80 ideas
| 19579 | The history of philosophy is just experiments in how to do philosophy [Novalis] |
| Full Idea: The history of philosophy up to now is nothing but a history of attempts to discover how to do philosophy. | |
| From: Novalis (Logological Fragments I [1798], 01) | |
| A reaction: I take post-Fregean analytic metaphysics to be another experiment in how to do philosophy. I suspect that the experiment of Husserl, Heidegger, Derrida etc has been a failure. |
| 19583 | Philosophy only begins when it studies itself [Novalis] |
| Full Idea: All philosophy begins where philosophizing philosophises itself. | |
| From: Novalis (Logological Fragments I [1798], 79) | |
| A reaction: The modern trend for doing metaphilosophy strikes me as wholly admirable, though I suspect that the enemies of philosophy (who are legion) see it as a decadence. |
| 22026 | Philosophy is homesickness - the urge to be at home everywhere [Novalis] |
| Full Idea: Philosophy is actually homesickness - the urge to be everywhere at home. | |
| From: Novalis (General Draft [1799], 45) | |
| A reaction: The idea of home [heimat] is powerful in German culture. The point of romanticism was seen as largely concerning restless souls like Byron and his heroes, who do not feel at home. Hence ironic detachment. |
| 19588 | The highest aim of philosophy is to combine all philosophies into a unity [Novalis] |
| Full Idea: He attains the maximum of a philosopher who combines all philosophies into a single philosophy | |
| From: Novalis (Logological Fragments II [1798], 31) | |
| A reaction: I have found the epigraph for my big book! Recently a few narrowly analytical philosophers have attempted big books about everything (Sider, Heil, Chalmers), and they get a huge round of applause from me. |
| 19598 | Philosophy relies on our whole system of learning, and can thus never be complete [Novalis] |
| Full Idea: Now all learning is connected - thus philosophy will never be complete. Only in the complete system of all learning will philosophy be truly visible. | |
| From: Novalis (Logological Fragments II [1798], 39) | |
| A reaction: Philosophy is evidently the unifying subject, which reveals the point of all the other subjects. It matches my maxim that 'science is the servant of philosophy'. |
| 19586 | Philosophers feed on problems, hoping they are digestible, and spiced with paradox [Novalis] |
| Full Idea: The philosopher lives on problems as the human being does on food. An insoluble problem is an indigestible food. What spice is to food, the paradoxical is to problems. | |
| From: Novalis (Logological Fragments II [1798], 09) | |
| A reaction: Novalis would presumably have disliked Hegel's dialectic, where the best food seems to be the indigestible. |
| 19587 | Philosophy aims to produce a priori an absolute and artistic world system [Novalis] |
| Full Idea: Philosophy ...is the art of producing all our conceptions according to an absolute, artistic idea and of developing the thought of a world system a priori out of the depths of our spirit. | |
| From: Novalis (Logological Fragments II [1798], 19) | |
| A reaction: A lovely statement of the dream of building world systems by pure thought - embodying perfectly the view of philosophy despised by logical positivists and modern logical metaphysicians. The Novalis view will never die! I like 'artistic'. |
| 23728 | Analysis aims to express the full set of platitudes surrounding a given concept [Smith,M] |
| Full Idea: The aim of analysis is to give us knowledge of all and only the platitudes surrounding our use of the concept that is up for analysis. | |
| From: Michael Smith (The Moral Problem [1994], 1.10) | |
| A reaction: His earlier specimen concept is 'redness'. For other concepts there might be considerable disagreement about which propositions are or are not the relevant platitudes. Smith emphasises that analysis need not be reductive. |
| 23744 | Defining a set of things by paradigms doesn't pin them down enough [Smith,M] |
| Full Idea: The discussion of colour concepts shows that permutation problems arise when a set of concepts, acquired inter alia via the presentation of paradigms, is largely interdefined. | |
| From: Michael Smith (The Moral Problem [1994], 5.9) | |
| A reaction: Smith says that our normative moral concepts are largely interdefined in this way. The 'permutation' problem is that they can change places in the definition set, and so their intrinsic individual character is not pinned down. Sounds right. |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| Full Idea: Dedkind gave a rigorous proof of the principle of definition by recursion, permitting recursive definitions of addition and multiplication, and hence proofs of the familiar arithmetical laws. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 13 'Deriv' |
| 19574 | If man sacrifices truth he sacrifices himself, by acting against his own convictions [Novalis] |
| Full Idea: Man has his being in truth - if he sacrifices truth he sacrifices himself. Whoever betrays truth betrays himself. It is not a question of lying - but of acting against one's conviction. | |
| From: Novalis (Miscellaneous Observations [1798], 038) | |
| A reaction: Does he condone lying here, as long as you don't believe the lie? We would call it loss of integrity. |
| 19571 | Delusion and truth differ in their life functions [Novalis] |
| Full Idea: The distinction between delusion and truth lies in the difference in their life functions. | |
| From: Novalis (Miscellaneous Observations [1798], 008) | |
| A reaction: Pure pragmatism, it seems. We might expect doubts about objective truth from a leading light of the Romantic movement. |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| Full Idea: A set is 'Dedekind-infinite' iff there exists a one-to-one function that maps a set into a proper subset of itself. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §64) by E Reck / M Price - Structures and Structuralism in Phil of Maths n 7 | |
| A reaction: Sounds as if it is only infinite if it is contradictory, or doesn't know how big it is! |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| Full Idea: Dedekind had an interesting proof of the Axiom of Infinity. He held that I have an a priori grasp of the idea of my self, and that every idea I can form the idea of that idea. Hence there are infinitely many objects available to me a priori. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], no. 66) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 12 'Numb' | |
| A reaction: Who said that Descartes' Cogito was of no use? Frege endorsed this, as long as the ideas are objective and not subjective. |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| Full Idea: Dedekind plainly had fusions, not collections, in mind when he avoided the empty set and used the same symbol for membership and inclusion - two tell-tale signs of a mereological conception. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], 2-3) by Michael Potter - Set Theory and Its Philosophy 02.1 | |
| A reaction: Potter suggests that mathematicians were torn between mereology and sets, and eventually opted whole-heartedly for sets. Maybe this is only because set theory was axiomatised by Zermelo some years before Lezniewski got to mereology. |
| 19597 | Logic (the theory of relations) should be applied to mathematics [Novalis] |
| Full Idea: Ought not logic, the theory of relations, be applied to mathematics? | |
| From: Novalis (Logological Fragments II [1798], 38) | |
| A reaction: Bolzano was 19 when his was written. I presume Novalis would have been excited by set theory (even though he was a hyper-romantic). |
| 19581 | A problem is a solid mass, which the mind must break up [Novalis] |
| Full Idea: A problem is a solid, synthetic mass which is broken up by means of the penetrating power of the mind. | |
| From: Novalis (Logological Fragments I [1798], 04) |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| Full Idea: Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: Does this fit real numbers and complex numbers, as well as natural numbers? Frege was concerned by the lack of objectivity in this sort of view. What sort of arithmetic might the Martians have created? Numbers register sameness too. |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| Full Idea: It was primarily Dedekind's accomplishment to define the integers, rationals and reals, taking only the system of natural numbers for granted. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by A.George / D.J.Velleman - Philosophies of Mathematics Intro |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| Full Idea: Dedekind and Cantor said the cardinals may be defined in terms of the ordinals: The cardinal number of a set S is the least ordinal onto whose predecessors the members of S can be mapped one-one. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 5 |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| Full Idea: Dedekind said that the notion of order, rather than that of quantity, is the central notion in the definition of number. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
| A reaction: Compare Aristotle's nice question in Idea 646. My intuition is that quantity comes first, because I'm not sure HOW you could count, if you didn't think you were changing the quantity each time. Why does counting go in THAT particular order? Cf. Idea 8661. |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| Full Idea: Dedekind's ordinals are not essentially either ordinals or cardinals, but the members of any progression whatever. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §243 | |
| A reaction: This is part of Russell's objection to Dedekind's structuralism. The question is always why these beautiful structures should actually be considered as numbers. I say, unlike Russell, that the connection to counting is crucial. |
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| Full Idea: It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], Intro) | |
| A reaction: [He seeks the origin of the theorem that differential calculus deals with continuous magnitude, and he wants an arithmetical rather than geometrical demonstration; the result is his famous 'cut']. |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| Full Idea: Whenever we have to do a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §4) | |
| A reaction: Fine quotes this to show that the Dedekind Cut creates the irrational numbers, rather than hitting them. A consequence is that the irrational numbers depend on the rational numbers, and so can never be identical with any of them. See Idea 10573. |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| Full Idea: Dedekind set up the axiom that the gap in his 'cut' must always be filled …The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - Introduction to Mathematical Philosophy VII | |
| A reaction: This remark of Russell's is famous, and much quoted in other contexts, but I have seen the modern comment that it is grossly unfair to Dedekind. |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| Full Idea: One view, favoured by Dedekind, is that the cut postulates a real number for each cut in the rationals; it does not identify real numbers with cuts. ....A view favoured by later logicists is simply to identify a real number with a cut. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 | |
| A reaction: Dedekind is the patriarch of structuralism about mathematics, so he has little interest in the existenc of 'objects'. |
| 18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
| Full Idea: Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power. | |
| From: Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
| A reaction: Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects. |
| 19584 | Whoever first counted to two must have seen the possibility of infinite counting [Novalis] |
| Full Idea: Whoever first understood how to count to two, even if he still found it difficult to keep on counting, saw nonetheless the possibility of infinite counting according to the same laws. | |
| From: Novalis (Logological Fragments I [1798], 84) | |
| A reaction: Presumably it is the discerning of the 'law' which triggers this. Is the key concept 'addition' or 'successor' (or are those the same?). |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| Full Idea: If we scrutinize closely what is done in counting an aggregate of things, we see the ability of the mind to relate things to things, to let a thing correspond to a thing, or to represent a thing by a thing, without which no thinking is possible. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: I don't suppose it occurred to Dedekind that he was reasserting Hume's observation about the fundamental psychology of thought. Is the origin of our numerical ability of philosophical interest? |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| Full Idea: I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself is nothing else than the successive creation of the infinite series of positive integers. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §1) | |
| A reaction: Thus counting roots arithmetic in the world, the successor operation is the essence of counting, and the Dedekind-Peano axioms are built around successors, and give the essence of arithmetic. Unfashionable now, but I love it. Intransitive counting? |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| Full Idea: A system S is said to be infinite when it is similar to a proper part of itself. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], V.64) |
| 18087 | If x changes by less and less, it must approach a limit [Dedekind] |
| Full Idea: If in the variation of a magnitude x we can for every positive magnitude δ assign a corresponding position from and after which x changes by less than δ then x approaches a limiting value. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], p.27), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.7 | |
| A reaction: [Kitcher says he 'showed' this, rather than just stating it] |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| Full Idea: Dedekind's natural numbers: an object is in a set (0 is a number), a function sends the set one-one into itself (numbers have unique successors), the object isn't a value of the function (it isn't a successor), plus induction. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William D. Hart - The Evolution of Logic 5 | |
| A reaction: Hart notes that since this refers to sets of individuals, it is a second-order account of numbers, what we now call 'Second-Order Peano Arithmetic'. |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| Full Idea: Dedekind's idea is that the set of natural numbers has zero as a member, and also has as a member the successor of each of its members, and it is the smallest set satisfying this condition. It is the intersection of all sets satisfying the condition. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| Full Idea: It is Dedekind's categoricity result that convinces most of us that he has articulated our implicit conception of the natural numbers, since it entitles us to speak of 'the' domain (in the singular, up to isomorphism) of natural numbers. | |
| From: comment on Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ian Rumfitt - The Boundary Stones of Thought 9.1 | |
| A reaction: The main rival is set theory, but that has an endlessly expanding domain. He points out that Dedekind needs second-order logic to achieve categoricity. Rumfitt says one could also add to the 1st-order version that successor is an ancestral relation. |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| Full Idea: Dedekind proves mathematical induction, while Peano regards it as an axiom, ...and Peano's method has the advantage of simplicity, and a clearer separation between the particular and the general propositions of arithmetic. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §241 |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| Full Idea: Dedekind is the philosopher-mathematician with whom the structuralist conception originates. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §3 n13) by Fraser MacBride - Structuralism Reconsidered | |
| A reaction: Hellman says the idea grew naturally out of modern mathematics, and cites Hilbert's belief that furniture would do as mathematical objects. |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| Full Idea: Dedekindian abstraction says mathematical objects are 'positions' in a model, while Cantorian abstraction says they are the result of abstracting on structurally similar objects. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §6 | |
| A reaction: The key debate among structuralists seems to be whether or not they are committed to 'objects'. Fine rejects the 'austere' version, which says that objects have no properties. Either version of structuralism can have abstraction as its basis. |
| 22025 | Novalis thought self-consciousness cannot disclose 'being', because we are temporal creatures [Novalis, by Pinkard] |
| Full Idea: Novalis came to think that the kind of existence , or 'being', that is disclosed in self-consciousness remains, as it were, forever out of our reach because of the kind of temporal creatures we are. | |
| From: report of Novalis (Logological Fragments I [1798]) by Terry Pinkard - German Philosophy 1760-1860 06 | |
| A reaction: It looks here as if Novalis kicked Heidegger's Dasein into the long grass before it even got started, but maybe they have different notions of 'being', with Novalis seeking timeless being, and Heidegger, influenced by Bergson, accepting temporality. |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| Full Idea: A thing (an object of our thought) is completely determined by all that can be affirmed or thought concerning it. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], I.1) | |
| A reaction: How could you justify this as an observation? Why can't there be unthinkable things (even by God)? Presumably Dedekind is offering a stipulative definition, but we may then be confusing epistemology with ontology. |
| 19575 | Refinement of senses increasingly distinguishes individuals [Novalis] |
| Full Idea: The more our senses are refined, the more capable they become of distinguishing between individuals. The highest sense would be the highest receptivity to particularity in human nature. | |
| From: Novalis (Miscellaneous Observations [1798], 072) | |
| A reaction: I adore this idea!! It goes into the collection of support I am building for individual essences, against the absurd idea of kinds as essences (when they are actually categorisations). It also accompanies particularism in ethics. |
| 22067 | Poetry is true idealism, and the self-consciousness of the universe [Novalis] |
| Full Idea: Poetry is true idealism - contemplation of the world as contemplation of a large mind - self-consciousness of the universe. | |
| From: Novalis (Logological Fragments I [1798], vol 3 p.640), quoted by Ernst Behler - Early German Romanticism | |
| A reaction: It looks like the step from Fichte's idealism to the Absolute is poetry, which embraces the ultimate Spinozan substance through imagination. Or something... |
| 19572 | Experiences tests reason, and reason tests experience [Novalis] |
| Full Idea: Experience is the test of the rational - and vice versa. | |
| From: Novalis (Miscellaneous Observations [1798], 010) | |
| A reaction: A wonderful remark. Surely we can't ignore our need to test claims of pure logic by filling in the variables with concrete instances, to assess validity? And philosophy without examples is doomed to be abstract waffle. Coherence is the combined aim. |
| 19590 | Empiricists are passive thinkers, given their philosophy by the external world and fate [Novalis] |
| Full Idea: An empiricist is one whose way of thinking is an effect of the external world and of fate - the passive thinker - to whom his philosophy is given. | |
| From: Novalis (Teplitz Fragments [1798], 33) | |
| A reaction: Novalis goes on to enthuse about 'magical idealism', so he rejects empiricism. This is an early attack on the Myth of the Given, found in Sellars and McDowell. |
| 19594 | General statements about nature are not valid [Novalis] |
| Full Idea: General statements are not valid in the study of nature. | |
| From: Novalis (Last Fragments [1800], 17) | |
| A reaction: This is his striking obsession with the particularity and fine detail of nature. Alexander von Humbolt was exploring nature in S.America in this year. It sounds wrong about physics, but possibly right about biology. |
| 19591 | Desire for perfection is an illness, if it turns against what is imperfect [Novalis] |
| Full Idea: An absolute drive toward perfection and completeness is an illness, as soon as it shows itself to be destructive and averse toward the imperfect, the incomplete. | |
| From: Novalis (General Draft [1799], 33) | |
| A reaction: Deep and true! Novalis seems to be a particularist - hanging on to the fine detail of life, rather than being immersed in the theory. These are the philosophers who also turn to literature. |
| 19596 | The whole body is involved in the formation of thoughts [Novalis] |
| Full Idea: In the formation of thoughts all parts of the body seem to me to be working together. | |
| From: Novalis (Last Fragments [1800], 20) | |
| A reaction: I can only think that Spinoza must be behind this thought, or La Mettrie. It seems a strikingly unusual intuition for its time, when almost everyone takes a spiritual sort of dualism for granted. |
| 19573 | The seat of the soul is where our inner and outer worlds interpenetrate [Novalis] |
| Full Idea: The seat of the soul is the point where the inner and the outer worlds touch. Wherever they penetrate each other - it is there at every point of penetration. | |
| From: Novalis (Miscellaneous Observations [1798], 020) | |
| A reaction: I surmise that Spinoza's dual-aspect monism is behind this interesting remark. See the related idea from Schopenhauer. |
| 23743 | Capturing all the common sense facts about rationality is almost impossible [Smith,M] |
| Full Idea: It would be a superhuman task just to write down an explicit, non-summary style, statement of the platitudes that capture our idea of what it is to be fully rational. | |
| From: Michael Smith (The Moral Problem [1994], 5.9) | |
| A reaction: Well said. Philosophers are inclined to make simplistic binary judgements about whether persons or animals are rational. A visit to YouTube will show fish acting extremely rationally. |
| 19577 | Everything is a chaotic unity, then we abstract, then we reunify the world into a free alliance [Novalis] |
| Full Idea: Before abstraction everything is one - but one as chaos is - after abstraction everything is again unified - but in a free alliance of independent, self-determined beings. A crowd has become a society - a chaos is transformed into a manifold world. | |
| From: Novalis (Miscellaneous Observations [1798], 094) | |
| A reaction: Personally I take (unfashionably) psychological abstraction to one of the key foundations of human thought, so I love this idea, which gives a huge picture of how the abstracting mind relates to reality. |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| Full Idea: By applying the operation of abstraction to a system of objects isomorphic to the natural numbers, Dedekind believed that we obtained the abstract system of natural numbers, each member having only properties consequent upon its position. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Dummett - The Philosophy of Mathematics | |
| A reaction: Dummett is scornful of the abstractionism. He cites Benacerraf as a modern non-abstractionist follower of Dedekind's view. There seems to be a suspicion of circularity in it. How many objects will you abstract from to get seven? |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| Full Idea: If in an infinite system, set in order, we neglect the special character of the elements, simply retaining their distinguishability and their order-relations to one another, then the elements are the natural numbers, created by the human mind. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], VI.73) | |
| A reaction: [compressed] This is the classic abstractionist view of the origin of number, but with the added feature that the order is first imposed, so that ordinals remain after the abstraction. This, of course, sounds a bit circular, as well as subjective. |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| Full Idea: Dedekind's conception is psychologistic only if that is the only way to understand the abstraction that is involved, which it is not. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William W. Tait - Frege versus Cantor and Dedekind IV | |
| A reaction: This is a very important suggestion, implying that we can retain some notion of abstractionism, while jettisoning the hated subjective character of private psychologism, which seems to undermine truth and logic. |
| 19585 | Every person has his own language [Novalis] |
| Full Idea: Every person has his own language. Language is the expression of the spirit. | |
| From: Novalis (Logological Fragments I [1798], 91) | |
| A reaction: Nice to see someone enthusiastically affirming what was later famously denied, and maybe even disproved. |
| 23724 | A pure desire could be criticised if it were based on a false belief [Smith,M] |
| Full Idea: There is a minor proviso to Hume's view, which is that desires are subject to rational criticism, but only insofar as they are based on beliefs that are subject to rational criticism. | |
| From: Michael Smith (The Moral Problem [1994], 1.3) | |
| A reaction: He says this is not a refutation of the basic Humean claim. He has in mind a desire such as to consume cyanide because you believe it will be good for you. |
| 23736 | A person can have a desire without feeling it [Smith,M] |
| Full Idea: We should concede that a desire may be had in the absence of its being felt. | |
| From: Michael Smith (The Moral Problem [1994], 4.5) | |
| A reaction: A nice observation. An example he gives is a father's desire that his child does well. Smith is discussing Hume's account of motivation in terms of desires and beliefs. |
| 23723 | In the Humean account, desires are not true/false, or subject to any rational criticism [Smith,M] |
| Full Idea: According to the standard picture of human psychology that we get from Hume, not only are desires not assessable in terms of truth and falsehood, they are not subject to any sort of rational criticism at all. | |
| From: Michael Smith (The Moral Problem [1994], 1.3) | |
| A reaction: This is where action theory meets metaethics. The separation of facts from values underlies this, because a desire is a fact, but the wickedness of a desire is not. Surely a desire could be a failure of practical reason? |
| 23735 | Subjects may be fallible about the desires which explain their actions [Smith,M] |
| Full Idea: It is an adequacy constraint on any conception of desire that the epistemology of desire it recommends allows that subjects may be fallible about the desires they have. | |
| From: Michael Smith (The Moral Problem [1994], 4.5) | |
| A reaction: [I do wish authors would write my short versions instead of their rambling sentences!] Even after the event we may be unsure why we did something. If someone observes self-interest when I thought my action was altruistic, I don't know how to respond. |
| 23738 | Humeans (unlike their opponents) say that desires and judgements can separate [Smith,M] |
| Full Idea: Humeans claim that agents who believe they should act may nevertheless lack the desire to do so, where anti-Humeans must say the two go together, and someone with the belief thereby has the desire. | |
| From: Michael Smith (The Moral Problem [1994], 4.7) | |
| A reaction: [very compressed] A very helpful distinction about the classic debates over the motivations of action. Smith defends the Humean view, and makes it very plausible. No mere sense of rightness or duty can compel us to act. |
| 23742 | If first- and second-order desires conflict, harmony does not require the second-order to win [Smith,M] |
| Full Idea: Even if we assume that reason prefers harmony between first- and second-order desires, there is no reason to assume that reason is on the side of achieving that harmony by changing first-order desires to suit second-order, rather than vice versa. | |
| From: Michael Smith (The Moral Problem [1994], 5.7) | |
| A reaction: [Smith is discussing David Lewis 1989 on second-order desires] Smith says that on the Humean view the rational winner should simply be the stronger of the two. Since this sounds like an endorsement for weakness of will, Smith relies on beliefs. |
| 23746 | Objective reasons to act might be the systematic desires of a fully rational person [Smith,M] |
| Full Idea: One way to decide what we have normative reasons to do …is by trying to find a set of desires that is systematically justifiable, which is our best assessment of the desires we would have under conditions of full rationality. | |
| From: Michael Smith (The Moral Problem [1994], 5.9) | |
| A reaction: This is Smith accepting the Humean view that desires are essential for motivation, but trying to find a marriage of desires with reason to produce the more objective aspects of morality. An interesting aspiration… |
| 23739 | Goals need desires, and so only desires can motivate us [Smith,M] |
| Full Idea: Only an agent's desires may constitute her having certain goals, and it follows from this that only her desires may constitute her motivating reasons. | |
| From: Michael Smith (The Moral Problem [1994], 4.8) | |
| A reaction: We might distinguish between reasons which direct us towards certain ends, and reasons which motivate us to pursue those ends. Most mornings I have a reason to get out of bed, which precedes my motivation to actually do it. |
| 23733 | Motivating reasons are psychological, while normative reasons are external [Smith,M] |
| Full Idea: There are motivating reasons for action, which are psychological states, and normative reasons, which are propositions of the general form 'a person's doing this is desirable or required'. | |
| From: Michael Smith (The Moral Problem [1994], 4.2) | |
| A reaction: Motivating reasons are locatable entities in minds, whereas normative reasons are either abstract, or perhaps motivating reasons expressed by other people. Smith says the two types are unconnected. |
| 23740 | Humeans take maximising desire satisfaction as the normative reasons for actions [Smith,M] |
| Full Idea: The distinctive Humean view of normative reasons for action is that the rational thing for an agent to do is simply to act so as to maximally satisfy her desires, whatever the content of those desires. | |
| From: Michael Smith (The Moral Problem [1994], 5.1) | |
| A reaction: Smith disagrees with this view (though he agrees with Hume about motivating reasons). An obvious problem for the Humean view would be a strong desire to do something excessively dangerous. |
| 23745 | We cannot expect even fully rational people to converge on having the same desires for action [Smith,M] |
| Full Idea: We cannot expect that, even under conditions of full rationality, agents would all converge on the same desires about what is to be done in the various circumstances they might face. | |
| From: Michael Smith (The Moral Problem [1994], 5.9) | |
| A reaction: A very good argument in favour of the Humean view that desires are an essential part of moral motivation. Possible convergence of view is a standard hallmark of communal rationality. |
| 19578 | Only self-illuminated perfect individuals are beautiful [Novalis] |
| Full Idea: Everything beautiful is a self-illuminated, perfect individual. | |
| From: Novalis (Miscellaneous Observations [1798], 101) | |
| A reaction: It is a commonplace to describe something beautiful as being 'perfect'. Unfinished masterpieces are interesting exceptions. Are only 'individuals' beautiful? Is unity a necessary condition of beauty? Bad art fails to be self-illuminated. |
| 19582 | Morality and philosophy are mutually dependent [Novalis] |
| Full Idea: Without philosophy there is no true morality, and without morality no philosophy. | |
| From: Novalis (Logological Fragments I [1798], 21) | |
| A reaction: Challenging! Maybe unthinking people drift in a sea of vague untethered morality, and people who seem to have a genuine moral strength are always rooted in some sort of philosophy. Maybe. Is the passion for philosophy a moral passion? |
| 23731 | 'Externalists' say moral judgements are not reasons, and maybe not even motives [Smith,M] |
| Full Idea: The 'externalist' view of morality says either that judgements of rightness are motives but not reasons, or (more strongly) that they are neither, meaning that moral judgements do not have practical implications. | |
| From: Michael Smith (The Moral Problem [1994], 3.1) | |
| A reaction: [Philippa Foot's untypical 1972 article is cited for the strong view. Hare and Blackburn are typical of the first view]. I would say that such judgements are both reasons and motives - but not necessarily for me! 'Someone should do something about this!'. |
| 23732 | A person could make a moral judgement without being in any way motivated by it [Smith,M] |
| Full Idea: Amoralists make moral judgements without being motivated accordingly, and without suffering any sort of practical irrationality either; the practicality requirement of moral judgement is thus false. | |
| From: Michael Smith (The Moral Problem [1994], 3.3) | |
| A reaction: It is hard to imagine an immoralist with this nihilistic attitude bothering to make any moral judgements at all. Why would someone indifferent to art make aesthetic judgements? What could a 'judgement of rightness' mean to an amoralist? |
| 23729 | Moral internalism says a judgement of rightness is thereby motivating [Smith,M] |
| Full Idea: Moral 'internalism' says if an agent judges an action as right in some circumstance, then they are either thereby motivated to do it, or they are irrational (e.g. their will is weak). | |
| From: Michael Smith (The Moral Problem [1994], 3.1) | |
| A reaction: [Somewhat reworded] So the motivation comes from an internal judgement, not from external factors. Is it not tautological that 'this is the right thing to do' means it should be done (ceteris paribus)? |
| 23730 | 'Rationalism' says the rightness of an action is a reason to perform it [Smith,M] |
| Full Idea: Moral 'rationalism' says if an action is right for agents in some circumstances, then there is a reason for the agents to do it. | |
| From: Michael Smith (The Moral Problem [1994], 3.1) | |
| A reaction: That is, there is not merely a motivation to act (the 'internalist' view), but there is a reason to act. Smith calls both views the 'practicality requirement' of normal moral judgements. Smith defends the rationalist view. |
| 23727 | Expressivists count attitudes as 'moral' if they concern features of things, rather than their mere existence [Smith,M] |
| Full Idea: The pro- and con- attitudes of the expressivists count as 'moral' only if they are had towards particular people, actions or states of affairs in virtue of their natural features, ….rather than in virtue of being the particulars that they are. | |
| From: Michael Smith (The Moral Problem [1994], 2.4) | |
| A reaction: So whereas emotivists don't have to have any reasons for their moral feelings, other expressivists seem to require reasons (i.e. indicating features of things) to endorse their attitudes. What of reasonless emotionless attitudes? |
| 23741 | Is valuing something a matter of believing or a matter of desiring? [Smith,M] |
| Full Idea: What is it to value something? That is, equivalently, what is it to accept that we have a normative reason to do something? In Hume's terms, is it a matter of believing? Or is it a matter of desiring? We seem to face a dilemma. | |
| From: Michael Smith (The Moral Problem [1994], 5.4) | |
| A reaction: Smith is discussing moral motivation, and there is obviously more to valuing something than acting on it. Nice question, though. Personally I value St Paul's Cathedral, but I don't desire it. I value heart surgeons, but don't want to emulate them. |
| 22027 | Life isn't given to us like a novel - we write the novel [Novalis] |
| Full Idea: Life must not be a novel that is given to us, but one that is made by us. | |
| From: Novalis (Logological Fragments I [1798], 99) | |
| A reaction: The roots of existentialism are in the Romantic movement. Sartre seems to have taken this idea literally. |
| 19589 | The whole point of a monarch is that we accept them as a higher-born, ideal person [Novalis] |
| Full Idea: The distinguishing character of the monarchy lies precisely in the fact of belief in a higher-born person, of voluntary acceptance of an ideal person. I cannot choose a leader from among my peers. | |
| From: Novalis (Fath and Love, or the King and Queen [1798], 18) | |
| A reaction: Novalis was passionately devoted to the new king and queen of Prussia, only a few years after the French Revolution. This attitude seems to me unchanged among monarchists in present day Britain. Genetics has undermined 'higher-born'. |
| 19580 | If the pupil really yearns for the truth, they only need a hint [Novalis] |
| Full Idea: If a pupil genuinely desires truth is requires only a hint to show him how to find what he is seeking. | |
| From: Novalis (Logological Fragments I [1798], 02) | |
| A reaction: The tricky job for the teacher or supervisor is assessing whether the pupil genuinely desires truth, or needs motivating. |
| 19593 | Persons are shaped by a life history; splendid persons are shaped by world history [Novalis] |
| Full Idea: What is it that shapes a person if not his life history? And in the same way a splendid person is shaped by nothing other than world history. Many people live better in the past and in the future than in the present. | |
| From: Novalis (Last Fragments [1800], 15) | |
| A reaction: Clearly there is a lot to be said for splendid people who live entirely in the present (such as jazz musicians). Some people do have an awesomely wide historical perspective on their immediate lives. Palaeontology is not the master discipline though! |
| 19595 | Nature is a whole, and its individual parts cannot be wholly understood [Novalis] |
| Full Idea: Nature is a whole - in which each part in itself can never be wholly understood. | |
| From: Novalis (Last Fragments [1800], 18) | |
| A reaction: This doesn't seem right when studying some item in a laboratory, but it seems undeniable when you consider the history and future of each item. |
| 19592 | The basic relations of nature are musical [Novalis] |
| Full Idea: Musical relations seem to me to be actually the basic relations of nature. | |
| From: Novalis (Last Fragments [1800], 10) | |
| A reaction: Novalis shows no signs of being a pythagorean, and then suddenly comes out with this. I suppose if you love music, this thought should float into your mind at regular intervals, because the power of music is so strong. Does he mean ratios? |
| 19576 | Religion needs an intermediary, because none of us can connect directly to a godhead [Novalis] |
| Full Idea: Nothing is more indispensable for true religious feeling than an intermediary - which connects us to the godhead. The human being is absolutely incapable of sustaining an immediate relation with this. | |
| From: Novalis (Miscellaneous Observations [1798], 073) | |
| A reaction: I take this to be a defence of priests and organised religion, and an implied attack on protestants who give centrality to private prayer and conscience. |