124 ideas
| 3240 | There is more insight in fundamental perplexity about problems than in their supposed solutions [Nagel] |
| Full Idea: Certain forms of perplexity (say about freedom, knowledge and the meaning of life) seem to me to embody more insight than any of the supposed solutions to those problems. | |
| From: Thomas Nagel (The View from Nowhere [1986], Intro) | |
| A reaction: Obviously false solutions won't embody much insight. This sounds good, but I suspect that the insight is in the recognition of the facts which give rise to the perplexity. I can't think of anything in favour of perplexity for its own sake. |
| 3269 | If your life is to be meaningful as part of some large thing, the large thing must be meaningful [Nagel] |
| Full Idea: Those seeking to give their lives meaning usually envision a role in something larger than themselves, …but such a role can't confer significance unless that enterprise is itself significant. | |
| From: Thomas Nagel (The Absurd [1971], §3) | |
| A reaction: Which correctly implies that this way of finding meaning for one's life is doomed. |
| 3242 | Philosophy is the childhood of the intellect, and a culture can't skip it [Nagel] |
| Full Idea: Philosophy is the childhood of the intellect, and a culture that tries to skip it will never grow up. | |
| From: Thomas Nagel (The View from Nowhere [1986], Intro) | |
| A reaction: Can he really mean that a mature culture doesn't need philosophy? |
| 3241 | It seems mad, but the aim of philosophy is to climb outside of our own minds [Nagel] |
| Full Idea: We are trying to climb outside of our own minds, an effort that some would regard as insane and that I regard as philosophically fundamental. | |
| From: Thomas Nagel (The View from Nowhere [1986], Intro) | |
| A reaction: It is not only philosophers who do this. It is an essential feature of the mind, and is inherent in the concept of truth. |
| 1489 | Modern philosophy tends to be a theory-constructing extension of science, but there is also problem-solving [Nagel] |
| Full Idea: Philosophy is now dominated by a spirit of theory construction which sees philosophy as continuous with science, but the other problem-centred style is still in existence and it is important to keep it alive. | |
| From: Thomas Nagel (The Philosophical Culture [1995], §6) |
| 3248 | Realism invites scepticism because it claims to be objective [Nagel] |
| Full Idea: The search for objective knowledge, because of its commitment to realism, cannot refute scepticism and must proceed under its shadow, and scepticism is only a problem because of the realist claims of objectivity. | |
| From: Thomas Nagel (The View from Nowhere [1986], V.1) |
| 20989 | Views are objective if they don't rely on a person's character, social position or species [Nagel] |
| Full Idea: A view or form of thought is more objective than another if it relies less on the specifics of the individual's makeup and position in the world, or on the character of the particular type of creature he is. | |
| From: Thomas Nagel (The View from Nowhere [1986], Intro) | |
| A reaction: Notice that this defines comparative objectivity, rather than an absolute. I take it that something must be entirely objective to qualify as a 'fact', and so anything about which there is a consensus that it is a fact can be taken as wholly objective. |
| 22354 | Things cause perceptions, properties have other effects, hence we reach a 'view from nowhere' [Nagel, by Reiss/Sprenger] |
| Full Idea: First we realise that perceptions are caused by things, second we realise that properties have other effects (as well as causing perceptions), and third we conceive of a thing's true nature without perspectives. That is the 'view from nowhere'. | |
| From: report of Thomas Nagel (The View from Nowhere [1986], p.14) by Reiss,J/Spreger,J - Scientific Objectivity 2.1 | |
| A reaction: [My summary of their summary] This is obviously an optimistic view. I''m not sure how he can justify three precise stages, given than animals probably jump straight to the third stage, and engage with the nature's of things. |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| Full Idea: Cohen's method of 'forcing' produces a new model of ZFC from an old model by appending a carefully chosen 'generic' set. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.4) |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| Full Idea: A possible axiom is the Large Cardinal Axiom, which asserts that there are more and more stages in the cumulative hierarchy. Infinity can be seen as the first of these stages, and Replacement pushes further in this direction. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.5) |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| Full Idea: In current set theory, the search is on for new axioms to determine the size of the continuum. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §0) | |
| A reaction: This sounds the wrong way round. Presumably we seek axioms that fix everything else about set theory, and then check to see what continuum results. Otherwise we could just pick our continuum, by picking our axioms. |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| Full Idea: Most writers agree that if any sense can be made of the distinction between analytic and synthetic, then the Axiom of Extensionality should be counted as analytic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [Boolos is the source of the idea] In other words Extensionality is not worth discussing, because it simply tells you what the world 'set' means, and there is no room for discussion about that. The set/class called 'humans' varies in size. |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| Full Idea: The extensional view of sets is preferable because it is simpler, clearer, and more convenient, because it individuates uniquely, and because it can simulate intensional notions when the need arises. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [She cites Fraenkel, Bar-Hillet and Levy for this] The difficulty seems to be whether the extensional notion captures our ordinary intuitive notion of what constitutes a group of things, since that needs flexible size and some sort of unity. |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| Full Idea: The Axiom of Infinity is a simple statement of Cantor's great breakthrough. His bold hypothesis that a collection of elements that had lurked in the background of mathematics could be infinite launched modern mathematics. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: It also embodies one of those many points where mathematics seems to depart from common sense - but then most subjects depart from common sense when they get more sophisticated. Look what happened to art. |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| Full Idea: If one is interested in analysis then infinite sets are indispensable since even the notion of a real number cannot be developed by means of finite sets alone. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: [Maddy is citing Fraenkel, Bar-Hillel and Levy] So Cantor's great breakthrough (Idea 13021) actually follows from the earlier acceptance of the real numbers, so that's where the departure from common sense started. |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| Full Idea: The axiom of infinity: that there are infinite sets is to claim that completed infinite collections can be treated mathematically. In its standard contemporary form, the axioms assert the existence of the set of all finite ordinals. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.3) |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| Full Idea: The Power Set Axiom is indispensable for a set-theoretic account of the continuum, ...and in so far as those attempts are successful, then the power-set principle gains some confirmatory support. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.6) | |
| A reaction: The continuum is, of course, notoriously problematic. Have we created an extra problem in our attempts at solving the first one? |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| Full Idea: In the presence of other axioms, the Axiom of Foundation is equivalent to the claim that every set is a member of some Vα. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.3) |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| Full Idea: Jordain made consistent and ill-starred efforts to prove the Axiom of Choice. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This would appear to be the fate of most axioms. You would presumably have to use a different system from the one you are engaged with to achieve your proof. |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| Full Idea: Resistance to the Axiom of Choice centred on opposition between existence and construction. Modern set theory thrives on a realistic approach which says the choice set exists, regardless of whether it can be defined, constructed, or given by a rule. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This seems to be a key case for the ontology that lies at the heart of theory. Choice seems to be an invaluable tool for proofs, so it won't go away, so admit it to the ontology. Hm. So the tools of thought have existence? |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| Full Idea: Many theorems depend on the Axiom of Choice, including that a countable union of sets is countable, and results in analysis, topology, abstract algebra and mathematical logic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: The modern attitude seems to be to admit anything if it leads to interesting results. It makes you wonder about the modern approach of using mathematics and logic as the cutting edges of ontological thinking. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| Full Idea: The Axiom of Reducibility states that every propositional function is extensionally equivalent to some predicative proposition function. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| Full Idea: The Iterative Conception (Zermelo 1930) says everything appears at some stage. Given two objects a and b, let A and B be the stages at which they first appear. Suppose B is after A. Then the pair set of a and b appears at the immediate stage after B. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: Presumably this all happens in 'logical time' (a nice phrase I have just invented!). I suppose we might say that the existence of the paired set is 'forced' by the preceding sets. No transcendental inferences in this story? |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| Full Idea: The 'limitation of size' is a vague intuition, based on the idea that being too large may generate the paradoxes. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: This is an intriguing idea to be found right at the centre of what is supposed to be an incredibly rigorous system. |
| 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. |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| Full Idea: Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups. |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| Full Idea: Henkin-style semantics seem to me more plausible for plural logic than for second-order logic. | |
| From: Penelope Maddy (Second Philosophy [2007], III.8 n1) | |
| A reaction: Henkin-style semantics are presented by Shapiro as the standard semantics for second-order logic. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| Full Idea: A 'propositional function' is generated when one of the terms of the proposition is replaced by a variable, as in 'x is wise' or 'Socrates'. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: This implies that you can only have a propositional function if it is derived from a complete proposition. Note that the variable can be in either subject or in predicate position. It extends Frege's account of a concept as 'x is F'. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| Full Idea: The line of development that finally led to a coherent foundation for the calculus also led to the explicit introduction of completed infinities: each real number is identified with an infinite collection of rationals. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.3) | |
| A reaction: Effectively, completed infinities just are the real numbers. |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| Full Idea: Both Cantor's real number (Cauchy sequences of rationals) and Dedekind's cuts involved regarding infinite items (sequences or sets) as completed and subject to further manipulation, bringing the completed infinite into mathematics unambiguously. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1 n39) | |
| A reaction: So it is the arrival of the real numbers which is the culprit for lumbering us with weird completed infinites, which can then be the subject of addition, multiplication and exponentiation. Maybe this was a silly mistake? |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| Full Idea: The stunning discovery that infinity comes in different degrees led to the theory of infinite cardinal numbers, the heart of contemporary set theory. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: It occurs to me that these huge cardinals only exist in set theory. If you took away that prop, they would vanish in a puff. |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| Full Idea: By the mid 1890s Cantor was aware that there could be no set of all sets, as its cardinal number would have to be the largest cardinal number, while his own theorem shows that for any cardinal there is a larger. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: There is always a larger cardinal because of the power set axiom. Some people regard that with suspicion. |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| Full Idea: An 'inaccessible' cardinal is one that cannot be reached by taking unions of small collections of smaller sets or by taking power sets. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.5) | |
| A reaction: They were introduced by Hausdorff in 1908. |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| Full Idea: Even the fundamental theorems about limits could not [at first] be proved because the reals themselves were not well understood. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: This refers to the period of about 1850 (Weierstrass) to 1880 (Dedekind and Cantor). |
| 18182 | The extension of concepts is not important to me [Maddy] |
| Full Idea: I attach no decisive importance even to bringing in the extension of the concepts at all. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], §107) | |
| A reaction: He almost seems to equate the concept with its extension, but that seems to raise all sorts of questions, about indeterminate and fluctuating extensions. |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| Full Idea: In the ZFC cumulative hierarchy, Frege's candidates for numbers do not exist. For example, new three-element sets are formed at every stage, so there is no stage at which the set of all three-element sets could he formed. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: Ah. This is a very important fact indeed if you are trying to understand contemporary discussions in philosophy of mathematics. |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| Full Idea: To solve the Julius Caesar problem, Frege requires explicit definitions of the numbers, and he proposes his well-known solution: the number of Fs = the extension of the concept 'equinumerous with F' (based on one-one correspondence). | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: Why do there have to be Fs before there can be the corresponding number? If there were no F for 523, would that mean that '523' didn't exist (even if 522 and 524 did exist)? |
| 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. |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| Full Idea: Maddy takes a natural number to be a certain property of sui generis sets, the property of having a certain number of members. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990], 3 §2) by Alex Oliver - The Metaphysics of Properties | |
| A reaction: [I believe Maddy has shifted since then] Presumably this will make room for zero and infinities as natural numbers. Personally I want my natural numbers to count things. |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| Full Idea: The set theory axioms developed in producing foundations for mathematics also have strong consequences for existing fields, and produce a theory that is immensely fruitful in its own right. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: [compressed] Second of Maddy's three benefits of set theory. This benefit is more questionable than the first, because the axioms may be invented because of their nice fruit, instead of their accurate account of foundations. |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| Full Idea: The single unified area of set theory provides a court of final appeal for questions of mathematical existence and proof. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: Maddy's third benefit of set theory. 'Existence' means being modellable in sets, and 'proof' means being derivable from the axioms. The slightly ad hoc character of the axioms makes this a weaker defence. |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| Full Idea: Set theoretic foundations bring all mathematical objects and structures into one arena, allowing relations and interactions between them to be clearly displayed and investigated. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: The first of three benefits of set theory which Maddy lists. The advantages of the one arena seem to be indisputable. |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| Full Idea: The identification of geometric points with real numbers was among the first and most dramatic examples of the power of set theoretic foundations. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: Hence the clear definition of the reals by Dedekind and Cantor was the real trigger for launching set theory. |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| Full Idea: The structure of a geometric line by rational points left gaps, which were inconsistent with a continuous line. Set theory provided an ordering that contained no gaps. These reals are constructed from rationals, which come from integers and naturals. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: This completes the reduction of geometry to arithmetic and algebra, which was launch 250 years earlier by Descartes. |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| Full Idea: Our much loved mathematical knowledge rests on two supports: inexorable deductive logic (the stuff of proof), and the set theoretic axioms. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I Intro) |
| 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) |
| 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. |
| 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. |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| Full Idea: Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things. |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| Full Idea: Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5 | |
| A reaction: Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory. |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| Full Idea: Crudely, the scientist posits only those entities without which she cannot account for observations, while the set theorist posits as many entities as she can, short of inconsistency. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.5) |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| Full Idea: It could turn out that all applications of continuum mathematics in natural sciences are actually instances of idealisation. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.6) |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 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] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| Full Idea: Recent commentators have noted that Frege's versions of the basic propositions of arithmetic can be derived from Hume's Principle alone, that the fatal Law V is only needed to derive Hume's Principle itself from the definition of number. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: Crispin Wright is the famous exponent of this modern view. Apparently Charles Parsons (1965) first floated the idea. |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| Full Idea: It seems unavoidable that the facts about logically necessary relations between levels of facts are themselves logically distinct further facts, irreducible to the microphysical facts. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: I'm beginning to think that rejecting every theory of reality that is proposed by carefully exposing some infinite regress hidden in it is a rather lazy way to do philosophy. Almost as bad as rejecting anything if it can't be defined. |
| 4242 | Pure supervenience explains nothing, and is a sign of something fundamental we don't know [Nagel] |
| Full Idea: Pure, unexplained supervenience is never a solution to a problem but a sign that there is something fundamental we don't know. | |
| From: Thomas Nagel (The Psychophysical Nexus [2000], §III) | |
| A reaction: This seems right. It is not a theory or an explanation, merely the observation of a correlation which will require explanation. Why are they correlated? |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| Full Idea: Logical supervenience, restricted to individuals, seems to imply strong reduction. It is said that where the B-facts logically supervene on the A-facts, the B-facts simply re-describe what the A-facts describe, and the B-facts come along 'for free'. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: This seems to be taking 'logically' to mean 'analytically'. Presumably an entailment is logically supervenient on its premisses, and may therefore be very revealing, even if some people think such things are analytic. |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| Full Idea: The root intuition behind nonreductive materialism is that reality is composed of ontologically distinct layers or levels. …The upper levels depend on the physical without reducing to it. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], B) | |
| A reaction: A nice clear statement of a view which I take to be false. This relationship is the sort of thing that drives people fishing for an account of it to use the word 'supervenience', which just says two things seem to hang out together. Fluffy materialism. |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| Full Idea: Jessica Wilson (1999) says what makes physicalist accounts different from emergentism etc. is that each individual causal power associated with a supervenient property is numerically identical with a causal power associated with its base property. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], n 11) | |
| A reaction: Hence the key thought in so-called (serious, rather than self-evident) 'emergentism' is so-called 'downward causation', which I take to be an idle daydream. |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| Full Idea: The case of atoms makes it clear that the indispensable appearance of an entity in our best scientific theory is not generally enough to convince scientists that it is real. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.6) | |
| A reaction: She refers to the period between Dalton and Einstein, when theories were full of atoms, but there was strong reluctance to actually say that they existed, until the direct evidence was incontrovertable. Nice point. |
| 3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
| Full Idea: The supposition that a diamond or organism should truly have emergent properties is that they appear at certain complex levels of organisation, but are not explainable (even in principle) in terms of any more fundamental properties of the system. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |
| 3249 | Modern science depends on the distinction between primary and secondary qualities [Nagel] |
| Full Idea: The distinction between primary and secondary qualities is the precondition for the development of modern physics and chemistry. | |
| From: Thomas Nagel (The View from Nowhere [1986], V.3) |
| 22429 | We achieve objectivity by dropping secondary qualities, to focus on structural primary qualities [Nagel] |
| Full Idea: At the end [of the three stages of objectivity] the secondary qualities drop out of our picture of the external world, and the underlyiing primary qualities such as shape, size, weight, and motion are thought of structurally. | |
| From: Thomas Nagel (The View from Nowhere [1986], II) | |
| A reaction: This is the orthodox view for realists about the external world, and I largely agree. The only problem I see is that secondary qualities contain information, such as the colour of rotting fruit - but then colour is not an essential feature of rot. |
| 3296 | Sense-data are a false objectification of what is essentially subjective [Nagel] |
| Full Idea: The private object or sense datum view is an instance of the false objectification of what is essentially subjective. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.207) |
| 3247 | Epistemology is centrally about what we should believe, not the definition of knowledge [Nagel] |
| Full Idea: The central problem of epistemology is what to believe and how to justify one's beliefs, not the impersonal problem of whether my beliefs can be said to be knowledge. | |
| From: Thomas Nagel (The View from Nowhere [1986], V.1) | |
| A reaction: Wrong. The question of whether what one has is 'knowledge' is not impersonal at all - it is having the social status of a knower or expert. |
| 3271 | We can't control our own beliefs [Nagel] |
| Full Idea: Our beliefs are always due to factors outside of our control. | |
| From: Thomas Nagel (Moral Luck [1976], p.27) |
| 3270 | Justifications come to an end when we want them to [Nagel] |
| Full Idea: Justifications come to an end when we are content to have them end. | |
| From: Thomas Nagel (The Absurd [1971], §3) | |
| A reaction: This is the correct account, with the vital proviso that where justification comes to an end is usually a social matter. Robinson Crusoe doesn't care whether he 'knows' - he just acts on his beliefs. |
| 3252 | Scepticism is based on ideas which scepticism makes impossible [Nagel] |
| Full Idea: The sceptic reaches scepticism through thoughts that scepticism makes unthinkable. | |
| From: Thomas Nagel (The View from Nowhere [1986], V.6) |
| 1490 | You would have to be very morally lazy to ignore criticisms of your own culture [Nagel] |
| Full Idea: One would have to be very morally lazy to be unconcerned with the possibility that the prevailing morality of one's culture had something fundamentally wrong with it. | |
| From: Thomas Nagel (MacIntyre versus the Enlightenment [1988], 203) |
| 3251 | Observed regularities are only predictable if we assume hidden necessity [Nagel] |
| Full Idea: Observed regularities provide reason to believe that they will be repeated only to the extent that they provide evidence of hidden necessary connections, which hold timelessly. | |
| From: Thomas Nagel (The View from Nowhere [1986], V.5) |
| 3295 | Inner v outer brings astonishment that we are a particular person [Nagel] |
| Full Idea: The problem of reconciling the objective and subjective points of view takes its purest form in a sense of incredulity that one should be anyone in particular. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.206) | |
| A reaction: Nice observation. This idea has always struck me forcibly, and seems to be one of those basic intuitions which motivates philosophy, and yet the subject has almost nothing to say about it. Of course you are you, or you wouldn't be amazed by it… |
| 2957 | Brain bisection suggests unity of mind isn't all-or-nothing [Nagel, by Lockwood] |
| Full Idea: Nagel argues (because of brain bisection experiments) that we should jettison our commonsense assumption that the unity of consciousness is an all-or-nothing affair. | |
| From: report of Thomas Nagel (Brain Bisection and Unity of Consciousness [1971]) by Michael Lockwood - Mind, Brain and the Quantum p.84 | |
| A reaction: It seems wrong to call it 'commonsense'. It is an assumption that precedes any judgement, but if you rapidly grasp that your mind is in your brain, it becomes common sense that you can cut lumps out of your mind. |
| 3286 | An organism is conscious if and only if there is something it is like to be that organism [Nagel] |
| Full Idea: An organism only has conscious mental states if and only if there is something that it is like to be that organism. | |
| From: Thomas Nagel (What is it like to be a bat? [1974], p.166) | |
| A reaction: It is hard to argue with this, but one should push on and ask what features of its consciousness make it such that there is a 'what it is like'. What is it like to have a subconscious mind, or be deeply asleep, or drive while daydreaming? |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| Full Idea: In science we treat the earth's surface as flat, we assume the ocean to be infinitely deep, we use continuous functions for what we know to be quantised, and we take liquids to be continuous despite atomic theory. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.6) | |
| A reaction: If fussy people like scientists do this all the time, how much more so must the confused multitude be doing the same thing all day? |
| 3285 | We may be unable to abandon personal identity, even when split-brains have undermined it [Nagel] |
| Full Idea: As a result of the evidence of split-brains, it is possible that the ordinary, simple idea of a single person will come to seem quaint some day, …but we may be unable to abandon the idea, no matter what we discover. | |
| From: Thomas Nagel (Brain Bisection and Unity of Consciousness [1971], p.164) | |
| A reaction: I'm not sure what grounds you can have for a claim that we can't abandon our current view of selves, even when the new reality will be utterly different. Rather conservative? I would expect future concepts to roughly match future reality. |
| 3293 | If you assert that we have an ego, you can still ask if that future ego will be me [Nagel] |
| Full Idea: The metaphysical ego, if it is a continuing individual with its identity over time, is just one more thing about which the same problem can be raised - will that ego still be me? | |
| From: Thomas Nagel (Subjective and Objective [1979], p.200) | |
| A reaction: You can worry too much about some philosophical questions. If it is me now, and it has continuing individual identity over time, I'm not going to lose sleep over the possibility that it might nevertheless somehow cease to be me. I'm overrated. |
| 3244 | Personal identity cannot be fully known a priori [Nagel] |
| Full Idea: The full conditions of personal identity cannot be extracted from the concept of a person at all: they cannot be arrived at a priori. | |
| From: Thomas Nagel (The View from Nowhere [1986], III.2) | |
| A reaction: However, if you turn to experience to get the hang of what a person is, it is virtually impossible to disentangle the essentials from the accidental features of being a person. How essential are memories or reasoning or hopes or understandings or plans? |
| 3245 | The question of whether a future experience will be mine presupposes personal identity [Nagel] |
| Full Idea: The identity of the self must have some sort of objectivity, otherwise the subjective question whether a future experience will be mine or not will be contentless. | |
| From: Thomas Nagel (The View from Nowhere [1986], III.3) | |
| A reaction: This sounds a bit circular and question-begging. If there is no objective self, then the question of whether a future experience will be mine would be a misconceived question. I sympathise with Nagel's attempt to show how personal identity is a priori. |
| 3246 | I can't even conceive of my brain being split in two [Nagel] |
| Full Idea: It is hard to think of myself as being identical with my brain. If my brain is to be split, with one half miserable and the other half euphoric, my expectations can take no form, as my idea of myself doesn't allow for divisibility. | |
| From: Thomas Nagel (The View from Nowhere [1986], III.4) | |
| A reaction: Nagel is trying to imply that there is some sort of conceptual impossibility here, but it may just be very difficult. I can think about my lovely lunch while doing my miserable job. Does Nagel want to hang on to a unified thing which doesn't exist? |
| 3292 | The most difficult problem of free will is saying what the problem is [Nagel] |
| Full Idea: The most difficult problem of free will is saying what the problem is. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.198) |
| 3288 | Can we describe our experiences to zombies? [Nagel] |
| Full Idea: The goal of an objective phenomenology would be to describe, at least in part, the subjective character of experiences in a form comprehensible to beings incapable of having those experiences. | |
| From: Thomas Nagel (What is it like to be a bat? [1974], p.179) | |
| A reaction: This seems a bizarre expectation. We can already explain visual experience to the blind up to a point, but no one is dreaming of an "objective phenomenology" which will give blind people total understanding, just by reading about it in braille. |
| 4883 | Nagel's title creates an impenetrable mystery, by ignoring a bat's ways that may not be "like" anything [Dennett on Nagel] |
| Full Idea: Nagel's title invites us to ignore all the different ways in which bats might accomplish their cunning feats without its "being like" anything for them. We create an impenetrable mystery for ourselves if we assume that Nagel's title makes sense. | |
| From: comment on Thomas Nagel (What is it like to be a bat? [1974]) by Daniel C. Dennett - Kinds of Minds Ch.6 | |
| A reaction: This could well be correct about bats, but the question applies to humans as well, and we can't deny that "what it is like" is a feature of some creatures' realities. On the fringes of our own consciousness there are mental events that are "like" nothing. |
| 3287 | We can't be objective about experience [Nagel] |
| Full Idea: If the subjective character of experience is fully comprehensible only from one point of view, then any shift to greater objectivity does not take us nearer to the real nature of the phenomenon: it takes us further away from it. | |
| From: Thomas Nagel (What is it like to be a bat? [1974], p.174) | |
| A reaction: We can, however, talk to one another about our subjectivity, and compare notes, and such 'inter-subjectivity' may be one approach to objectivity. We must concede Nagel's point, but we also miss something about a stone if we must remain outside of it. |
| 4989 | Physicalism should explain how subjective experience is possible, but not 'what it is like' [Kirk,R on Nagel] |
| Full Idea: A physicalist account of conscious experience must explain how it is possible for a physical system to be a conscious subject, but not 'what it is like' for some organism. | |
| From: comment on Thomas Nagel (What is it like to be a bat? [1974]) by Robert Kirk - Mind and Body §4.2 | |
| A reaction: You can't entirely evade Nagel's challenge. We are trying to discover the 'neural correlate of consciousness', which will explain why we are conscious, but we also want to know why we experience green for one wavelength, and red for another. |
| 4001 | The meaning of a word contains all its possible uses as well as its actual ones [Nagel] |
| Full Idea: The meaning of a word contains all its possible uses, true and false, not only its actual ones. | |
| From: Thomas Nagel (What Does It All Mean? [1987], Ch.5) | |
| A reaction: It has always seemed to me that meaning is not use, because you can't use it if it hasn't already got a meaning. What use is a meaningless word? |
| 6479 | Noninterference requires justification as much as interference does [Nagel] |
| Full Idea: Noninterference requires justification as much as interference does. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.10) | |
| A reaction: I'm not convinced by this, as a simple rule. If I spend my whole life doing just the minimum for my own survival, I don't see why I should have to justify that, and I don't see a state is obliged to justify it either. |
| 6450 | Morality must be motivating, and not because of pre-moral motives [Nagel] |
| Full Idea: My own view is that moral justification must be capable of motivating, but not in virtue of reliance on pre-moral motives. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.5) | |
| A reaction: This may well be the core and essence of Kantian moral theory. I'm inclined to think of it as 'Kant's dream', which is of ultra-rational beings who are driven by pure rationality as a motivator. People who fit this bill tend to be academics. |
| 3284 | There is no one theory of how to act (or what to believe) [Nagel] |
| Full Idea: To look for a single general theory of how to decide the right thing to do is like looking for a single theory of how to decide what to believe. | |
| From: Thomas Nagel (The Fragmentation of Value [1977], p.135) | |
| A reaction: Depends on your level of generality. Values and virtues are general guides which should be brought to every action, with 'higher' values guiding choice of what is relevant. |
| 3257 | Total objectivity can't see value, but it sees many people with values [Nagel] |
| Full Idea: A purely objective view has no way of knowing whether anything has any value, but actually its data include the appearance of value to individuals with particular perspectives, including oneself. | |
| From: Thomas Nagel (The View from Nowhere [1986], VIII.2) | |
| A reaction: I would have thought that a very objective assessment of someone's health is an obvious revelation of value, irrespective of anyone's particular perspective. |
| 3265 | We don't worry about the time before we were born the way we worry about death [Nagel] |
| Full Idea: We do not regard the period before we were born in the same way that we regard the prospect of death. | |
| From: Thomas Nagel (The View from Nowhere [1986], XI.3) | |
| A reaction: This is a challenge to Epicurus, who said death is no worse than pre-birth. This idea may be true of the situation immediately post-death, but a thousand years from now it is hard to distinguish them. |
| 3263 | If our own life lacks meaning, devotion to others won't give it meaning [Nagel] |
| Full Idea: If no one's life has any meaning in itself, how can it acquire meaning through devotion to the meaningless lives of others? | |
| From: Thomas Nagel (The View from Nowhere [1986], XI.2) | |
| A reaction: This is one of the paradoxes of compassion. The other is that the virtue requires other people to be in need of help, which can't be a desirable situation. |
| 3256 | Pain doesn't have a further property of badness; it gives a reason for its avoidance [Nagel] |
| Full Idea: The objective badness of pain is not some mysterious further property that all pains have, but just the fact that there is reason for anyone capable of viewing the world objectively to want it to stop. | |
| From: Thomas Nagel (The View from Nowhere [1986], VIII.2) | |
| A reaction: Presumably all pains (e.g. of grief and of toothache) have something in common, to qualify as pains. It must be more than being disliked, because we can dislike a food. |
| 3272 | Moral luck can arise in character, preconditions, actual circumstances, and outcome [Nagel] |
| Full Idea: Moral luck involves one's character, the antecedent circumstances of the act, the actual circumstances of the act, and the outcome of the act. | |
| From: Thomas Nagel (Moral Luck [1976], p.28) | |
| A reaction: Meaning, I take it, that there can be luck in any one of those four. A neat slicing up that doesn't quite fit the real world, where things flow. Helpful, though. |
| 6447 | Game theory misses out the motivation arising from the impersonal standpoint [Nagel] |
| Full Idea: I do not favour the route taken by Hobbes's modern descendants, using game theory, since I believe the impersonal standpoint makes an essential contribution to individual motivation which must be addressed by any ethically acceptable theory. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.4) | |
| A reaction: The assumption of self-seeking at the core of game theory seems very bizarre, and leads to moral approval of free riders. Nagel offers the best response, which is the Kantian impersonal view. Nagel may be optimistic about motivation, though. |
| 3261 | Something may be 'rational' either because it is required or because it is acceptable [Nagel] |
| Full Idea: "Rational" may mean rationally required or rationally acceptable | |
| From: Thomas Nagel (The View from Nowhere [1986], X.4) |
| 3258 | If cockroaches can't think about their actions, they have no duties [Nagel] |
| Full Idea: If cockroaches cannot think about what they should do, there is nothing they should do. | |
| From: Thomas Nagel (The View from Nowhere [1986], VIII.3) |
| 6446 | In ethics we abstract from our identity, but not from our humanity [Nagel] |
| Full Idea: In pursuit of the kind of objectivity needed in the physical sciences, we abstract even from our humanity; but nothing further than abstraction from our identity (that is, who we are) enters into ethical theory. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.2) | |
| A reaction: The 'brief' summary of this boils down to a nice and interesting slogan. It epitomises the modern Kantian approach to ethics. But compare Idea 4122, from Bernard Williams. |
| 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) |
| 3294 | As far as possible we should become instruments to realise what is best from an eternal point of view [Nagel] |
| Full Idea: The right thing to do is to turn oneself as far as possible into an instrument for the realisation of what is best 'sub specie aeternitatis'. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.204) |
| 3254 | If we can decide how to live after stepping outside of ourselves, we have the basis of a moral theory [Nagel] |
| Full Idea: If we can make judgements about how we should live even after stepping outside of ourselves, they will provide the material for moral theory. | |
| From: Thomas Nagel (The View from Nowhere [1986], VIII.1) |
| 3264 | We should see others' viewpoints, but not lose touch with our own values [Nagel] |
| Full Idea: One should occupy a position far enough outside your own life to reduce the importance of the difference between yourself and other people, yet not so far outside that all human values vanish in a nihilistic blackout (i.e.aim for a form of humility). | |
| From: Thomas Nagel (The View from Nowhere [1986], XI.2) |
| 6477 | I can only universalise a maxim if everyone else could also universalise it [Nagel] |
| Full Idea: It is implicit in the categorical imperative that I can will that everyone should adopt as a maxim only what everyone else can also will that everyone should adopt as a maxim. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.5) | |
| A reaction: This is a nice move, because it shifts the theory away from a highly individualistic Cartesian view of morality towards the idea that morality is a community activity. |
| 3255 | We find new motives by discovering reasons for action different from our preexisting motives [Nagel] |
| Full Idea: There are reasons for action, and we must discover them instead of deriving them from our preexisting motives - and in that way we can acquire new motives superior to the old. | |
| From: Thomas Nagel (The View from Nowhere [1986], VIII.1) |
| 3262 | Utilitarianism is too demanding [Nagel] |
| Full Idea: Utilitarianism is too demanding. | |
| From: Thomas Nagel (The View from Nowhere [1986], X.5) |
| 3268 | If a small brief life is absurd, then so is a long and large one [Nagel] |
| Full Idea: If life is absurd because it only lasts seventy years, wouldn't it be infinitely absurd if it lasted for eternity? And if we are absurd because we are small, would we be any less absurd if we filled the universe? | |
| From: Thomas Nagel (The Absurd [1971], §1) |
| 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) |
| 6448 | A legitimate system is one accepted as both impartial and reasonably partial [Nagel] |
| Full Idea: A legitimate system is one which reconciles the two universal principles of impartiality and reasonable partiality so that no one can object that his interests are not being accorded sufficient weight or that the demands on him are excessive. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.4) | |
| A reaction: This seems an appealing principle, and a nice attempt at stating the core of Kantian liberalism. It is obviously influenced by Scanlon's contractualist view, in the idea that 'no one can object', because everyone sees the justification. |
| 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. |
| 6478 | Democracy is opposed to equality, if the poor are not a majority [Nagel] |
| Full Idea: As things are, democracy is the enemy of comprehensive equality, once the poor cease to be a majority. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.9) | |
| A reaction: This is obvious once you think about it, but it is well worth saying, because it is tempting to think that we live in an 'equal' society, merely because we are equal in things such as voting rights and equality before the law. |
| 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) |
| 3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |
| Full Idea: Given what heat is and what water is, it is literally impossible for water to be heated beyond a certain point at normal atmospheric pressure without boiling. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |