10 ideas
| 18261 | A simplification which is complete constitutes a definition [Kant] |
| Full Idea: By dissection I can make the concept distinct only by making the marks it contains clear. That is what analysis does. If this analysis is complete ...and in addition there are not so many marks, then it is precise and so constitutes a definition. | |
| From: Immanuel Kant (Wiener Logik [1795], p.455), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
| A reaction: I think Aristotle would approve of this. We need to grasp that a philosophical definition is quite different from a lexicographical definition. 'Completeness' may involve quite a lot. |
| 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… |
| 22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
| Full Idea: In logic the question is not one of contingent but of necessary rules, not how to think, but how we ought to think. | |
| From: Immanuel Kant (Wiener Logik [1795], p.16), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Trans' | |
| A reaction: Presumably it aspires to the objectivity of a single correct account of how we all ought to think. I'm sympathetic to that, rather than modern cultural relativism about reason. Logic is rooted in nature, not in arbitrary convention. |
| 18260 | If we knew what we know, we would be astonished [Kant] |
| Full Idea: If we only know what we know ...we would be astonished by the treasures contained in our knowledge. | |
| From: Immanuel Kant (Wiener Logik [1795], p.843), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
| A reaction: Nice remark. He doesn't require immediat recall of knowledge. You can't be required to know that you know something. That doesn't imply externalism, though. I believe in securely founded internal knowledge which is hard to recall. |
| 19555 | People begin to doubt whether they 'know' when the answer becomes more significant [Conee] |
| Full Idea: Fluent speakers typically become increasingly hesitant about 'knowledge' attributions as the practical significance of the right answer increases. | |
| From: Earl Conee (Contextualism Contested (and reply) [2005], 'Epistemic') | |
| A reaction: The standard examples of this phenomenon are in criminal investigations, and in philosophical discussions of scepticism. Simple observations I take to have maximum unshakable confidence, except in extreme global scepticism contexts. |
| 19557 | Maybe low knowledge standards are loose talk; people will deny that it is 'really and truly' knowledge [Conee] |
| Full Idea: Maybe variable knowledge ascriptions are just loose talk. This is shown when we ask whether weakly supported knowledge is 'really' or 'truly' or 'really and truly' known. Fluent speakers have a strong inclination to doubt or deny that it is. | |
| From: Earl Conee (Contextualism Contested (and reply) [2005], 'Loose') | |
| A reaction: [bit compressed] Conee is suggesting the people are tacitly invariantist about knowledge (they have a fixed standard). But it may be that someone who asks 'do you really and truly know?' is raising the contextual standard. E.g. a barrister. |
| 19556 | Maybe knowledge has fixed standards (high, but attainable), although people apply contextual standards [Conee] |
| Full Idea: It may be that all 'knowledge' attributions have the same truth conditions, but people apply contextually varying standards. The most plausible standard for truth is very high, but not unreachably high. | |
| From: Earl Conee (Contextualism Contested (and reply) [2005], 'Loose') | |
| A reaction: This is the 'invariantist' alternative to contextualism about knowledge. Is it a standard 'for truth'? Either it is or it isn't true, so there isn't a standard. I take the standard to concern the justification. |