7 ideas
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
| Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.4) |
| 10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
| Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.2) |
| 10885 | Computer proofs don't provide explanations [Horsten] |
| Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.3) |
| 10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
| Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.3) |
| 18892 | Suppose a world where I'm from different gametes; add my gametes; which one is more me? [McGinn] |
| Full Idea: It seems essential that you come from your gametes. Suppose (for reductio) that I come from Nixon's actual gametes. Now add my actual gametes to that possible world, and suppose they become an adult. Which has the stronger title to be me? | |
| From: Colin McGinn (On the Necessity of Origin [1976], p.132), quoted by Nathan Salmon - Reference and Essence (1st edn) 7.25.5 | |
| A reaction: [See Nathan Salmon 1981:209] Feels like the Ship of Theseus. You say 'that's Theseus Ship', until the rival ship appears around the headland. Confusion. If Nixon's gametes can produce McGinn, the second gametes could produce a Nixon! Then what? |
| 12019 | McGinn falsely claims necessity of origin is a special case of the necessity of identity [Forbes,G on McGinn] |
| Full Idea: McGinn assimilates the origin relation among organisms to the identity relation, so that the necessity of origin becomes a special case of the necessity of identity. We argue that this assimilation is illegitimate. | |
| From: comment on Colin McGinn (On the Necessity of Origin [1976]) by Graeme Forbes - The Metaphysics of Modality 6.1 | |
| A reaction: Not sure about this. I have long suspected what McGinn suspects. Once you have identified the organism with a particular origin, it hardly seems surprising that this particular origin has become inescapable. |
| 5954 | All inventions of the mind aim at pleasure, and those that don't are worthless [Metrodorus of Lamp., by Plutarch] |
| Full Idea: Metrodorus says that all the wonderful, ingenious and brilliant inventions of the mind have been contrived for the sake of pleasure of the flesh or for the sake of looking forward to it, and any accomplishment not leading to this end is worthless. | |
| From: report of Metrodorus (Lamp) (fragments/reports [c.291 BCE], Fr 6) by Plutarch - 74: Reply to Colotes §1125 | |
| A reaction: It is very hard to think of counterexamples! Would anyone bother to work out the theorems of number theory if they didn't enjoy doing it? Would any sensible person make great sacrifices if they didn't think that increased happiness would result? |