55 ideas
| 15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
| Full Idea: The problem with the Axiom of Choice is that it allows an initiate (by an ingenious train of reasoning) to cut a golf ball into a finite number of pieces and put them together again to make a globe as big as the sun. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 9) | |
| A reaction: I'm not sure how this works (and I think it was proposed by the young Tarski), but it sounds like a real problem to me, for all the modern assumptions that Choice is fine. |
| 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? |
| 15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
| Full Idea: You have 1 and 0, something and nothing. Adding gives us the naturals. Subtracting brings the negatives into light; dividing, the rationals; only with a new operation, taking of roots, do the irrationals show themselves. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 1 'Mind') | |
| A reaction: The suggestion is constructivist, I suppose - that it is only operations that produce numbers. They go on to show that complex numbers don't quite fit the pattern. |
| 15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
| Full Idea: The rationals are everywhere - the irrationals are everywhere else. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 1 'Nameless') | |
| A reaction: Nice. That is, the rationals may be dense (you can always find another one in any gap), but the irrationals are continuous (no gaps). |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| Full Idea: The 'commutative' laws say the order in which you add or multiply two numbers makes no difference; ...the 'associative' laws declare that regrouping couldn't change a sum or product (e.g. a+(b+c)=(a+b)+c ). | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Tablets') | |
| A reaction: This seem utterly self-evident, but in more complex systems they can break down, so it is worth being conscious of them. |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| Full Idea: The 'distributive' law says you will get the same result if you first add two numbers, and then multiply them by a third, or first multiply each by the third and then add the results (i.e. a · (b+c) = a · b + a · c ). | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Tablets') | |
| A reaction: Obviously this will depend on getting the brackets right, to ensure you are indeed doing the same operations both ways. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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? |
| 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. |
| 15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
| Full Idea: The claim that no number is greater than a million is confirmed by the first million test cases. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Intro') | |
| A reaction: Extrapolate from this, and you can have as large a number of cases as you could possibly think of failing to do the inductive job. Love it! Induction isn't about accumulations of cases. It is about explanation, which is about essence. Yes! |
| 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. |
| 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. |
| 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). |
| 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 |
| 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'. |