display all the ideas for this combination of texts
2 ideas
| 8884 | The phenomenal concept of an eleven-dot pattern does not include the concept of eleven [Sosa] |
| Full Idea: You could detect the absence of an eleven-dot pattern without having counted the dots, so your phenomenal concept of that array is not an arithmetical concept, and its content will not yield that its dots do indeed number eleven. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 7.3) | |
| A reaction: Sosa is discussing foundational epistemology, but this draws attention to the gulf that has to be leaped by structuralists. If eleven is not derived from the pattern, where does it come from? Presumably two eleven-dotters are needed, to map them. |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |