley, and Robert van Rooij, "Tolerant, classical, strict" (Journal of Philosophical Logic, 2012), introduced for vagueness; Ripley, "Paradoxes and failures of cut" (2013) and "Conservatively extending classical logic with transparent truth" (2012), turned it on the semantic paradoxes. The claim that made it notorious: ST is classical logic, and it has a transparent truth predicate.
• CRITERIA ⤓ .txt 2026-07-15T233655.000 000000000012008
  Not sufficient: A cut-elimination theorem, which shows cut is admissible and is a result about proofs (Metatheory/Proof-Systems). A logic that drops contraction to block Curry while keeping cut—that is noncontractive and belongs in Linear or Affine by which rule it drops, and is cross-listed here where the paradox motivation is the subject. A paraconsistent or paracomplete matrix (Algebraic/Many-Valued): the point here is that the matrix is not what changed.