63 ideas
| 11147 | Naturalistic philosophers oppose analysis, preferring explanation to a priori intuition [Margolis/Laurence] |
| Full Idea: Philosophers who oppose conceptual analysis identify their approach as being 'naturalistic'. Philosophy is supposed to be continuous with science, and philosophical theories are to be defended on explanatory grounds, not by a priori intuitions. | |
| From: E Margolis/S Laurence (Concepts [2009], 5.2) | |
| A reaction: [They cite Papineau 1993, Devitt 1996 aand Kornblith 2002] I think there is a happy compromise here. I agree that any philosophical knowledge should be continuous with science, but we shouldn't prejudge how the analytic branch of science is done. |
| 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. |
| 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. |
| 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. |
| 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... |
| 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. |
| 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). |
| 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). |
| 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. |
| 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. |
| 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. |
| 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. |
| 11141 | Modern empiricism tends to emphasise psychological connections, not semantic relations [Margolis/Laurence] |
| Full Idea: A growing number of philosophers are attracted to modified forms of empiricism, emphasizing psychological relations between the conceptual system and perceptual and motor states, not semantic relations. | |
| From: E Margolis/S Laurence (Concepts [2009], 3.2) | |
| A reaction: I suddenly spot that this is what I have been drifting towards for some time! The focus is concept formation, where the philosophers need to join forces with the cognitive scientists. |
| 21833 | Research suggest that we overrate conscious experience [Flanagan] |
| Full Idea: The emerging consensus is that we probably overrate the power of conscious experience in our lives. Freud, of course, said the same thing for different reasons. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 3 'Ontology') | |
| A reaction: [He cites Pockett, Banks and Gallagher 2006]. Freud was concerned with big deep secrets, but the modern view concerns ordinary decisions and perceptions. An important idea, which should incline us all to become Nietzscheans. |
| 11142 | Body-type seems to affect a mind's cognition and conceptual scheme [Margolis/Laurence] |
| Full Idea: It is claimed, on the basis of empirical research, that the type of body that an organism has profoundly affects it cognitive operations and the way it conceptualises the world. We can't assume that human minds could inhere in wildly different body types. | |
| From: E Margolis/S Laurence (Concepts [2009], 3.2) | |
| A reaction: Sounds interesting. They cite Lawrence Shapiro 2004. It needs a large effort of imagination to think how a snake or whale or albatross might conceptualise the world, in relation to their bodies. |
| 21834 | Sensations may be identical to brain events, but complex mental events don't seem to be [Flanagan] |
| Full Idea: There is still some hope for something like identity theory for sensations. But almost no one believes that strict identity theory will work for more complex mental states. Strict identity is stronger than type neurophysicalism. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 3 'Ontology') | |
| A reaction: It is so hard to express the problem. What needs to be explained? How can one bunch of neurons represent many different things? It's not like computing. That just transfers the data to brains, where the puzzling stuff happens. |
| 11121 | Language of thought has subject/predicate form and includes logical devices [Margolis/Laurence] |
| Full Idea: The language of thought is taken to have subject/predicate form and include logical devices, such as quantifiers and variables. | |
| From: E Margolis/S Laurence (Concepts [2009], 1.1) |
| 11120 | Concepts are either representations, or abilities, or Fregean senses [Margolis/Laurence] |
| Full Idea: The three main options for the ontological status of concepts are to identify them with mental representations, or with abilities, or with Fregean senses. | |
| From: E Margolis/S Laurence (Concepts [2009], 1) |
| 11122 | A computer may have propositional attitudes without representations [Margolis/Laurence] |
| Full Idea: It may be possible to have propositional attitudes without having the mental representations tokened in one's head. ...We may say a chess-playing computer thinks it should develop its queen early, though we know it has no representation with that content. | |
| From: E Margolis/S Laurence (Concepts [2009], 1.1) | |
| A reaction: [Thye cite Dennett - who talks of the 'intentional stance'] It is, of course, a moot point whether we would attribute a propositional attitude (such as belief) to a machine once we knew that it wasn't representing the relevant concepts. |
| 11124 | Do mental representations just lead to a vicious regress of explanations [Margolis/Laurence] |
| Full Idea: A standard criticism is that the mental representation view of concepts creates just another item whose significance bears explaining. Either we have a vicious regress, or we might as well explain external language directly. | |
| From: E Margolis/S Laurence (Concepts [2009], 1.2) | |
| A reaction: [They cite Dummett, with Wittgenstein in the background] I don't agree, because I think that explanation of concepts only stops when it dovetails into biology. |
| 11123 | Maybe the concept CAT is just the ability to discriminate and infer about cats [Margolis/Laurence] |
| Full Idea: The view that concepts are abilities (e.g. found in Brandom, Dummett and Millikan) would say that the concept CAT amounts to the ability to discriminate cats from non-cats and to draw certain inferences about cats. | |
| From: E Margolis/S Laurence (Concepts [2009], 1.2) | |
| A reaction: Feels wrong. The concept is what makes these abilities possible, but it seems rather behaviourist to identify the concept with what is enabled by the concept. You might understand 'cat', but fail to recognise your first cat (though you might suspect it). |
| 11125 | The abilities view cannot explain the productivity of thought, or mental processes [Margolis/Laurence] |
| Full Idea: The abilities view of concepts, by its rejection of mental representation, is ill-equipped to explain the productivity of thought; and it can say little about mental processes. | |
| From: E Margolis/S Laurence (Concepts [2009], 1.2) | |
| A reaction: The latter point arises from its behaviouristic character, which just gives us a black box with some output of abilities. In avoiding a possible regress, it offers no explanation at all. |
| 11140 | Concept-structure explains typicality, categories, development, reference and composition [Margolis/Laurence] |
| Full Idea: The structures of concepts are invoked to explain typicality effects, reflective categorization, cognitive development, reference determination, and compositionality. | |
| From: E Margolis/S Laurence (Concepts [2009], 2.5) |
| 11128 | Classically, concepts give necessary and sufficient conditions for falling under them [Margolis/Laurence] |
| Full Idea: The classical theory is that a concept has a definitional structure in that it is composed of simpler concepts that express necessary and sufficient conditions for falling under the concept, the stock example being unmarried and a man for 'bachelor'. | |
| From: E Margolis/S Laurence (Concepts [2009], 2.1) | |
| A reaction: This is the background idea to philosophy as analysis, and it makes concepts essentially referential, in that they are defined by their ability to pick things out. There must be some degree of truth in the theory. |
| 11130 | Typicality challenges the classical view; we see better fruit-prototypes in apples than in plums [Margolis/Laurence] |
| Full Idea: The classical view is challenged by the discovery that certain categories are taken to be more typical, with typicality widely correlating with other data. Apples are judged to be more typical of (and have more common features with) fruit than plums are. | |
| From: E Margolis/S Laurence (Concepts [2009], 2.1) | |
| A reaction: This discovery that people use prototypes in thinking has been the biggest idea to ever hit the philosophy of concepts, and simply cannot be ignored (as long as the research keeps reinforcing it, which I believe it does). The classical view might adapt. |
| 11129 | The classical theory explains acquisition, categorization and reference [Margolis/Laurence] |
| Full Idea: The appeal of the classical theory of concepts is that it offers unified treatments of concept acquisition (assembling constituents), categorization (check constituents against target), and reference determination (whether they apply). | |
| From: E Margolis/S Laurence (Concepts [2009], 2.1) | |
| A reaction: [See Idea 11128 for the theory] As so often, I find myself in sympathy with the traditional view which has been relegated to ignominy by our wonderful modern philosophers. |
| 11131 | It may be that our concepts (such as 'knowledge') have no definitional structure [Margolis/Laurence] |
| Full Idea: In the light of problems such as the definition of knowledge, many philosophers now take seriously the possibility that our concepts lack definitional structure. | |
| From: E Margolis/S Laurence (Concepts [2009], 2.1) | |
| A reaction: This challenges the classical view, that there are precise conditions for each concept. That view would obviously be in difficulties with atomic concepts, so our account of those might be applied all the way up. |
| 11132 | The prototype theory is probabilistic, picking something out if it has sufficient of the properties [Margolis/Laurence] |
| Full Idea: In the prototype theory of concepts, a lexical concept has probabilistic structure in that something falls under it if it satisfies a sufficient number of properties encoded by the constituents. It originates in Wittgenstein's 'family resemblance'. | |
| From: E Margolis/S Laurence (Concepts [2009], 2.2) | |
| A reaction: It would seem unlikely to be a matter of the 'number' of properties, and would have to involve some notion of what was essential to the prototype. |
| 11133 | Prototype theory categorises by computing the number of shared constituents [Margolis/Laurence] |
| Full Idea: On the prototype theory, categorization is to be understood as a similarity comparison process, where similarity is computed as a function of the number of constituents that two concepts hold in common. | |
| From: E Margolis/S Laurence (Concepts [2009], 2.2) | |
| A reaction: Again it strikes me that 'computing' similarity by mere 'number' of shared constituents won't do, as there is a prior judgement about which constituents really matter, or are essential. That may even be hard-wired. |
| 11134 | People don't just categorise by apparent similarities [Margolis/Laurence] |
| Full Idea: When it comes to more reflexive judgements, people go beyond the outcome of a similarity comparison. Even children say that a dog surgically altered to look like a raccoon is still a dog. | |
| From: E Margolis/S Laurence (Concepts [2009], 2.2) | |
| A reaction: We can defend the theory by not underestimating people so much. Most categorisation is done on superficial grounds, but even children know there may be hidden similarities (behind the mask, under the bonnet) which are more important. |
| 11135 | Complex concepts have emergent properties not in the ingredient prototypes [Margolis/Laurence] |
| Full Idea: An objection to the prototype view concerns compositionality. A complex concept often has emergent properties, as when it seems that 'pet fish' encodes for brightly coloured, which has no basis in the prototypes for 'pet' or 'fish'. | |
| From: E Margolis/S Laurence (Concepts [2009], 2.2) | |
| A reaction: I would take 'pet fish' to work like a database query. 'Fish' has a very vague prototype, and then 'pet fish' narrows the search to fish which are appropriate to be pets. We might say that the prototype is refined, or the Mk 2 prototype appears. |
| 11136 | Many complex concepts obviously have no prototype [Margolis/Laurence] |
| Full Idea: Many patently complex concepts don't even have a prototype structure, such as 'Chairs that were purchased on a Wednesday'. | |
| From: E Margolis/S Laurence (Concepts [2009], 2.2) | |
| A reaction: [The example seems to be from Fodor] I disagree. If we accept the notion of 'refining' the prototype (see Idea 11135), then the compositionality of the expression will produce a genuine but very unusual prototype. |
| 11137 | The theory theory of concepts says they are parts of theories, defined by their roles [Margolis/Laurence] |
| Full Idea: The theory theory of concepts says that terms are related as in a scientific theory, and that categorization resembles theorising. It is generally assumed that scientific terms are interdefined so that content is determined by its role in the theory. | |
| From: E Margolis/S Laurence (Concepts [2009], 2.3) | |
| A reaction: I never like this sort of account. What are the characteristics of the thing which enable it to fulfil its role? You haven't defined a car when you've said it gets you from A to B. |
| 11138 | The theory theory is holistic, so how can people have identical concepts? [Margolis/Laurence] |
| Full Idea: A problem with the theory theory of concepts is that it is holistic, saying a concept is determined by its role, not by its constituents. It then seems difficult for different people to possess the same concepts (or even the same person, over time). | |
| From: E Margolis/S Laurence (Concepts [2009], 2.3) | |
| A reaction: This seems a good objection to any holistic account of concepts or meaning - spotted by Plato in motivating his theory of Forms, to give the necessary stability to communication. |
| 11139 | Maybe concepts have no structure, and determined by relations to the world, not to other concepts [Margolis/Laurence] |
| Full Idea: According to conceptual atomism, lexical concepts have no semantic structure, and the content of a concept isn't determined by its relation to other concepts but by its relations to the world. | |
| From: E Margolis/S Laurence (Concepts [2009], 2.4) | |
| A reaction: [They cite Fodor 1998 and Millikan 2000] I like the sound of that, because I take the creation of concepts to be (in the first instance) a response to the world, not a response to other concepts. |
| 11146 | People can formulate new concepts which are only named later [Margolis/Laurence] |
| Full Idea: People seem to be able to formulate novel concepts which are left to be named later; the concept comes first, the name second. | |
| From: E Margolis/S Laurence (Concepts [2009], 4.2) | |
| A reaction: [This seems to have empirical support, and he cites Pinker 1994] I do not find this remotely surprising, since I presume that human concepts are a continuous kind with animal concepts, including non-conscious concepts (why not?). |
| 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. |
| 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. |
| 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). |
| 21837 | Morality is normative because it identifies best practices among the normal practices [Flanagan] |
| Full Idea: Morality is 'normative' in the sense that it consists of the extraction of ''good' or 'excellent' practices from common practices. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 4 'Naturalism') |
| 21830 | For Darwinians, altruism is either contracts or genetics [Flanagan] |
| Full Idea: Two explanations came forward in the neo-Darwinian synthesis. Altruism is either 1) person-based reciprocal altruism, or 2) gene-based kin altruism. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 2 'Darwin') | |
| A reaction: Flanagan obviously thinks there is also 'genuine psychological atruism'. Presumably we don't explain mathematics or music or the desire to travel as either contracts or genetics, so we have other explanations available. |
| 21835 | We need Eudaimonics - the empirical study of how we should flourish [Flanagan] |
| Full Idea: It would be nice if I could advance the case for Eudaimonics - empirical enquiry into the nature, causes, and constituents of flourishing, …and the case for some ways of living and being as better than others. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 4 'Normative') | |
| A reaction: Things seem to be moving in that direction. Lots of statistics about happiness have been appearing. |
| 21831 | Alienation is not finding what one wants, or being unable to achieve it [Flanagan] |
| Full Idea: What Marx called 'alienation' is the widespread condition of not being able to discover what one wants, or not being remotely positioned to achieve. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 2 'Expanding') | |
| A reaction: I took alienation to concern people's relationship to the means of production in their trade. On Flanagan's definition I would expect almost everyone aged under 20 to count as alienated. |
| 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. |
| 21832 | Buddhists reject God and the self, and accept suffering as key, and liberation through wisdom [Flanagan] |
| Full Idea: Buddhism rejected the idea of a creator God, and the unchanging self [atman]. They accept the appearance-reality distinction, reward for virtue [karma], suffering defining our predicament, and that liberation [nirvana] is possible through wisdom. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 3 'Buddhism') | |
| A reaction: [Compressed] Flanagan is an analytic philosopher and a practising Buddhist. Looking at a happiness map today which shows Europeans largely happy, and Africans largely miserable, I can see why they thought suffering was basic. |