77 ideas
| 9376 | A sentence may simultaneously define a term, and also assert a fact [Boghossian] |
| Full Idea: It doesn't follow from the fact that a given sentence is being used to implicitly define one of its ingredient terms, that it is not a factual statement. 'This stick is a meter long at t' may define an ingredient terms and express something factual. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: This looks like a rather good point, but it is tied in with a difficulty about definition, which is deciding which sentences are using a term, and which ones are defining it. If I say 'this stick in Paris is a meter long', I'm not defining it. |
| 9161 | Maybe reasonableness requires circular justifications - that is one coherentist view [Field,H] |
| Full Idea: It is not out of the question to hold that without circular justifications there is no reasonableness at all. That is the view of a certain kind of coherence theorist. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 2) | |
| A reaction: This nicely captures a gut feeling I have had for a long time. Being now thoroughly converted to coherentism, I am drawn to the idea - like a moth to a flame. But how do we distinguish cuddly circularity from its cruel and vicious cousin? |
| 10825 | The notion of truth is to help us make use of the utterances of others [Field,H] |
| Full Idea: I suspect that the original purpose of the notion of truth was to aid us in utilizing the utterances of others in drawing conclusions about the world,...so we must attend to its social role, and that being in a position to assert something is what counts. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], §5) | |
| A reaction: [Last bit compressed] This sounds excellent. Deflationary and redundancy views are based on a highly individualistic view of utterances and truth, but we need to be much more contextual and pragmatic if we are to get the right story. |
| 10820 | In the early 1930s many philosophers thought truth was not scientific [Field,H] |
| Full Idea: In the early 1930s many philosophers believed that the notion of truth could not be incorporated into a scientific conception of the world. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], §3) | |
| A reaction: This leads on to an account of why Tarski's formal version was so important, and Field emphasises Tarski's physicalist metaphysic. |
| 13499 | Tarski reduced truth to reference or denotation [Field,H, by Hart,WD] |
| Full Idea: Tarski can be viewed as having reduced truth to reference or denotation. | |
| From: report of Hartry Field (Tarski's Theory of Truth [1972]) by William D. Hart - The Evolution of Logic 4 |
| 10818 | Tarski really explained truth in terms of denoting, predicating and satisfied functions [Field,H] |
| Full Idea: A proper account of Tarski's truth definition explains truth in terms of three other semantic notions: what it is for a name to denote something, and for a predicate to apply to something, and for a function symbol to be fulfilled by a pair of things. | |
| From: Hartry Field (Tarski's Theory of Truth [1972]) | |
| A reaction: This is Field's 'T1' version, which is meant to spell out what was really going on in Tarski's account. |
| 10817 | Tarski just reduced truth to some other undefined semantic notions [Field,H] |
| Full Idea: It is normally claimed that Tarski defined truth using no undefined semantic terms, but I argue that he reduced the notion of truth to certain other semantic notions, but did not in any way explicate these other notions. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], §0) |
| 6345 | Minimalism is incoherent, as it implies that truth both is and is not a property [Boghossian, by Horwich] |
| Full Idea: Boghossian argues that minimalism is incoherent because it says truth both is and is not a property; the essence of minimalism is that, unlike traditional theories, truth is not a property, yet properties are needed to explain the theory. | |
| From: report of Paul Boghossian (The Status of Content [1990]) by Paul Horwich - Truth (2nd edn) Post.8 | |
| A reaction: I doubt whether this is really going to work as a demolition, because it seems to me that no philosophers are even remotely clear about what a property is. If properties are defined causally, it is not quite clear how truth would ever be a property. |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| Full Idea: A proof of the consistency of propositional logic was given by Emil Post in 1921. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.2.1) |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| Full Idea: Propositional language is very rudimentary and has limited powers of expression. The only relation between various statements it can handle is that of identity and difference. As are all the same, but Bs can be different from As. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 7 Intro) | |
| A reaction: [second sentence a paraphrase] In predicate logic you could represent two statements as being the same except for one element (an object or predicate or relation or quantifier). |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| Full Idea: Boolean connectives are interpreted as functions on the set {1,0}. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 5.1) | |
| A reaction: 1 and 0 are normally taken to be true (T) and false (F). Thus the functions output various combinations of true and false, which are truth tables. |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| Full Idea: The empty set is mainly a mathematical convenience - defining a set by describing the properties of its members in an involved way, we may not know from the very beginning what its members are. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 1.1) |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| Full Idea: Without the assumption of the empty set, one would often have to take special precautions for the case where a set happened to contain no elements. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 1.1) | |
| A reaction: Compare the introduction of the concept 'zero', where special precautions are therefore required. ...But other special precautions are needed without zero. Either he pays us, or we pay him, or ...er. Intersecting sets need the empty set. |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| Full Idea: Ordinals play the central role in set theory, providing the paradigmatic well-orderings. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
| A reaction: When you draw the big V of the iterative hierarchy of sets (built from successive power sets), the ordinals are marked as a single line up the middle, one ordinal for each level. |
| 9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
| Full Idea: Field commits himself to a Platonic view of mathematics. The theorems of set theory are held to imply or presuppose the existence of things that don't in fact exist. That is why he believes that these theorems are false. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Charles Chihara - A Structural Account of Mathematics 11.1 | |
| A reaction: I am sympathetic to Field, but this sounds wrong. A response that looks appealing is that maths is hypothetical ('if-thenism') - the truth is in the logical consequences, not in the ontological presuppositions. |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| Full Idea: In order to construct precise and valid patterns of arguments one has to determine their 'building blocks'. One has to identify the basic terms, their kinds and means of combination. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History Intro) | |
| A reaction: A deceptively simple and important idea. All explanation requires patterns and levels, and it is the idea of building blocks which makes such things possible. It is right at the centre of our grasp of everything. |
| 10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
| Full Idea: Field defines logical consequence by taking the notion of 'logical possibility' as primitive. Hence q is a consequence of P if the conjunction of the items in P with the negation of q is not possible. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Stewart Shapiro - Philosophy of Mathematics 7.2 | |
| A reaction: The question would then be whether it is plausible to take logical possibility as primitive. Presumably only intuition could support it. But then intuition will equally support natural and metaphysical possibilities. |
| 9375 | Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian] |
| Full Idea: Conventualism is a factualist view: it presupposes that sentences of logic have truth values. It differs from a realist view in its conception of the source of those truth values, not on their existence. I call the denial of truths Non-Factualism. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: It barely seems to count as truth is we say 'p is true because we say so'. It is a truth about an agreement, not a truth about logic. Driving on the left isn't a truth about which side of the road is best. |
| 10819 | Tarski gives us the account of truth needed to build a group of true sentences in a model [Field,H] |
| Full Idea: Model theory must choose the denotations of the primitives so that all of a group of sentences come out true, so we need a theory of how the truth value of a sentence depends on the denotation of its primitive nonlogical parts, which Tarski gives us. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], §1) |
| 10827 | Model theory is unusual in restricting the range of the quantifiers [Field,H] |
| Full Idea: In model theory we are interested in allowing a slightly unusual semantics for quantifiers: we are willing to allow that the quantifier not range over everything. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], n 5) |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| Full Idea: A specification of a domain of objects, and of the rules for interpreting the symbols of a logical language in this domain such that all the theorems of the logical theory are true is said to be a 'model' of the theory. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.1.3) | |
| A reaction: The basic ideas of this emerged 1915-30, but it needed Tarski's account of truth to really get it going. |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| Full Idea: The L-S Theorem is ...a shocking result, since it implies that any consistent formal theory of everything - even about biology, physics, sets or the real numbers - can just as well be understood as being about natural numbers. It says nothing more. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.2) | |
| A reaction: Illuminating. Particularly the point that no theory about the real numbers can say anything more than a theory about the natural numbers. So the natural numbers contain all the truths we can ever express? Eh????? |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| Full Idea: Having such a compact [axiomatic] presentation of a complicated field [such as Euclid's], makes it possible to relate not only to particular theorems but also to the whole field as such. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| Full Idea: Axiomatic systems, their primitive terms and proofs, are purely syntactic, that is, do not presuppose any interpretation. ...[142] They never address the world directly, but address a possible semantic model which formally represents the world. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
| 9226 | If mathematical theories conflict, it may just be that they have different subject matter [Field,H] |
| Full Idea: Unlike logic, in the case of mathematics there may be no genuine conflict between alternative theories: it is natural to think that different theories, if both consistent, are simply about different subjects. | |
| From: Hartry Field (Recent Debates on the A Priori [2005], 7) | |
| A reaction: For this reason Field places logic at the heart of questions about a priori knowledge, rather than mathematics. My intuitions make me doubt his proposal. Given the very simple basis of, say, arithmetic, I would expect all departments to connect. |
| 8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
| Full Idea: Field's nominalist version of science develops a version of Newtonian gravitational theory, where no quantifiers range over mathematical entities, and space-time points and regions play the role of surrogates for real numbers. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Zoltán Gendler Szabó - Nominalism 5.1 | |
| A reaction: This seems to be a very artificial contrivance, but Field has launched a programme for rewriting science so that numbers can be omitted. All of this is Field's rebellion against the Indispensability Argument for mathematics. I sympathise. |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| Full Idea: An ordinal can be defined as a transitive set of transitive sets, or else, as a transitive set totally ordered by set inclusion. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| Full Idea: The collection of ordinals is defined inductively: Basis: the empty set is an ordinal; Ind: for an ordinal x, the union with its singleton is also an ordinal; and any arbitrary (possibly infinite) union of ordinals is an ordinal. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
| A reaction: [symbolism translated into English] Walicki says they are called 'ordinal numbers', but are in fact a set. |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| Full Idea: We can form infinite ordinals by taking unions of ordinals. We can thus form 'limit ordinals', which have no immediate predecessor. ω is the first (the union of all finite ordinals), ω + ω = sω is second, 3ω the third.... | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| Full Idea: There may be several ordinals for the same cardinality. ...Two ordinals can represent different ways of well-ordering the same number (aleph-0) of elements. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
| A reaction: This only applies to infinite ordinals and cardinals. For the finite, the two coincide. In infinite arithmetic the rules are different. |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| Full Idea: Every member of an ordinal is itself an ordinal, and every ordinal is a transitive set (its members are also its subsets; a member of a member of an ordinal is also a member of the ordinal). | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
| 18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
| Full Idea: There are two approaches to axiomatising geometry. The 'metric' approach uses a function which maps a pair of points into the real numbers. The 'synthetic' approach is that of Euclid and Hilbert, which does without real numbers and functions. | |
| From: Hartry Field (Science without Numbers [1980], 5) |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| Full Idea: Since non-Euclidean geometry preserves all Euclid's postulates except the fifth one, all the theorems derived without the use of the fifth postulate remain valid. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| Full Idea: Inductive proof is not guaranteed to work in all cases and, particularly, it depends heavily on the choice of the ordering. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.1.1) | |
| A reaction: There has to be an well-founded ordering for inductive proofs to be possible. |
| 8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
| Full Idea: There is one and only one serious argument for the existence of mathematical entities, and that is the Indispensability Argument of Putnam and Quine. | |
| From: Hartry Field (Science without Numbers [1980], p.5), quoted by Stewart Shapiro - Thinking About Mathematics 9.1 | |
| A reaction: Personally I don't believe (and nor does Field) that this gives a good enough reason to believe in such things. Quine (who likes 'desert landscapes' in ontology) ends up believing that sets are real because of his argument. Not for me. |
| 18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
| Full Idea: The most popular approach of nominalistically inclined philosophers is to try to reinterpret mathematics, so that its terms and quantifiers only make reference to, say, physical objects, or linguistic expressions, or mental constructions. | |
| From: Hartry Field (Science without Numbers [1980], Prelim) | |
| A reaction: I am keen on naturalism and empiricism, but only referring to physical objects is a non-starter. I think I favour constructions, derived from the experience of patterns, and abstracted, idealised and generalised. Field says application is the problem. |
| 10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
| Full Idea: Field argues that to account for the applicability of mathematics, we need to assume little more than the possibility of the mathematics, not its truth. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Stewart Shapiro - Philosophy of Mathematics 7.2 | |
| A reaction: Very persuasive. We can apply chess to real military situations, provided that chess isn't self-contradictory (or even naturally impossible?). |
| 18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
| Full Idea: Facts about geometric laws receive satisfying explanations, by the intrinsic facts about physical space, i.e. those laid down without reference to numbers in Hilbert's axioms. | |
| From: Hartry Field (Science without Numbers [1980], 3) | |
| A reaction: Hilbert's axioms mention points, betweenness, segment-congruence and angle-congruence (Field 25-26). Field cites arithmetic and geometry (as well as Newtonian mechanics) as not being dependent on number. |
| 9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
| Full Idea: Field needs the notion of logical consequence in second-order logic, but (since this is not recursively axiomatizable) this is a semantical notion, which involves the idea of 'true in all models', a set-theoretic idea if there ever was one. | |
| From: comment on Hartry Field (Science without Numbers [1980], Ch.4) by James Robert Brown - Philosophy of Mathematics | |
| A reaction: Brown here summarises a group of critics. Field was arguing for modern nominalism, that actual numbers could (in principle) be written out of the story, as useful fictions. Popper's attempt to dump induction seemed to need induction. |
| 18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
| Full Idea: No clear explanation of the idea that the conclusion was 'implicitly contained in' the premises was ever given, and I do not believe that any clear explanation is possible. | |
| From: Hartry Field (Science without Numbers [1980], 1) |
| 18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
| Full Idea: Abstract entities are useful because we can use them to formulate abstract counterparts of concrete statements. | |
| From: Hartry Field (Science without Numbers [1980], 3) | |
| A reaction: He defends the abstract statements as short cuts. If the concrete statements were 'true', then it seems likely that the abstract counterparts will also be true, which is not what fictionalism claims. |
| 18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
| Full Idea: Mathematics is in a sense empirical, but only in the rather Pickwickian sense that is an empirical question as to which mathematical theory is useful. | |
| From: Hartry Field (Science without Numbers [1980], 1) | |
| A reaction: Field wants mathematics to be fictions, and not to be truths. But can he give an account of 'useful' that does not imply truth? Only in a rather dubiously pragmatist way. A novel is not useful. |
| 8714 | Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H] |
| Full Idea: The fictionalist can say that the sense in which '2+2=4' is true is pretty much the same as the sense in which 'Oliver Twist lived in London' is true. They are true 'according to a well-known story', or 'according to standard mathematics'. | |
| From: Hartry Field (Realism, Mathematics and Modality [1989], 1.1.1), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 6.3 | |
| A reaction: The roots of this idea are in Carnap. Fictionalism strikes me as brilliant, but poisonous in large doses. Novels can aspire to artistic truth, or to documentary truth. We invent a fiction, and nudge it slowly towards reality. |
| 18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
| Full Idea: Why regard the axioms of standard mathematics as truths, rather than as fictions that for a variety of reasons mathematicians have become interested in? | |
| From: Hartry Field (Science without Numbers [1980], p.viii) |
| 18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
| Full Idea: One can often reduce one's ontological commitments by expanding one's logic. | |
| From: Hartry Field (Science without Numbers [1980], p.ix) | |
| A reaction: I don't actually understand this idea, but that's never stopped me before. Clearly, this sounds like an extremely interesting thought, and hence I should aspire to understand it. So I do aspire to understand it. First, how do you 'expand' a logic? |
| 8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
| Full Idea: Field regards the eliminability of apparent reference to properties from the language of science as a foregone result. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Zoltán Gendler Szabó - Nominalism 5.1 n50 | |
| A reaction: Field is a nominalist who also denies the existence of mathematics as part of science. He has a taste for ontological 'desert landscapes'. I have no idea what a property really is, so I think he is on to something. |
| 18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
| Full Idea: To be able to apply any postulated abstract entities to the physical world, we need impure abstact entities, e.g. functions that map physical objects into pure abstract objects. | |
| From: Hartry Field (Science without Numbers [1980], 1) | |
| A reaction: I am a fan of 'impure metaphysics', and this pinpoints my reason very nicely. |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| Full Idea: The link between time and modality was severed by Duns Scotus, who proposed a notion of possibility based purely on the notion of semantic consistency. 'Possible' means for him logically possible, that is, not involving contradiction. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History B.4) |
| 9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
| Full Idea: Isn't it overwhelmingly obvious that 'Either snow is white or it isn't' was true before anyone stipulated a meaning for it, and that it would have been true even if no one had thought about it, or chosen it to be expressed by one of our sentences? | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
| A reaction: Boghossian would have to believe in propositions (unexpressed truths) to hold this - which he does. I take the notion of truth to only have relevance when there are minds around. Otherwise the so-called 'truths' are just the facts. |
| 9160 | Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H] |
| Full Idea: Propositions such as 'People usually tell the truth' seem to count as default reasonable, but it is odd to count them as a priori. Empirical indefeasibility seems the obvious way to distinguish those default reasonable propositions that are a priori. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 1) | |
| A reaction: Sounds reasonable, but it would mean that all the uniformities of nature would then count as a priori. 'Every physical object exerts gravity' probably has no counterexamples, but doesn't seem a priori (even if it is necessary). See Idea 9164. |
| 9164 | We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence [Field,H] |
| Full Idea: I argue not that our most basic rules are a priori or empirically indefeasible, but that we treat them as empirically defeasible and indeed a priori; we don't regard anything as evidence against them. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 4) | |
| A reaction: This is the fictionalist view of a priori knowledge (and of most other things, such as mathematics). I can't agree. Most people treat heaps of a posteriori truths (like the sun rising) as a priori. 'Mass involves energy' is indefeasible a posteriori. |
| 9367 | The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian] |
| Full Idea: The central impetus behind the analytic explanation of the a priori is a desire to explain the possibility of a priori knowledge without having to postulate a special evidence-gathering faculty of intuition. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
| A reaction: I don't see at all why one has to postulate a 'faculty' in order to talk about intuition. I take an intuition to be an apprehension of a probable truth, combined with an inability to articulate how the conclusion was arrived at. |
| 9373 | That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian] |
| Full Idea: The analytic theory of the apriority of logic arose indirectly, as a by-product of the attempt to explain in what a grasp of the meaning of the logical constants consists. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: Preumably he is referring to Wittgenstein's anguish over the meaning of the word 'not' in his World War I notebooks. He first defined the constants by truth tables, then asserted that they were purely conventional - so logic is conventional. |
| 9380 | We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian] |
| Full Idea: If there is no sentence I must hold true if it is to mean what it does, then there is no basis on which to argue that I am entitled to hold it true without evidence. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: He is exploring Quine's view. Truth by convention depends on agreeing which part of the usage of a term constitutes its defining sentence(s), and that may be rather tricky. Boghossian says this slides into the 'dreaded indeterminacy of meaning'. |
| 9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |
| Full Idea: It is consistent with a belief's being a priori in the strong sense that we should have pragmatic reasons for dropping it from our best overall theory. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], n 6) | |
| A reaction: Does 'dropping it' from the theory mean just ignoring it, or actually denying it? C.I. Lewis is the ancestor of this view. Could it be our 'best' theory, while conflicting with beliefs that were strongly a priori? Pragmatism can embrace falsehoods. |
| 9374 | If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian] |
| Full Idea: If we learn geometrical truths by intuition, how could this faculty have misled us for so long? | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: This refers to the development of non-Euclidean geometries, though the main misleading concerns parallels, which involves infinity. Boghossian cites 'distance' as a concept the Euclideans had misunderstood. Why shouldn't intuitions be wrong? |
| 9165 | Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H] |
| Full Idea: Reliability is not a 'factual property'; in calling a rule reasonable we are evaluating it, and all that makes sense to ask about is what we value. We place a high value on the reliability of our inductive and perceptual rules that lead to truth. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 5) | |
| A reaction: This doesn't seem to be a contradiction of reliabilism, since truth is a pretty widespread epistemological value. If you do value truth, then eyes are pretty reliable organs for attaining it. Reliabilism is still wrong, but not for this reason. |
| 9162 | Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H] |
| Full Idea: Reliability is not all we want in an inductive rule. Completely reliable methods are available, such as believing nothing, or only believing logical truths. But we don't value them, but value less reliable methods with other characteristics. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 3) | |
| A reaction: I would take this excellent point to be an advertisement for inference to the best explanation, which requires not only reliable inputs of information, but also a presiding rational judge to assess the mass of evidence. |
| 9166 | People vary in their epistemological standards, and none of them is 'correct' [Field,H] |
| Full Idea: We should concede that different people have slightly different basic epistemological standards. ..I doubt that any clear sense could be given to the notion of 'correctness' here. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 5) | |
| A reaction: I think this is dead right. There is a real relativism about knowledge, which exists at the level of justification, rather than of truth. The scientific revolution just consisted of making the standards tougher, and that seems to have been a good idea. |
| 9163 | If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H] |
| Full Idea: If some inductive rule is basic for us, in the sense that we never assess it using any rules other than itself, then it must be one that we treat as empirically indefeasible (hence as fully a priori, given that it will surely have default status). | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 4) | |
| A reaction: This follows on from Field's account of a priori knowledge. See Ideas 9160 and 9164. I think of induction as simply learning from experience, but if experience goes mad I will cease to trust it. (A rationalist view). |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| Full Idea: A plausible methodological principle is that underlying every good extrinsic explanation there is an intrinsic explanation. | |
| From: Hartry Field (Science without Numbers [1980], 5) | |
| A reaction: I'm thinking that Hartry Field is an Aristotelian essentialist, though I bet he would never admit it. |
| 10826 | 'Valence' and 'gene' had to be reduced to show their compatibility with physicalism [Field,H] |
| Full Idea: 'Valence' and 'gene' were perfectly clear long before anyone succeeded in reducing them, but it was their reducibility and not their clarity before reduction that showed them to be compatible with physicalism. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], §5) |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| Full Idea: The term 'abstract entities' may not be entirely clear, but one thing that does seem clear is that such alleged entities as numbers, functions and sets are abstract. | |
| From: Hartry Field (Science without Numbers [1980], p.1), quoted by JP Burgess / G Rosen - A Subject with No Object I.A.1.a | |
| A reaction: Field firmly denies the existence of such things. Sets don't seem a great problem, if the set is a herd of elephants, but the null and singleton sets show up the difficulties. |
| 9378 | If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian] |
| Full Idea: Conceptual Role Semantics must explain what properties an inference or sentence involving a logical constant must have, if that inference or sentence is to be constitutive of its meaning. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: This is my perennial request that if something is to be defined by its function (or role), we must try to explain what properties it has that make its function possible, and those properties will be the more basic explanation. |
| 9377 | 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian] |
| Full Idea: 'Conceptual role semantics' says the logical constants mean what they do by virtue of figuring in certain inferences and/or sentences involving them and not others, ..so some inferences and sentences are constitutive of an expression's meaning. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: If the meaning of the terms derives from the sentences in which they figure, that seems to be meaning-as-use. The view that it depends on the inferences seems very different, and is a more interesting but more risky claim. |
| 9372 | Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian] |
| Full Idea: Could there be a fact of the matter about what each expression means, but no fact of the matter about whether they mean the same? | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §II) | |
| A reaction: He is discussing Quine's attack on synonymy, and his scepticism about meaning. Boghossian and I believe in propositions, so we have no trouble with two statements having the same meaning. Denial of propositions breeds trouble. |
| 22244 | 'Partial reference' is when the subject thinks two objects are one object [Field,H, by Recanati] |
| Full Idea: A subject's thought is about A, but, unbeknownst to the subject, B is substituted for A. Then there is Field's 'partial reference', because the subject's thought is still partially about A, even though they are following B. | |
| From: report of Hartry Field (Theory Change and the Indeterminacy of Reference [1973]) by François Recanati - Mental Files in Flux 2 | |
| A reaction: Used to interpret a well-known case: Wally says of Udo 'he needs a haircut'; Zach looks at someone else and says 'he sure does'. Recanati explains it by mental files. |
| 7615 | Field says reference is a causal physical relation between mental states and objects [Field,H, by Putnam] |
| Full Idea: In Field's view reference is a 'physicalistic relation', i.e. a complex causal relation between words or mental representations and objects or sets of objects; it is up to physical science to discover what that physicalistic relation is. | |
| From: report of Hartry Field (Tarski's Theory of Truth [1972]) by Hilary Putnam - Reason, Truth and History Ch.2 | |
| A reaction: I wouldn't hold your breath while the scientists do their job. If physicalism is right then Field is right, but physics seems no more appropriate for giving a theory of reference than it does for giving a theory of music. |
| 17721 | There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins] |
| Full Idea: Boghossian distinguishes metaphysical analyticity (truth purely in virtue of meaning, debunked by Quine, he says) from epistemic analyticity (knowability purely in virtue of understanding - a notion in good standing). | |
| From: report of Paul Boghossian (Analyticity Reconsidered [1996]) by Carrie Jenkins - Grounding Concepts 2.4 | |
| A reaction: [compressed] This fits with Jenkins's claim that we have a priori knowledge just through understanding and relating our concepts. She, however, rejects that idea that a priori is analytic. |
| 9368 | Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian] |
| Full Idea: The epistemological notion of analyticity: a statement is 'true by virtue of meaning' provided that grasp of its meaning alone suffices for justified belief in its truth; the metaphysical reading is that it owes its truth to its meaning, not to facts. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
| A reaction: Kripke thinks it is neither, but is a purely semantic notion. How could grasp of meaning alone be a good justification if it wasn't meaning which was the sole cause of the statement's truth? I'm not convinced by his distinction. |
| 8404 | Explain single events by general rules, or vice versa, or probability explains both, or they are unconnected [Field,H] |
| Full Idea: Some think singular causal claims should be explained in terms of general causal claims; some think the order should be reversed; some think a third thing (e.g. objective probability) will explain both; and some think they are only loosely connected. | |
| From: Hartry Field (Causation in a Physical World [2003], 2) | |
| A reaction: I think Ducasse gives the best account, which is the second option, of giving singular causal claims priority. Probability (Mellor) strikes me as a non-starter, and the idea that they are fairly independent seems rather implausible. |
| 8401 | Physical laws are largely time-symmetric, so they make a poor basis for directional causation [Field,H] |
| Full Idea: It is sometimes pointed out that (perhaps with a few minor exceptions) the fundamental physical laws are completely time-symmetric. If so, then if one is inclined to found causation on fundamental physical law, it isn't evident how directionality gets in. | |
| From: Hartry Field (Causation in a Physical World [2003], 1) | |
| A reaction: All my instincts tell me that causation is more fundamental than laws, and that directionality is there at the start. That, though, raises the nice question of how, if causation explains laws, the direction eventually gets left OUT! |
| 8400 | Identifying cause and effect is not just conventional; we explain later events by earlier ones [Field,H] |
| Full Idea: It is not just that the earlier member of a cause-effect pair is conventionally called the cause; it is also connected with other temporal asymmetries that play an important role in our practices. We tend to explain later events in terms of earlier ones. | |
| From: Hartry Field (Causation in a Physical World [2003], 1) | |
| A reaction: We also interfere with the earlier one to affect the later one, and not vice versa (Idea 8363). I am inclined to think that attempting to explain the direction of causation is either pointless or hopeless. |
| 8402 | The only reason for adding the notion of 'cause' to fundamental physics is directionality [Field,H] |
| Full Idea: Although it is true that the notion of 'cause' is not needed in fundamental physics, even statistical physics, still directionality considerations don't preclude this notion from being consistently added to fundamental physics. | |
| From: Hartry Field (Causation in a Physical World [2003], 1) | |
| A reaction: This only makes sense if the notion of cause already has directionality built into it, which I think is correct. The physicist might reply that they don't care about directionality, but the whole idea of an experiment seems to depend on it (Idea 8363). |
| 18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
| Full Idea: According to theories that take the notion of a field seriously, space-time points or regions are fully-fledge causal agents. | |
| From: Hartry Field (Science without Numbers [1980], n 23) |
| 18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
| Full Idea: In general, it seems to me that recent developments in both philosophy and physics have made substantivalism a much more attractive position than it once was. | |
| From: Hartry Field (Science without Numbers [1980], 4) | |
| A reaction: I'm intrigued as to what philosophical developments are involved in this. The arrival of fields is the development in physics. |
| 18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |
| Full Idea: The problem of the relational view of space is especially acute in the context of physical theories that take the notion of a field seriously, e.g. classical electromagnetic theory. | |
| From: Hartry Field (Science without Numbers [1980], 4) | |
| A reaction: In the Leibniz-Clarke debate I sided with the Newtonian Clarke (defending absolute space), and it looks like modern science agrees with me. Nothing exists purely as relations. |