13 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) |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
A reaction: Each expansion brings a limitation, but then you can expand again. |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
16188 | Serious Actualism says there are no facts at all about something which doesn't exist [Simchen] |
Full Idea: Serious Actualism is the view that in possible circumstances in which something does not exist there are no facts about it of any kind, including its very non-existence | |
From: Ori Simchen (The Barcan Formula and Metaphysics [2013], §1 n4) | |
A reaction: He suggests that the Converse Barcan Formula implies this view. It sounds comparable to the view of Presentism about time, that no future or past truthmakers exist right now. If a new square table were to exist, it would have four corners. |
20887 | A rape disregards the status of being a person - but so does all assault [Foa] |
Full Idea: In a rape a person is used without proper regard for her personhood - but this is true of every kind of assault. | |
From: Pamela Foa (What's Wrong with Rape? [1977], 1) | |
A reaction: This is a good step towards her attempt to pin down what is specifically wrong with rape, which strikes me as an extremely important question, and not merely in order to justify punishments. |
20888 | Rape of children is dreadful, but no one thinks children should have a right of consent [Foa] |
Full Idea: Rape of children is at least as heinous as rape of adults, though few believe that children have or ought to have the same large domain of consent adults (male and female) ought to have. | |
From: Pamela Foa (What's Wrong with Rape? [1977], 1) | |
A reaction: A powerful point. She is not quite spelling out the crux, which is that no one thinks children should have a right to consent to sexual intercourse, which means that consent is irrelevant in such a case of rape. So it can't be the key to adult rape? |
20889 | If men should lust and women shouldn't, that makes rape the prevalent sexual model [Foa] |
Full Idea: We are taught that sexual desires are desires women ought not to have and men must have. This is the model which makes necessary an eternal battle of the sexes. It explains why rape is the prevalent model of sexuality. | |
From: Pamela Foa (What's Wrong with Rape? [1977], 3) | |
A reaction: A striking thought. See 'The Origins of Sex' by F.Dabhoiwala, which claims that women used to be seen as the sexual predators, and the balance shifted in the 18thC. Are women obliged to exhibit lust, in order to defuse rapacious desires? |