4 ideas
| 16974 | The nature of each logical concept is given by a collection of inference rules [Correia] |
| Full Idea: The view presented here presupposes that each logical concept is associated with some fixed and well defined collection of rules of inference which characterize its basic logical nature. | |
| From: Fabrice Correia (On the Reduction of Necessity to Essence [2012], 4) | |
| A reaction: [He gives Fine's 'Senses of Essences' 57-8 as a source] He seems to have in mind natural deduction, where the rules are for the introduction and elimination of the concepts. |
| 16973 | Explain logical necessity by logical consequence, or the other way around? [Correia] |
| Full Idea: One view is that logical consequence is to be understood in terms of logical necessity (some proposition holds necessarily, if some group of other propositions holds). Alternatively, logical necessity is a logical consequence of the empty set. | |
| From: Fabrice Correia (On the Reduction of Necessity to Essence [2012], 3) | |
| A reaction: I think my Finean preference is for all necessities to have a 'necessitator', so logical necessity results from logic in some way, perhaps from logical consequence, or from the essences of the connectives and operators. |
| 9155 | An a priori proof is independent of experience [Leibniz] |
| Full Idea: An a priori proof is a proof independent of experience. | |
| From: Gottfried Leibniz (Primary Truths [1686]) | |
| A reaction: Burge says Leibniz gave the first modern account of a priori knowledge. There may be no explicit reference to experience involved, but it would beg many questions to deny that implicit experience may be at the root of the proof. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |