18 ideas
| 8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
| Full Idea: Chihara's programme is to replace talk of sets with talk of open sentences. Instead of speaking of the set of all cats, we talk about the open sentence 'x is a cat'. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2 | |
| A reaction: As Shapiro points out, this is following up Russell's view that sets should be replaced with talk of properties. Chihara is expressing it more linguistically. I'm in favour of any attempt to get rid of sets. |
| 10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
| Full Idea: Chihara's system is a version of type theory. Translate thus: replace variables of sets of type n with level n variables over open sentences, replace membership/predication with satisfaction, and high quantifiers with constructability quantifiers. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4 |
| 8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
| Full Idea: Chihara's system is similar to simple type theory; he replaces each type with variables over open sentences, replaces membership (or predication) with satisfaction, and replaces quantifiers over level 1+ variables with constructability quantifiers. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2 | |
| A reaction: This is interesting for showing that type theory may not be dead. The revival of supposedly dead theories is the bread-and-butter of modern philosophy. |
| 10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
| Full Idea: Chihara has proposal a modal primitive, a 'constructability quantifier'. Syntactically it behaves like an ordinary quantifier: Φ is a formula, and x a variable. Then (Cx)Φ is a formula, read as 'it is possible to construct an x such that Φ'. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4 | |
| A reaction: We only think natural numbers are infinite because we see no barrier to continuing to count, i.e. to construct new numbers. We accept reals when we know how to construct them. Etc. Sounds promising to me (though not to Shapiro). |
| 15642 | If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle] |
| Full Idea: If the kinds there are depend not on the essences of the objects but on their observed distinguishing particulars, ...then for any kind that we think there is, it is possible that there are many underlying essences which are observably indistinguishable. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: Eagle is commenting on Locke's reliance on nominal essences. This seems to be the genuine problem with jadeite and nephrite (both taken to be 'jade'), or with 'fool's gold'. This isn't an objection to Locke; it just explains the role of science. |
| 15645 | Nominal essence are the observable properties of things [Eagle] |
| Full Idea: It is clear the nominal essences really are the properties of the things which have them: they are (a subset of) the observable properties of the things. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: I think this is wrong. The surface characteristics are all that is available to us, so our classifications must be based on those, but it is on the ideas of them, not their intrinsic natures. That is empiricsm! What makes the properties 'essential'? |
| 15643 | Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle] |
| Full Idea: Nominal essence does not allow for gradations in significance for the underlying properties. Those are all essential for the object behaving as it observably does, and they must all be given equal weight when deciding what the object does. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: This is where 'scientific' essentialism comes in. If we take one object, or one kind of object, in isolation, Eagle is right. When we start to compare, and to set up controlled conditions tests, we can dig into the 'gradations' he cares about. |
| 2181 | It is an absurd Kantian idea that at the limit rationality and freedom coincide [Williams,B] |
| Full Idea: There is a deluded Kantian idea that at the limit rationality and freedom will totally coincide. | |
| From: Bernard Williams (Shame and Necessity [1993], VI - p.158) |
| 2176 | There is only a problem of free will if you think the notion of 'voluntary' can be metaphysically deepened [Williams,B] |
| Full Idea: There is a problem of free will only for those who think that the notion of voluntary can be metaphysically deepened. | |
| From: Bernard Williams (Shame and Necessity [1993], III - p.68) | |
| A reaction: Years later, I now see that his refers to a pet hate of mine in discussions of free will, which is the idea that a person can have something called 'ultimate' responsibility for an action (which is the 'deep' version of 'you did it'). |
| 4317 | We judge weakness of will by an assessment after the event is concluded [Williams,B, by Cottingham] |
| Full Idea: Williams has shown that whether an action was weakness of will depends on an evaluation after the event, as in the question of whether Gauguin was right to abandon his family to pursue his art. | |
| From: report of Bernard Williams (Shame and Necessity [1993]) by John Cottingham - Reason, Emotions and Good Life p.1 | |
| A reaction: The 'Gauguin Problem' is that Gauguin's actions only become weakness of will if the pictures are no good, and he can't know that till he's painted them. Good point. |
| 2174 | Responsibility involves cause, intention, state of mind, and response after the event [Williams,B] |
| Full Idea: The four elements of any conception of responsibility are cause, intention, state of mind, and response after the event. | |
| From: Bernard Williams (Shame and Necessity [1993], III - p.53) |
| 2178 | In bad actions, guilt points towards victims, and shame to the agent [Williams,B] |
| Full Idea: In what I have done, the guilt points in one direction towards what has happened to others, and the shame in another direction to what I am. | |
| From: Bernard Williams (Shame and Necessity [1993], IV - p.92) | |
| A reaction: Not convinced. I think shame has the fear of being observed as an inescapable component. Even when alone shame involves imagining what others might think. |
| 2169 | Greek moral progress came when 'virtue' was freed from social status [Williams,B] |
| Full Idea: There was moral progress in the ancient Greek world, notably to the extent that the idea of areté, human excellence, was freed to some extent from determination by social position. | |
| From: Bernard Williams (Shame and Necessity [1993], I - p.7) |
| 2172 | The modern idea of duty is unknown in archaic Greece [Williams,B] |
| Full Idea: Duty in some abstract modern sense is largely unknown to the Greeks, in particular to archaic Greeks. | |
| From: Bernard Williams (Shame and Necessity [1993], II - p.41) |
| 2179 | If the moral self is seen as characterless, then other people have a very limited role in our moral lives [Williams,B] |
| Full Idea: The conception of the moral self as characterless leaves only a limited positive role to other people in one's moral life. | |
| From: Bernard Williams (Shame and Necessity [1993], IV - p.95) |
| 2180 | If reason cannot lead people to good, we must hope they have an internal voice [Williams,B] |
| Full Idea: If we think the power of reason is not enough by itself to distinguish good and bad, then we would hope that people have limited autonomy, that there is an internalised other in them that carries some social weight. | |
| From: Bernard Williams (Shame and Necessity [1993], IV - p.100) |
| 15641 | Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle] |
| Full Idea: The natural thought is to think that real kinds are given only by classification on the basis of essential properties: properties that make an object the kind of thing that it is. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], II) | |
| A reaction: Circularity alert! Circularity alert! Essence gives a thing its kind - and hence we can see what the kind is? Test for a trivial property! Eagle is not unaware of these issues. Does he mean 'necessary' rather than 'essential'? |
| 2175 | There is a problem of evil only if you expect the world to be good [Williams,B] |
| Full Idea: There is a "problem of evil" only for those who expect the world to be good. | |
| From: Bernard Williams (Shame and Necessity [1993], III - p.68) |