27 ideas
| 13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
| Full Idea: Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv | |
| A reaction: Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'. |
| 9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
| Full Idea: Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66) | |
| A reaction: Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher. |
| 10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
| Full Idea: Only what is logically complex can be defined; what is simple can only be pointed to. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §180), quoted by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.137 | |
| A reaction: Frege presumably has in mind his treasured abstract objects, such as cardinal numbers. It is hard to see how you could 'point to' anything in the phenomenal world that had atomic simplicity. Hodes calls this a 'desperate Kantian move'. |
| 9886 | Cardinals say how many, and reals give measurements compared to a unit quantity [Frege] |
| Full Idea: The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19 | |
| A reaction: We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals. |
| 9889 | Real numbers are ratios of quantities [Frege, by Dummett] |
| Full Idea: Frege fixed on construing real numbers as ratios of quantities (in agreement with Newton). | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege philosophy of mathematics Ch.20 | |
| A reaction: If 3/4 is the same real number as 6/8, which is the correct ratio? Why doesn't the square root of 9/16 also express it? Why should irrationals be so utterly different from rationals? In what sense are they both 'numbers'? |
| 10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
| Full Idea: For Frege, in 'Grundgesetze', a number is a class of classes of the same cardinality. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 |
| 10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
| Full Idea: The inconsistency of Grundgesetze was only a minor flaw. Its fundamental flaw was its inability to account for the way in which the senses of number terms are determined. It leaves the reference-magnetic nature of the standard numberer a mystery. | |
| From: comment on Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.139 | |
| A reaction: A point also made by Hofweber. As a logician, Frege was only concerned with the inferential role of number terms, and he felt he had captured their logical form, but it is when you come to look at numbers in natural language that he seem in trouble. |
| 9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
| Full Idea: Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising. |
| 8751 | Only applicability raises arithmetic from a game to a science [Frege] |
| Full Idea: It is applicability alone which elevates arithmetic from a game to the rank of a science. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §91), quoted by Stewart Shapiro - Thinking About Mathematics 6.1.2 | |
| A reaction: This is the basic objection to Formalism. It invites the question of why it is applicable, which platonists like Frege don't seem to answer (though Plato himself has reality modelled on the Forms). This is why I like structuralism. |
| 19347 | Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins] |
| Full Idea: For individuation, substance needs three properties: independence, to separate it from other things; unity, to call it one thing, rather than an aggregate; and permanence or stability over time. Its other role is as subject for predicates. | |
| From: Franklin Perkins (Leibniz: Guide for the Perplexed [2007], 3.1) | |
| A reaction: Perkins is describing the Aristotelian view, which is taken up by Leibniz. 'Substance' is not a controversial idea, if we see that it only means that the world is full of 'things'. It is an unusual philosopher wholly totally denies that. |
| 9891 | The first demand of logic is of a sharp boundary [Frege] |
| Full Idea: The first demand of logic is of a sharp boundary. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §160), quoted by Michael Dummett - Frege philosophy of mathematics Ch.22 | |
| A reaction: Nothing I have read about vagueness has made me doubt Frege's view of this, although precisification might allow you to do logic with vague concepts without having to finally settle where the actual boundaries are. |
| 9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
| Full Idea: From geometry we retain the interpretation of a real number as a ratio of quantities or measurement-number; but in more recent times we detach it from geometrical quantities, and from all particular types of quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §159), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Dummett glosses the 'recent' version as by Cantor and Dedekind in 1872. This use of 'detach' seems to me startlingly like the sort of psychological abstractionism which Frege was so desperate to avoid. |
| 11846 | If we abstract the difference between two houses, they don't become the same house [Frege] |
| Full Idea: If abstracting from the difference between my house and my neighbour's, I were to regard both houses as mine, the defect of the abstraction would soon be made clear. It may, though, be possible to obtain a concept by means of abstraction... | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §99) | |
| A reaction: Note the important concession at the end, which shows Frege could never deny the abstraction process, despite all the modern protests by Geach and Dummett that he totally rejected it. |
| 23110 | Human injustice is not a permanent feature of communities [Rawls] |
| Full Idea: Men's propensity to injustice is not a permanent aspect of community life. | |
| From: John Rawls (A Theory of Justice [1972], p.245), quoted by John Kekes - Against Liberalism | |
| A reaction: This attitude is dismissed by Kekes, with some justification, as naïve optimism. What could be Rawls's grounds for making such a claim? It couldn't be the facts of human history. |
| 15676 | Rawls defends the priority of right over good [Rawls, by Finlayson] |
| Full Idea: Rawls defends the thesis of the priority of the right over the good. | |
| From: report of John Rawls (A Theory of Justice [1972]) by James Gordon Finlayson - Habermas Ch.7:100 | |
| A reaction: It depends whether you are talking about actions, or about states of affairs. I don't see how any state of affairs can be preferred to the good one. It may be that the highest duty of action is to do what is right, rather than to achieve what is good. |
| 4123 | A fair arrangement is one that parties can agree to without knowing how it will benefit them personally [Rawls, by Williams,B] |
| Full Idea: Rawls's theory is an elaboration of a simple idea: a fair system of arrangements is one that the parties can agree to without knowing how it will benefit them personally. | |
| From: report of John Rawls (A Theory of Justice [1972]) by Bernard Williams - Ethics and the Limits of Philosophy Ch.5 | |
| A reaction: The essence of modern Kantian contractualism. It is an appealing principle for building a rational world, but I hear Nietzsche turning in his grave. |
| 3279 | Utilitarianism inappropriately scales up the individual willingness to make sacrifices [Rawls, by Nagel] |
| Full Idea: Rawls claims that utilitarianism applies to the problem of many interests a method appropriate for one individual. A single person may accept disadvantages in exchange for benefits, but in society other people get the benefits. | |
| From: report of John Rawls (A Theory of Justice [1972], p.74,104) by Thomas Nagel - Equality §7 |
| 3280 | Why does the rational agreement of the 'Original Position' in Rawls make it right? [Nagel on Rawls] |
| Full Idea: Why does what it is rational to agree to in Rawls' 'Original Position' determine what is right? | |
| From: comment on John Rawls (A Theory of Justice [1972]) by Thomas Nagel - Equality §7 |
| 20552 | The original position models the idea that citizens start as free and equal [Rawls, by Swift] |
| Full Idea: The original position is presented by Rawls as modelling the sense in which citizens are to be understood as free and equal. | |
| From: report of John Rawls (A Theory of Justice [1972]) by Adam Swift - Political Philosophy (3rd ed) 3 'Strikes' | |
| A reaction: In other words, Rawls's philosophy is not a demonstration of why we should be liberals, but a guidebook for how liberals should go about organising society. |
| 18636 | Choose justice principles in ignorance of your own social situation [Rawls] |
| Full Idea: The principles of justice are chosen behind a veil of ignorance. ...Since all are similarly situated and no one is able to design principles to favor his particular condition, the principles of justice are the rest of a fair agreement or bargain. | |
| From: John Rawls (A Theory of Justice [1972], §03) | |
| A reaction: A famous idea. It tries to impose a Kantian impartiality onto the assessment of political principles. It is a beautifully simple idea, and saying that such impartiality never occurs is no objection to it. Think of a planet far far away. |
| 18631 | All desirable social features should be equal, unless inequality favours the disadvantaged [Rawls] |
| Full Idea: All social primary goods - liberty and opportunity, income and wealth, and the bases of self-respect - are to be distributed equally unless an unequal distribution of any or all of these goods is to the advantage of the least favoured. | |
| From: John Rawls (A Theory of Justice [1972], §46) | |
| A reaction: In the wholehearted capitalism of the 21st century this sounds like cloud-cuckoo land. As an 'initial position' (just as in the 'Republic') the clean slate brings out some interesting principles. Actual politics takes vested interests as axiomatic. |
| 20538 | Utilitarians lump persons together; Rawls somewhat separates them; Nozick wholly separates them [Swift on Rawls] |
| Full Idea: Rawls objects to utilitarianism because it fails to take seriously the separateness of persons (because there is no overall person to enjoy the overall happiness). But Nozick thinks Rawls does not take the separateness of persons seriously enough. | |
| From: comment on John Rawls (A Theory of Justice [1972]) by Adam Swift - Political Philosophy (3rd ed) 1 'Nozick' | |
| A reaction: In this sense, Nozick seems to fit our picture of a liberal more closely than Rawls does. I think they both exaggerate the separateness of persons, based on a false concept of human nature. |
| 9277 | Rawls's account of justice relies on conventional fairness, avoiding all moral controversy [Gray on Rawls] |
| Full Idea: Rawls's account of justice works only with widely accepted intuitions of fairness and relies at no point on controversial positions in ethics. The fruit of this modesty is a pious commentary on conventional moral beliefs. | |
| From: comment on John Rawls (A Theory of Justice [1972]) by John Gray - Straw Dogs 3.6 | |
| A reaction: Presumably this is the thought which provoked Nozick to lob his grenade on the subject. It resembles the charges of Schopenhauer and Nietzsche against Kant, that he was just dressing up conventional morality. Are 'controversial' ethics good? |
| 20527 | Liberty Principle: everyone has an equal right to liberties, if compatible with others' liberties [Rawls] |
| Full Idea: First Principle [Liberty]: Each person is to have an equal right to the most extensive total system of equal basic liberties compatible with a similar system of liberty for all. | |
| From: John Rawls (A Theory of Justice [1972], 46) | |
| A reaction: This is the result of consensus after the initial ignorant position of assessment. It is characteristic of liberalism. I'm struggling to think of a disagreement. |
| 21018 | The social contract has problems with future generations, national boundaries, disabilities and animals [Rawls, by Nussbaum] |
| Full Idea: Rawls saw four difficulties for justice in the social contract approach: future generations; justice across national boundaries; fair treatment of people with disabilities; and moral issues involving non-human animals. | |
| From: report of John Rawls (A Theory of Justice [1972]) by Martha Nussbaum - Creating Capabilities 4 | |
| A reaction: These are all classic examples of groups who do not have sufficient power to negotiate contracts. |
| 21041 | Justice concerns not natural distributions, or our born location, but what we do about them [Rawls] |
| Full Idea: The natural distribution is neither just nor unjust; nor is it unjust that persons are born into society at some particular position. These are simply natural facts. What is just and unjust is the way that institutions deal with these facts. | |
| From: John Rawls (A Theory of Justice [1972], 17) | |
| A reaction: Lovely quotation. There is no point in railing against the given, and that includes what is given by history, as well as what is given by nature. It comes down to intervening, in history and in nature. How much intervention will individuals tolerate? |
| 23583 | If an aggression is unjust, the constraints on how it is fought are much stricter [Rawls] |
| Full Idea: When a country's right to war is questionable and uncertain, the constraints on the means it can use are all the more severe. | |
| From: John Rawls (A Theory of Justice [1972], p.379), quoted by Michael Walzer - Just and Unjust Wars 14 | |
| A reaction: This is Rawls opposing the idea that combatants are moral equals. The restraints are, of course, moral. In practice aggressors are usually the worst behaved. |