10 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) |
| 6019 | If someone squashed a horse to make a dog, something new would now exist [Mnesarchus] |
| Full Idea: If, for the sake of argument, someone were to mould a horse, squash it, then make a dog, it would be reasonable for us on seeing this to say that this previously did not exist but now does exist. | |
| From: Mnesarchus (fragments/reports [c.120 BCE]), quoted by John Stobaeus - Anthology 179.11 | |
| A reaction: Locke would say it is new, because the substance is the same, but a new life now exists. A sword could cease to exist and become a new ploughshare, I would think. Apply this to the Ship of Theseus. Is form more important than substance? |
| 12580 | Experiences have no conceptual content [Evans, by Greco] |
| Full Idea: In Evans's work experiences are conceived of as not having a conceptual content at all. | |
| From: report of Gareth Evans (The Varieties of Reference [1980]) by John Greco - Justification is not Internal | |
| A reaction: I presume it is this view which provoked McDowell's contrary view in 'Mind and World'. I say this is a job for neuroscience, and I struggle to see what philosophical questions hang on the outcome. I think I side with Evans. |
| 7643 | We have far fewer colour concepts than we have discriminations of colour [Evans] |
| Full Idea: Do we really understand the proposal that we have as many colour concepts as there are shades colour that we can sensibly discriminate? | |
| From: Gareth Evans (The Varieties of Reference [1980], 7.5) | |
| A reaction: This is the argument (rejected by McDowell) that experience cannot be conceptual because experience is too rich. We should not confuse lack of concepts with lack of words. I may have a concept of a colour between two shades, but no word for it. |
| 23794 | Some representational states, like perception, may be nonconceptual [Evans, by Schulte] |
| Full Idea: Evans introduced the idea that there are some representational states, for example perceptual experiences, which have content that is nonconceptual. | |
| From: report of Gareth Evans (The Varieties of Reference [1980]) by Peter Schulte - Mental Content 3.4 | |
| A reaction: McDowell famously disagree, and whether all experience is inherently conceptualised is a main debate from that period. Hard to see how it could be settled, but I incline to McDowell, because minimal perception hardly counts as 'experience'. |
| 16366 | The Generality Constraint says if you can think a predicate you can apply it to anything [Evans] |
| Full Idea: If a subject can be credited with the thought that a is F, then he must have the conceptual resources for entertaining the thought that a is G, for every property of being G of which he has conception. This condition I call the 'Generality Constraint'. | |
| From: Gareth Evans (The Varieties of Reference [1980], p.104), quoted by François Recanati - Mental Files 5.3 | |
| A reaction: Recanati endorses the Constraint in his account of mental files. Apparently if I can entertain the thought of a circle being round, I can also entertain the thought of it being square, so I am not too sure about this one. |
| 12575 | Concepts have a 'Generality Constraint', that we must know how predicates apply to them [Evans, by Peacocke] |
| Full Idea: Evans's 'Generality Constraint' says that if a thinker is capable of attitudes to the content Fa and possesses the singular concept b, then he is capable of having attitudes to the content Fb. | |
| From: report of Gareth Evans (The Varieties of Reference [1980], 4.3) by Christopher Peacocke - A Study of Concepts 1.1 | |
| A reaction: So having an attitude becomes the test of whether one possesses a concept. I suppose if one says 'You know you've got a concept when you are capable of thinking about it', that is much the same thing. Sounds fine. |