103 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. |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 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. |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 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. |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 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)). |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 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? |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 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.... |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 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. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 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. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 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. |
| 2392 | Properties supervene if you can't have one without the other [Chalmers] |
| Full Idea: B-properties supervene on A-properties if no two possible situations are identical with respect to their A-properties while differing in their B-properties. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.1) | |
| A reaction: Personally I would have thought that if this condition is achieved, then we could go on to say B-properties supervene on A because A is causing them. We shouldn't be shy about this. Personally I think the Bs are necessary. |
| 2393 | Logical supervenience is when one set of properties must be accompanied by another set [Chalmers] |
| Full Idea: B-properties logically supervene on A-properties if no two logically possible situations are identical with respect to their A-properties but distinct with respect to their B-properties. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.1) | |
| A reaction: This is the gap into which Chalmers wants to slip zombies. He's wrong. He thinks that because he can imagine Bs without As, that this makes their separation logically possible. No doubt he can imagine a bonfire on the moon. |
| 2394 | Natural supervenience is when one set of properties is always accompanied by another set [Chalmers] |
| Full Idea: B-properties supervene naturally on A-properties if any two naturally possible situations with the same A-properties have the same B-properties. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.1) | |
| A reaction: Since it is hard to imagine a healthy working brain failing to produce consciousness, given the current laws of nature, almost everyone (except extreme dualists) must concede that they are naturally supervenient. I wonder why they are. |
| 2398 | Reduction requires logical supervenience [Chalmers] |
| Full Idea: Reductive explanation requires a logical supervenience relation. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.3) | |
| A reaction: Why can't you say that in another world there are zombies, but in this world the mind is explained by its natural supervenience on the brain (given the current natural laws)? Driving on the left in Britain is explained by current laws. |
| 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. |
| 16048 | Physicalism says in any two physically indiscernible worlds the positive facts are the same [Chalmers, by Bennett,K] |
| Full Idea: Chalmers says that physicalism is true in a world w just in case every positive fact that obtains in w also obtains in any world physically indiscernible from w. | |
| From: report of David J.Chalmers (The Conscious Mind [1996], 2.1) by Karen Bennett - Supervenience | |
| A reaction: [Bennett summarises Chalmers' argument on pp.39-40] Chalmers says negative facts depend on the world's limits, which aren't part of the physical facts of the world. |
| 2401 | All facts are either physical, experiential, laws of nature, second-order final facts, or indexical facts about me [Chalmers] |
| Full Idea: Facts about the world are exhausted by physical facts, conscious experiences, laws of nature, a second-order that's-all fact, and perhaps an indexical fact about my location. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.5) |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 16424 | Strong metaphysical necessity allows fewer possible worlds than logical necessity [Chalmers] |
| Full Idea: The hypothesized modality of 'strong' metaphysical necessity says there are fewer metaphysically possible worlds than there are logically possible worlds, and the a posteriori necessities can stem from factors independent of the semantics of terms. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.4.2) | |
| A reaction: Chalmers sets this up in order to reject it. He notes that it involves a big gap between conceivability and possibility. If a world is logically possible but metaphysically impossible, then it is impossible, surely? |
| 16425 | Metaphysical necessity is a bizarre, brute and inexplicable constraint on possibilities [Chalmers] |
| Full Idea: Strong metaphysical necessities will put constraints on the space of possible worlds that are brute and inexplicable. That's fine for our world, but bizarre for possible worlds. The realm of the possible has no room for such arbitrary constraint. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.4.2) | |
| A reaction: He would say this, given that he wants zombies to be possible, just because he thinks he can conceive of them. Presumably he thinks a raging bonfire with no flames is also possible. His objection here is weak. |
| 16426 | How can we know the metaphysical impossibilities; the a posteriori only concerns this world [Chalmers] |
| Full Idea: If some worlds are metaphysically impossible, it seems that we could never know it. By assumption the information is not available a priori, and a posteriori information only tells us about our world. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.4.2) | |
| A reaction: You need essentialism to reply to this. If you discover the essence of something, you can predict its possibilities. You discover the natures of the powers and dispositions of actuality. |
| 13956 | Kripke is often taken to be challenging a priori insights into necessity [Chalmers] |
| Full Idea: At various points in this book, I use a priori methods to gain insight into necessity; this is the sort of thing that Kripke's account is often taken to challenge. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.4) | |
| A reaction: Chalmers uses his 2-D approach to split off an a priori part from Kripke's a posterior part of our insight into necessity. |
| 13963 | Maybe logical possibility does imply conceivability - by an ideal mind [Chalmers] |
| Full Idea: If we understand conceivability as conceivability-in-principle (by a superbeing?) then it is plausible that logical possibility of a world implies conceivability of the world, so logical possibility of a statement implies its conceivability. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.4) | |
| A reaction: I see nothing incoherent in the possibility that there might be aspects of existence which are utterly inconceivable to any conscious mind. Infinity might be a start, if an 'infinite' mind were impossible. |
| 2407 | One can wrongly imagine two things being non-identical even though they are the same (morning/evening star) [Chalmers] |
| Full Idea: Just because one can imagine that A and B are not identical, it does not follow that A and B are not identical (think of the morning star and the evening star). | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.4.1) |
| 2390 | We attribute beliefs to people in order to explain their behaviour [Chalmers] |
| Full Idea: Belief is something of an explanatory construct: we attribute beliefs to others largely in order to explain their behaviour. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.1.3) |
| 2397 | 'Perception' means either an action or a mental state [Chalmers] |
| Full Idea: 'Perception' can be used to refer either to the act of perceiving, or the internal state that arises as a result. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.2) |
| 2422 | The structure of the retina has already simplified the colour information which hits it [Chalmers] |
| Full Idea: In vision three varieties of cones abstract out information according to the amount of light present in various overlapping wavelength ranges. Immediately, many distinctions present in the original light wave are lost. | |
| From: David J.Chalmers (The Conscious Mind [1996], 3.8.3) |
| 2396 | Reductive explanation is not the be-all and the end-all of explanation [Chalmers] |
| Full Idea: Reductive explanation is not the be-all and the end-all of explanation. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.2) |
| 2426 | Why are minds homogeneous and brains fine-grained? [Chalmers] |
| Full Idea: The 'grain problem' for materialism was raised by Sellars: how could an experience be identical with a vast collection of physiological events, given the homogeneity of the former, and the fine-grainedness of the latter? | |
| From: David J.Chalmers (The Conscious Mind [1996], 3.8.5) | |
| A reaction: An interesting question, but it doesn't sound like a huge problem, given the number of connections in the brain. If the brain were expanded (as Leibniz suggested), the 'grains' might start to appear. We can't propose a 'deceived homunculus' to solve it. |
| 2391 | Can we be aware but not conscious? [Chalmers] |
| Full Idea: Consciousness is always accompanied by awareness, but awareness as I have described it need not be accompanied by consciousness. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.1.5) | |
| A reaction: One should consult Chalmers, but he is stretching the English word 'awareness' rather far. This road leads to saying that thermostats are 'aware', and information is aware of its content, which is probably very wrong indeed. Compare Idea 2415. |
| 2412 | Can we explain behaviour without consciousness? [Chalmers] |
| Full Idea: However the metaphysics of causation turns out, it seems relatively straightforward that a physical explanation of behaviour can be given that neither appeals to nor implies the existence of consciousness. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.5.2) | |
| A reaction: Chalmers needs this to support his idea that zombies are possible, but it strikes me as implausible. I find it inconceivable that our behaviour would be unchanged if we retained 'awareness' but lost consciousness. Try visiting an art gallery. |
| 2386 | Hard Problem: why brains experience things [Chalmers] |
| Full Idea: The Hard Problem is: why is all this brain processing accompanied by an experienced inner life? | |
| From: David J.Chalmers (The Conscious Mind [1996], Intro) | |
| A reaction: The word 'accompanied' is interesting. A very epiphenomenal word! The answer to this neo-dualist question may be: if you do enough complex representational brain processing at high speed, it adds up to some which we call 'experience'. |
| 2416 | What turns awareness into consciousness? [Chalmers] |
| Full Idea: Given the necessity of awareness, any candidate for an underlying law will have the form "Awareness plus something gives rise to consciousness" (…but simplicity suggests leaving out the 'something'). | |
| From: David J.Chalmers (The Conscious Mind [1996], 3.6.5) | |
| A reaction: You can't leave out the 'something' if you think awareness without consciousness is possible. The phenomenon of blindsight suggests that a whole extra brain area must come into play to produce the consciousness. It may not have a distinct ontology. |
| 2423 | Going down the scale, where would consciousness vanish? [Chalmers] |
| Full Idea: Moving down the scale from lizards to slugs, there doesn't seem much reason to suppose that phenomenology should wink out while a reasonably complex perceptual psychology persists….and if you move on down to thermostats, where would it wink out? | |
| From: David J.Chalmers (The Conscious Mind [1996], 3.8.4) | |
| A reaction: This doesn't seem much of an argument, particularly if its conclusion is that there is phenomenology in thermostats. When day changes into night, where does it 'wink out'? Are we to conclude that night doesn't exist, or that day doesn't exist? |
| 2403 | Nothing in physics even suggests consciousness [Chalmers] |
| Full Idea: Even if we knew every last detail about the physics of the universe, that information would not lead us to postulate the existence of conscious experience. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.3.1.3) | |
| A reaction: I find this a very strange claim. Given that the biggest gap in our physical knowledge is that concerning the brain and consciousness, Chalmer is no position to say this. Why shouldn't a physical revelation suddenly make consciousness inevitable? |
| 2400 | Is intentionality just causal connections? [Chalmers] |
| Full Idea: Intentional properties should be analyzable in terms of causal connections to behaviour and the environment….so there is no separate ontological problem of intentionality. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.5) | |
| A reaction: There could only be no ontological problem if intentional states were purely physical. Everything is made of something (I presume). |
| 2389 | Sometimes we don't notice our pains [Chalmers] |
| Full Idea: What of the fact that we speak of pains that last for a day, even though there are times that they are not conscious? | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.1.3) | |
| A reaction: This is hardly proof that there are non-conscious pains. Otherwise we might say we have a pain even after it has left us for good (because it might return), which seems daft. Not a crucial issue. The word 'pain' has two uses… |
| 2419 | Why should qualia fade during silicon replacement? [Chalmers] |
| Full Idea: If parts of the brain are gradually replaced, perhaps by silicon chips, ...the most reasonable hypothesis is that qualia do not fade at all. | |
| From: David J.Chalmers (The Conscious Mind [1996], 3.7.3) | |
| A reaction: As it stands this could either assert dualism or functionalism. Personally I think the most reasonable hypothesis is that qualia would fade. Chalmers needs more imagination (or less?). What is it like to experience Alzheimer's Disease? |
| 2402 | It seems possible to invert qualia [Chalmers] |
| Full Idea: It seems entirely coherent that experiences could be inverted while physical structure is duplicated exactly. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.3.1.2) | |
| A reaction: Strange how what seems 'entirely coherent' to a leading philosopher strikes me as totally incoherent. I would have thought it was only coherent to a dualist. I don't believe God makes the physics on Thursday, and adds experiences on Friday. |
| 2415 | In blindsight both qualia and intentionality are missing [Chalmers] |
| Full Idea: In blindsight, the information does not qualify as directly available for global control, and subjects are not truly aware of the information. The lack of experience corresponds directly to a lack of awareness. | |
| From: David J.Chalmers (The Conscious Mind [1996], 3.6.3) | |
| A reaction: Blindsight patients give correct answers about objects in their visual field, and you need 'global control' to speak the truth, even if you lack confidence in what you are saying. Philosophers should not be frightened of blindsight. Cf Idea 2391. |
| 2414 | When distracted we can totally misjudge our own experiences [Chalmers] |
| Full Idea: If one is distracted one may make judgements about one's experiences that are quite false. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.5.5) | |
| A reaction: Of course, when one is distracted one can make mistakes about anything. This does imply that if there is indeed infallible knowledge to be had from introspection, it will at least require full concentration to achieve it. Cf Idea 8883. |
| 2409 | Maybe dualist interaction is possible at the quantum level? [Chalmers] |
| Full Idea: The only form of interactionist dualism that has seemed even remotely tenable in the contemporary picture is one that exploits certain properties of quantum mechanics. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.4.4) | |
| A reaction: I think he is bluffing. No doubt quantum mechanics offers many intriguing possibilities, such as the interaction of many worlds within the mind, but I am not aware that anything non-physical is ever postulated. Physicists don't deal in the non-physical. |
| 2411 | Supervenience makes interaction laws possible [Chalmers] |
| Full Idea: There is an objection to dualism that it cannot explain how the physical and the nonphysical interact, but the answer is simple on a natural supervenience framework - they interact by virtue of psychophysical laws (…which are as eternal as physics). | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.4.6) | |
| A reaction: There are different sorts of laws. What Chalmers is hoping for would be a mere regularity, like the connection of cancer to smoking, but the objection is that the discovery of causal mechanisms, to give truly explanatory laws, is simply impossible. |
| 2424 | It is odd if experience is a very recent development [Chalmers] |
| Full Idea: It would be odd for a fundamental property like experience to be instantiated for the first time only relatively late in the history of the universe, and even then only in occasional complex systems. | |
| From: David J.Chalmers (The Conscious Mind [1996], 3.8.4) | |
| A reaction: The assumption of this remark is that experience is 'fundamental', which seems to claim that it is a separate ontological category. Maybe, but experience doesn't seem to be a thing. 'Process' seems a better term, and that is not a novelty in the universe. |
| 2413 | If I can have a zombie twin, my own behaviour doesn't need consciousness [Chalmers] |
| Full Idea: The explanation of my zombie twin's claims does not depend on consciousness, as there is none in his world. It follows that the explanation of my claims is also independent of the existence of consciousness. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.5.2) | |
| A reaction: Epiphenomenalism says my accounts of my consciousness are NOT because of my consciousness (which seems daft). Chalmers here gives a very good reason why we should not be a friend of philosophical zombies. |
| 2417 | Does consciousness arise from fine-grained non-reductive functional organisation? [Chalmers] |
| Full Idea: I claim that conscious experience arises from fine-grained functional organisation….. we might call it 'non-reductive functionalism'. | |
| From: David J.Chalmers (The Conscious Mind [1996], 3.7.1) | |
| A reaction: This is Chalmers' final position. If consciousness is 'emergent' and cannot be reduced, what has fine-grained got to do with it? I take 'fine-grained' to be a hint at why the brain becomes conscious. Fine-grained functions cause something. |
| 2428 | Maybe the whole Chinese Room understands Chinese, though the person doesn't [Chalmers] |
| Full Idea: Opponents typically reply to Searle's argument by conceding that the person in the room does not understand Chinese, and arguing that the understanding should instead be attributed to the system consisting of the person and the pieces of paper. | |
| From: David J.Chalmers (The Conscious Mind [1996], 4.9.4) | |
| A reaction: Searle himself spotted this reply. It seems plausible to say that a book contains 'understanding', so the translation dictionary may have it. A good Room would cope with surprise questions. |
| 2418 | The Chinese Mind doesn't seem conscious, but then nor do brains from outside [Chalmers] |
| Full Idea: While it may be intuitively implausible that Block's 'mind' made of the population of China would give rise to conscious experience, it is equally intuitively implausible that a brain should give rise to experience. | |
| From: David J.Chalmers (The Conscious Mind [1996], 3.7.2) | |
| A reaction: This sounds like good support for functionalism, but I am more inclined to see it as a critique of 'intuition' as a route to truth where minds are concerned. Intuition isn't designed for that sort of work. |
| 2406 | H2O causes liquidity, but no one is a dualist about that [Chalmers] |
| Full Idea: Searle argues that H2O causes liquidity, but no one is a dualist about liquidity. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.4.1) | |
| A reaction: Good! |
| 2405 | Perhaps consciousness is physically based, but not logically required by that base [Chalmers] |
| Full Idea: It remains plausible that consciousness arises from a physical basis, even though it is not entailed by that basis. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.4.1) | |
| A reaction: Personally I find this totally implausible. Since every other property or process in the known universe seems to be entailed by its physical basis, I don't expect the mind to be an exception. |
| 2395 | Zombies imply natural but not logical supervenience [Chalmers] |
| Full Idea: It seems logically possible that a creature physically identical to a conscious creature might have no conscious experiences (a zombie)…so conscious experience supervenes naturally but not logically on the physical. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.1) | |
| A reaction: "It seems possible" isn't much of an argument. This claim by Chalmers has been a great incentive to reassess what is or isn't possible. Can a brain lack consciousness? Can a tree fall over silently? Can cyanide stop poisoning us? |
| 9318 | Phenomenal consciousness is fundamental, with no possible nonphenomenal explanation [Chalmers, by Kriegel/Williford] |
| Full Idea: In Chalmers's non-reductive theory, phenomenal consciousness is treated as a fundamental feature of the world, that cannot be explained in nonphenomenal terms. Theory is still possible, in the regularities of interaction. | |
| From: report of David J.Chalmers (The Conscious Mind [1996]) by U Kriegel / K Williford - Intro to 'Self-Representational Consciousness' n2 | |
| A reaction: I can't make much sense of this view without a backing of panpsychism. How could a 'fundamental' feature of reality only begin to appear when life evolves on one particular planet? But 'panpsychism' is a warning of big misunderstandings. See Idea 2424. |
| 2404 | Nothing external shows whether a mouse is conscious [Chalmers] |
| Full Idea: It is consistent with the physical facts about a mouse that it has conscious experiences, and it is consistent with the physical facts that it does not. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.3.1.4) | |
| A reaction: No. It is consistent with our KNOWLEDGE of a mouse that it may or may not be conscious. I take this to be the key error of Chalmers, which led him to the mistaken idea that zombies are possible. The usual confusion of ontology and epistemology…. |
| 2429 | Temperature (etc.) is agreed to be reducible, but it is multiply realisable [Chalmers] |
| Full Idea: Many physical phenomena that are often taken to be paradigms of reducibility (e.g. temperature) are in fact multiply realizable. | |
| From: David J.Chalmers (The Conscious Mind [1996], n 2.20) | |
| A reaction: So multiple realisability isn't such a big problem for physicalism. I take it, though, that all hot things have some physical type of event in common (a level of molecular energy). Finding the level of commonality is the challenge. |
| 18403 | Indexicals may not be objective, but they are a fact about the world as I see it [Chalmers] |
| Full Idea: Even if the indexical is not an objective fact about the world, it is a fact about the world as I find it, and it is the world as I find it that needs explanation. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.5) | |
| A reaction: Chalmers treats them as important, whereas the way he expresses it could make them eliminable, if the world seen by him is eliminable. |
| 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). |
| 14708 | Rationalist 2D semantics posits necessary relations between meaning, apriority, and possibility [Chalmers, by Schroeter] |
| Full Idea: Chalmers seeks a rationalist interpretation of the 2D framework, situated in the tradition which posits a golden triangle of necessary constitutive relations between meaning, apriority, and possibility. | |
| From: report of David J.Chalmers (The Conscious Mind [1996]) by Laura Schroeter - Two-Dimensional Semantics 2.3.1 | |
| A reaction: The first prize of the project is to get some sort of apriori knowledge about these crucial relations. I suppose the superduper prize is to get apriori knowledge of the possibilities of the world, but I wouldn't hold your breath waiting for that. |
| 13958 | The 'primary intension' is non-empirical, and fixes extensions based on the actual-world reference [Chalmers] |
| Full Idea: The 'primary intension' of a concept is a function from worlds to extensions reflecting the way the actual-world reference is fixed, ...which is independent of empirical factors. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.4) | |
| A reaction: This bit is a priori because the concept picks out something, no matter what its essence turns out to be. I take it to be a priori because it is stipulative. |
| 2399 | Meaning has split into primary ("watery stuff"), and secondary counterfactual meaning ("H2O") [Chalmers] |
| Full Idea: The single Fregean intension has fragmented into two: a primary intension ("watery stuff") that fixes reference in the actual world, and a secondary intension ("H2O") that picks out reference in counterfactual possible worlds. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.4) | |
| A reaction: No one actually performs this schizoid double operation, so this is theory disconnected from life. What is the role of 'H2O' in the actual world, and 'watery stuff' in the others? |
| 13959 | The 'secondary intension' is determined by rigidifying (as H2O) the 'water' picked out in the actual world [Chalmers] |
| Full Idea: The 'secondary intension' of 'water' picks out the water (H2O) in all worlds. ..It is determined by first evaluating the primary intension at the actual world, and then rigidifying it so that the same sort of thing is picked out in all possible worlds. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.4) | |
| A reaction: No wonder Soames calls 2-D semantics 'Byzantine'. If we don't actually do this psychologically, what exactly is Chalmers describing? Is this revisionary semantics - i.e. how we ought to do it if we want to talk about the world properly? |
| 13957 | Primary and secondary intensions are the a priori (actual) and a posteriori (counterfactual) aspects of meaning [Chalmers] |
| Full Idea: Primary intension picks out a referent in a world considered as actual; secondary considers it as counterfactual. ...(62) We can think of the primary and secondary intensions as the a priori and a posteriori aspects of meaning, respectively. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.4) | |
| A reaction: Primary intension is a priori because, it seems, it is stipulative ('water' means 'the watery stuff'), whereas the secondary intension (in counterfactual worlds) is empirical ('water' is used to refer to H2O/XYZ). We get internalism and externalism. |
| 13961 | We have 'primary' truth-conditions for the actual world, and derived 'secondary' ones for counterfactual worlds [Chalmers] |
| Full Idea: 'Primary' truth-conditions tell us how the actual world has to be for an utterance of the statement to be true in that world; ....'secondary' truth-conditions give the truth-value in counterfactual worlds, given that the actual world turned out some way. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.4) | |
| A reaction: This is the reinterpretation of the truth-conditions account in terms of two-dimensional semantics. My first reaction is not very positive. Why can't we fix our references in counterfactual worlds, and then apply them to the actual (like inventions)? |
| 13962 | Two-dimensional semantics gives a 'primary' and 'secondary' proposition for each statement [Chalmers] |
| Full Idea: If we see a proposition as a function from possible worlds to truth-values, then the two sets of truth-conditions yield two propositions associated with any statement. A 'primary' for those which express a truth, and 'secondary' for counterfactual truth. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.4) | |
| A reaction: This is where 2-D semantics becomes increasingly 'Byzantine'. Intuition and introspection don't seem to offer me two different propositions for every sentence I utter. I can't see this theory catching on, even if it is technically beautiful. |
| 13960 | In two-dimensional semantics we have two aspects to truth in virtue of meaning [Chalmers] |
| Full Idea: Both the 'primary' and 'secondary' intension qualify as truths in virtue of meaning; they are simply true in virtue of different aspects of meaning. | |
| From: David J.Chalmers (The Conscious Mind [1996], 1.2.4) | |
| A reaction: This is the view of two-dimensional semantics, which has split Fregean sense into an a priori and an a posterior part. Chalmers is trying to hang onto the idea that we might see necessity as largely analytic. |
| 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. |
| 16427 | Presumably God can do anything which is logically possible [Chalmers] |
| Full Idea: Presumably it is in God's powers, when creating the world, to do anything that is logically possible. | |
| From: David J.Chalmers (The Conscious Mind [1996], 2.4.2) | |
| A reaction: I don't really understand why anyone would say that the only constraint on God is logic. Presumably no logic is breached if God places in object simultaneously in two spacetime locations, but it would be an impressive achievement. |