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) |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
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. |