23 ideas
| 17824 | The master science is physical objects divided into sets [Maddy] |
| Full Idea: The master science can be thought of as the theory of sets with the entire range of physical objects as ur-elements. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: This sounds like Quine's view, since we have to add sets to our naturalistic ontology of objects. It seems to involve unrestricted mereology to create normal objects. |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| Full Idea: If you wonder why multiplication is commutative, you could prove it from the Peano postulates, but the proof offers little towards an answer. In set theory Cartesian products match 1-1, and n.m dots when turned on its side has m.n dots, which explains it. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: 'Turning on its side' sounds more fundamental than formal set theory. I'm a fan of explanation as taking you to the heart of the problem. I suspect the world, rather than set theory, explains the commutativity. |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| Full Idea: The standard account of the relationship between numbers and sets is that numbers simply are certain sets. This has the advantage of ontological economy, and allows numbers to be brought within the epistemology of sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Maddy votes for numbers being properties of sets, rather than the sets themselves. See Yourgrau's critique. |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| Full Idea: I propose that ...numbers are properties of sets, analogous, for example, to lengths, which are properties of physical objects. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Are lengths properties of physical objects? A hole in the ground can have a length. A gap can have a length. Pure space seems to contain lengths. A set seems much more abstract than its members. |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| Full Idea: A set of things is located where the aggregate of those things is located, ...but a number is simultaneously located at many different places (10 in my hand, and a baseball team) ...so numbers seem more like universals than particulars. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: My gut feeling is that Maddy's master idea (of naturalising sets by building them from ur-elements of natural objects) won't work. Sets can work fine in total abstraction from nature. |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| Full Idea: I am not suggesting a reduction of number theory to set theory ...There are only sets with number properties; number theory is part of the theory of finite sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], V) |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| Full Idea: The popular challenges to platonism in philosophy of mathematics are epistemological (how are we able to interact with these objects in appropriate ways) and ontological (if numbers are sets, which sets are they). | |
| From: Penelope Maddy (Sets and Numbers [1981], I) | |
| A reaction: These objections refer to Benacerraf's two famous papers - 1965 for the ontology, and 1973 for the epistemology. Though he relied too much on causal accounts of knowledge in 1973, I'm with him all the way. |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| Full Idea: Number words are not like normal adjectives. For example, number words don't occur in 'is (are)...' contexts except artificially, and they must appear before all other adjectives, and so on. | |
| From: Penelope Maddy (Sets and Numbers [1981], IV) | |
| A reaction: [She is citing Benacerraf's arguments] |
| 21059 | General rules of action also need a judgement about when to apply them [Kant] |
| Full Idea: A concept of the understanding, which contains the general rule, must be supplemented by an act of judgement whereby the practitioner distinguishes instances where the rule applies from those where it does not. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], Intro) | |
| A reaction: This is Aristotle's phronesis, and Hart's 'rules of recognition' in law courts. So is the link between theory and practice an intellectual one, or a sort of inarticulate intuition? I like 'common sense' for this ability. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 21061 | Duty does not aim at an end, but gives rise to universal happiness as aim of the will [Kant] |
| Full Idea: My conception of duty does not need to be based on any particular end, but rather itself occasions a new end for the human will, that of striving with all one's power towards the highest good possible on earth, the universal happiness of the whole world. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 1B) | |
| A reaction: I see nothing in the categorical imperative that demands 'all one's power', and nothing that specifies happiness as what has to be universalised. Nietzsche, for one, thinks happiness is overrated. |
| 21060 | It can't be a duty to strive after the impossible [Kant] |
| Full Idea: It would not be a duty to strive after a certain effect of our will if this effect were impossible in experience. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], Intro) | |
| A reaction: 'Ought implies can' has become a familiar slogan. The quickest way to get shot of a tiresome duty is to persuade yourself that it is impossible. The seemingly impossible is occasionally achieved. |
| 21062 | The will's motive is the absolute law itself, and moral feeling is receptivity to law [Kant] |
| Full Idea: The will must have motives. But these are not objects of physical feeling as predetermined ends in themselves. They are none other than the absolute law itself, and the will's receptivity to it as an absolute compulsion is known as moral feeling. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 1Bb) | |
| A reaction: This sounds like our natural motivation to get the right answer when doing arithmetic, which is the innate motivation towards truth. I once heard it said that truth is the only value. So why does Donald Trump fail to value truth? |
| 21071 | There can be no restraints on freedom if reason does not reveal some basic rights [Kant] |
| Full Idea: If there is nothing which commands immediate respect through reason, such as the basic rights of man, no influence can prevail upon man's arbitrary will and restrain his freedom. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-Concl) | |
| A reaction: I think this is the nearest Kant gets to natural rights. It is hard to see how basic rights can be identified by pure reason, without some inbuilt human values. Kant's usual move is to say denial of them leads to a contradiction, but I'm going off that. |
| 21063 | Personal contracts are for some end, but a civil state contract involves a duty to share [Kant] |
| Full Idea: In all social contracts, we find a union of many individuals for some common end which they all share. But a union as an end in itself which they all ought to share …is only found in a society insofar as it constitutes a civil state i.e. a commonwealth. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 2 Intro) | |
| A reaction: This makes a nice link between the contractarian individual morality of Hobbes and his social contract view of society. Kant seems to reject the first but accept the second. Presumably because the first implies benefit and the second implies duty. |
| 21068 | There must be a unanimous contract that citizens accept majority decisions [Kant] |
| Full Idea: The actual principle of being content with majority decisions must be accepted unanimously and embodied in a contract, and this itself must be the ultimate basis on which a civil constitution is established. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-3) | |
| A reaction: This is the contract which combines a social contract with democracy. We unanimously agree not to be unanimous? Cf Idea 21065. What should the minority do when the majority elect criminal Nazi leaders? |
| 21069 | A contract is theoretical, but it can guide rulers to make laws which the whole people will accept [Kant] |
| Full Idea: The original contract …is merely an idea of reason, which nonetheless has undoubted practical reality; for it can oblige every legislator to frame his laws in such a way that they could have been produced by the united will of a whole nation. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-Concl) | |
| A reaction: The contractualist theory of morality of Thomas Scanlon approaches this. Note that Kant says it 'can' oblige the legislators. Nothing would compel them to follow such a principle. |
| 21070 | A law is unjust if the whole people could not possibly agree to it [Kant] |
| Full Idea: If the law is such that a whole people could not possibly agree to it …it is unjust. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-Concl) | |
| A reaction: Kant is explicitly trying to approximate Rousseau's general will. The categorical imperative was greatly influenced by Rousseau. The key point is not whether they accept it, but that unanimous acceptance is unthinkable. Unfair laws will fail. |
| 21067 | A citizen must control his own life, and possess property or an important skill [Kant] |
| Full Idea: The only qualification required by a citizen (apart, of course, from being an adult male) is that he must be his own master, and must have some property (which can include any skill, trade, fine art or science) to support himself. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-3) | |
| A reaction: Of course! Being one's own master evidently allows for being an employee, as long as this is a free contract, and not exploitation. Invites lots of interesting test cases. We need a Marxist commentary on this idea. |
| 21064 | A lawful civil state must embody freedom, equality and independence for its members [Kant] |
| Full Idea: The civil state, regarded purely as a lawful state, is based on the following a priori principles. 1) the freedom of every member as a human being, 2) the equality of each as a subject, 3) the independence of each as a subject. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 2 Intro) | |
| A reaction: Written in 1792, three years after the start of the French Revolution. He says that a state with an inbuilt hierarchy or aristocracy is unlawful. Which freedoms, equality in what respects, and independence from what? |
| 21066 | Citizens can rise to any rank that talent, effort and luck can achieve [Kant] |
| Full Idea: Every member of the commonwealth must be entitled to reach any degree of rank which a subject can earn through his talent, his industry and his good fortune. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-2) | |
| A reaction: This is equality of opportunity, which is a mantra for liberals, but has been subjected to good criticisms in modern times. The main question is whether there is formal and legal equality, or actual practical equality. |
| 21065 | You can't make a contract renouncing your right to make contracts! [Kant] |
| Full Idea: No one can voluntarily renounce his rights by a contract ..to the effect that he has no rights but only duties, for such a contract would deprive him of the right to make a contract, and would thus invalidate the one he had already made. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-2) | |
| A reaction: Kant tries to establish all of his principles by showing that their denial is contradictory. But this example is blatantly wrong. King Lear didn't nullify his previous legislation when he abdicated, and his two daughters legally kept their territories. |
| 21072 | The people (who have to fight) and not the head of state should declare a war [Kant] |
| Full Idea: Each state must be organised so that the head of state, for whom the war costs nothing (for he wages it at the expense of the people) must no longer have the deciding vote on whether war is to be declared or not, for the people who pay for it must decide. | |
| From: Immanuel Kant (True in Theory, but not in Practice [1792], 3) | |
| A reaction: I would guess that he has Louis XIV particularly in mind. Imagine if Kant's proposal had been implemented in 1914. A referendum takes ages, and the people would need the facts (from the intelligence agencies). |