74 ideas
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| Full Idea: Dedkind gave a rigorous proof of the principle of definition by recursion, permitting recursive definitions of addition and multiplication, and hence proofs of the familiar arithmetical laws. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 13 'Deriv' |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| Full Idea: A set is 'Dedekind-infinite' iff there exists a one-to-one function that maps a set into a proper subset of itself. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §64) by E Reck / M Price - Structures and Structuralism in Phil of Maths n 7 | |
| A reaction: Sounds as if it is only infinite if it is contradictory, or doesn't know how big it is! |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| Full Idea: Dedekind had an interesting proof of the Axiom of Infinity. He held that I have an a priori grasp of the idea of my self, and that every idea I can form the idea of that idea. Hence there are infinitely many objects available to me a priori. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], no. 66) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 12 'Numb' | |
| A reaction: Who said that Descartes' Cogito was of no use? Frege endorsed this, as long as the ideas are objective and not subjective. |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| Full Idea: Dedekind plainly had fusions, not collections, in mind when he avoided the empty set and used the same symbol for membership and inclusion - two tell-tale signs of a mereological conception. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], 2-3) by Michael Potter - Set Theory and Its Philosophy 02.1 | |
| A reaction: Potter suggests that mathematicians were torn between mereology and sets, and eventually opted whole-heartedly for sets. Maybe this is only because set theory was axiomatised by Zermelo some years before Lezniewski got to mereology. |
| 4098 | The theory of descriptions supports internalism, since they are thinkable when the object is non-existent [Crane] |
| Full Idea: The theory of descriptions gives a model of internalist intentionality, in that it describes cases where the thinkability of a belief does not depend on the existence of a specific object. | |
| From: Tim Crane (Elements of Mind [2001], 4.36) | |
| A reaction: So what do externalists say about the theory? Surely a reference to 'water' can't entail the existence of water? |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| Full Idea: Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: Does this fit real numbers and complex numbers, as well as natural numbers? Frege was concerned by the lack of objectivity in this sort of view. What sort of arithmetic might the Martians have created? Numbers register sameness too. |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| Full Idea: It was primarily Dedekind's accomplishment to define the integers, rationals and reals, taking only the system of natural numbers for granted. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by A.George / D.J.Velleman - Philosophies of Mathematics Intro |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| Full Idea: Dedekind said that the notion of order, rather than that of quantity, is the central notion in the definition of number. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
| A reaction: Compare Aristotle's nice question in Idea 646. My intuition is that quantity comes first, because I'm not sure HOW you could count, if you didn't think you were changing the quantity each time. Why does counting go in THAT particular order? Cf. Idea 8661. |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| Full Idea: Dedekind and Cantor said the cardinals may be defined in terms of the ordinals: The cardinal number of a set S is the least ordinal onto whose predecessors the members of S can be mapped one-one. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 5 |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| Full Idea: Dedekind's ordinals are not essentially either ordinals or cardinals, but the members of any progression whatever. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §243 | |
| A reaction: This is part of Russell's objection to Dedekind's structuralism. The question is always why these beautiful structures should actually be considered as numbers. I say, unlike Russell, that the connection to counting is crucial. |
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| Full Idea: It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], Intro) | |
| A reaction: [He seeks the origin of the theorem that differential calculus deals with continuous magnitude, and he wants an arithmetical rather than geometrical demonstration; the result is his famous 'cut']. |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| Full Idea: Whenever we have to do a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §4) | |
| A reaction: Fine quotes this to show that the Dedekind Cut creates the irrational numbers, rather than hitting them. A consequence is that the irrational numbers depend on the rational numbers, and so can never be identical with any of them. See Idea 10573. |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| Full Idea: Dedekind set up the axiom that the gap in his 'cut' must always be filled …The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - Introduction to Mathematical Philosophy VII | |
| A reaction: This remark of Russell's is famous, and much quoted in other contexts, but I have seen the modern comment that it is grossly unfair to Dedekind. |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| Full Idea: One view, favoured by Dedekind, is that the cut postulates a real number for each cut in the rationals; it does not identify real numbers with cuts. ....A view favoured by later logicists is simply to identify a real number with a cut. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 | |
| A reaction: Dedekind is the patriarch of structuralism about mathematics, so he has little interest in the existenc of 'objects'. |
| 18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
| Full Idea: Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power. | |
| From: Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
| A reaction: Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects. |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| Full Idea: If we scrutinize closely what is done in counting an aggregate of things, we see the ability of the mind to relate things to things, to let a thing correspond to a thing, or to represent a thing by a thing, without which no thinking is possible. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: I don't suppose it occurred to Dedekind that he was reasserting Hume's observation about the fundamental psychology of thought. Is the origin of our numerical ability of philosophical interest? |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| Full Idea: I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself is nothing else than the successive creation of the infinite series of positive integers. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §1) | |
| A reaction: Thus counting roots arithmetic in the world, the successor operation is the essence of counting, and the Dedekind-Peano axioms are built around successors, and give the essence of arithmetic. Unfashionable now, but I love it. Intransitive counting? |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| Full Idea: A system S is said to be infinite when it is similar to a proper part of itself. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], V.64) |
| 18087 | If x changes by less and less, it must approach a limit [Dedekind] |
| Full Idea: If in the variation of a magnitude x we can for every positive magnitude δ assign a corresponding position from and after which x changes by less than δ then x approaches a limiting value. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], p.27), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.7 | |
| A reaction: [Kitcher says he 'showed' this, rather than just stating it] |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| Full Idea: Dedekind's natural numbers: an object is in a set (0 is a number), a function sends the set one-one into itself (numbers have unique successors), the object isn't a value of the function (it isn't a successor), plus induction. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William D. Hart - The Evolution of Logic 5 | |
| A reaction: Hart notes that since this refers to sets of individuals, it is a second-order account of numbers, what we now call 'Second-Order Peano Arithmetic'. |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| Full Idea: Dedekind's idea is that the set of natural numbers has zero as a member, and also has as a member the successor of each of its members, and it is the smallest set satisfying this condition. It is the intersection of all sets satisfying the condition. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| Full Idea: It is Dedekind's categoricity result that convinces most of us that he has articulated our implicit conception of the natural numbers, since it entitles us to speak of 'the' domain (in the singular, up to isomorphism) of natural numbers. | |
| From: comment on Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ian Rumfitt - The Boundary Stones of Thought 9.1 | |
| A reaction: The main rival is set theory, but that has an endlessly expanding domain. He points out that Dedekind needs second-order logic to achieve categoricity. Rumfitt says one could also add to the 1st-order version that successor is an ancestral relation. |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| Full Idea: Dedekind proves mathematical induction, while Peano regards it as an axiom, ...and Peano's method has the advantage of simplicity, and a clearer separation between the particular and the general propositions of arithmetic. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §241 |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| Full Idea: Dedekind is the philosopher-mathematician with whom the structuralist conception originates. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §3 n13) by Fraser MacBride - Structuralism Reconsidered | |
| A reaction: Hellman says the idea grew naturally out of modern mathematics, and cites Hilbert's belief that furniture would do as mathematical objects. |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| Full Idea: Dedekindian abstraction says mathematical objects are 'positions' in a model, while Cantorian abstraction says they are the result of abstracting on structurally similar objects. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §6 | |
| A reaction: The key debate among structuralists seems to be whether or not they are committed to 'objects'. Fine rejects the 'austere' version, which says that objects have no properties. Either version of structuralism can have abstraction as its basis. |
| 4077 | Aesthetic properties of thing supervene on their physical properties [Crane] |
| Full Idea: It is sometimes said that the aesthetic properties of a thing supervene on its physical properties. | |
| From: Tim Crane (Elements of Mind [2001], 2.16) | |
| A reaction: A confusing example, as aesthetic properties only exist if there is an observer. Is 'supervenience' just an empty locution which tries to avoid reduction? |
| 4078 | Constitution (as in a statue constituted by its marble) is supervenience without identity [Crane] |
| Full Idea: A statue is constituted by the marble that makes it up. It is plausible to say that constitution is not the same as identity - since identity is symmetrical and identity is not - but nonetheless constitution is a supervenience relation. | |
| From: Tim Crane (Elements of Mind [2001], 2.16) | |
| A reaction: So what makes it a statue, as opposed to a piece of marble? It may well be an abstraction which only exists relative to observers. |
| 8386 | Events are picked out by descriptions, and facts by whole sentences [Crane] |
| Full Idea: Events are picked out using descriptions ('The death of Caesar'), while facts are picked out using whole sentences ('Caesar died'). | |
| From: Tim Crane (Causation [1995], 1.4.2) | |
| A reaction: Useful, and interesting. He mentions that Kim's usage doesn't agree with this. For analysis purposes, this means that an event is a more minimal item than a fact, and many facts will contain events as components. |
| 4083 | If mental properties are emergent they add a new type of causation, and physics is not complete [Crane] |
| Full Idea: Whatever the causal process is, it remains true that if emergentism is true, the completeness of physics is false; there are some effects which would not have come about if mental things were absent from the world. | |
| From: Tim Crane (Elements of Mind [2001], 2.18) | |
| A reaction: Emergentism looks to me like an incoherent concept, unless it is another word for dualism. |
| 4082 | The distinction between 'resultant' properties (weight) and 'emergent' properties is a bit vague [Crane] |
| Full Idea: The distinction between 'resultant' properties like weight, and 'emergent' properties like colour, seems intuitive enough, but on examination it is very hard to make precise. | |
| From: Tim Crane (Elements of Mind [2001], 2.18) | |
| A reaction: It is no coincidence that the examples are of primary and secondary qualities. If 'the physical entails the mental' then all mental properties are resultant. |
| 4079 | Properties are causes [Crane] |
| Full Idea: Properties are causes. | |
| From: Tim Crane (Elements of Mind [2001], 2.17) | |
| A reaction: We can't detect properties if they lack causal powers. This may be a deep confusion. Properties are what make causal powers possible, but that isn't what properties are? |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| Full Idea: A thing (an object of our thought) is completely determined by all that can be affirmed or thought concerning it. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], I.1) | |
| A reaction: How could you justify this as an observation? Why can't there be unthinkable things (even by God)? Presumably Dedekind is offering a stipulative definition, but we may then be confusing epistemology with ontology. |
| 4068 | Traditional substance is separate from properties and capable of independent existence [Crane] |
| Full Idea: The traditional concept of substance says substances bear properties which are distinct from them, and substances are capable of independent existence. | |
| From: Tim Crane (Elements of Mind [2001], 2.9) | |
| A reaction: Put like that, it sounds ridiculous as a physical theory. It is hard to dislodge substance, though, from a priori human metaphysics. |
| 4096 | Maybe beliefs don't need to be conscious, if you are not conscious of the beliefs guiding your actions [Crane] |
| Full Idea: The beliefs that are currently guiding your actions do not need to be in your stream of consciousness, which suggests that beliefs do not need to be conscious at all. | |
| From: Tim Crane (Elements of Mind [2001], 4.31) | |
| A reaction: Too bold, I think. Presumably this would eliminate all the other propositional attitudes from consciousness. There would only be qualia left! |
| 4097 | Maybe there are two kinds of belief - 'de re' beliefs and 'de dicto' beliefs [Crane] |
| Full Idea: Some philosophers have claimed that there are two kinds of belief, 'de re' belief and 'de dicto' belief. | |
| From: Tim Crane (Elements of Mind [2001], 4.35) | |
| A reaction: Interesting, though it may only distinguish two objects of belief, not two types. Internalist and externalist views are implied. |
| 4093 | Many cases of knowing how can be expressed in propositional terms (like how to get somewhere) [Crane] |
| Full Idea: There are plenty of cases of knowing how to do something, where that knowledge can also be expressed - without remainder, as it were - in propositional terms (such as knowing how to get to the Albert Hall). | |
| From: Tim Crane (Elements of Mind [2001], 3.28) | |
| A reaction: Presumably all knowing how could be expressed propositionally by God. |
| 4108 | Phenol-thio-urea tastes bitter to three-quarters of people, but to the rest it is tasteless, so which is it? [Crane] |
| Full Idea: Phenol-thio-urea tastes bitter to three-quarters of people, but to the rest it is tasteless. Is it really bitter, or really tasteless? | |
| From: Tim Crane (Elements of Mind [2001], 5.44) | |
| A reaction: A nice reinforcement of a classic Greek question. Good support for the primary/secondary distinction. Common sense, really. |
| 4105 | The traditional supports for the sense datum theory were seeing double and specks before one's eyes [Crane] |
| Full Idea: The traditional examples used to support the sense datum theory were seeing double and specks before one's eyes. | |
| From: Tim Crane (Elements of Mind [2001], 5.43) | |
| A reaction: Presumably, though, direct realists can move one eye, or having something wrong with a retina. |
| 4104 | One can taste that the wine is sour, and one can also taste the sourness of the wine [Crane] |
| Full Idea: One can taste that the wine is sour, and one can also taste the sourness of the wine. | |
| From: Tim Crane (Elements of Mind [2001], 5.42) | |
| A reaction: …so sense data are optional? We create sense data by objectifying them, but animals just taste the wine, and are direct realists. Tasting the sourness seems to be a case of abstraction. |
| 4101 | If we smell something we are aware of the smell separately, but we don't perceive a 'look' when we see [Crane] |
| Full Idea: Visual perception seems to differ from some of the other senses; when we become aware of burning toast, we become aware of the smell, ...but we don't see a garden by seeing a 'look' of the garden. | |
| From: Tim Crane (Elements of Mind [2001], 5.40) | |
| A reaction: Interesting. Do blind people transfer this more direct perception to a different sense (e.g. the one they rely on most)? |
| 4102 | The problems of perception disappear if it is a relation to an intentional state, not to an object or sense datum [Crane] |
| Full Idea: The solution to the problem of perception is to deny that it is related to real objects (things or sense-data); rather, perception is an intentional state (with a subject, mode and content), a relation to the intentional content. | |
| From: Tim Crane (Elements of Mind [2001], 5.42) | |
| A reaction: Not clear. This definition makes it sound like a propositional attitude. |
| 4109 | If perception is much richer than our powers of description, this suggests that it is non-conceptual [Crane] |
| Full Idea: The richness in information of perceptual experience outruns our modes of description of it, which has led some philosophers to claim that the content of perceptual experience is non-conceptual. | |
| From: Tim Crane (Elements of Mind [2001], 5.45) | |
| A reaction: It certainly implies that it can't be entirely conceptual, but it still may be that in humans concepts are always involved. Not when I'm waking up in the morning, though. |
| 4103 | The adverbial theory of perceptions says it is the experiences which have properties, not the objects [Crane] |
| Full Idea: The Adverbial Theory of perception holds that the predicates which other theories take as picking out the properties of objects are really adverbs of the perceptual verb; ..instead of strange objects, we just have properties of experiences. | |
| From: Tim Crane (Elements of Mind [2001], 5.42) | |
| A reaction: Promising. It fits secondary qualities all right, but what about primary? I 'see bluely', but can I 'see squarely'? |
| 4065 | Is knowledge just a state of mind, or does it also involve the existence of external things? [Crane] |
| Full Idea: It is controversial whether knowledge is a state of mind, or a composite state involving a thought about something, plus its existence. | |
| From: Tim Crane (Elements of Mind [2001], 1.5) | |
| A reaction: Pinpoints the internalism/externalism problem. Knowledge is a special type of belief (but maybe belief with external links!). Tricky. I vote for internalism. |
| 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? |
| 4092 | The core of the consciousness problem is the case of Mary, zombies, and the Hard Question [Crane] |
| Full Idea: The three arguments that have been used to articulate the problem of consciousness are the knowledge argument ('Mary'), the possibility of 'zombies' (creatures like us but lacking phenomenal consciousness), and the explanatory gap (the Hard Question). | |
| From: Tim Crane (Elements of Mind [2001], 3.26) | |
| A reaction: All of these push towards the implausible claim that there could never be a physical explanation of why we experience things. Zombies are impossible, in my opinion. |
| 4087 | Intentionalism does not require that all mental states be propositional attitudes [Crane] |
| Full Idea: Intentionalism (the doctrine that all mental states are intentional) need not be the thesis that all mental states are propositional attitudes. | |
| From: Tim Crane (Elements of Mind [2001], 3.22) | |
| A reaction: This points to the requirement for an intentionalist to prove that so-called 'qualia' states are essentially intentional, which is not implausible. |
| 4095 | Object-directed attitudes like love are just as significant as propositional attitudes [Crane] |
| Full Idea: Love, hate, and the other object-directed attitudes have as much of a role in explaining behaviour as the propositional attitudes. | |
| From: Tim Crane (Elements of Mind [2001], 4.34) | |
| A reaction: A good clarification of the range of intentional states. Objects seem to be external, where propositions are clearly internal. |
| 4106 | If someone removes their glasses the content of experience remains, but the quality changes [Crane] |
| Full Idea: There is a phenomenal difference between a short-sighted person wearing glasses and not; they do not judge that the world is different, but the properties of the experience (the qualia) have changed. | |
| From: Tim Crane (Elements of Mind [2001], 5.43) | |
| A reaction: Could be challenged. If a notice becomes unreadable, that is more than the qualia changing. |
| 4089 | Pains have a region of the body as their intentional content, not some pain object [Crane] |
| Full Idea: The intentional object of a pain-state is a part or region of the body, not a pain-object. | |
| From: Tim Crane (Elements of Mind [2001], 3.24) | |
| A reaction: Plausible. Has anyone ever suffered from pain without some sense of what part of the body is actually in pain? |
| 4090 | Weak intentionalism says qualia are extra properties; strong intentionalism says they are intentional [Crane] |
| Full Idea: Weak intentionalism says all mental states are intentional, but qualia are higher-order properties of these states. ..Strong intentionalists say the phenomenal character of a sensation consists purely in that state's intentionality. | |
| From: Tim Crane (Elements of Mind [2001], 3.25) | |
| A reaction: The weak version sounds better. Asking 'how could a thought have a quality of experience just by being about something?' is a restatement of the traditional problem, which won't go away. The Hard Question. |
| 4107 | With inverted qualia a person's experiences would change, but their beliefs remain the same [Crane] |
| Full Idea: The right thing to say about inverted qualia is that the person's experiences are different from other people's, but their beliefs are the same. | |
| From: Tim Crane (Elements of Mind [2001], 5.44) | |
| A reaction: Right - which reinforces the idea that all beliefs are the result of judgement, and none come directly from perception. |
| 4069 | Descartes did not think of minds as made of a substance, because they are not divisible [Crane] |
| Full Idea: It would be wrong to represent Descartes' view as the idea that bodies are made of one kind of stuff and minds of another; he did not think minds are made of stuff at all, because then they would be divisible. | |
| From: Tim Crane (Elements of Mind [2001], 2.10) | |
| A reaction: I'm not convinced. It could be an indivisible substance. Without a mental substance, Descartes may have to say the mind is an abstraction, perhaps a pattern of Platonic forms. |
| 4074 | Functionalism defines mental states by their causal properties, which rules out epiphenomenalism [Crane] |
| Full Idea: Functionalism holds that it is in the nature of certain mental states to have certain effects; therefore there can be no mental epiphenomena. | |
| From: Tim Crane (Elements of Mind [2001], 2.14) | |
| A reaction: I strongly resist the idea that a thing's identity is its function. Functionalism may not say that. Mind is an abstraction referring to a causal nexus of unknowable components. |
| 4091 | The problems of misrepresentation and error have dogged physicalist reductions of intentionality [Crane] |
| Full Idea: The fundamental problems of misrepresentation and error have dogged physicalist reductions of intentionality. | |
| From: Tim Crane (Elements of Mind [2001], 3.26) | |
| A reaction: If footprints or tree-rings are the model for reductions of intentionality, there doesn't seem much scope in them for giving false information, except by some freak event. |
| 4070 | Properties dualism says mental properties are distinct from physical, despite a single underlying substance [Crane] |
| Full Idea: According to property dualism, mental properties are distinct from physical properties, even though they are properties of one substance. | |
| From: Tim Crane (Elements of Mind [2001], 2.10) | |
| A reaction: Two properties may be phenomenologically different (transparent and magnetic), but that doesn't put them in different ontological categories. |
| 4084 | Non-reductive physicalism seeks an explanation of supervenience, but emergentists accept it as basic [Crane] |
| Full Idea: While the non-reductive physicalist believes that mental/physical supervenience must be explained, the emergentist is willing to accept it as a fact of nature. | |
| From: Tim Crane (Elements of Mind [2001], 2.18) | |
| A reaction: A good reason not to be an emergentist. No philosopher should abandon the principle of sufficient reason. |
| 4080 | If mental supervenes on the physical, then every physical cause will be accompanied by a mental one [Crane] |
| Full Idea: If the mental supervenes on the physical, then whenever a physical cause brings about some effect, a mental cause comes along for the ride. | |
| From: Tim Crane (Elements of Mind [2001], 2.17) | |
| A reaction: This is why supervenience seems to imply epiphenomenalism. The very concept of supervenience is dubious. |
| 4085 | Physicalism may be the source of the mind-body problem, rather than its solution [Crane] |
| Full Idea: Physicalism may be the source of the mind-body problem, rather than its solution. | |
| From: Tim Crane (Elements of Mind [2001], 2.19) | |
| A reaction: Certainly if the physical is seen as just a pile of atoms, it is hard to see how they could ever think (see idea 1909). |
| 4075 | Identity theory is either of particular events, or of properties, depending on your theory of causation [Crane] |
| Full Idea: If causation concerns events, then we have an identity theory of mental and physical events (particulars) [Davidson]. If causation is by properties, then it is mental and physical properties which are identical [Lewis and Armstrong]. | |
| From: Tim Crane (Elements of Mind [2001], 2.14) | |
| A reaction: Events are tokens, and properties are types. Tricky. Events are dynamic, but properties can be static. |
| 4073 | Overdetermination occurs if two events cause an effect, when each would have caused it alone [Crane] |
| Full Idea: Causal overdetermination is when an effect has more than one cause, and each event would have caused the effect if the other one had not done so. | |
| From: Tim Crane (Elements of Mind [2001], 2.13) | |
| A reaction: Overdetermination is a symptom that an explanation is questionable, but it can occur. Two strong people can join to push over a light hatstand. |
| 4072 | The completeness of physics must be an essential component of any physicalist view of mind [Crane] |
| Full Idea: I claim that the completeness of physics must be an essential component of any physicalist view of mind. | |
| From: Tim Crane (Elements of Mind [2001], 2.12) | |
| A reaction: He does not convince me of this. The mind may be within physics, but why should we say a priori that no exceptions to physical law will ever be discovered. Crane is setting up straw men. |
| 4094 | Experience teaches us propositions, because we can reason about our phenomenal experience [Crane] |
| Full Idea: In experience we learn propositions, since someone can reason using the sentence 'Red looks like this' (e.g. 'If red looks like this, then either it looks like this to dogs or it doesn't'). | |
| From: Tim Crane (Elements of Mind [2001], 3.28) | |
| A reaction: The fact that we can create propositions about experiences doesn't prove that experience is inherently propositional. |
| 4100 | The Twin Earth argument depends on reference being determined by content, which may be false. [Crane] |
| Full Idea: The Twin Earth argument does not refute internalism, since it depends on the 'Content-Determines-Reference' principle, which internalists can reject. | |
| From: Tim Crane (Elements of Mind [2001], 4.37) | |
| A reaction: The idea is that content should be understood in a context (e.g. on a particular planet). Indexicals count against a totally narrow view of content (Twins thinking 'I am here'). |
| 4067 | Broad content entails the existence of the object of the thought [Crane] |
| Full Idea: If a mental state is broad, then the existence of the mental state entails the existence of its object. | |
| From: Tim Crane (Elements of Mind [2001], 1.7) | |
| A reaction: Hence thinking of non-existent things like unicorns is problematic for externalists. However, externalists can think about numbers or Platonic ideals. |
| 4063 | In intensional contexts, truth depends on how extensions are conceived. [Crane] |
| Full Idea: Intensional contexts are those where truth or falsehood depends on the way the extensions are conceived. | |
| From: Tim Crane (Elements of Mind [2001], 1.4) | |
| A reaction: An important distinction for anyone defending an internalist view of concepts or of knowledge |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| Full Idea: By applying the operation of abstraction to a system of objects isomorphic to the natural numbers, Dedekind believed that we obtained the abstract system of natural numbers, each member having only properties consequent upon its position. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Dummett - The Philosophy of Mathematics | |
| A reaction: Dummett is scornful of the abstractionism. He cites Benacerraf as a modern non-abstractionist follower of Dedekind's view. There seems to be a suspicion of circularity in it. How many objects will you abstract from to get seven? |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| Full Idea: If in an infinite system, set in order, we neglect the special character of the elements, simply retaining their distinguishability and their order-relations to one another, then the elements are the natural numbers, created by the human mind. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], VI.73) | |
| A reaction: [compressed] This is the classic abstractionist view of the origin of number, but with the added feature that the order is first imposed, so that ordinals remain after the abstraction. This, of course, sounds a bit circular, as well as subjective. |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| Full Idea: Dedekind's conception is psychologistic only if that is the only way to understand the abstraction that is involved, which it is not. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William W. Tait - Frege versus Cantor and Dedekind IV | |
| A reaction: This is a very important suggestion, implying that we can retain some notion of abstractionism, while jettisoning the hated subjective character of private psychologism, which seems to undermine truth and logic. |
| 4071 | Causation can be seen in counterfactual terms, or as increased probability, or as energy flow [Crane] |
| Full Idea: A theory of causation might say 'If A had not existed, B would not have existed' (counterfactual theory), or 'B is more likely if A occurs' (probabilistic), or 'energy flows from A to B'. | |
| From: Tim Crane (Elements of Mind [2001], 2.11) | |
| A reaction: As always, it is vital to separate epistemology from ontology. Energy won't cover agents. Whisper "Fire!" in a theatre. |
| 8387 | A cause has its effects in virtue of its properties [Crane] |
| Full Idea: Some philosophers say that a cause has its effects in virtue of its properties. | |
| From: Tim Crane (Causation [1995], 1.4.2) | |
| A reaction: The trouble with this approach, I think, is that it encourages us to invent dubious properties, because every explanation of an effect will require one. Dormative properties, for example, are ascribed to sleeping pills. |
| 4076 | Causes are properties, not events, because properties are what make a difference in a situation [Crane] |
| Full Idea: My view is that causes are properties (not events); when we look for causes, we look for the aspect of a situation which made a difference, and aspects are properties or qualities. | |
| From: Tim Crane (Elements of Mind [2001], 2.14) | |
| A reaction: He is talking about explanations, which may not be causes, or at least they have a different emphasis. Don't events 'make a difference'? Events are ontologically weird |
| 8384 | The regularity theory explains a causal event by other items than the two that are involved [Crane] |
| Full Idea: An unsatisfactory aspect of the regularity thesis is that it explains why this A caused this B in terms of facts about things other that this A and this B. But we want to know what it is about this A and this B that makes one the cause of the other? | |
| From: Tim Crane (Causation [1995], 1.3) | |
| A reaction: Well said. This is the failing of any attempt to define things by their relationships (e.g. functional definitions). Hume, of course, was only relying on regularity because when he focused on the actual A and B, they had no helpful experiences to offer. |
| 4066 | It seems that 'exists' could sometimes be a predicate [Crane] |
| Full Idea: The view that 'exists' is never a predicate is not plausible. | |
| From: Tim Crane (Elements of Mind [2001], 1.7) | |
| A reaction: He doesn't enlarge. Russell says 'exists' is a quantifier. 'Your very existence offends me - I hope it is confiscated'. |