Source
Barry Smith and Achille C. Varzi (2000), “Fiat and Bona Fide Boundaries”, LIT-1024, Philosophy and Phenomenological Research 60(2): 401–420, read in full in NOTE-721. The OCR garbled the logical symbols, and the formulas were restored by eye; axioms A≤1–A≤3 and A≈2–A≈3 were given from the prose.
What was actually shown
The typology (§1). “Inner boundaries involving spatial discontinuity (holes, fissures, slits) or qualitative heterogeneity (of material constitution, texture, electric charge) we shall call bona fide boundaries.” The rest are fiat: the hemispheres of a homogeneous sphere, national borders “at least in those cases where they lie skew to any qualitative differentiations or spatial discontinuities”, the equator. Fiat boundaries may be social, individual, perceptual, linguistic or mathematical. Any object with a fiat portion of boundary is a fiat object: the North Sea, and also “A mountain, a bay, the branches of a tree, or the stem of a champagne glass”.
Not arbitrary. “Real properties of the underlying factual material … both enable the drawing of fiat borders and constrain the types and location of fiat borders which can be drawn.”
No contact between bodies (§§1.2, 2). “As far as bona fide outer boundaries are concerned, however, no genuine contact or coincidence of boundaries between John and Mary is possible at all.” Bona fide objects are connected; fiat objects may be scattered (Polynesia, Orion).
The distinction is absolute (§2.1). Cutting, or building a fence along a border, makes a new bona fide boundary; “this is not a process of transformation”.
Two theories (§§3.3–3.4). Bona fide boundaries take a primitive B(x, y), a mereologised closure c(x) := x + b(x), and the Kuratowski axioms. Contact is external connection, and two closed things cannot touch (TB4). Fiat boundaries take B*(x, y) with B*(x, y) → x ≤ y: they “are necessarily parts of the entities they bound”, so there is no closure operator and no open/closed distinction. Each side owns its own, and “each hemisphere has its own equator, and the two equators coincide”.
One formal surprise (§3.5). A boundary needs a self-connected host, and self-connection has to be defined by fiat connection: “A self-connected entity is one all of whose parts are separated at most by fiat”. So “the theory of bona fide boundaries presupposes the theory of fiat boundaries”.
What could have come out otherwise. A single topology could have handled both kinds, or the puzzles of contact and division could have survived the split. The paper argues case by case that they do not (sphere, disk, equator, Mason–Dixon line).
What this does not say
- Who or what made a boundary. A cell membrane and a beam joining two pendulums are both bona fide. The equator is fiat and imposed. The paper has no category for a boundary the bounded thing draws and keeps for itself.
- Anything about time or process. The axioms are read synchronically (fn. 15). Boundaries that come and go, or are maintained by a process, are outside the theory.
- That the theory is consistent. It is “illustrative”: no models, no consistency or completeness result.
- That bona fide boundaries exist at the physical level. The authors grant that physics shows macroscopic objects “do not have boundaries of the sort countenanced by common sense at all”. The theory is of the common-sense world.
- That reality is vague. Vagueness “pertains ontologically only to the fiat world”, and every candidate aggregate is “precisely determinate”. NOTE-721 rates this claim weak.
- That an interaction gap is a bona fide boundary. The heterogeneity is of “material constitution, texture, electric charge”, not of coupling strength. Reading a near-decomposability gap as bona fide would extend the paper.
Connections
- QUESTION-035. Every combined form of separate bodies comes out fiat, the
dancing couple (CASE-046) and the coupled pendulums included. The distinction
classifies the question’s answers rather than supplying one, so no
answersedge is claimed. What it offers is a vocabulary: a fiat boundary that real coupling strengths enable and constrain, which fits a target-relative block (CLAIM-157). That use is the record’s. - CLAIM-194. It sorts the membrane and the beam together, as the counter says the gap criterion does. That is indirect support for the counter’s point and no answer to it. The paper’s “imposition” is an observer’s demarcation, not the externally maintained constraint CLAIM-194 means.
- Production and self-production. THEORY-072’s production and Weber and Varela (LIT-1018) are about causal maintenance; the paper’s dependence of a boundary on a host is ontological.
- Mereology. Varzi’s SEP entry (LIT-124; THEORY-493, THEORY-589) is the parthood theory this extends with topology.
- The problem of the many. Lewis (LIT-1015, THEORY-452) likewise puts vagueness in our terms, not in the material.