11 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) |
| 22868 | The value and truth of knowledge are measured by success in activity [Dewey] |
| Full Idea: What measures knowledge's value, its correctness and truth, is the degree of its availability for conducting to a successful issue the activities of living beings. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 4:180), quoted by David Hildebrand - Dewey 2 'Critique' | |
| A reaction: Note that this is the measure of truth, not the nature of truth (which James seemed to believe). Dewey gives us a clear and perfect statement of the pragmatic view of knowledge. I don't agree with it. |
| 22865 | Habits constitute the self [Dewey] |
| Full Idea: All habits are demands for certain kinds of activity; and they constitute the self. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 14:22), quoted by David Hildebrand - Dewey 1 'Acts' | |
| A reaction: Not an idea I have encountered elsewhere. He emphasises that habits are not repeated actions, but are dispositions. I'm not clear whether these habits must be conscious. |
| 22871 | The good people are those who improve; the bad are those who deteriorate [Dewey] |
| Full Idea: The bad man is the man who no matter how good he has been is beginning to deteriorate, to grow less good. The good man is the man who no matter how morally unworthy he has been is moving to become better. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 12:181), quoted by David Hildebrand - Dewey 3 'Reconstruct' | |
| A reaction: Although a slightly improving rat doesn't sound as good as a slightly deteriorating saint, I have some sympathy with this thought. The desire to improve seems to be right at the heart of what makes good character. |
| 22876 | Democracy is the development of human nature when it shares in the running of communal activities [Dewey] |
| Full Idea: Democracy is but a name for the fact that human nature is developed only when its elements take part in directing things which are common, things for the sake of which men and women form groups. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 12:199), quoted by David Hildebrand - Dewey 4 'Democracy' | |
| A reaction: It is hard to prove that human nature develops when it particpates in groups. If people are excluded from power, their loyalty tends to switch to sub-groups, such as friends in a pub, or a football team. Powerless nationalists baffle me. |
| 22875 | Democracy is not just a form of government; it is a mode of shared living [Dewey] |
| Full Idea: A democracy is more than a form of government; it is primarily a mode of associated living, of conjoint communicated experience | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 9:93), quoted by David Hildebrand - Dewey 4 'Democracy' | |
| A reaction: This precisely pinpoints the heart of the culture wars in 2021. A huge swathe of western populations believe in Dewey's idea, but a core of wealthy right-wingers and their servants only see democracy as the mechanism for obtaining power. |
| 22874 | Individuality is only developed within groups [Dewey] |
| Full Idea: Only in social groups does a person have a chance to develop individuality. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 15:176), quoted by David Hildebrand - Dewey 4 'Individuals' | |
| A reaction: This is a criticism of both Rawls and Nozick. Rawls's initial choosers don't consult, or have much social background. Nozick's property owners ignore everything except contracts. |
| 18639 | If we assess what people would buy in an imaginary insurance market, our taxes could copy it [Dworkin, by Kymlicka] |
| Full Idea: If we can make sense of a hypothetical insurance market, and find a determinate answer to the question of what insurance people would buy in it, then we could use the tax system to duplicate the results. | |
| From: report of Ronald Dworkin (A Matter of Principle [1985]) by Will Kymlicka - Contemporary Political Philosophy (1st edn) 2.4.b | |
| A reaction: This is a nice alternative from Dworkin to Rawls's 'veil of ignorance' approach. |