68 ideas
| 6891 | Quine's naturalistic and empirical view is based entirely on first-order logic and set theory [Quine, by Mautner] |
| Full Idea: Quine has aimed at a naturalistic and empirical world-view, and claims that first-order logic and set theory provide a framework sufficient for the articulation of our knowledge of the world. | |
| From: report of Willard Quine (Word and Object [1960]) by Thomas Mautner - Penguin Dictionary of Philosophy p.465 | |
| A reaction: Consequently he is fairly eliminativist about meaning and mental states, and does without universals in his metaphysics. An impressively puritanical enterprise, taking Ockham's Razor to the limit, but I find it hard to swallow. |
| 6310 | Enquiry needs a conceptual scheme, so we should retain the best available [Quine] |
| Full Idea: No enquiry is possible without some conceptual scheme, so we may as well retain and use the best one we know. | |
| From: Willard Quine (Word and Object [1960], §01) | |
| A reaction: This remark leads to Davidson's splendid paper 'On the Very Idea of a Conceptual Scheme'. Quine's remark raises the question of how we know which conceptual scheme is 'best'. |
| 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. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 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. |
| 12798 | Plurals can in principle be paraphrased away altogether [Quine] |
| Full Idea: By certain standardizations of phrasing the contexts that call for plurals can in principle be paraphrased away altogether. | |
| From: Willard Quine (Word and Object [1960], §19) | |
| A reaction: Laycock, who quotes this, calls it 'unduly optimistic', but I presume that it was the standard view of plural reference until Boolos raised the subject. |
| 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. |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 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)). |
| 17905 | Any progression will do nicely for numbers; they can all then be used to measure multiplicity [Quine] |
| Full Idea: The condition on an explication of number can be put succinctly: any progression will do nicely. Russell once held that one must also be able to measure multiplicity, but this was a mistake; any progression can be fitted to that further condition. | |
| From: Willard Quine (Word and Object [1960], §54) | |
| A reaction: [compressed] This is the strongest possible statement that the numbers are the ordinals, and the Peano Axioms will define them. The Fregean view that cardinality comes first is redundant. |
| 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. |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 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? |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 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... |
| 9556 | Nearly all of mathematics has to quantify over abstract objects [Quine] |
| Full Idea: Mathematics, except for very trivial portions such as very elementary arithmetic, is irredeemably committed to quantification over abstract objects. | |
| From: Willard Quine (Word and Object [1960], §55) | |
| A reaction: Personally I would say that we are no more committed to such things than actors in 'The Tempest' are committed to the existence of Prospero and Caliban (which is quite a strong commitment, actually). |
| 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. |
| 16462 | The quest for ultimate categories is the quest for a simple clear pattern of notation [Quine] |
| Full Idea: The quest of a simplest, clearest overall pattern of canonical notation is not to be distinguished from a quest of ultimate categories, a limning of the most general traits of reality. | |
| From: Willard Quine (Word and Object [1960], §33) | |
| A reaction: I won't disagree, as long as we recognise that reality calls the shots, not the notation, and that even animals must have some sort of system of categories, achieved without 'notation'. |
| 15723 | Either dispositions rest on structures, or we keep saying 'all things being equal' [Quine] |
| Full Idea: The further a disposition is from those that can confidently be pinned on molecular structure or something comparably firm, the more our talk of it tends to depend on a vague factor of 'caeteris paribus' | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: I approve of this. It is precisely the point of scientific essentialism, I take it. We are faced with innumerable uncertain dispositions, but once the underlying mechanisms are known, their role in nature becomes fairly precise. |
| 15490 | Explain unmanifested dispositions as structural similarities to objects which have manifested them [Quine, by Martin,CB] |
| Full Idea: Quine claims that an unmanifested disposition is explicable in terms of an object having a structure similar to a structure of an object that has manifested the supposed disposition. | |
| From: report of Willard Quine (Word and Object [1960], §46) by C.B. Martin - The Mind in Nature 07.4 | |
| A reaction: This is probably the best account available for the firm empiricist who denies modal features in the actual world. In other words, a disposition is the result of an induction, not a conditional statement. |
| 8504 | Quine aims to deal with properties by the use of eternal open sentences, or classes [Quine, by Devitt] |
| Full Idea: Quine is not an 'ostrich', because his strategy for dealing with property sentences is clear enough: all talk of attributes is to be dispensed with in favour of talk of eternal open sentences or talk of classes. | |
| From: report of Willard Quine (Word and Object [1960], §43) by Michael Devitt - 'Ostrich Nominalism' or 'Mirage Realism'? p.100 | |
| A reaction: [See p.209 'Word and Object'] The proposal seems to be that a property like being-human (a category) would be dealt with by classes, and qualitative properties would be dealt with simply as predicates. I like the split, and the first half, not the second. |
| 8464 | Physical objects in space-time are just events or processes, no matter how disconnected [Quine] |
| Full Idea: Physical objects, conceived four-dimensionally in space-time, are not to be distinguished from events or concrete processes. Each comprises simply the content, however heterogeneous, of a portion of space-time, however disconnected and gerrymandered. | |
| From: Willard Quine (Word and Object [1960], §36) | |
| A reaction: I very much like the suggestion that objects should be thought of as 'processes', but I dislike the idea that they can be gerrymandered. This is a refusal to cut nature at the joints (Idea 7953), which I find very counterintuitive. |
| 7924 | The notion of a physical object is by far the most useful one for science [Quine] |
| Full Idea: In a contest of sheer systematic utility to science, the notion of physical object still leads the field. | |
| From: Willard Quine (Word and Object [1960], §48) | |
| A reaction: A delightful circumlocution from someone who seems terrified to assert that there just are objects. Not that I object to Quine's caution. It would be disturbing if his researches had revealed that we could manage without objects. But compare Idea 6124. |
| 8482 | Mathematicians must be rational but not two-legged, cyclists the opposite. So a mathematical cyclist? [Quine] |
| Full Idea: Mathematicians are necessarily rational, and not necessarily two-legged; cyclists are the opposite. But what of an individual who counts among his eccentricities both mathematics and cycling? | |
| From: Willard Quine (Word and Object [1960], §41) | |
| A reaction: Quine's view is that the necessity (and essence) depends on how this eccentric is described. If he loses a leg, he must give up cycling; if he loses his rationality, he must give up the mathematics. Quine is wrong. |
| 12136 | Cyclist are not actually essentially two-legged [Brody on Quine] |
| Full Idea: Cyclists are not essentially two-legged (a one-legged cyclist exists, but can't cycle any more), and mathematicians are not essentially rational (as they can lose rationality and continue to exist, though unable to do mathematics). | |
| From: comment on Willard Quine (Word and Object [1960], §41.5) by Baruch Brody - Identity and Essence 5.1 | |
| A reaction: Was Quine thinking of the nominal essence of this person - that 'cyclists' necessarily cylce, and 'mathematicians' necessarily do some maths? It is as bad to confuse 'necessary' with 'essential' as to confuse 'use' with 'mention'. |
| 17594 | We can paraphrase 'x=y' as a sequence of the form 'if Fx then Fy' [Quine] |
| Full Idea: For general terms write 'if Fx then Fy' and vice versa, and 'if Fxz then Fyz'..... The conjunction of all these is coextensive with 'x=y' if any formula constructible from the vocabulary is; and we can adopt that conjunction as our version of identity. | |
| From: Willard Quine (Word and Object [1960], §47) | |
| A reaction: [first half compressed] The main rival views of equality are this and Wiggins (1980:199). Quine concedes that his account implies a modest version of the identity of indiscernibles. Wiggins says identity statements need a sortal. |
| 15725 | Normal conditionals have a truth-value gap when the antecedent is false. [Quine] |
| Full Idea: In its unquantified form 'If p then q' the indicative conditional is perhaps best represented as suffering a truth-value gap whenever its antecedent is false. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: That is, the clear truth-functional reading of the conditional (favoured by Lewis, his pupil) is unacceptable. Quine favours the Edgington line, that we are only interested in situations where the antecedent might be true. |
| 15722 | Conditionals are pointless if the truth value of the antecedent is known [Quine] |
| Full Idea: The ordinary conditional loses its point when the truth value of its antecedent is known. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: A beautifully simple point that reveals a lot about what conditionals are. |
| 15719 | We feign belief in counterfactual antecedents, and assess how convincing the consequent is [Quine] |
| Full Idea: The subjunctive conditional depends, like indirect quotation and more so, on a dramatic projection: we feign belief in the antececent and see how convincing we then find the consequent. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: This seems accurate. It means that we are only interested in when the antecedent is true, and when it is false is irrelevant. |
| 15721 | Counterfactuals are plausible when dispositions are involved, as they imply structures [Quine] |
| Full Idea: The subjunctive conditional is seen at its most respectable in the disposition terms. ...The reason is that they are conceived as built-in, enduring structural traits. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: Surprisingly, this is very sympathetic to a metaphysical view that seems a long way from Quine, since dispositions seem to invite commitment to modal features of reality. But the structural traits are not, of course, modal, in any way! |
| 15724 | Counterfactuals have no place in a strict account of science [Quine] |
| Full Idea: The subjunctive conditional has no place in an austere canonical notation for science - but that ban is less restrictive than would at first appear. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: Idea 15723 shows what he has in mind - that what science aims for is accounts of dispositional mechanisms, which then leave talk of other possible worlds (in Lewis style) as unnecessary. I may be with Quine one this one. |
| 15720 | What stays the same in assessing a counterfactual antecedent depends on context [Quine] |
| Full Idea: The traits to suppose preserved in a counterfactual depend on sympathy for the fabulist's purpose. Compare 'If Caesar were in command, he would use the atom bomb', and 'If Caesar were in command, he would use catapults'. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: This seems to be an important example for the Lewis approach, since you are asked to consider the 'nearest' possible world, but that will depend on context. |
| 4630 | Two theories can be internally consistent and match all the facts, yet be inconsistent with one another [Quine, by Baggini /Fosl] |
| Full Idea: Duhem and Quine have maintained that it may be possible to develop two or more theories that are 1) internally consistent, 2) inconsistent with one another, and 3) perfectly consistent with all the data we can muster. | |
| From: report of Willard Quine (Word and Object [1960]) by J Baggini / PS Fosl - The Philosopher's Toolkit §1.06 | |
| A reaction: Obviously this may be a contingent truth about our theories, but why not presume that this is because we are unable to collect the crucial data (e.g. about prehistoric biology), rather than denigrate the whole concept of a theory, and undermine science? |
| 3131 | Quine expresses the instrumental version of eliminativism [Quine, by Rey] |
| Full Idea: Quine expresses the instrumental version of eliminativism. | |
| From: report of Willard Quine (Word and Object [1960]) by Georges Rey - Contemporary Philosophy of Mind Int.3 |
| 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). |
| 3988 | Indeterminacy of translation also implies indeterminacy in interpreting people's mental states [Dennett on Quine] |
| Full Idea: Quine's thesis of the indeterminacy of radical translation carries all the way in, as the thesis of the indeterminacy of radical interpretation of mental states and processes. | |
| From: comment on Willard Quine (Word and Object [1960]) by Daniel C. Dennett - Daniel Dennett on himself p.239 | |
| A reaction: Strong scepticism seems wrong here. Davidson's account of charity in interpretation, and the role of truth, seems closer. |
| 6311 | The firmer the links between sentences and stimuli, the less translations can diverge [Quine] |
| Full Idea: The firmer the direct links of a sentence with non-verbal stimulation, the less drastically its translations can diverge from one another from manual to manual. | |
| From: Willard Quine (Word and Object [1960], §07) | |
| A reaction: This implies (plausibly) that talk about farming will have fairly determinate translations into foreign languages, but talk of philosophy will not. An interesting case is logic, where we might expect tight translation with little non-verbal stimulation. |
| 6312 | We can never precisely pin down how to translate the native word 'Gavagai' [Quine] |
| Full Idea: There is no evident criterion whereby to strip extraneous effects away and leave just the meaning of 'Gavagai' properly so-called - whatever meaning properly so-called may be. | |
| From: Willard Quine (Word and Object [1960], §09) | |
| A reaction: Quine's famous assertion that translation is ultimately 'indeterminate'. Huge doubts about meaning and language and truth follow from his claim. Personally I think it is rubbish. People become fluent in very foreign languages, and don't have breakdowns. |
| 6313 | Stimulus synonymy of 'Gavagai' and 'Rabbit' does not even guarantee they are coextensive [Quine] |
| Full Idea: Stimulus synonymy of the occasion sentences 'Gavagai' and 'Rabbit' does not even guarantee that 'gavagai' and 'rabbit' are coextensive terms, terms true of the same things. | |
| From: Willard Quine (Word and Object [1960], §12) | |
| A reaction: Since this scepticism eventually seems to result in the reader no longer knowing what they mean themselves by the word 'rabbit', I doubt Quine's claim. Problems after hearing one word of a foreign language disappear after years of residence. |
| 6317 | Dispositions to speech behaviour, and actual speech, are never enough to fix any one translation [Quine] |
| Full Idea: Rival systems of analytical hypotheses can fit the totality of speech behaviour to perfection, and can fit the totality of dispositions to speech behaviour as well, and still specify mutually incompatible translations of countless sentences. | |
| From: Willard Quine (Word and Object [1960], §15) | |
| A reaction: This is Quine's final assertion of indeterminacy, having explored charity, bilingual speakers etc. It seems to me that he is a victim of his underlying anti-realism, which won't allow nature to dictate ways of cutting up the world. |
| 6315 | We should be suspicious of a translation which implies that a people have very strange beliefs [Quine] |
| Full Idea: The more absurd or exotic the beliefs imputed to a people, the more suspicious we are entitled to be of the translations. | |
| From: Willard Quine (Word and Object [1960], §15) | |
| A reaction: Quine is famous for his relativist and indeterminate account of translation, but he gradually works his way towards the common sense which Davidson later brought out into the open. |
| 6314 | Weird translations are always possible, but they improve if we impose our own logic on them [Quine] |
| Full Idea: Wanton translation can make natives sound as queer as one pleases; better translation imposes our logic upon them. | |
| From: Willard Quine (Word and Object [1960], §13) | |
| A reaction: This begins to point towards the principle of charity, on which Davidson is so keen, and even on doubts whether two different conceptual schemes are possible. Personally I think there is only one logic (deep down), and the natives will have it. |
| 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. |