4 ideas
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 15282 | Facts should be deducible from the theory and initial conditions, and prefer the simpler theory [Osiander, by Harré/Madden] |
| Full Idea: The two positivist criteria for a scientific theory are that the facts must be deducible from the theory together with initial conditions, and if there is more than one theory the simplest must be chosen. | |
| From: report of Andreas Osiander (Preface to 'De Revolutionibus' [1543]) by Harré,R./Madden,E.H. - Causal Powers 7.I | |
| A reaction: Harré and Madden cite this as a famous early statement of positivism. It seems to combine Hempel and Lewis very concisely. Wrong, of course. It does not, though, appear to mention 'laws'. |
| 7350 | The Torah just says: do not do to your neighbour what is hateful to you [Hillel the Elder] |
| Full Idea: What is hateful to you, do not unto your neighbour: this is the entire Torah. All the rest is commentary - go and study it. | |
| From: Hillel the Elder (reports [c.10]), quoted by Paul Johnson - The History of the Jews Pt II | |
| A reaction: Johnson suggests that this idea, of stripping everything from the Torah except its basic morality, was passed on to Jesus by Hillel. Suppose you hate Arsenal, but your neighbour supports them, and they just won the European Cup? What should you do? |