9 ideas
| 10163 | Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman] |
| Full Idea: At the age of 19 Saul Kripke published a completeness proof of propositional modal logic. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Feferman / Feferman - Alfred Tarski: life and logic Int V |
| 10760 | With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg] |
| Full Idea: Kripke gave a possible worlds semantics to a whole range of modal logics, and S4 and S5 turned out to be both sound and complete with this semantics. Hence more systems could be designed. S1-S3 failed in soundness, leading to 'impossible worlds'. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Marcus Rossberg - First-order Logic, 2nd-order, Completeness §4 |
| 16189 | The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen] |
| Full Idea: Kripke's variable domain approach to quantified modal logic famously invalidates the Barcan Formula. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Ori Simchen - The Barcan Formula and Metaphysics §3 | |
| A reaction: [p.9 and p.16] In a single combined domain all the possibilia must be present, but with variable domains objects in remote domains may not exist in your local domain. BF is committed to those possible objects. |
| 15132 | The Barcan formulas fail in models with varying domains [Kripke, by Williamson] |
| Full Idea: Kripke showed that the Barcan formula ∀x□A⊃□∀xA and its converse fail in models which require varying domains. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Timothy Williamson - Truthmakers and Converse Barcan Formula §1 | |
| A reaction: I think this is why I reject the Barcan formulas for metaphysics - because the domain of metaphysics should be seen as varying, since some objects are possible in some contexts and not in others. Hmm… |
| 15533 | We can quantify over fictions by quantifying for real over their names [Lewis] |
| Full Idea: Substitutionalists simulate quantification over fictional characters by quantifying for real over fictional names. | |
| From: David Lewis (Noneism or Allism? [1990], p.159) | |
| A reaction: I would say that a fiction is a file of conceptual information, identified by a label. The label brings baggage with it, and there is no existence in the label. |
| 15534 | We could quantify over impossible objects - as bundles of properties [Lewis] |
| Full Idea: We can quantify over Meinongian objects by quantifying for real over property bundles (such as the bundle of roundness and squareness). | |
| From: David Lewis (Noneism or Allism? [1990], p.159) |
| 15532 | 'Allists' embrace the existence of all controversial entities; 'noneists' reject all but the obvious ones [Lewis] |
| Full Idea: An expansive friend of the controversial entities who says they all exist may be called an 'allist'; a tough desert-dweller who says that none of them exist may be called a 'noneist'. | |
| From: David Lewis (Noneism or Allism? [1990], p.152) | |
| A reaction: Lewis gives examples of the obvious and the controversial entities. Lewis implies that he himself is in between. The word 'desert' is a reference to Quine. |
| 15535 | We can't accept a use of 'existence' that says only some of the things there are actually exist [Lewis] |
| Full Idea: If 'existence' is understood so that it can be a substantive thesis that only some of the things there are exist, we will have none of it. | |
| From: David Lewis (Noneism or Allism? [1990], p.163) | |
| A reaction: Lewis is a strong advocate, following Quine, of the univocal sense of the word 'exist', and I agree with them. |
| 5495 | Instances of pain are physical tokens, but the nature of pain is more abstract [Putnam, by Lycan] |
| Full Idea: In machine functionalism, pain tokens (individual instances of pain) are identical with particular neurophysiological states, but pain itself, the kind, universal, or 'type', can be identified only with something more abstract. | |
| From: report of Hilary Putnam (The Mental Life of Some Machines [1967]) by William Lycan - Introduction - Ontology p.6 | |
| A reaction: This is where the "what is it like?" question seems important. Pain doesn't seem like a physical object, or an abstract idea. Personally I think the former is more likely to be correct than the latter. Causation by pain is not like causation by gravity. |