10 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. |
| 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? |
| 1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
| Full Idea: Prodicus insists that contradiction is impossible, since if two people are contradicting each other, they cannot both be speaking of the same fact. Only the one who is speaking the truth is speaking of facts as they are; the other does not speak facts. | |
| From: report of Prodicus (fragments/reports [c.423 BCE]) by Didymus the Blind - Commentary on Ecclesiastes (frags) | |
| A reaction: cf. Kant's 100 thalers example |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 1555 | People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus] |
| Full Idea: In the old days people regarded the sun, the moon, rivers, springs, and everything else which is helpful for life as gods, because we are helped by them, just as the Egyptians regard the Nile as a god. | |
| From: Prodicus (fragments/reports [c.423 BCE], B05), quoted by Sextus Empiricus - Against the Professors (six books) 9.18 |
| 535 | The gods are just personified human benefits [Prodicus] |
| Full Idea: Things from which benefits to human life have been derived have come to be considered deities, such as Demeter and Dionysus. | |
| From: Prodicus (fragments/reports [c.423 BCE], B5), quoted by (who?) - where? |
| 1543 | He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus] |
| Full Idea: He says that the gods worshipped by men neither exist nor have knowledge, but that the ancients exalted crops and everything else which is useful for life. | |
| From: Prodicus (fragments/reports [c.423 BCE]), quoted by Anon (Herc) - fragments 1428 19.12 |