63 ideas
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| Full Idea: The standard requirement of definitions involves 'eliminability' (any defined terms must be replaceable by primitives) and 'non-creativity' (proofs of theorems should not depend on the definition). | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7) | |
| A reaction: [He cites Russell and Whitehead as a source for this view] This is the austere view of the mathematician or logician. But almost every abstract concept that we use was actually defined in a creative way. |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| Full Idea: The set-theory account of infinity doesn't just say that we can keep on counting, but that the natural numbers are an actual infinite set. This is necessary to make sense of the powerset of ω, as the set of all its subsets, and thus even bigger. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
| A reaction: I don't personally find this to be sufficient reason to commit myself to the existence of actual infinities. In fact I have growing doubts about the whole role of set theory in philosophy of mathematics. Shows how much I know. |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| Full Idea: In current set theory Russell's Paradox is avoided by saying that a condition can only be defined on already existing sets. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: A response to Idea 9613. This leaves us with no account of how sets are created, so we have the modern notion that absolutely any grouping of daft things is a perfectly good set. The logicians seem to have hijacked common sense. |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| Full Idea: In the early versions of set theory ('naïve' set theory), the axiom of comprehension assumed that for any condition there is a set of objects satisfying that condition (so P(x)↔x∈{x:P(x)}), but this led directly to Russell's Paradox. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: How rarely any philosophers state this problem clearly (as Brown does here). This is incredibly important for our understanding of how we classify the world. I'm tempted to just ignore Russell, and treat sets in a natural and sensible way. |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| Full Idea: The modern 'iterative' concept of a set starts with the empty set φ (or unsetted individuals), then uses set-forming operations (characterized by the axioms) to build up ever more complex sets. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: The only sets in our system will be those we can construct, rather than anything accepted intuitively. It is more about building an elaborate machine that works than about giving a good model of reality. |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| Full Idea: Neither a flock of birds nor a pack of wolves is strictly a set, since a flock can fly south, and a pack can be on the prowl, whereas sets go nowhere and menace no one. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7) | |
| A reaction: To say that the pack menaced you would presumably be to commit the fallacy of composition. Doesn't the number 64 have properties which its set-theoretic elements (whatever we decide they are) will lack? |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| Full Idea: The law of excluded middle says if a proposition is false, then its negation is true | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1) | |
| A reaction: Surely that is the best statement of the law? How do you write that down? ¬(P)→¬P? No, because it is a semantic claim, not a syntactic claim, so a truth table captures it. Semantic claims are bigger than syntactic claims. |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| Full Idea: The three views one could adopt concerning axioms are that they are self-evident truths, or that they are arbitrary stipulations, or that they are fallible attempts to describe how things are. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10) | |
| A reaction: Presumably modern platonists like the third version, with others choosing the second, and hardly anyone now having the confidence to embrace the first. |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| Full Idea: Berry's Paradox refers to 'the least integer not namable in fewer than nineteen syllables' - a paradox because it has just been named in eighteen syllables. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
| A reaction: Apparently George Boolos used this quirky idea as a basis for a new and more streamlined proof of Gödel's Theorem. Don't tell me you don't find that impressive. |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| Full Idea: Mathematics seems to be the one and only place where we humans can be absolutely sure that we got it right. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1) | |
| A reaction: Apart from death and taxes, that is. Personally I am more certain of the keyboard I am typing on than I am of Pythagoras's Theorem, but the experts seem pretty confident about the number stuff. |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| Full Idea: 'There are two apples' can be recast as 'x is an apple and y is an apple, and x isn't y, and if z is an apple it is the same as x or y', which makes no appeal at all to mathematics. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4) | |
| A reaction: He cites this as the basis of Hartry Field's claim that science can be done without numbers. The logic is ∃x∃y∀z(Ax&Ay&(x¬=y)&(Az→z=x∨z=y)). |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| Full Idea: The number π is not only irrational, but it is also (unlike √2) a 'transcendental' number, because it is not the solution of an algebraic equation. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10) | |
| A reaction: So is that a superficial property, or a profound one? Answers on a post card. |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| Full Idea: Mathematics hooks onto the world by providing representations in the form of structurally similar models. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4) | |
| A reaction: This is Brown's conclusion. It needs notions of mapping, one-to-one correspondence, and similarity. I like the idea of a 'model', as used in both logic and mathematics, and children's hobbies. The mind is a model-making machine. |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| Full Idea: I'm tempted to say that mathematics is so rich that there are indefinitely many ways to prove anything - verbal/symbolic derivations and pictures are just two. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 9) | |
| A reaction: Brown has been defending pictures as a form of proof. I wonder how long his list would be, if we challenged him to give more details? Some people have very low standards of proof. |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| Full Idea: The celebrity of the famous proof in 1976 of the four-colour theorem of maps is that a computer played an essential role in the proof. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10) | |
| A reaction: The problem concerns the reliability of the computers, but then all the people who check a traditional proof might also be unreliable. Quis custodet custodies? |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| Full Idea: Maybe all of mathematics can be represented in set theory, but we should not think that mathematics is set theory. Functions can be represented as order pairs, but perhaps that is not what functions really are. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7) | |
| A reaction: This seems to me to be the correct view of the situation. If 2 is represented as {φ,{φ}}, why is that asymmetrical? The first digit seems to be the senior and original partner, but how could the digits of 2 differ from one another? |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| Full Idea: The basic definition of a graph can be given in set-theoretic terms,...but then what could an unlabelled graph be? | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7) | |
| A reaction: An unlabelled graph will at least need a verbal description for it to have any significance at all. My daily mood-swings look like this.... |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| Full Idea: Epistemology is a big worry for structuralists. ..To conjecture that something has a particular structure, we must already have conceived of the idea of the structure itself; we cannot be discovering structures by conjecturing them. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4) | |
| A reaction: This has to be a crucial area of discussion. Do we have our heads full of abstract structures before we look out of the window? Externalism about the mind is important here; mind and world are not utterly distinct things. |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| Full Idea: Set theory is at the very heart of mathematics; it may even be all there is to mathematics. The notion of set, however, seems quite contrary to the spirit of structuralism. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4) | |
| A reaction: So much the worse for sets, I say. You can, for example, define ordinality in terms of sets, but that is no good if ordinality is basic to the nature of numbers, rather than a later addition. |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| Full Idea: We could not discover irrational numbers by physical measurement. The discovery of the irrationality of the square root of two was an intellectual achievement, not at all connected to sense experience. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1) | |
| A reaction: Brown declares himself a platonist, and this is clearly a key argument for him, and rather a good one. Hm. I'll get back to you on this one... |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| Full Idea: Numbers are not 'abstract' (in the old sense, of universals abstracted from particulars), since each of the integers is a unique individual, a particular, not a universal. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: An interesting observation which I have not seen directly stated before. Compare Idea 645. I suspect that numbers should be thought of as higher-order abstractions, which don't behave like normal universals (i.e. they're not distributed). |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| Full Idea: A simple argument makes it clear that all mathematical arguments are abstract: there are infinitely many numbers, but only a finite number of physical entities, so most mathematical objects are non-physical. The best assumption is that they all are. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: This, it seems to me, is where constructivists score well (cf. Idea 9608). I don't have an infinity of bricks to build an infinity of houses, but I can imagine that the bricks just keep coming if I need them. Imagination is what is unbounded. |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| Full Idea: Perhaps, instead of objects, numbers are associated with properties of objects. Basing them on objects is strongly empiricist and uses first-order logic, whereas the latter view is somewhat Platonistic, and uses second-order logic. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4) | |
| A reaction: I don't seem to have a view on this. You can count tomatoes, or you can count red objects, or even 'instances of red'. Numbers refer to whatever can be individuated. No individuation, no arithmetic. (It's also Hume v Armstrong on laws on nature). |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| Full Idea: For the instinctive nominalist in mathematics, there are no numbers, only numerals. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
| A reaction: Maybe. A numeral is a specific sign, sometimes in a specific natural language, so this seems to miss the fact that cardinality etc are features of reality, not just conventions. |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| Full Idea: In mathematics, the most brilliant formalist of all was Hilbert | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
| A reaction: He seems to have developed his fully formalist views later in his career. See Mathematics|Basis of Mathematic|Formalism in our thematic section. Kreisel denies that Hilbert was a true formalist. |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| Full Idea: Are there mathematical properties which can only be discovered using a particular notation? | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 6) | |
| A reaction: If so, this would seem to be a serious difficulty for platonists. Brown has just been exploring the mathematical theory of knots. |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| Full Idea: Constuctivists link truth with constructive proof, but necessarily lack constructions for many highly desirable results of classical mathematics, making their account of mathematical truth rather implausible. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: The tricky word here is 'desirable', which is an odd criterion for mathematical truth. Nevertheless this sounds like a good objection. How flexible might the concept of a 'construction' be? |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| Full Idea: If we define p as '3 if Goldbach's Conjecture is true' and '5 if Goldbach's Conjecture is false', it seems that p must be a prime number, but, amazingly, constructivists would not accept this without a proof of Goldbach's Conjecture. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 8) | |
| A reaction: A very similar argument structure to Schrödinger's Cat. This seems (as Brown implies) to be a devastating knock-down argument, but I'll keep an open mind for now. |
| 12270 | Being is one [Melissus, by Aristotle] |
| Full Idea: Being is one. | |
| From: report of Melissus (fragments/reports [c.443 BCE]) by Aristotle - Topics 104b23 | |
| A reaction: I can only really understand this in terms of physics, as the belief that ultimately there is one simple theory which explains everything. That project doesn't look terribly promising, despite the lovely simplifications of modern physics. |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| Full Idea: David's painting of Napoleon (on a white horse) is a 'picture' of Napoleon, and a 'symbol' of leadership, courage, adventure. It manages to be about something concrete and something abstract. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 3) | |
| A reaction: This strikes me as the germ of an extremely important idea - that abstraction is involved in our perception of the concrete, so that they are not two entirely separate realms. Seeing 'as' involves abstraction. |
| 6504 | For physicalists, the only relations are spatial, temporal and causal [Robinson,H] |
| Full Idea: Spatial, temporal and causal relations are the only respectable candidates for relations for a physicalist. | |
| From: Howard Robinson (Perception [1994], V.4) | |
| A reaction: This seems to be true, and is an absolutely crucial principle upon which any respectable physicalist account of the world must be built. It means that physicalists must attempt to explain all mental events in causal terms. |
| 6520 | If reality just has relational properties, what are its substantial ontological features? [Robinson,H] |
| Full Idea: Some thinkers claim the physical world consists just of relational properties - generally of active powers or fields; ..but an ontology of mutual influences is not an ontology at all unless the possessors of the influence have more substantial features. | |
| From: Howard Robinson (Perception [1994], IX.3) | |
| A reaction: I think this idea is one of the keys to wisdom. It is the same problem with functional explanations - you are left asking WHY this thing can have this particular function. Without the buck stopping at essences you are chasing your explanatory tail. |
| 6485 | When a red object is viewed, the air in between does not become red [Robinson,H] |
| Full Idea: When the form of red passes from an object to the eye, the air in between does not become red. | |
| From: Howard Robinson (Perception [1994], 1.2) | |
| A reaction: This strikes me as a crucial and basic fact which must be faced by any philosopher offering a theory of perception. I would have thought it instantly eliminated any sort of direct or naïve realism. The quale of red is created by my brain. |
| 6521 | Representative realists believe that laws of phenomena will apply to the physical world [Robinson,H] |
| Full Idea: One thing which is meant by saying that the phenomenal world represents or resembles the transcendental physical world is that the scientific laws devised to apply to the former, if correct, also apply (at least approximately) to the latter. | |
| From: Howard Robinson (Perception [1994], IX.3) | |
| A reaction: This is not, of course, an argument, or a claim which can be easily substantiated, but it does seem to be a nice statement of a central article of faith for representative realists. The laws of the phenomenal world are the only ones we are going to get. |
| 6509 | Representative realists believe some properties of sense-data are shared by the objects themselves [Robinson,H] |
| Full Idea: A representative realist believes that at least some of the properties that are ostensively demonstrable in virtue of being exemplified in sense-data are of the same kind as some of those exemplified in physical objects. | |
| From: Howard Robinson (Perception [1994], VII.5) | |
| A reaction: It is hard to pin down exactly what is being claimed here. Locke's primary qualities will obviously qualify, but could properties be 'exemplified' in sense-data without them actually being the same as those of the objects? |
| 6522 | Phenomenalism can be theistic (Berkeley), or sceptical (Hume), or analytic (20th century) [Robinson,H] |
| Full Idea: It is useful to identify three kinds of phenomenalism: theistic, sceptical and analytic; the first is represented by Berkeley, the second by Hume, and the third by most twentieth-century phenomenalists. | |
| From: Howard Robinson (Perception [1994], IX.4) | |
| A reaction: In Britain the third group is usually represented by A.J.Ayer. My simple objection to all phenomenalists is that they are intellectual cowards because they won't venture to give an explanation of the phenomena which confront them. |
| 6502 | Can we reduce perception to acquisition of information, which is reduced to causation or disposition? [Robinson,H] |
| Full Idea: Many modern physicalists first analyse perception as no more than the acquisition of beliefs or information through the senses, and then analyse belief and the possession of information in causal or dispositional terms. | |
| From: Howard Robinson (Perception [1994], V.1) | |
| A reaction: (He mentions Armstrong, Dretske and Pitcher). A reduction to dispositions implies behaviourism. This all sounds more like an eliminativist strategy than a reductive one. I would start by saying that perception is only information after interpretation. |
| 6513 | Would someone who recovered their sight recognise felt shapes just by looking? [Robinson,H] |
| Full Idea: Molyneux's Problem is whether someone who was born blind and acquired sight would be able to recognise, on sight, which shapes were which; that is, would they see which shape was the one that felt so-and-so? | |
| From: Howard Robinson (Perception [1994], VIII.7) | |
| A reaction: (Molyneux wrote a letter to John Locke about this). It is a good question, and much discussed in modern times. My estimation is that the person would recognise the shapes. We are partly synaesthetic, and see sharpness as well as feeling it. |
| 6512 | Secondary qualities have one sensory mode, but primary qualities can have more [Robinson,H] |
| Full Idea: Primary qualities and secondary qualities are often distinguished on the grounds that secondaries are restricted to one sensory modality, but primaries can appear in more. | |
| From: Howard Robinson (Perception [1994], VIII.7) | |
| A reaction: This distinction seems to me to be accurate and important. It is not just that the two types are phenomenally different - it is that the best explanation is that the secondaries depend on their one sense, but the primaries are independent. |
| 6497 | We say objects possess no intrinsic secondary qualities because physicists don't need them [Robinson,H] |
| Full Idea: The idea that objects do not possess secondary qualities intrinsically rests on the thought that they do not figure in the physicist's account of the world; ..as they are causally idle, no purpose is served by attributing them to objects. | |
| From: Howard Robinson (Perception [1994], III.1) | |
| A reaction: On the whole I agree with this, but colours (for example) are not causally idle, as they seem to affect the behaviour of insects. They are properties which can only have a causal effect if there is a brain in their vicinity. Physicists ignore brains. |
| 6494 | If objects are not coloured, and neither are sense-contents, we are left saying that nothing is coloured [Robinson,H] |
| Full Idea: If there are good reasons for thinking that physical objects are not literally coloured, and one also refuses to attribute them to sense-contents, then one will have the bizarre theory (which has been recently adopted) that nothing is actually coloured. | |
| From: Howard Robinson (Perception [1994], 1.7) | |
| A reaction: It seems to me that objects are not literally coloured, that the air in between does not become coloured, and that my brain doesn't turn a funny colour, so that only leaves colour as an 'interior' feature of certain brain states. That's how it is. |
| 6499 | Shape can be experienced in different ways, but colour and sound only one way [Robinson,H] |
| Full Idea: Shape can be directly experienced by either touch or sight, which are subjectively different; but colour and sound can be directly experienced only through experiences which are subjectively like sight and hearing. | |
| From: Howard Robinson (Perception [1994], III.1) | |
| A reaction: This seems to be a key argument in support of the distinction between primary and secondary qualities. It seems to me that the distinction may be challenged and questioned, but to deny it completely (as Berkeley and Hume do) is absurd. |
| 6500 | If secondary qualities match senses, would new senses create new qualities? [Robinson,H] |
| Full Idea: As secondary qualities are tailored to match senses, a proliferation of senses would lead to a proliferation of secondary qualities. | |
| From: Howard Robinson (Perception [1994], III.1) | |
| A reaction: One might reply that if we experienced, say, magnetism, we would just be discerning a new fine grained primary quality, not adding something new to the ontological stock of properties in the world. It is a matter of HOW we experience the magnetism. |
| 6484 | Most moderate empiricists adopt Locke's representative theory of perception [Robinson,H] |
| Full Idea: The representative theory of perception is found in Locke, and is adopted by most moderate empiricists. | |
| From: Howard Robinson (Perception [1994], 1.2) | |
| A reaction: This is, I think, my own position. Anything less than fairly robust realism strikes me as being a bit mad (despite Berkeley's endless assertions that he is preaching common sense), and direct realism seems obviously false. |
| 6508 | Sense-data leads to either representative realism or phenomenalism or idealism [Robinson,H] |
| Full Idea: The sense-datum theorist is either a representative realist or a phenomenalist (with which we can classify idealism for present purposes). | |
| From: Howard Robinson (Perception [1994], VII.5) | |
| A reaction: The only alternative to these two positions seems to be some sort of direct realism. I class myself as a representative realist, as this just seems (after a very little thought about colour blindness) to be common sense. I'm open to persuasion. |
| 6482 | For idealists and phenomenalists sense-data are in objects; representative realists say they resemble objects [Robinson,H] |
| Full Idea: For idealists and phenomenalists sense-data are part of physical objects, for objects consist only of actual or actual and possible sense-data; representative realists say they just have an abstract and structural resemblance to objects. | |
| From: Howard Robinson (Perception [1994], 1.1) | |
| A reaction: He puts Berkeley, Hume and Mill in the first group, and Locke in the second. Russell belongs in the second. The very fact that there can be two such different theories about the location of sense-data rather discredits the whole idea. |
| 6480 | Sense-data do not have any intrinsic intentionality [Robinson,H] |
| Full Idea: I understand sense-data as having no intrinsic intentionality; that is, though it may suggest, by habit, things beyond it, in itself it possesses only sensible qualities which do not refer beyond themselves. | |
| From: Howard Robinson (Perception [1994], 1.1) | |
| A reaction: This seems right, as the whole point of proposing sense-data was as something neutral between realism and anti-realism |
| 6505 | Sense-data are rejected because they are a veil between us and reality, leading to scepticism [Robinson,H] |
| Full Idea: Resistance to the sense-datum theory is inspired mainly by the fear that such data constitute a veil of perception which stands between the observer and the external world, threatening scepticism, or even solipsism. | |
| From: Howard Robinson (Perception [1994], VII.1) | |
| A reaction: It is very intellectually dishonest to reject any theory because it leads to scepticism or relativism. This is a common failing among quite good professional philosophers. See Idea 241. |
| 6506 | 'Sense redly' sounds peculiar, but 'senses redly-squarely tablely' sounds far worse [Robinson,H] |
| Full Idea: 'Sense redly' sounds peculiar, but 'senses redly-squarely' or 'red-squarely' or 'senses redly-squarely-tablely' and other variants sound far worse. | |
| From: Howard Robinson (Perception [1994], VII.5) | |
| A reaction: This is a comment on the adverbial theory, which is meant to replace representative theories based on sense-data. The problem is not that it sounds weird; it is that while plain red can be a mode of perception, being a table obviously can't. |
| 6507 | Adverbialism sees the contents of sense-experience as modes, not objects [Robinson,H] |
| Full Idea: The defining claim of adverbialism is that the contents of sense-experience are modes, not objects, of sensory activity. | |
| From: Howard Robinson (Perception [1994], VII.5) | |
| A reaction: This seems quite a good account of simple 'modes' like colour, but not so good when you instantly perceive a house. It never seems wholly satisfactory to sidestep the question of 'what are you perceiving when you perceive red or square?' |
| 6511 | If there are only 'modes' of sensing, then an object can no more be red or square than it can be proud or lazy. [Robinson,H] |
| Full Idea: If only modes of sensing are ostensively available, ..then it is a category mistake to see any resemblance between what is available and properties of bodies; one could as sensibly say that a physical body is proud or lazy as that it is red or square. | |
| From: Howard Robinson (Perception [1994], VII.5) | |
| A reaction: This is an objection to the 'adverbial' theory of perception. It looks to me like a devastating objection, if the theory is meant to cover primary qualities as well as secondary. Red could be a mode of perception, but not square, surely? |
| 6515 | An explanation presupposes something that is improbable unless it is explained [Robinson,H] |
| Full Idea: Any search for an explanation presupposes that there is something in need of an explanation - that is, something which is improbable unless explained. | |
| From: Howard Robinson (Perception [1994], IX.3) | |
| A reaction: Elementary enough, but it underlines the human perspective of all explanations. I may need an explanation of baseball, where you don't. |
| 6517 | If all possibilities are equal, order seems (a priori) to need an explanation - or does it? [Robinson,H] |
| Full Idea: The fact that order requires an explanation seems to be an a priori principle; ..we assume all possibilities are equally likely, and so no striking regularities should emerge; the sceptic replies that a highly ordered sequence is as likely as any other. | |
| From: Howard Robinson (Perception [1994], IX.3) | |
| A reaction: An independent notion of 'order' is required. If I write down '14356', and then throw 1 4 3 5 6 on a die, the match is the order; instrinsically 14356 is nothing special. If you threw the die a million times, a run of six sixes seems quite likely. |
| 6481 | If intentional states are intrinsically about other things, what are their own properties? [Robinson,H] |
| Full Idea: Intentional states are mysterious things; if they are intrinsically about other things, what properties, if any, do they possess intrinsically? | |
| From: Howard Robinson (Perception [1994], 1.1) | |
| A reaction: A very nice question, which I suspect to be right at the heart of the tendency towards externalist accounts of the mind. Since you can only talk about the contents of the thoughts, you can't put forward a decent internalist account of what is going on. |
| 6503 | Physicalism cannot allow internal intentional objects, as brain states can't be 'about' anything [Robinson,H] |
| Full Idea: It is generally conceded by reductive physicalists that a state of the brain cannot be intrinsically about anything, for intentionality is not an intrinsic property of anything, so there can be no internal objects for a physicalist. | |
| From: Howard Robinson (Perception [1994], V.4) | |
| A reaction: Perhaps it is best to say that 'aboutness' is not a property of physics. We may say that a brain state 'represents' something, because the something caused the brain state, but representations have to be recognised |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| Full Idea: The current usage of 'abstract' simply means outside space and time, not concrete, not physical. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: This is in contrast to Idea 9609 (the older notion of being abstracted). It seems odd that our ancestors had a theory about where such ideas came from, but modern thinkers have no theory at all. Blame Frege for that. |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| Full Idea: The older sense of 'abstract' applies to universals, where a universal like 'redness' is abstracted from red particulars; it is the one associated with the many. In mathematics, the notion of 'group' or 'vector space' perhaps fits this pattern. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2) | |
| A reaction: I am currently investigating whether this 'older' concept is in fact dead. It seems to me that it is needed, as part of cognitive science, and as the crucial link between a materialist metaphysic and the world of ideas. |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| Full Idea: In addition to the sense and reference of term, there is the 'computational' role. The name '2' has a sense (successor of 1) and a reference (the number 2). But the word 'two' has little computational power, Roman 'II' is better, and '2' is a marvel. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 6) | |
| A reaction: Very interesting, and the point might transfer to natural languages. Synonymous terms carry with them not just different expressive powers, but the capacity to play different roles (e.g. slang and formal terms, gob and mouth). |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| Full Idea: There seem to be no actual infinites in the physical realm. Given the correctness of atomism, there are no infinitely small things, no infinite divisibility. And General Relativity says that the universe is only finitely large. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
| A reaction: If time was infinite, you could travel round in a circle forever. An atom has size, so it has a left, middle and right to it. Etc. They seem to be physical, so we will count those too. |
| 6519 | Locke's solidity is not matter, because that is impenetrability and hardness combined [Robinson,H] |
| Full Idea: Notoriously, Locke's filler for Descartes's geometrical matter, solidity, will not do, for that quality collapses on examination into a composite of the dispositional-cum-relational propery of impenetrability, and the secondary quality of hardness. | |
| From: Howard Robinson (Perception [1994], IX.3) | |
| A reaction: I would have thought the problem was that 'matter is solidity' turns out on analysis to be a tautology. We have a handful of nearly synonymous words for matter and our experiences of it, but they boil down to some 'given' thing for which we lack words. |
| 3059 | There is no real motion, only the appearance of it [Melissus, by Diog. Laertius] |
| Full Idea: There is no such thing as real motion, but there only appears to be such. | |
| From: report of Melissus (fragments/reports [c.443 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.4.3 |
| 5100 | The void is not required for change, because a plenum can alter in quality [Aristotle on Melissus] |
| Full Idea: There is no need for void to be the cause of all change, because it is perfectly possible for a plenum to alter qualitatively (which is something Melissus overlooked). | |
| From: comment on Melissus (fragments/reports [c.443 BCE]) by Aristotle - Physics 214a27 | |
| A reaction: In modern physics this presumably gives us fluctuations in a force field. Motion is like a cat being digested by a python. The atomist claim that emptiness is needed if anything is to move still has intuitive appeal. |
| 456 | Nothing could come out of nothing [Melissus] |
| Full Idea: If Nothing existed, in no way could anything come into being out of nothing. | |
| From: Melissus (fragments/reports [c.443 BCE], B1), quoted by (who?) - where? |