80 ideas
| 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) |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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) |
| 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) |
| 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. |
| 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. |
| 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. |
| 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) |
| 21382 | Things get smaller without end [Anaxagoras] |
| Full Idea: Of the small there is no smallest, but always a smaller. | |
| From: Anaxagoras (fragments/reports [c.460 BCE], B03), quoted by Gregory Vlastos - The Physical Theory of Anaxagoras II | |
| A reaction: Anaxagoras seems to be speaking of the physical world (and probably writing prior to the emergence of atomism, which could have been a rebellion against he current idea). |
| 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. |
| 481 | Nothing is created or destroyed; there is only mixing and separation [Anaxagoras] |
| Full Idea: No thing comes into being or passes away, but it is mixed together or separated from existing things. Thus it would be correct if coming into being was called 'mixing', and passing away 'separation-off''. | |
| From: Anaxagoras (fragments/reports [c.460 BCE], B17), quoted by Simplicius - On Aristotle's 'Physics' 163.20 |
| 21822 | Anaxagoras's concept of supreme Mind has a simple First and a multiple One [Anaxagoras, by Plotinus] |
| Full Idea: Anaxagoras, in his assertion of a Mind pure and unmixed, affirms a simplex First and a sundered One, though writing long ago he failed in precision. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plotinus - The Enneads 5.1.09 | |
| A reaction: The crunch question is whether the supreme One or Mind is part of Being, or is above and beyond Being. Plotinus claims that Anaxagoras was on his side (with Plato, against Parmenides). |
| 17995 | Basic is the potentially perceptible, then comes the contrary qualities, and finally the 'elements' [Anaxagoras] |
| Full Idea: We must recognise three 'originative sources': first that which is potentially perceptible body, secondly the contrarities (e.g hot and cold), and thirdly Fire, Water, and the like. Only thirdly, however, for these bodies change into one another. | |
| From: Anaxagoras (fragments/reports [c.460 BCE]), quoted by Aristotle - The History of Animals 529a34 | |
| A reaction: The 'potentially perceptible' seems to be matter. The surprise here is that the contraries are more basic than the elements, rather than being properties of them. Reality is modes of matter, it seems. |
| 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. |
| 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. |
| 20802 | Snow is not white, and doesn't even appear white, because it is made of black water [Anaxagoras, by Cicero] |
| Full Idea: Anaxagoras not only denied that snow was white, but because he knew that the water from which it was composed was black, even denied that it appeared white to himself. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by M. Tullius Cicero - Academica II.100 | |
| A reaction: Not ridiculous. Can you deny that red and yellow balls look orange from a distance? A failure of discrimination on your part. It sounds okay to say 'what I am really perceiving is red and yellow'. [see 'Anaxagoras' poem by D.H.Lawrence!] |
| 13257 | The senses are too feeble to determine the truth [Anaxagoras] |
| Full Idea: Owing to the feebleness of the sense, we are not able to determine the truth. | |
| From: Anaxagoras (fragments/reports [c.460 BCE], B21), quoted by Patricia Curd - Anaxagoras 5.1 | |
| A reaction: Anaxagoras offers a corresponding elevation of the power of mind (Idea 13256), so I now realise that he is, along with Pythagoras and Parmenides, one of the fathers of rationalism in philosophy. They probably overrate reason. |
| 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. |
| 22761 | We reveal unreliability in the senses when we cannot discriminate a slow change of colour [Anaxagoras, by Sext.Empiricus] |
| Full Idea: Our lack of sureness in the senses is shown if we take two colours, back and white, and pour one into the other drop by drop, we are unable to distinguish the gradual alterations although they subsist as actual facts. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Sextus Empiricus - Against the Logicians (two books) I.090 | |
| A reaction: [Sextus calls Anaxagoras 'the greatest of the physicists'] I'm not sure what this proves. People with bad eyesight can distinguish very little, but that doesn't prove scepticism. And there are things too small for anyone to see. |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
| From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
| A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
| 13256 | Nous is unlimited, self-ruling and pure; it is the finest thing, with great discernment and strength [Anaxagoras] |
| Full Idea: Nous is unlimited and self-ruling and has been mixed with no thing, but is alone itself by itself. ...For it is the finest of all things and the purest, and indeed it maintains all discernment about everything and has the greatest strength. | |
| From: Anaxagoras (fragments/reports [c.460 BCE], B12), quoted by Patricia Curd - Anaxagoras 3.3 | |
| A reaction: Anaxagoras seems to have been a pioneer in elevating the status of the mind, which is a prop to the rationalist view, and encourages dualism. More naturalistic accounts are, in my view, much healthier. |
| 13784 | Mind is self-ruling, pure, ordering and ubiquitous [Anaxagoras, by Plato] |
| Full Idea: Anaxagoras says that mind is self-ruling, mixes with nothing else, orders the things that are, and travels through everything. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plato - Cratylus 413c | |
| A reaction: This elevation of the mind in the natural scheme of things by Anaxagoras looks increasingly significant in western culture to me. Without this line of thought, Descartes and Kant are inconceivable. |
| 5118 | Anaxagoras says mind remains pure, and so is not affected by what it changes [Anaxagoras, by Aristotle] |
| Full Idea: Anaxagoras says that intellect (which is a cause of change) is not affected by or mixed in with anything else; for this is the only way in which it can cause change, while being itself changeless, and control things without mixing with them. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Physics 256b24 | |
| A reaction: I suggest that this is the germ of the original concept of freewill - of the mind as somehow outside the causal processes of the world, so that it can initiate change without itself being affected by other causes. Aristotle says he's right; I disagree. |
| 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. |
| 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. |
| 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). |
| 18231 | Anaxagoras said a person would choose to be born to contemplate the ordered heavens [Anaxagoras] |
| Full Idea: When Anaxagoras was asked what it was for which a person would choose to be born rather than not, he said it would be to apprehend the heavens and the order in the whole universe. | |
| From: Anaxagoras (fragments/reports [c.460 BCE], 1216), quoted by Aristotle - Eudemian Ethics 8 'Finality' | |
| A reaction: [Anaxagoras, quoted by Aristotle, quoted by Korsgaard, quoted by me, and then quoted by you, perhaps] |
| 631 | For Anaxagoras the Good Mind has no opposite, and causes all movement, for a higher reason [Anaxagoras, by Aristotle] |
| Full Idea: Anaxagoras says the good is a principle as the source of movement, in the form of Mind. However it does it for the sake of something else, which is a further factor. And he allows no opposite to the good Mind. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Metaphysics 1075b |
| 22727 | Mind creates the world from a mixture of pure substances [Anaxagoras, by ] |
| Full Idea: Anaxagoras assumed that Mind, which is God, is the efficient principle, and the multi-mixture of homoeomeries is the material principle. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by - I.6 | |
| A reaction: The choice of homoeomeries as basic is a good one. They are much better candidates than materials which are made of parts of a quite different kind, where the parts are a better candidate than the whole. |
| 550 | Anaxagoras said that the number of principles was infinite [Anaxagoras, by Aristotle] |
| Full Idea: Anaxagoras said that the number of principles was infinite. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Metaphysics 984a |
| 21383 | The ultimate constituents of reality are the homoeomeries [Anaxagoras, by Vlastos] |
| Full Idea: Anaxagoras contrasts with other thinkers in the formula that his 'elements' were not the air of Anaximenes or the fire of Heraclitus or the roots of Empedocles or the atoms of Leucippus, but the infinite variety of homoiomereia. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Gregory Vlastos - The Physical Theory of Anaxagoras III | |
| A reaction: Not sure about the 'roots' of Empedocles. Anaxagoras is particularly thinking of the basic stuffs that make up the body, such as hair, bone and blood. It is plausible to reduce everything to stuffs that seem to have no further structure. |
| 13208 | Anaxagoreans regard the homoeomeries as elements, which compose earth, air, fire and water [Anaxagoras, by Aristotle] |
| Full Idea: The followers of Anaxagoras regard the 'homoeomeries' as 'simple' and elements, whilst they affirm that Earth, Fire, Water and Air are composite; for each of these is (according to them) a 'common seminary' of all the homoeomeries. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314a28 | |
| A reaction: Compare Idea 13207. Aristotle is amused that the followers of Empedocles and of Anaxagoras have precisely opposite views on this subject. |
| 367 | Anaxagoras says mind produces order and causes everything [Anaxagoras, by Plato] |
| Full Idea: Anaxagoras asserted that it is mind that produces order and is the cause of everything. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plato - Phaedo 097d |
| 21381 | Germs contain microscopic organs, which become visible as they grow [Anaxagoras] |
| Full Idea: In the germ there are hair, nails, arteries, sinews, bones, which are not manifest because of the smallness of their parts, but become distinct little by little as they grow. For how could hair come from not-hair, or flesh from non-flesh. | |
| From: Anaxagoras (fragments/reports [c.460 BCE], B10), quoted by Gregory Vlastos - The Physical Theory of Anaxagoras I | |
| A reaction: Compare Aristotle's apparent view that the physical world has no microscopic structure, and Democritus's view that hair can come from not-hair by the organisation of atoms. Is this the first suggestion that we need to know what is microscopic? |
| 22726 | When things were unified, Mind set them in order [Anaxagoras] |
| Full Idea: All things were together, and Mind came and set them in order. | |
| From: Anaxagoras (fragments/reports [c.460 BCE]) | |
| A reaction: This is presumably the source for the passionate belief of Plato in the importance of order. Existence seems like chaos, with order residing beneath it, but we can wonder whether if we go even deeper it is chaos again. |
| 2629 | Anaxagoras was the first to say that the universe is directed by an intelligence [Anaxagoras, by Cicero] |
| Full Idea: Anaxagoras, pupil of Anaximenes, was the first to maintain that the form and motion of the universe was determined and directed by the power and purpose of an infinite intelligence. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.26 |
| 480 | Past, present and future, and the movements of the heavens, were arranged by Mind [Anaxagoras] |
| Full Idea: Whatever was then in existence which is not now, and all things that now exist, and whatever shall exist - all were arranged by Mind, as also the revolution followed now by the stars, the sun and the moon. | |
| From: Anaxagoras (fragments/reports [c.460 BCE], B12), quoted by Simplicius - On Aristotle's 'Physics' 164.24 |
| 5956 | Anaxagoras was charged with impiety for calling the sun a lump of stone [Anaxagoras, by Plutarch] |
| Full Idea: Anaxagoras was charged with impiety because he called the sun a lump of stone. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plutarch - 14: Superstition §9 | |
| A reaction: The point is that he was supposed to say that the sun is a god. |
| 7488 | Anaxagoras was the first recorded atheist [Anaxagoras, by Watson] |
| Full Idea: Anaxagoras was the first recorded atheist. | |
| From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Peter Watson - Ideas Ch.25 | |
| A reaction: He was a very lively character, right in the middle of the Athenian golden age. |