5 ideas
| 10190 | From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki] |
| Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures. | |
| From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79 | |
| A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s. |
| 7458 | The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking] |
| Full Idea: The credibility of a witness is in part a function of the story being reported. When the story claims to have infinite value, the temptation to lie for personal benefit is asymptotically infinite. | |
| From: report of Pierre Simon de Laplace (Philosophical Essay on Probability [1820], Ch.XI) by Ian Hacking - The Emergence of Probability Ch.8 | |
| A reaction: Laplace seems to especially have reports of miracles in mind. This observation certainly dashes any dreams one might have of producing a statistical measure of the reliability of testimony. |
| 3441 | If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace] |
| Full Idea: An intelligence knowing at an instant the whole universe could know the movement of the largest bodies and atoms in one formula, provided his intellect were powerful enough to subject all data to analysis. Past and future would be present to his eyes. | |
| From: Pierre Simon de Laplace (Philosophical Essay on Probability [1820]), quoted by Mark Thornton - Do we have free will? p.70 |
| 7071 | Life and rationality are pointless if we can only contemplate the freedom of our own ego [Jacobi] |
| Full Idea: If the highest upon which I can reflect, what I can contemplate, is my empty and pure, naked and mere ego, with its autonomy and freedom: then rational self-contemplation, then rationality is for me a curse - I deplore my existence. | |
| From: Friedrich Jacobi (Letters to Fichte [1799], Ch.2), quoted by Simon Critchley - Continental Philosophy - V. Short Intro | |
| A reaction: This is a rebellion against Fichte's interpretation of Kant. It is a lovely cry from the heart on behalf of everyone who resents lines of philosophical thinking that seem to imprison the mind and cut us off from the ordinary world and real life. |
| 7072 | Jacobi was the first philosopher to talk of nihilism [Jacobi, by Critchley] |
| Full Idea: Jacobi was the first to philosophically employ the concept of nihilism. | |
| From: report of Friedrich Jacobi (Letters to Fichte [1799]) by Simon Critchley - Continental Philosophy - V. Short Intro Ch.2 | |
| A reaction: Critchley explains that it was Jacobi's fear that Fichte was drawing nihilist conclusions from Kant's philosophy. This fear may be seen as the beginning of what is loosely called 'continental philosophy'. A worthy subject for thinkers... |