Weakly Discerning Vertices in a Plenitude of Graphs
E.E. Sheng · dialectica · 2022
De Clercq [-@declercq_r:2012] proposes a strategy for denying purported graph-theoretic counterexamples to the Principle of the Identity of Indiscernibles (PII) by assuming that any vertex is contained by multiple graphs. @duguid_c:2016 objects that De Clercq fails to show that the relevant vertices are discernible. Duguid is right, but De Clercq’s strategy can be rescued. This note clarifies what assumptions about graph ontology are needed by De Clercq and shows that, given those assumptions, any two vertices are weakly discernible and, so, are not counterexamples to the version of PII that requires only weak discernibility.