49 ideas
| 9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
| Full Idea: Field commits himself to a Platonic view of mathematics. The theorems of set theory are held to imply or presuppose the existence of things that don't in fact exist. That is why he believes that these theorems are false. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Charles Chihara - A Structural Account of Mathematics 11.1 | |
| A reaction: I am sympathetic to Field, but this sounds wrong. A response that looks appealing is that maths is hypothetical ('if-thenism') - the truth is in the logical consequences, not in the ontological presuppositions. |
| 10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
| Full Idea: Field defines logical consequence by taking the notion of 'logical possibility' as primitive. Hence q is a consequence of P if the conjunction of the items in P with the negation of q is not possible. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Stewart Shapiro - Philosophy of Mathematics 7.2 | |
| A reaction: The question would then be whether it is plausible to take logical possibility as primitive. Presumably only intuition could support it. But then intuition will equally support natural and metaphysical possibilities. |
| 8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
| Full Idea: Field's nominalist version of science develops a version of Newtonian gravitational theory, where no quantifiers range over mathematical entities, and space-time points and regions play the role of surrogates for real numbers. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Zoltán Gendler Szabó - Nominalism 5.1 | |
| A reaction: This seems to be a very artificial contrivance, but Field has launched a programme for rewriting science so that numbers can be omitted. All of this is Field's rebellion against the Indispensability Argument for mathematics. I sympathise. |
| 18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
| Full Idea: There are two approaches to axiomatising geometry. The 'metric' approach uses a function which maps a pair of points into the real numbers. The 'synthetic' approach is that of Euclid and Hilbert, which does without real numbers and functions. | |
| From: Hartry Field (Science without Numbers [1980], 5) |
| 8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
| Full Idea: There is one and only one serious argument for the existence of mathematical entities, and that is the Indispensability Argument of Putnam and Quine. | |
| From: Hartry Field (Science without Numbers [1980], p.5), quoted by Stewart Shapiro - Thinking About Mathematics 9.1 | |
| A reaction: Personally I don't believe (and nor does Field) that this gives a good enough reason to believe in such things. Quine (who likes 'desert landscapes' in ontology) ends up believing that sets are real because of his argument. Not for me. |
| 18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
| Full Idea: The most popular approach of nominalistically inclined philosophers is to try to reinterpret mathematics, so that its terms and quantifiers only make reference to, say, physical objects, or linguistic expressions, or mental constructions. | |
| From: Hartry Field (Science without Numbers [1980], Prelim) | |
| A reaction: I am keen on naturalism and empiricism, but only referring to physical objects is a non-starter. I think I favour constructions, derived from the experience of patterns, and abstracted, idealised and generalised. Field says application is the problem. |
| 10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
| Full Idea: Field argues that to account for the applicability of mathematics, we need to assume little more than the possibility of the mathematics, not its truth. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Stewart Shapiro - Philosophy of Mathematics 7.2 | |
| A reaction: Very persuasive. We can apply chess to real military situations, provided that chess isn't self-contradictory (or even naturally impossible?). |
| 18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
| Full Idea: Facts about geometric laws receive satisfying explanations, by the intrinsic facts about physical space, i.e. those laid down without reference to numbers in Hilbert's axioms. | |
| From: Hartry Field (Science without Numbers [1980], 3) | |
| A reaction: Hilbert's axioms mention points, betweenness, segment-congruence and angle-congruence (Field 25-26). Field cites arithmetic and geometry (as well as Newtonian mechanics) as not being dependent on number. |
| 9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
| Full Idea: Field needs the notion of logical consequence in second-order logic, but (since this is not recursively axiomatizable) this is a semantical notion, which involves the idea of 'true in all models', a set-theoretic idea if there ever was one. | |
| From: comment on Hartry Field (Science without Numbers [1980], Ch.4) by James Robert Brown - Philosophy of Mathematics | |
| A reaction: Brown here summarises a group of critics. Field was arguing for modern nominalism, that actual numbers could (in principle) be written out of the story, as useful fictions. Popper's attempt to dump induction seemed to need induction. |
| 18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
| Full Idea: No clear explanation of the idea that the conclusion was 'implicitly contained in' the premises was ever given, and I do not believe that any clear explanation is possible. | |
| From: Hartry Field (Science without Numbers [1980], 1) |
| 18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
| Full Idea: Abstract entities are useful because we can use them to formulate abstract counterparts of concrete statements. | |
| From: Hartry Field (Science without Numbers [1980], 3) | |
| A reaction: He defends the abstract statements as short cuts. If the concrete statements were 'true', then it seems likely that the abstract counterparts will also be true, which is not what fictionalism claims. |
| 18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
| Full Idea: Mathematics is in a sense empirical, but only in the rather Pickwickian sense that is an empirical question as to which mathematical theory is useful. | |
| From: Hartry Field (Science without Numbers [1980], 1) | |
| A reaction: Field wants mathematics to be fictions, and not to be truths. But can he give an account of 'useful' that does not imply truth? Only in a rather dubiously pragmatist way. A novel is not useful. |
| 18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
| Full Idea: Why regard the axioms of standard mathematics as truths, rather than as fictions that for a variety of reasons mathematicians have become interested in? | |
| From: Hartry Field (Science without Numbers [1980], p.viii) |
| 18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
| Full Idea: One can often reduce one's ontological commitments by expanding one's logic. | |
| From: Hartry Field (Science without Numbers [1980], p.ix) | |
| A reaction: I don't actually understand this idea, but that's never stopped me before. Clearly, this sounds like an extremely interesting thought, and hence I should aspire to understand it. So I do aspire to understand it. First, how do you 'expand' a logic? |
| 8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
| Full Idea: Field regards the eliminability of apparent reference to properties from the language of science as a foregone result. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Zoltán Gendler Szabó - Nominalism 5.1 n50 | |
| A reaction: Field is a nominalist who also denies the existence of mathematics as part of science. He has a taste for ontological 'desert landscapes'. I have no idea what a property really is, so I think he is on to something. |
| 18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
| Full Idea: To be able to apply any postulated abstract entities to the physical world, we need impure abstact entities, e.g. functions that map physical objects into pure abstract objects. | |
| From: Hartry Field (Science without Numbers [1980], 1) | |
| A reaction: I am a fan of 'impure metaphysics', and this pinpoints my reason very nicely. |
| 20146 | 'Luck' is the unpredictable and inexplicable intersection of causal chains [Kekes] |
| Full Idea: 'Luck' is loose shorthand. It stands for various causal chains that intersect and whose intersection we can neither predict nor explain, because we lack the relevant knowledge. | |
| From: John Kekes (The Human Condition [2010], 01.2) | |
| A reaction: Aristotle's example is a chance meeting in the market place. The point about 'intersection' seems good, since luck doesn't seem to arise for an event in isolation. |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| Full Idea: A plausible methodological principle is that underlying every good extrinsic explanation there is an intrinsic explanation. | |
| From: Hartry Field (Science without Numbers [1980], 5) | |
| A reaction: I'm thinking that Hartry Field is an Aristotelian essentialist, though I bet he would never admit it. |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| Full Idea: The term 'abstract entities' may not be entirely clear, but one thing that does seem clear is that such alleged entities as numbers, functions and sets are abstract. | |
| From: Hartry Field (Science without Numbers [1980], p.1), quoted by JP Burgess / G Rosen - A Subject with No Object I.A.1.a | |
| A reaction: Field firmly denies the existence of such things. Sets don't seem a great problem, if the set is a herd of elephants, but the null and singleton sets show up the difficulties. |
| 20169 | An action may be intended under one description, but not under another [Kekes] |
| Full Idea: People can usually be described as intending an action under one description, but not under another. ...Consequently the same action may reasonably be said to be both intentional and unintentional. | |
| From: John Kekes (The Human Condition [2010], 07.2) | |
| A reaction: This is the terrorist/freedom fighter problem. The problem seems to arise with long-term intentions, rather than immediate ones. Maybe it is the significance of the intention, rather than the intention itself? |
| 20149 | To control our actions better, make them result from our attitudes, not from circumstances [Kekes] |
| Full Idea: We increase our control by making our actions more and more the effects of our attitudes, and less and less the effects of external forces acting on us independently of our attitudes. | |
| From: John Kekes (The Human Condition [2010], 02.4) | |
| A reaction: He says that the attitudes should be focused on our well-being. Attitudes may also, however, serve some exernal ideal, such as altruism or patriotism. He has built a case for 'control' being a much more important value than 'free will'. |
| 19738 | Values are an attempt to achieve well-being by bringing contingencies under control [Kekes] |
| Full Idea: Our system of values should be understood, among other things, as our attempt to cope with contingencies by making the connection between our well-being and actions less contingent and more within our control. | |
| From: John Kekes (The Human Condition [2010], Intro) | |
| A reaction: He gives an account in which every aspect of morality focuses on human well-being. Of course, the values will dictate what constitutes that well-being, as well as good means of attaining it. |
| 20145 | Values help us to control life, by connecting it to what is stable and manageable [Kekes] |
| Full Idea: Values are ...an attempt to cope with contingencies by making the connection between our well-being and actions less contingent and more within our control. | |
| From: John Kekes (The Human Condition [2010], Intro) | |
| A reaction: This sounds more like principles than values, since the former tell you what to do, but a value in itself is just a picture of possibilities. |
| 20170 | Responsibility is unprovoked foreseeable harm, against society, arising from vicious character [Kekes] |
| Full Idea: Full responsibility is when evil-doers can fully foresee the harm that results, their victims have not provoked it, it violates the requirements of physical protection in a society, the action reflects character, and it is viciously motivated. | |
| From: John Kekes (The Human Condition [2010], 07.4) | |
| A reaction: [compressed] The point of this is to omit any reference to an explicit intention to perform an evil act. The Nazi Franz Stangl claimed that he never intended evil, but Kekes says that if true he is innocent, but the above definition makes him guilty. |
| 20165 | Reason and morality do not coincide; immorality can be reasonable, with an ideology [Kekes] |
| Full Idea: A central assumption of Western moral thought is mistaken: the requirements of reason and morality do not coincide. Immorality need not be unreasonable. ...Malevolent motives in combination with ideologies supply reasons for doing evil. | |
| From: John Kekes (The Human Condition [2010], 06.5) | |
| A reaction: I presume that Kant would say the malevolent motives are irrational. If I perform an evil act because someone gives me a stupid reason for doing it, I am not thereby rational because I am acting for a reason. Wrong. |
| 20171 | Practical reason is not universal and impersonal, because it depends on what success is [Kekes] |
| Full Idea: The assumption that the requirements of reason are universal and impersonal ...is false of practical reason that aims at successful action. Whether a belief is true depends on the facts. Whether an action is successful depends on what success consists in. | |
| From: John Kekes (The Human Condition [2010], 08.5) | |
| A reaction: Kekes is trying to eliminate the Kantian idea that reason can lead us to the 'right' thing to do. He rightly points to the complex demands of human, cultural and personal values. |
| 20175 | If morality has to be rational, then moral conflicts need us to be irrational and immoral [Kekes] |
| Full Idea: The absurdity follows [from Kant's categorical imperative] that in the case of moral conflicts reason and morality require us to act irrationally and immorally. | |
| From: John Kekes (The Human Condition [2010], 10.4) | |
| A reaction: We can't pick one from two equals if we must have a reason for the preference, but that does not make it 'irrational' to choose one of them, when it doesn't matter which one is chosen. Taking one of the cheese sandwiches is not irrational. |
| 20174 | Relativists say all values are relative; pluralists concede much of that, but not 'human' values [Kekes] |
| Full Idea: We must distinguish between pluralism and relativism about values. Pluralists accept that the validity of cultural and personal values is relative to societies and individuals. But they also hold that human values are objectively valid. | |
| From: John Kekes (The Human Condition [2010], 09.4) | |
| A reaction: This is a very attractive response to global moral relativism. I see a problem in the neat division into three distinct forms of value. Each of the three sets of values ought to be sensitive to the other two areas. Humans are cultured individuals. |
| 20159 | Cultural values are interpretations of humanity, conduct, institutions, and evaluations [Kekes] |
| Full Idea: I distinguish four types of cultural values likely to be found in a particular society: interpretations of human values; forms of expression and conduct; institutions and practices within them; and modes of evaluation. | |
| From: John Kekes (The Human Condition [2010], 05.2) | |
| A reaction: He proceeds to enlarge on these four. This sub-divides the second of his three main areas of value. I like philosophers who do that sort of thing. It gives you the reassuring feeling that you can break a problem down into elements we understand.... |
| 20161 | The big value problems are evil (humanity), disenchantment (cultures), and boredom (individuals) [Kekes] |
| Full Idea: The major problem for the human dimension of values is the prevalence of evil; for the cultural dimension it is widespread disenchantment; and for the personal dimension it is pervasive boredom. | |
| From: John Kekes (The Human Condition [2010], 05.5) | |
| A reaction: Boldly simple claims, but quite persuasive. Presumably it is the evil in human beings, rather than natural evil (like earthquakes) that is the problem. Disenchantment must come through alienation from social values. Powerlessness, rather than boredom? |
| 20156 | We are bound to regret some values we never aspired to [Kekes] |
| Full Idea: We inevitably feel regret for the many values we could have, but did not, try to realize. | |
| From: John Kekes (The Human Condition [2010], 04.5) | |
| A reaction: He's obviously talking about working harder at our projects. |
| 20150 | There are far more values than we can pursue, so they are optional possibilities [Kekes] |
| Full Idea: A significant feature of our system of values is that it provides many more values than we could pursue. ...We encounter values as possibilities, and we must accept or reject them. | |
| From: John Kekes (The Human Condition [2010], 03.1) | |
| A reaction: This immediately invites the lovely question of what values you are going to invoke when you discriminate among the values available in your culture. Nietzsche says it comes down to 'taste'. |
| 20158 | Innumerable values arise for us, from our humanity, our culture, and our individuality [Kekes] |
| Full Idea: There is an irreducible plurality of values that follow from the universal requirements of human well-being, from a shared cultural identity, and from individual conceptions of well-being. | |
| From: John Kekes (The Human Condition [2010], 05 Intro) | |
| A reaction: This strikes me as a very helpful division. It seems reasonably obvious, but I have not encountered it elsewhere. It is an obvious foundation for international negotiations. We can criticise another culture by appealing to human values. |
| 20151 | Our attitudes include what possibilities we value, and also what is allowable, and unthinkable [Kekes] |
| Full Idea: The beliefs, emotions, motives, and desires that form our attitudes ...include not only what possibilities we value, but also the limits we should not transgress. ...The strongest limit is what I call 'the unthinkable'. | |
| From: John Kekes (The Human Condition [2010], 03.2) | |
| A reaction: Another chance to link to my favourite idea from Democritus! Ideally we want a theory which shows how a vision of the possibilities immediately points to the limits, and to what is unthinkable. |
| 20152 | Unconditional commitments are our most basic convictions, saying what must never be done [Kekes] |
| Full Idea: Unconditional commitments are the most basic convictions we have. They tell us what we must not do no matter what, what we regard as outrageous, horrible, beyond the pale, or, in religious language, as sacrilegious. | |
| From: John Kekes (The Human Condition [2010], 03.3) | |
| A reaction: The Aztecs should have made rather different unconditional commitments from the ones they ended up with. How do you persuade someone to make such an unconditional commitment. Abortion seems to involve huge clashes here. |
| 20153 | Doing the unthinkable damages ourselves, so it is more basic than any value [Kekes] |
| Full Idea: Doing the unthinkable causes deep, often irreparable, damage to our sense of ourselves. ...That is why the unthinkable indicates a more basic commitment than what we have to any value. | |
| From: John Kekes (The Human Condition [2010], 03.3) | |
| A reaction: Kekes makes the interesting claim that what is unthinkable is so basic that it doesn't even count as a value - it is more like a fact of your own nature, which is prior to your values. Not sure about that. |
| 20162 | Evil isn't explained by nature, by monsters, by uncharacteristic actions, or by society [Kekes] |
| Full Idea: Four inadequate explanations of human evil attribute it to natural causes, moral monsters, uncharacteristic actions, and corrupting social conditions. | |
| From: John Kekes (The Human Condition [2010], 06.3) | |
| A reaction: He is addressing the 'secular problem of evil', which arises if you assume that human beings are essentially good, and then look around you. He says evil explains corrupting social conditions, so we can't be circular about it. |
| 20157 | Well-being needs correct attitudes and well-ordered commitments to local values [Kekes] |
| Full Idea: A reasonable conception of well-being requires mistake-free attitudes and well-ordered commitments to some values selected from our society's system of values. | |
| From: John Kekes (The Human Condition [2010], 05 Intro) | |
| A reaction: This summarises where he has got to so far. |
| 5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |
| Full Idea: For Bradley, the happiness of the individual is not to be understood in terms of his desires and needs, but rather in terms of his values - which is to say, in terms of those of his desires which he incorporates into his self. | |
| From: report of F.H. Bradley (Ethical Studies [1876]) by Roger Scruton - Short History of Modern Philosophy Ch.16 | |
| A reaction: Good. Bentham will reduce the values to a further set of desires, so that a value is a complex (second-level?) desire. I prefer to think of values as judgements, but I like Scruton's phrase of 'incorporating into his self'. Kant take note (Idea 1452). |
| 20154 | Control is the key to well-being [Kekes] |
| Full Idea: Increasing control is the key to our well-being. | |
| From: John Kekes (The Human Condition [2010], 04 Intro) | |
| A reaction: This slogan emerges from a sustained discussion. Hitler and Stalin increased control rather impressively, so we obviously need a bit more than this to get proper well-being. There's also something to be said for going with the flow. |
| 20172 | Boredom destroys our ability to evaluate [Kekes] |
| Full Idea: The threat of boredom is the dissolution of the evaluative dimension of our life. | |
| From: John Kekes (The Human Condition [2010], 09.1) | |
| A reaction: This seems right. If nothing is interesting, then there is no scale of values left, except perhaps 'of possible interest to other people'. |
| 20173 | Boredom is apathy and restlessness, yearning for something interesting [Kekes] |
| Full Idea: Boredom combines apathy and restlessness. ...We crave stimulation, worthwhile activities, and objects that engage our interest. | |
| From: John Kekes (The Human Condition [2010], 09.1) |
| 20155 | Society is alienating if it lacks our values, and its values repel us [Kekes] |
| Full Idea: We feel estranged from our society if the values we prize are not available, and if we do not want to live by the available values. | |
| From: John Kekes (The Human Condition [2010], 04.4) | |
| A reaction: There are two pictures here, for a monolithic culture, and for pluralism. For example, the values of Islam are fairly available in the Christian/atheist UK - but not sharia law. Pluralism can embrace a huge array of moderate values, but not extremes? |
| 20164 | The ideal of an ideology is embodied in a text, a role model, a law of history, a dream of the past... [Kekes] |
| Full Idea: The ideal in an ideology may be set down in a sacred text, exemplified in an exceptional life, dictated by laws of history, sociology, or psychology, located in a past uncorrupted idyllic past, or in a future Utopia of perfected human nature, and so on. | |
| From: John Kekes (The Human Condition [2010], 06.4) | |
| A reaction: A bit grumpy, but a fair observation about an awful lot of slightly mad social endeavours. |
| 20163 | Ideologies have beliefs about reality, ideals, a gap with actuality, and a program [Kekes] |
| Full Idea: Ideologies have a set of beliefs about the world, an ideal of life, an explanation of the gap between the ideal and actuality, and a program for closing the gap. | |
| From: John Kekes (The Human Condition [2010], 06.4) | |
| A reaction: [compressed] Kekes emerges as a bit right of centre in his politics. He clearly despises such ideologies, yet his book is an optimistic program for correcting things. Maybe the enemy is dogmatic ideologies. Kekes gives an undogmatic account of values. |
| 20148 | Equal distribution is no good in a shortage, because there might be no one satisfied [Kekes] |
| Full Idea: It is useless to distribute insufficient resources equally, because the equal distribution of insufficient resources may result in the even worse outcome that no one's reasonable expectations are met. | |
| From: John Kekes (The Human Condition [2010], 01.5) | |
| A reaction: He gives a shortage of oxygen tanks as a persuasive example, but that is hardly typical of the sorts of things that we normally want to distribute. |
| 18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
| Full Idea: According to theories that take the notion of a field seriously, space-time points or regions are fully-fledge causal agents. | |
| From: Hartry Field (Science without Numbers [1980], n 23) |
| 18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
| Full Idea: In general, it seems to me that recent developments in both philosophy and physics have made substantivalism a much more attractive position than it once was. | |
| From: Hartry Field (Science without Numbers [1980], 4) | |
| A reaction: I'm intrigued as to what philosophical developments are involved in this. The arrival of fields is the development in physics. |
| 18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |
| Full Idea: The problem of the relational view of space is especially acute in the context of physical theories that take the notion of a field seriously, e.g. classical electromagnetic theory. | |
| From: Hartry Field (Science without Numbers [1980], 4) | |
| A reaction: In the Leibniz-Clarke debate I sided with the Newtonian Clarke (defending absolute space), and it looks like modern science agrees with me. Nothing exists purely as relations. |