17 ideas
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 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. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 3282 | The general form of moral reasoning is putting yourself in other people's shoes [Nagel] |
| Full Idea: I believe the general form of moral reasoning is to put yourself in other people's shoes. | |
| From: Thomas Nagel (Equality [1977], §9) |
| 3278 | An egalitarian system must give priority to those with the worst prospects in life [Nagel] |
| Full Idea: What makes a system egalitarian is the priority it gives to the claims of those whose overall life prospects put them at the bottom. | |
| From: Thomas Nagel (Equality [1977], §6) |
| 3275 | Equality was once opposed to aristocracy, but now it opposes public utility and individual rights [Nagel] |
| Full Idea: Egalitarianism was once opposed to aristocratic values, but now it is opposed by adherents of two non-aristocratic values: utility (increase benefit, even if unequally) and individual rights (which redistribution violates). | |
| From: Thomas Nagel (Equality [1977], §2) |
| 3281 | The ideal of acceptability to each individual underlies the appeal to equality [Nagel] |
| Full Idea: The ideal of acceptability to each individual underlies the appeal to equality. | |
| From: Thomas Nagel (Equality [1977], §8) |
| 3277 | In judging disputes, should we use one standard, or those of each individual? [Nagel] |
| Full Idea: In assessing equality of claims, it must be decided whether to use a single, objective standard, or whether interests should be ranked by the person's own estimation. Also should they balance momentary or long-term needs? | |
| From: Thomas Nagel (Equality [1977], §6) |
| 3274 | Equality can either be defended as good for society, or as good for individual rights [Nagel] |
| Full Idea: The communitarian defence of equality says it is good for society as a whole, whereas the individualistic defence defends equality as a correct distributive principle. | |
| From: Thomas Nagel (Equality [1977], §2) |
| 3273 | Equality nowadays is seen as political, social, legal and economic [Nagel] |
| Full Idea: Contemporary political debate recognises four types of equality: political, social, legal and economic. | |
| From: Thomas Nagel (Equality [1977], §1) | |
| A reaction: Meaning equality of 1) power and influence, 2) status and respect, 3) rights and justice, 4) wealth. |
| 3276 | A morality of rights is very minimal, leaving a lot of human life without restrictions or duties [Nagel] |
| Full Idea: The morality of rights tends to be a limited, even minimal, morality. It leaves a great deal of human life ungoverned by moral restrictions or requirements. | |
| From: Thomas Nagel (Equality [1977], §5) |