92 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'. |
18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
Full Idea: There is surely no metaphysical basis for logic, but equally there is no logical basis for metaphysics, if that implies that we can settle the choice of logic in advance of settling any seriously contested metaphysical-cum-semantic issues. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.5) | |
A reaction: Is this aimed at Tim Williamson's book on treating modal logic as metaphysics? I agree with the general idea that logic won't deliver a metaphysics. I might want to defend a good metaphysics giving rise to a good logic. |
18819 | The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt] |
Full Idea: The realist principle that a statement may be true even though no one is able to recognise its truth is so deeply embedded in our ordinary conception of truth that any account that flouts it is liable to engender confusion. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 5.1) |
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. |
18826 | 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt] |
Full Idea: A statement is 'true at a possibility' if, necessarily, things would have been as the statement (actually) says they are, had the possibility obtained. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 6.6) | |
A reaction: This is deliberately vague about what a 'possibility' is, but it is intended to be more than a property instantiation, and less than a possible world. |
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. |
18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt] |
Full Idea: The classical semantics of natural language propositions says 1) valid arguments preserve truth, 2) no statement is both true and false, 3) each statement is either true or false, 4) the familiar truth tables. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) |
12204 | The logic of metaphysical necessity is S5 [Rumfitt] |
Full Idea: It is a widely accepted thesis that the logic of metaphysical necessity is S5. | |
From: Ian Rumfitt (Logical Necessity [2010], §5) | |
A reaction: Rumfitt goes on to defend this standard view (against Dummett's defence of S4). The point, I take it, is that one can only assert that something is 'true in all possible worlds' only when the worlds are all accessible to one another. |
18814 | 'Absolute necessity' would have to rest on S5 [Rumfitt] |
Full Idea: If there is such a notion as 'absolute necessity', its logic is surely S5. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 3.3) | |
A reaction: There are plenty of people (mainly in the strict empiricist tradition) who don't believe in 'absolute' necessity. |
18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
Full Idea: Although intuitionistic propositional and first-order logics are sub-systems of the corresponding classical systems, intuitionistic second-order logic affirms the negations of some classical theorems. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) |
18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |
Full Idea: Double Negation Elimination is a rule of inference which the classicist accepts without restriction, but which the intuitionist accepts only for decidable propositions. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) | |
A reaction: This cures me of my simplistic understanding that intuitionists just reject the rules about double negation. |
18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt] |
Full Idea: Many set theorists doubt if the Generalised Continuum Hypothesis must be either true or false; certainly, its bivalence is far from obvious. All the same, almost all set theorists use classical logic in their proofs. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.2) | |
A reaction: His point is that classical logic is usually taken to rest on bivalence. He offers the set theorists a helping hand, by defending classical logic without resorting to bivalence. |
18843 | The iterated conception of set requires continual increase in axiom strength [Rumfitt] |
Full Idea: We are doomed to postulate an infinite sequence of successively stronger axiom systems as we try to spell out what is involved in iterating the power set operation 'as far as possible'. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 9.3) | |
A reaction: [W.W. Tait is behind this idea] The problem with set theory, then, especially as a foundation of mathematics, is that it doesn't just expand, but has to keep reinventing itself. The 'large cardinal axioms' are what is referred to. |
18836 | A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt] |
Full Idea: There seem strong grounds for rejecting the thesis that a set consists of its members. For one thing, the empty set is a perpetual embarrassment for the thesis. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 8.4) | |
A reaction: Rumfitt also says that if 'red' has an extension, then membership of that set must be vague. Extensional sets are precise because their objects are decided in advance, but intensional (or logical) sets, decided by a predicate, can be vague. |
18837 | A set can be determinate, because of its concept, and still have vague membership [Rumfitt] |
Full Idea: Vagueness in respect of membership is consistent with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of the concept A. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 8.4) | |
A reaction: To be determinate, it must be presumed that there is some test which will decide what falls under the concept. The rule can say 'if it is vague, reject it' or 'if it is vague, accept it'. Without one of those, how could the set have a clear identity? |
18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt] |
Full Idea: Someone who is sympathetic to the thesis that the totality of sets is not well-defined ought to concede that we have no reason to think that the Power Set Axiom is true. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 9.6) | |
A reaction: The point is that it is only this Axiom which generates the vast and expanding totality. In principle it is hard, though, to see what is intrinsically wrong with the operation of taking the power set of a set. Hence 'limitation of size'? |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
Full Idea: On the conception of logic recommended here, logical laws are higher-order laws that can be applied to expand the range of any deductive principles. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 3.3) | |
A reaction: You need the concept of a 'deductive principle' to get this going, but I take it that might be directly known, rather than derived from a law. |
9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
Full Idea: Logic is part of a normative theory of thinking, not a substitute for thinking. | |
From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.13) | |
A reaction: There is some sort of logicians' dream, going back to Leibniz, of a reasoning engine, which accepts propositions and outputs inferences. I agree with this idea. People who excel at logic are often, it seems to me, modest at philosophy. |
18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt] |
Full Idea: There is not the slightest prospect of proving that the rules of classical logic are sound. ….All that the defender of classical logic can do is scrutinize particular attacks and try to repel them. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) | |
A reaction: This is the agenda for Rumfitt's book. |
18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt] |
Full Idea: I think it is a strategic mistake to rest the case for classical logic on the Principle of Bivalence: the soundness of the classical logic rules is far more compelling than the truth of Bivalence. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) | |
A reaction: The 'rules' to which he is referring are those of 'natural deduction', which make very few assumptions, and are intended to be intuitively appealing. |
18827 | If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt] |
Full Idea: If we specify the senses of the connectives by way of the standard truth-tables, then we must justify classical logic only by appeal to the Principle of Bivalence. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7) | |
A reaction: Rumfitt proposes to avoid the truth-tables, and hence not to rely on Bivalence for his support of classical logic. He accepts that Bivalence is doubtful, citing the undecidability of the Continuum Hypothesis as a problem instance. |
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). |
12195 | Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt] |
Full Idea: Our ordinary standards for deeming arguments to be sound vary greatly from context to context. Even the package tourist's syllogism ('It's Tuesday, so this is Belgium') may meet the operative standards for soundness. | |
From: Ian Rumfitt (Logical Necessity [2010], Intro) | |
A reaction: No doubt one could spell out the preconceptions of package tourist reasoning, and arrive at the logical form of the implication which is being offered. |
12199 | There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt] |
Full Idea: There is a modal element in consequence, in its applicability to assessing reasoning from suppositions. | |
From: Ian Rumfitt (Logical Necessity [2010], §2) |
12201 | We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt] |
Full Idea: A rule is to be rejected if it enables us to deduce from some premisses a purported conclusion that does not follow from them in the broad sense. The idea that deductions answer to consequence is incomprehensible if consequence consists in deducibility. | |
From: Ian Rumfitt (Logical Necessity [2010], §2) |
18813 | Logical consequence is a relation that can extended into further statements [Rumfitt] |
Full Idea: Logical consequence, I argue, is distinguished from other implication relations by the fact that logical laws may be applied in extending any implication relation so that it applies among some complex statements involving logical connectives. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 3.3) | |
A reaction: He offers implication in electronics as an example of a non-logical implication relation. This seems to indicate that logic must be monotonic, that consequence is transitive, and that the Cut Law always applies. |
18808 | Normal deduction presupposes the Cut Law [Rumfitt] |
Full Idea: Our deductive practices seem to presuppose the Cut Law. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 2.3) | |
A reaction: That is, if you don't believe that deductions can be transitive (and thus form a successful chain of implications), then you don't really believe in deduction. It remains a well known fact that you can live without the Cut Law. |
18840 | When faced with vague statements, Bivalence is not a compelling principle [Rumfitt] |
Full Idea: I do not regard Bivalence, when applied to vague statements, as an intuitively compelling principle which we ought to try to preserve. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 8.7) | |
A reaction: The point of Rumfitt's book is to defend classical logic despite failures of bivalence. He also cites undecidable concepts such as the Continuum Hypothesis. |
12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt] |
Full Idea: Overt contradictions include formal contradictions of form 'B and not B', but I also take them to include 'This is red all over and green all over' and 'This is red and not coloured'. | |
From: Ian Rumfitt (Logical Necessity [2010], Intro) |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
From: Ian Rumfitt ("Yes" and "No" [2000]) | |
A reaction: This is the standard view which Rumfitt sets out to challenge. |
18802 | In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt] |
Full Idea: There is no prospect whatever of giving the sense of a logical constant without using that very constant, and much else besides, in the metalinguistic principle that specifies that sense. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) |
12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt] |
Full Idea: The geometrical style of formalization of logic is now little more than a quaint anachronism, largely because it fails to show logical truths for what they are: simply by-products of rules of inference that are applicable to suppositions. | |
From: Ian Rumfitt (Logical Necessity [2010], §1) | |
A reaction: This is the rejection of Russell-style axiom systems in favour of Gentzen-style natural deduction systems (starting from rules). Rumfitt quotes Dummett in support. |
18800 | Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt] |
Full Idea: 'Introduction rules' state the conditions under which one may deduce a conclusion whose dominant logical operator is the connective. 'Elimination rules' state what may be deduced from some premises, where the major premise is dominated by the connective. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) | |
A reaction: So Introduction gives conditions for deduction, and Elimination says what can actually be deduced. If my magic wand can turn you into a frog (introduction), and so I turn you into a frog, how does that 'eliminate' the wand? |
18809 | Logical truths are just the assumption-free by-products of logical rules [Rumfitt] |
Full Idea: Gentzen's way of formalising logic has accustomed people to the idea that logical truths are simply the by-products of logical rules, that arise when all the assumptions on which a conclusion rests have been discharged. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 2.5) | |
A reaction: This is the key belief of those who favour the natural deduction account of logic. If you really believe in separate logic truths, then you can use them as axioms. |
18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
Full Idea: Monotonicity seems to mark the difference between cases in which a guarantee obtains and those where the premises merely provide inductive support for a conclusion. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 2.3) | |
A reaction: Hence it is plausible to claim that 'non-monotonic logic' is a contradiction in terms. |
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) |
18842 | Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt] |
Full Idea: Menzel proposes that an ordinal is something isomorphic well-ordered sets have in common, so while an ordinal can be represented as a set, it is not itself a set, but a 'property' of well-ordered sets. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 9.2) | |
A reaction: [C.Menzel 1986] This is one of many manoeuvres available if you want to distance mathematics from set theory. |
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?). |
17462 | A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt] |
Full Idea: One requirement for a successful count is that double counting should be avoided: a single object should not be counted twice. ...but that is to make a knowledgeable judgement of distinctness - to resolve a question of identity in the negative. | |
From: Ian Rumfitt (Concepts and Counting [2002], III) | |
A reaction: He also notes later (p.65) that you must count all and only the right things. |
18834 | Infinitesimals do not stand in a determinate order relation to zero [Rumfitt] |
Full Idea: Infinitesimals do not stand in a determinate order relation to zero: we cannot say an infinitesimal is either less than zero, identical to zero, or greater than zero. ….Infinitesimals are so close to zero as to be theoretically indiscriminable from it. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.4) |
18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt] |
Full Idea: One of the motivations behind Cantor's and Dedekind's pioneering explorations in the field was the ambition to give real analysis a new foundation in set theory - and hence a foundation independent of geometry. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 9.6) | |
A reaction: Rumfitt is inclined to think that the project has failed, although a weaker set theory than ZF might do the job (within limits). |
17461 | Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt] |
Full Idea: We hit trouble if we hear answers to some 'How many?' questions as predications about concepts. The correct answer to 'how many gallons of water are in the tank?' may be 'ten', but that doesn''t mean ten things instantiate 'gallon of water in the tank'. | |
From: Ian Rumfitt (Concepts and Counting [2002], I) | |
A reaction: Rumfitt makes the point that a huge number of things instantiate that concept in a ten gallon tank of water. No problem, says Rumfitt, because Frege wouldn't have counted that as a statement of number. |
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. |
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. |
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. |
9389 | Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt] |
Full Idea: Vagueness in respect of membership is consistency with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of a concept. | |
From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.5) | |
A reaction: I find this view of sets much more appealing than the one that identifies a set with its members. The empty set is less of a problem, as well as non-existents. Logicians prefer the extensional view because it is tidy. |
18839 | An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases [Rumfitt] |
Full Idea: A borderline red-orange object satisfies the disjunctive predicate 'red or orange', even though it satisfies neither 'red' or 'orange'. When applied to adjacent bands of colour, the disjunction 'sweeps up' objects which are reddish-orange. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 8.5) | |
A reaction: Rumfitt offers a formal principle in support of this. There may be a problem with 'adjacent'. Different colour systems will place different colours adjacent to red. In other examples the idea of 'adjacent' may make no sense. Rumfitt knows this! |
18838 | The extension of a colour is decided by a concept's place in a network of contraries [Rumfitt] |
Full Idea: On Sainsbury's picture, a colour has an extension that it has by virtue of its place in a network of contrary colour classifications. Something is determined to be 'red' by being a colour incompatible with orange, yellow, green, blue, indigo and violet. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 8.5) | |
A reaction: Along with Idea 18839, this gives quite a nice account of vagueness, by requiring a foil to the vague predicate, and using the disjunction of the predicate and its foil to handle anything caught in between them. |
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. |
14532 | A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A] |
Full Idea: Rumfitt argues that there is a distinctive notion of necessity implicated in the notion of logical consequence. | |
From: report of Ian Rumfitt (Logical Necessity [2010]) by Bob Hale/ Aviv Hoffmann - Introduction to 'Modality' 2 |
18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
Full Idea: The central characteristic mark of metaphysical necessity is that a metaphysical possibility respects the actual identities of things - in a capacious sense of 'thing'. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 3.4) | |
A reaction: He contrast this with logical necessity, and concludes that some truths are metaphysically but not logically necessary, such as 'Hesperus is identical with Phosphorus'. Personally I like the idea of a 'necessity-maker', so that fits. |
12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt] |
Full Idea: By the notion of 'logical necessity' I mean that there is a sense of 'necessary' for which 'It is necessary that A' implies and is implied by 'It is logically contradictory that not A'. ...From this, logical necessity is implicated in logical consequence. | |
From: Ian Rumfitt (Logical Necessity [2010], Intro) | |
A reaction: Rumfitt expresses a commitment to classical logic at this point. We will need to be quite sure what we mean by 'contradiction', which will need a clear notion of 'truth'.... |
12200 | A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt] |
Full Idea: There is no reason to suppose that any statement that is logically necessary (in the present sense) is knowable a priori. ..If a statement is logically necessary, its negation will yield a contradiction, but that does not imply that someone could know it. | |
From: Ian Rumfitt (Logical Necessity [2010], §2) | |
A reaction: This remark is aimed at Dorothy Edgington, who holds the opposite view. Rumfitt largely defends McFetridge's view (q.v.). |
18825 | S5 is the logic of logical necessity [Rumfitt] |
Full Idea: I accept the widely held thesis that S5 is the logic of logical necessity. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 6.4 n16) | |
A reaction: It seems plausible that S5 is also the logic of metaphysical necessity, but that does not make them the same thing. The two types of necessity have two different grounds. |
12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt] |
Full Idea: While Fine suggests defining a narrow notion of logical necessity in terms of metaphysical necessity by 'restriction' (to logical truths that can be defined in non-modal terms), this seems unpromising for broad logical necessity, which is modal. | |
From: Ian Rumfitt (Logical Necessity [2010], §2) | |
A reaction: [compressed] He cites Kit Fine 2002. Rumfitt glosses the non-modal definitions as purely formal. The metaphysics lurks somewhere in the proof. |
18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt] |
Full Idea: Some philosophers describe the colour scarlet as a determination of the determinable red; since the ways the world might be are naturally taken to be properties of the world, it helps to bear this analogy in mind. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 6.4) | |
A reaction: This fits nicely with the disposition accounts of modality which I favour. Hence being 'coloured' is a real property of objects, even in the absence of the name of its specific colour. |
18828 | If two possibilities can't share a determiner, they are incompatible [Rumfitt] |
Full Idea: Two possibilities are incompatible when no possibility determines both. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.1) | |
A reaction: This strikes me as just the right sort of language for building up a decent metaphysical picture of the world, which needs to incorporate possibilities as well as actualities. |
12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt] |
Full Idea: A world is usually taken to be a fully determinate way that things could have been; but then one might seriously wonder whether anyone is capable of 'considering' such a thing at all. | |
From: Ian Rumfitt (Logical Necessity [2010], §4) | |
A reaction: This has always worried me. If I say 'maybe my coat is in the car', I would hate to think that I had to be contemplating some entire possible world (including all the implications of my coat not being on the hat stand). |
18821 | Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt] |
Full Idea: Possibilities are things of the same general character as possible worlds, on one popular conception of the latter. They differ from worlds, though, in that they are not required to be fully determinate or complete. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 6) | |
A reaction: A rather promising approach to such things, even though a possibility is fairly determinate at its core, but very vague at the edges. It is possible that the UK parliament might be located in Birmingham, for example. Is this world 'complete'? |
18831 | Medieval logicians said understanding A also involved understanding not-A [Rumfitt] |
Full Idea: Mediaeval logicians had a principle, 'Eadem est scientia oppositorum': in order to attain a clear conception of what it is for A to be the case, one needs to attain a conception of what it is for A not to be the case. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.2) | |
A reaction: Presumably 'understanding' has to be a fairly comprehensive grasp of the matter, so understanding the negation sounds like a reasonable requirement for the real thing. |
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. |
18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
Full Idea: In English, the word 'evidence' behaves as a mass term: we speak of someone's having little evidence for an assertion, and of one thinker's having more evidence than another for a claim. One the other hand, we also speak of 'pieces' of evidence. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 5.2) | |
A reaction: And having 'more' evidence does not mean having a larger number of pieces of evidence, so it really is like an accumulated mass. |
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. |
18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
Full Idea: It is striking that our understanding of conditionals is not greatly impeded by widespread disagreement about their truth-conditions. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 4.2) | |
A reaction: Compare 'if you dig there you might find gold' with 'if you dig there you will definitely find gold'. The second but not the first invites 'how do you know that?', implying truth. Two different ifs. |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
Full Idea: The truth-grounds of '¬A' are precisely those possibilities that are incompatible with any truth-ground of A. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 7.1) | |
A reaction: This is Rumfitt's proposal for the semantics of 'not', based on the central idea of a possibility, rather than a possible world. The incompatibility tracks back to an absence of shared grounding. |
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. |