9 ideas
| 8956 | What is a singleton set, if a set is meant to be a collection of objects? [Szabó] |
| Full Idea: The relationship between an object and its singleton is puzzling. Our intuitive conception of a set is a collection of objects - what are we to make of a collection of a single object? | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 4.1) | |
| A reaction: The ontological problem seems to be the same as that of the empty set, and indeed the claim that a pair of entities is three things. For logicians the empty set is as real as a pet dog, but not for me. |
| 8447 | In 'Etna is higher than Vesuvius' the whole of Etna, including all the lava, can't be the reference [Frege] |
| Full Idea: The reference of 'Etna' cannot be Mount Etna itself, because each piece of frozen lava which is part of Mount Etna would then also be part of the thought that Etna is higher than Vesuvius. | |
| From: Gottlob Frege (Letters to Jourdain [1910], p.43) | |
| A reaction: This seems to be a straight challenge to Kripke's baptismal account of reference. I think I side with Kripke. Frege is allergic to psychological accounts, but the mind only has the capacity to think of the aspect of Etna that is relevant. |
| 8448 | Any object can have many different names, each with a distinct sense [Frege] |
| Full Idea: An object can be determined in different ways, and every one of these ways of determining it can give rise to a special name, and these different names then have different senses. | |
| From: Gottlob Frege (Letters to Jourdain [1910], p.44) | |
| A reaction: This seems right. No name is an entirely neutral designator. Imagine asking a death-camp survivor their name, and they give you their prison number. Sense clearly intrudes into names. But picking out the object is what really matters. |
| 8953 | Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things [Szabó] |
| Full Idea: It is better not to include in the definition of abstract entities that they ontologically depend on their concrete correlates. Note: ..but they may depend on the totality of concreta; maybe 'the supervenience of the abstract' is part of ordinary thought. | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 2.2) | |
| A reaction: [the quoted phrase is from Gideon Rosen] It certainly seems unlikely that the concept of the perfect hexagon depends on a perfect hexagon having existed. Human minds have intervened between the concrete and the abstract. |
| 8954 | Geometrical circles cannot identify a circular paint patch, presumably because they lack something [Szabó] |
| Full Idea: The vocabulary of geometry is sufficient to identify the circle, but could not be used to identify any circular paint patch. The reason must be that the circle lacks certain properties that can distinguish paint patches from one another. | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 2.2) | |
| A reaction: I take this to be support for the traditional view, that abstractions are created by omitting some of the properties of physical objects. I take them to be fictional creations, reified by language, and not actual hidden entities that have been observed. |
| 8955 | Abstractions are imperceptible, non-causal, and non-spatiotemporal (the third explaining the others) [Szabó] |
| Full Idea: In current discussions, abstract entities are usually distinguished as 1) in principle imperceptible, 2) incapable of causal interaction, 3) not located in space-time. The first is often explained by the second, which is in turn explained by the third. | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 2.2) | |
| A reaction: Szabó concludes by offering 3 as the sole criterion of abstraction. As Lewis points out, the Way of Negation for defining abstracta doesn't tell us very much. Courage may be non-spatiotemporal, but what about Alexander the Great's courage? |
| 8446 | We understand new propositions by constructing their sense from the words [Frege] |
| Full Idea: The possibility of our understanding propositions which we have never heard before rests on the fact that we construct the sense of a proposition out of parts that correspond to words. | |
| From: Gottlob Frege (Letters to Jourdain [1910], p.43) | |
| A reaction: This is the classic statement of the principle of compositionality, which seems to me so obviously correct that I cannot understand anyone opposing it. Which comes first, the thought or the word, may be a futile debate. |
| 8449 | Senses can't be subjective, because propositions would be private, and disagreement impossible [Frege] |
| Full Idea: If the sense of a name was subjective, then the proposition and the thought would be subjective; the thought one man connects with this proposition would be different from that of another man. One man could not then contradict another. | |
| From: Gottlob Frege (Letters to Jourdain [1910], p.44) | |
| A reaction: This is an implicit argument for the identity of 'proposition' and 'thought'. This argument resembles Plato's argument for universals (Idea 223). See also Kant on existence as a predicate (Idea 4475). But people do misunderstand one another. |
| 6017 | Nomos is king [Pindar] |
| Full Idea: Nomos is king. | |
| From: Pindar (poems [c.478 BCE], S 169), quoted by Thomas Nagel - The Philosophical Culture | |
| A reaction: This seems to be the earliest recorded shot in the nomos-physis wars (the debate among sophists about moral relativism). It sounds as if it carries the full relativist burden - that all that matters is what has been locally decreed. |