8 ideas
| 10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
| Full Idea: I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits ...which are permitted to increase without bound. | |
| From: Carl Friedrich Gauss (Letter to Shumacher [1831]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.7 |
| 14221 | Serious essentialism says everything has essences, they're not things, and they ground necessities [Shalkowski] |
| Full Idea: Serious essentialism is the position that a) everything has an essence, b) essences are not themselves things, and c) essences are the ground for metaphysical necessity and possibility. | |
| From: Scott Shalkowski (Essence and Being [2008], 'Intro') | |
| A reaction: If a house is being built, it might acquire an identity first, and only get an essence later. Essences can be physical, but if you extract them you destroy thing thing of which they were the essence. Does all of this apply to abstract 'things'. |
| 14222 | Essences are what it is to be that (kind of) thing - in fact, they are the thing's identity [Shalkowski] |
| Full Idea: The route into essentialism is, first, a recognition that the essence of a thing is "what it is to be" that (kind of) thing; the essence of a thing is just its identity. | |
| From: Scott Shalkowski (Essence and Being [2008], 'Essent') | |
| A reaction: The first half sounds right, and very Aristotelian. The second half is dramatically different, controversial, and far less plausible. Slipping in 'kind of' is also highly dubious. This remark shows, I think, some confusion about essences. |
| 14226 | We distinguish objects by their attributes, not by their essences [Shalkowski] |
| Full Idea: In ordinary contexts, we distinguish objects not by their essences but by their attributes. | |
| From: Scott Shalkowski (Essence and Being [2008], 'Ess and Know') | |
| A reaction: Hence we have a gap between what bestows identity intrinsically, and how we bestow identity conventionally. If you could grasp the essence of something, you might predict a new attribute, as yet unobserved. |
| 14225 | Critics say that essences are too mysterious to be known [Shalkowski] |
| Full Idea: According to critics, the thorniest problem for essentialism is the question of our knowledge of essence. It is usually at this point that terms of abuse such as 'dark', 'mysterious', and 'occult' are wheeled out. | |
| From: Scott Shalkowski (Essence and Being [2008], 'Ess and Know') | |
| A reaction: I'm inclined to think that the existence of essences can be fairly conclusively inferred, but that attributing a precise identity to them is the biggest challenge. |
| 14223 | De dicto necessity has linguistic entities as their source, so it is a type of de re necessity [Shalkowski] |
| Full Idea: De dicto necessity is a species of de re necessity. Anyone prone to countenance de dicto necessity must recognise mental and/or linguistic entities, thus counting each of them as a res to which necessity attaches. | |
| From: Scott Shalkowski (Essence and Being [2008], 'Essent') | |
| A reaction: This seems to rest on the Kit Fine thought that analytic necessities seem to derive from the essences of words such as 'bachelor'. I like this idea: all necessity is de re, but some of the 'things' are words. |
| 14224 | Equilateral and equiangular aren't the same, as we have to prove their connection [Shalkowski] |
| Full Idea: That 'all and only equilateral triangles are equiangular' required proof, and not for mere curiosity, is grounds for thinking that being an equilateral triangle is not the same property as being an equiangular triangle. | |
| From: Scott Shalkowski (Essence and Being [2008], 'Serious') | |
| A reaction: If you start with equiangularity, does equilateralness then require proof? This famous example is of two concepts which seem to be coextensional, but seem to have a different intension. Does a dependence relation drive a wedge between them? |
| 8113 | Art is like understanding a natural language, and needs a grasp of a symbol system [Goodman, by Gardner] |
| Full Idea: In Goodman's account, knowing what a painting represents is logically like understanding a sentence in a natural language. It requires a grasp of the 'symbol system' to which the painting belongs. | |
| From: report of Nelson Goodman (The Languages of Art [1976]) by Sebastian Gardner - Aesthetics 2.3.2 | |
| A reaction: This may fit some pictures well (e.g. early Flemish painting, with its complex iconography), but others hardly at all. You can enjoy a first experience of (say) ballet long before you get the hang of the 'symbol system' involved. |