11 ideas
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| Full Idea: Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups. |
| 10429 | It is best to say that a name designates iff there is something for it to designate [Sainsbury] |
| Full Idea: It is better to say that 'For all x ("Hesperus" stands for x iff x = Hesperus)', than to say '"Hesperus" stands for Hesperus', since then the expression can be a name with no bearer (e.g. "Vulcan"). | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.2) | |
| A reaction: In cases where it is unclear whether the name actually designates something, it seems desirable that the name is at least allowed to function semantically. |
| 10425 | Definite descriptions may not be referring expressions, since they can fail to refer [Sainsbury] |
| Full Idea: Almost everyone agrees that intelligible definite descriptions may lack a referent; this has historically been a reason for not counting them among referring expressions. | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.2) | |
| A reaction: One might compare indexicals such as 'I', which may be incapable of failing to refer when spoken. However 'look at that!' frequently fails to communicate reference. |
| 10438 | Definite descriptions are usually rigid in subject, but not in predicate, position [Sainsbury] |
| Full Idea: Definite descriptions used with referential intentions (usually in subject position) are normally rigid, ..but in predicate position they are normally not rigid, because there is no referential intention. | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.5) | |
| A reaction: 'The man in the blue suit is the President' seems to fit, but 'The President is the head of state' doesn't. Seems roughly right, but language is always too complex for philosophers. |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| Full Idea: Maddy takes a natural number to be a certain property of sui generis sets, the property of having a certain number of members. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990], 3 §2) by Alex Oliver - The Metaphysics of Properties | |
| A reaction: [I believe Maddy has shifted since then] Presumably this will make room for zero and infinities as natural numbers. Personally I want my natural numbers to count things. |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| Full Idea: Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things. |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| Full Idea: Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5 | |
| A reaction: Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory. |
| 10432 | A new usage of a name could arise from a mistaken baptism of nothing [Sainsbury] |
| Full Idea: A baptism which, perhaps through some radical mistake, is the baptism of nothing, is as good a propagator of a new use as a baptism of an object. | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.3) | |
| A reaction: An obvious example might be the Loch Ness Monster. There is something intuitively wrong about saying that physical objects are actually part of linguistic meaning or reference. I am not a meaning! |
| 10434 | Even a quantifier like 'someone' can be used referentially [Sainsbury] |
| Full Idea: A large range of expressions can be used with referential intentions, including quantifier phrases (as in 'someone has once again failed to close the door properly'). | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.5) | |
| A reaction: This is the pragmatic aspect of reference, where it can be achieved by all sorts of means. But are quantifiers inherently referential in their semantic function? Some of each, it seems. |
| 23565 | Our obedience to the king erases any crimes we commit for him [Shakespeare] |
| Full Idea: We know enough if we know we are the king's men. Our obedience to the king wipes the crime of it out of us. | |
| From: William Shakespeare (Henry V [1599]), quoted by Michael Walzer - Just and Unjust Wars 03 | |
| A reaction: He is referring to the slaughter of the French servants behind the lines at Agincourt. A classic expression of 'I was just obeying orders', which was rejected at Nurnberg in 1946. Depends on the seriousness of the crime. |
| 10431 | Things are thought to have a function, even when they can't perform them [Sainsbury] |
| Full Idea: On one common use of the notion of a function, something can possess a function which it does not, or even cannot, perform. A malformed heart is to pump blood, even if such a heart cannot in fact pump blood. | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.2) | |
| A reaction: One might say that the heart in a dead body had the function of pumping blood, but does it still have that function? Do I have the function of breaking the world 100 metres record, even though I can't quite manage it? Not that simple. |