display all the ideas for this combination of texts
5 ideas
| 16186 | The Barcan Formulas express how to combine modal operators with classical quantifiers [Simchen] |
| Full Idea: The Barcan Formula and its converse gives expression to the most straightforward way of combining modal operators with classical quantification. | |
| From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1) |
| 16187 | The Barcan Formulas are orthodox, but clash with the attractive Actualist view [Simchen] |
| Full Idea: The Barcan Formulas are a threat to 'actualism' in modal metaphysics, which seems regrettable since the Formulas are validated by standard modal logics, but clash with the plausible and attractive actualist view (that there are no merely possible things). | |
| From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1) | |
| A reaction: He notes that the Barcan Formulas 'appear to require quantification over possibilia'. So are you prepared to accept the 'possible elephant in your kitchen'? Conceptually yes, but actually no, I would have thought. So possibilia are conceptual. |
| 16190 | BF implies that if W possibly had a child, then something is possibly W's child [Simchen] |
| Full Idea: In accordance with the Barcan Formula we assume that if it is possible that Wittgenstein should have had a child, then something or other is possibly Wittgentein's child. | |
| From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §5) | |
| A reaction: Put like this it sounds unpersuasive. What is the something or other? Someone else's child? A dustbin? A bare particular? Wittgenstein's child? If it was the last one, how could it be Wittgenstein's child while only possibly being that thing? |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |