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2 ideas
| 19297 | The two Barcan principles are easily proved in fairly basic modal logic [Hale] |
| Full Idea: If the Brouwersche principle, p ⊃ □◊p is adjoined to a standard quantified vesion of the weakest modal logic K, then one can prove both the Barcan principle, and its converse. | |
| From: Bob Hale (Necessary Beings [2013], 09.2) | |
| A reaction: The Brouwersche principle (that p implies that p must be possible) sounds reasonable, but the Barcan principles strike me as false, so something has to give. They are theorems of S5. Hale proposes giving up classical logic. |
| 19301 | With a negative free logic, we can dispense with the Barcan formulae [Hale] |
| Full Idea: I reject both Barcan and Converse Barcan by adopting a negative free logic. | |
| From: Bob Hale (Necessary Beings [2013], 11.3) | |
| A reaction: See section 9.2 of Hale's book, where he makes his case. I can't evaluate this bold move, though I don't like the Barcan Formulae. We can anticipate objections to Hale: are you prepared to embrace the unexpected consequences of your new logic? |