46 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. |
| 21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
| Full Idea: Metaphysics is the most general attempt to make sense of things. | |
| From: A.W. Moore (The Evolution of Modern Metaphysics [2012], Intro) | |
| A reaction: This is the first sentence of Moore's book, and a touchstone idea all the way through. It stands up well, because it says enough without committing to too much. I have to agree with it. It implies explanation as the key. I like generality too. |
| 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'. |
| 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. |
| 10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
| Full Idea: In 1938 Gödel proved that the Axiom of Choice is consistent with the other axioms of set theory. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: Hence people now standardly accept ZFC, rather than just ZF. |
| 10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
| Full Idea: Zermelo's Axiom of Choice asserts that for any set of non-empty sets that (pairwise) have no elements in common, then there is a set that 'simultaneously chooses' exactly one element from each set. Note that this is an existential claim. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: The Axiom is now widely accepted, after much debate in the early years. Even critics of the Axiom turn out to be relying on it. |
| 10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
| Full Idea: The Axiom of Choice seems clearly true from the Platonistic point of view, independently of how sets may be defined, but is rejected by those who think such existential claims must show how to pick out or define the object claimed to exist. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: The typical critics are likely to be intuitionists or formalists, who seek for both rigour and a plausible epistemology in our theory. |
| 10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
| Full Idea: The Trichotomy Principle (any number is less, equal to, or greater than, another number) turned out to be equivalent to the Axiom of Choice. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: [He credits Sierpinski (1918) with this discovery] |
| 10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
| Full Idea: The Axiom of Choice is a pure existence statement, without defining conditions. It was necessary to provide a foundation for Cantor's theory of transfinite cardinals and ordinal numbers, but its nonconstructive character engendered heated controversy. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) |
| 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). |
| 10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
| Full Idea: A structure is said to be a 'model' of an axiom system if each of its axioms is true in the structure (e.g. Euclidean or non-Euclidean geometry). 'Model theory' concerns which structures are models of a given language and axiom system. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
| A reaction: This strikes me as the most interesting aspect of mathematical logic, since it concerns the ways in which syntactic proof-systems actually connect with reality. Tarski is the central theoretician here, and his theory of truth is the key. |
| 10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
| Full Idea: In the late 1950s Tarski and Vaught defined and established basic properties of the relation of elementary equivalence between two structures, which holds when they make true exactly the same first-order sentences. This is fundamental to model theory. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
| A reaction: This is isomorphism, which clarifies what a model is by giving identity conditions between two models. Note that it is 'first-order', and presumably founded on classical logic. |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
| Full Idea: The Löwenheim-Skolem Theorem, the earliest in model theory, states that if a countable set of sentences in a first-order language has a model, then it has a countable model. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
| A reaction: There are 'upward' (sentences-to-model) and 'downward' (model-to-sentences) versions of the theory. |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
| Full Idea: Before Tarski's work in the 1930s, the main results in model theory were the Löwenheim-Skolem Theorem, and Gödel's establishment in 1929 of the completeness of the axioms and rules for the classical first-order predicate (or quantificational) calculus. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) |
| 10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
| Full Idea: Completeness is when, if a sentences holds in every model of a theory, then it is logically derivable from that theory. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) |
| 10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
| Full Idea: 'Recursion theory' is the subject of what can and cannot be solved by computing machines | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Ch.9) | |
| A reaction: This because 'recursion' will grind out a result step-by-step, as long as the steps will 'halt' eventually. |
| 10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
| Full Idea: In 1936 Church showed that Principia Mathematica is undecidable if it is ω-consistent, and a year later Rosser showed that Peano Arithmetic is undecidable, and any consistent extension of it. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int IV) |
| 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) |
| 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?). |
| 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. |
| 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. |
| 21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
| Full Idea: Appearances in general are nothing outside our representations, which is just what we mean by transcendental ideality. | |
| From: A.W. Moore (The Evolution of Modern Metaphysics [2012], B535/A507) |
| 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. |
| 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. |
| 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. |
| 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? |
| 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. |