12 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. |
| 20475 | Maybe modal sentences cannot be true or false [Casullo] |
| Full Idea: Some people claim that modal sentences do not express truths or falsehoods. | |
| From: Albert Casullo (A Priori Knowledge [2002], 3.2) | |
| A reaction: I can only imagine this coming from a narrow hardline empiricist. It seems to me obvious that we make true or false statements about what is possible or impossible. |
| 20476 | If the necessary is a priori, so is the contingent, because the same evidence is involved [Casullo] |
| Full Idea: If one can only know a priori that a proposition is necessary, then one can know only a priori that a proposition is contingent. The evidence relevant to determining the latter is the same as that relevant to determining the former. | |
| From: Albert Casullo (A Priori Knowledge [2002], 3.2) | |
| A reaction: This seems a telling point, but I suppose it is obvious. If you see that the cat is on the mat, nothing in the situation tells you whether this is contingent or necessary. We assume it is contingent, but that may be an a priori assumption. |
| 20471 | Epistemic a priori conditions concern either the source, defeasibility or strength [Casullo] |
| Full Idea: There are three suggested epistemic conditions on a priori knowledge: the first regards the source of justification, the second regards the defeasibility of justification, and the third appeals to the strength of justification. | |
| From: Albert Casullo (A Priori Knowledge [2002], 2) | |
| A reaction: [compressed] He says these are all inspired by Kant. The non-epistemic suggested condition involve necessity or analyticity. The source would have to be entirely mental; the defeasibly could not be experiential; the strength would be certainty. |
| 20477 | The main claim of defenders of the a priori is that some justifications are non-experiential [Casullo] |
| Full Idea: The leading claim of proponents of the a priori is that sources of justification are of two significantly different types: experiential and nonexperiential. Initially this difference is marked at the phenomenological level. | |
| From: Albert Casullo (A Priori Knowledge [2002], 5) | |
| A reaction: He cites Plantinga and Bealer for the phenomenological starting point (that some knowledge just seems rationally obvious, certain, and perhaps necessary). |
| 20472 | Analysis of the a priori by necessity or analyticity addresses the proposition, not the justification [Casullo] |
| Full Idea: There is reason to view non-epistemic analyses of a priori knowledge (in terms of necessity or analyticity) with suspicion. The a priori concerns justification. Analysis by necessity or analyticity concerns the proposition rather than the justification. | |
| From: Albert Casullo (A Priori Knowledge [2002], 2.1) | |
| A reaction: [compressed] The fact that the a priori is entirely a mode of justification, rather than a type of truth, is the modern view, influenced by Kripke. Given that assumption, this is a good objection. |
| 20474 | 'Overriding' defeaters rule it out, and 'undermining' defeaters weaken in [Casullo] |
| Full Idea: A justified belief that a proposition is not true is an 'overriding' defeater, ...and the belief that a justification is inadequate or defective is an 'undermining' defeater. | |
| From: Albert Casullo (A Priori Knowledge [2002], n 40) | |
| A reaction: Sounds more like a sliding scale than a binary option. Quite useful, though. |
| 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? |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |