15 ideas
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought. | |
| From: report of David Hilbert (works [1900], 6.7) by Michčle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault. |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign. | |
| From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience. |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1). | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application. |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning. | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem. |
| 21075 | The state of nature always involves the threat of war [Kant] |
| Full Idea: The state of nature is a state of war. For even if it does not involve active hostilities, it involves a constant threat of their breaking out. | |
| From: Immanuel Kant (Perpetual Peace [1795], 2) | |
| A reaction: Kant is siding with Hobbes against Rousseau, despite Rousseau's claim that Hobbes's pessimism concerns a more advanced situation that the true (and peaceful) state of nature. |
| 20569 | Kant made the social contract international and cosmopolitan [Kant, by Oksala] |
| Full Idea: Kant developed the social contract theory into an international and cosmopolitan idea. | |
| From: report of Immanuel Kant (Perpetual Peace [1795]) by Johanna Oksala - Political Philosophy: all that matters Ch.6 | |
| A reaction: That is, the contract both operates between states, and rises above them. I found this idea rather thrilling when I first met it (listening to Onora O'Neill). But then I remain a child of the Englightenment. |
| 21079 | The a priori general will of a people shows what is right [Kant] |
| Full Idea: It is precisely the general will as it is given a priori, within a single people or in the mutual relationships of various peoples, which alone determines what is right among men. | |
| From: Immanuel Kant (Perpetual Peace [1795], App 1) | |
| A reaction: The clearest quotation for showing Kant's debt to Rousseau. Why should Rousseau bother to have a real assembly of the people, if the General Will can be worked out a priori? Indeed, the a priori version must be deemed superior to any meeting. |
| 21077 | Each nation should, from self-interest, join an international security constitution [Kant] |
| Full Idea: Each nation, for the sake of its own security, can and ought to demand of the others that they should enter along with it into a constitution, similar to the civil one, within which the rights of each could be secured. | |
| From: Immanuel Kant (Perpetual Peace [1795], 2.2nd) | |
| A reaction: Not sure how close the United Nations takes us to this. You have to admire Kant for this one. |
| 21078 | A constitution must always be improved when necessary [Kant] |
| Full Idea: Changes for the better are necessary, in order that the constitution may constantly approach the optimum end prescribed by laws of right. | |
| From: Immanuel Kant (Perpetual Peace [1795], App 1) | |
| A reaction: This should be a clause in every constitution. It is crazy to feel trapped by a misjudgement or outdated view of your ancestors. |
| 21076 | Equality is where you cannot impose a legal obligation you yourself wouldn't endure [Kant] |
| Full Idea: Rightful equality within a state is a relationship among citizens where no-one can put anyone else under a legal obligation without submitting simultaneously to a law which requires that he can be put under the same kind of obligation by the other person. | |
| From: Immanuel Kant (Perpetual Peace [1795], 2.1st n) | |
| A reaction: This appears only to be legal equality, rather than political or economic or social equality. |
| 20570 | There is now a growing universal community, and violations of rights are felt everywhere [Kant] |
| Full Idea: The peoples of the earth have entered in varying degrees into a universal community, and it has developed to the point where a violation of rights in one part of the world is felt everywhere. | |
| From: Immanuel Kant (Perpetual Peace [1795], 'Third') | |
| A reaction: I hope slavery was at the forefront of his mind when he wrote that. It is only in very recent times (since about 1960?) that major violations of rights are felt to matter to the whole human race. A long way to go, though. |
| 20571 | There are political and inter-national rights, but also universal cosmopolitan rights [Kant] |
| Full Idea: The idea of a cosmopolitan right is not fantastic and overstrained; it is a necessary complement to the unwritten code of political and international right, transforming it into a universal right of humanity. | |
| From: Immanuel Kant (Perpetual Peace [1795], 'Third') | |
| A reaction: The interesting thought is that there are no 'natural rights', but there can be universal rights insofar as there exists a universal community. See the UN Declaration of Human Rights c.1948. |
| 21073 | Hiring soldiers is to use them as instruments, ignoring their personal rights [Kant] |
| Full Idea: The hiring of men to kill or be killed seems to mean using them as mere machines and insturments in the hands of someone else (the state), which cannot easily be reconciled with the rights of man in one's own person. | |
| From: Immanuel Kant (Perpetual Peace [1795], 1.3) | |
| A reaction: Kant was not a pacificist, though this makes him sound like one. Some men go off to war with enthusiasm, and then regret it. Exploitation of rational beings may be the worst sin in Kant's Enlightenment world. |
| 21074 | Some trust in the enemy is needed during wartime, or peace would be impossible [Kant] |
| Full Idea: It must remain possible, even in wartime, to have some sort of trust in the attitude of the enemy, otherwise peace could not be concluded and the hostilities would turn into a war of extermination. | |
| From: Immanuel Kant (Perpetual Peace [1795], 1.6) | |
| A reaction: Consider the 'unconditional surrender' approach to the Nazis in 1944, and the peace of May 1945, made with very different Germans. How do you make peace with an enemy you cannot trust? |
| 19436 | Bare or primary matter is passive; it is clothed or secondary matter which contains action [Leibniz] |
| Full Idea: The active principle is not attributed by me to bare or primary matter, which is merely passive ...but to clothed or secondary matter which in addition contains a primitive entelechy, or active principle. | |
| From: Gottfried Leibniz (Letters to Wagner [1710], 1710 §2) | |
| A reaction: Secondary matter contains monads. The puzzling question is what primary matter consists of. It is not atoms, because it is infinitely divisible, and it seems to be composed of corpuscles. But what is it made of? Just gunge? He says it is 'flux'. |