Single Idea 15139

[catalogued under 4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula]

Full Idea

The converse Barcan is at least plausible, since its denial says there is something that could fail to meet a condition when everything met that condition; but how could everything meet that condition if that thing did not?

Gist of Idea

Converse Barcan: could something fail to meet a condition, if everything meets that condition?

Source

Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §3)

Book Reference

-: 'Dialectica' [-], p.264


A Reaction

Presumably the response involves a discussion of domains, since everything in a given domain might meet a condition, but something in a different domain might fail it.

Related Ideas

Idea 15132 The Barcan formulas fail in models with varying domains [Kripke, by Williamson]

Idea 15135 If the domain of propositional quantification is constant, the Barcan formulas hold [Williamson]