13 ideas
| 17818 | How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau] |
| Full Idea: We want to know How many what? You must first partition an aggregate into parts relevant to the question, where no partition is privileged. How the partitioned set is to be numbered is bound up with its unique members, and follows from logic alone. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'New Problem') | |
| A reaction: [Compressed wording of Yourgrau's summary of Frege's 'relativity argument'] Concepts do the partitioning. Yourgau says this fails, because the same argument applies to the sets themselves, as well as to the original aggregates. |
| 17822 | Nothing is 'intrinsically' numbered [Yourgrau] |
| Full Idea: Nothing at all is 'intrinsically' numbered. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'What the') | |
| A reaction: Once you are faced with distinct 'objects' of some sort, they can play the role of 'unit' in counting, so his challenge is that nothing is 'intrinsically' an object, which is the nihilism explored by Unger, Van Inwagen and Merricks. Aristotle disagrees... |
| 17817 | Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau] |
| Full Idea: The Frege-Maddy definition of number (as the 'property' of being-three) explains why the definitions of Von Neumann, Zermelo and others work, by giving the 'principle of collection' that ties together all threes. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'A Fregean') | |
| A reaction: [compressed two or three sentences] I am strongly in favour of the best definition being the one which explains the target, rather than just pinning it down. I take this to be Aristotle's view. |
| 17815 | We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau] |
| Full Idea: Sets could hardly serve as a foundation for number theory if we had to await detailed results in the upper reaches of the edifice before we could make our first move. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'Two') |
| 17821 | You can ask all sorts of numerical questions about any one given set [Yourgrau] |
| Full Idea: We can address a set with any question at all that admits of a numerical reply. Thus we can ask of {Carter, Reagan} 'How many feet do the members have?'. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'On Numbering') | |
| A reaction: This is his objection to the Fregean idea that once you have fixed the members of a set, you have thereby fixed the unique number that belongs with the set. |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
| From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
| A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
| 8122 | True works of art transmit completely new feelings [Tolstoy] |
| Full Idea: Only that is a true work of art which transmits fresh feelings not previously experienced by man. | |
| From: Leo Tolstoy (What is Art? [1898], Ch.9) | |
| A reaction: I think a great composer will probably not have any new feelings at all, but will discover new expressions which contain feelings by which even they are surprised (e.g. the Tristan chord). |
| 8121 | Art is when one man uses external signs to hand on his feelings to another man [Tolstoy] |
| Full Idea: Art is a human activity in which one man consciously by means of external signs, hands on to others feelings he has lived through, and other are infected by those feelings, and also experience them. | |
| From: Leo Tolstoy (What is Art? [1898], Ch.5) | |
| A reaction: Such definitions always work better for some art forms than for others. This may fit 'Anna Karenin' quite well, but probably not Bach's 'Art of Fugue'. Writing obscenities on someone's front door would fit this definition. |
| 8124 | The highest feelings of mankind can only be transmitted by art [Tolstoy] |
| Full Idea: The highest feelings to which mankind has attained can only be transmitted from man to man by art. | |
| From: Leo Tolstoy (What is Art? [1898], Ch.17) | |
| A reaction: We are much more nervous these days of talking about 'highest' feelings. Tolstoy obviously considers religion to be an ingredient of the highest feelings, but that prevents us from judging them purely as feelings. Music is the place to rank feelings. |
| 8123 | The purpose of art is to help mankind to evolve better, more socially beneficial feelings [Tolstoy] |
| Full Idea: The evolution of feeling proceeds by means of art - feelings less kind and less necessary for the well-being of mankind being replaced by others kinder and more needful for that end. That is the purpose of art. | |
| From: Leo Tolstoy (What is Art? [1898], Ch.16) | |
| A reaction: Underneath his superficially expressivist view of art, Tolstoy is really an old-fashioned moralist about it, like Dr Johnson. This is the moralism of the great age of the nineteenth century novel (which was, er, the greatest age of the novel!). |
| 22710 | People estimate art according to their moral values [Tolstoy] |
| Full Idea: The estimation of the value of art …depends on men's perception of the meaning of life; depends on what they hold to be the good and evil of life. | |
| From: Leo Tolstoy (What is Art? [1898]), quoted by Iris Murdoch - The Sublime and the Good p.206 | |
| A reaction: [No ref given] This is put to the test by the insightful depiction of wickedness. We condemn the wickedness and admire the insight. Every reading of a novel is a moral journey, though I'm not sure how the true psychopath reads a novel. |
| 8125 | The upper classes put beauty first, and thus freed themselves from morality [Tolstoy] |
| Full Idea: The people of the upper class, more and more frequently encountering the contradictions between beauty and goodness, put the ideal of beauty first, thus freeing themselves from the demands of morality. | |
| From: Leo Tolstoy (What is Art? [1898], Ch.17) | |
| A reaction: The rich are a great deal freer to pursue the demands of beauty than are the poor. They also have a tradition of 'immorality' (such as duels and adultery) which was in place long before they discovered art. |
| 8064 | We separate the concept of beauty from goodness, unlike the ancients [Tolstoy] |
| Full Idea: The ancients had not that conception of beauty separated from goodness which forms the basis and aim of aesthetics in our time. | |
| From: Leo Tolstoy (What is Art? [1898], Ch.3) | |
| A reaction: This is written at around the time of the Aesthetic Movement, but Tolstoy's own novels are intensely moral. This separation makes abstract painting possible. |