44 ideas
| 12223 | It is a fallacy to explain the obscure with the even more obscure [Hale/Wright] |
| Full Idea: The fallacy of 'ad obscurum per obscurius' is to explain the obscure by appeal to what is more obscure. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §3) | |
| A reaction: Not strictly a fallacy, so much as an example of inadequate explanation, along with circularity and infinite regresses. |
| 12230 | Singular terms refer if they make certain atomic statements true [Hale/Wright] |
| Full Idea: Anyone should agree that a justification for regarding a singular term as having objectual reference is provided just as soon as one has justification for regarding as true certain atomic statements in which it functions as a singular term. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: The meat of this idea is hidden in the word 'certain'. See Idea 10314 for Hale's explanation. Without that, the proposal strikes me as absurd. |
| 10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
| Full Idea: If we stipulate that 'x is heterological' iff it does not apply to itself, we speedily arrive at the contradiction that 'heterological' is itself heterological just in case it is not. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) |
| 10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
| Full Idea: The incompletability of formal arithmetic reveals, not arithmetical truths which are not truths of logic, but that logical truth likewise defies complete deductive characterization. ...Gödel's result has no specific bearing on the logicist project. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §2 n5) | |
| A reaction: This is the key defence against the claim that Gödel's First Theorem demolished logicism. |
| 8784 | Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright] |
| Full Idea: The result of joining Hume's Principle to second-order logic is a consistent system which is a foundation for arithmetic, in the sense that all the fundamental laws of arithmetic are derivable within it as theorems. This seems a vindication of logicism. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1) | |
| A reaction: The controversial part seems to be second-order logic, which Quine (for example) vigorously challenged. The contention against most attempts to improve Frege's logicism is that they thereby cease to be properly logical. |
| 8787 | The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright] |
| Full Idea: The Julius Caesar problem is the problem of supplying a criterion of application for 'number', and thereby setting it up as the concept of a genuine sort of object. (Why is Julius Caesar not a number?) | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 3) | |
| A reaction: One response would be to deny that numbers are objects. Another would be to derive numbers from their application in counting objects, rather than the other way round. I suspect that the problem only real bothers platonists. Serves them right. |
| 10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
| Full Idea: The relativization of ontology to theory in structuralism can't avoid carrying with it a relativization of truth-value, which would compromise the objectivity which structuralists wish to claim for mathematics. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26) | |
| A reaction: This is the attraction of structures which grow out of the physical world, where truth-value is presumably not in dispute. |
| 10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
| Full Idea: It is not clear how the view that natural numbers are purely intra-structural 'objects' can be squared with the widespread use of numerals outside purely arithmetical contexts. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26) | |
| A reaction: I don't understand this objection. If they refer to quantity, they are implicitly cardinal. If they name things in a sequence they are implicitly ordinal. All users of numbers have a grasp of the basic structure. |
| 8788 | Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright] |
| Full Idea: It is only if logic is metaphysically and epistemologically privileged that a reduction of mathematical theories to logical ones can be philosophically any more noteworthy than a reduction of any mathematical theory to any other. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 8) | |
| A reaction: It would be hard to demonstrate this privileged position, though intuitively there is nothing more basic in human rationality. That may be a fact about us, but it doesn't make logic basic to nature, which is where proper reduction should be heading. |
| 10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
| Full Idea: The neo-Fregean takes a more optimistic view than Frege of the prospects for the kind of contextual explanation of the fundamental concepts of arithmetic and analysis (cardinals and reals), which he rejected in 'Grundlagen' 60-68. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §1) |
| 8783 | Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright] |
| Full Idea: Two modern approaches to logicism are the quantificational approach of David Bostock, and the abstraction-free approach of Neil Tennant. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1 n2) | |
| A reaction: Hale and Wright mention these as alternatives to their own view. I merely catalogue them for further examination. My immediate reaction is that Bostock sounds hopeless and Tennant sounds interesting. |
| 12225 | Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright] |
| Full Idea: A third way has been offered to 'make sense' of neo-Fregeanism: we should reject Quine's well-known criterion of ontological commitment in favour of one based on 'truth-maker theory'. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §4 n19) | |
| A reaction: [The cite Ross Cameron for this] They reject this proposal, on the grounds that truth-maker theory is not sufficient to fix the grounding truth-conditions of statements. |
| 12224 | Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright] |
| Full Idea: It is claimed that neo-Fregeans are committed to 'maximalism' - that whatever can exist does. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §4) | |
| A reaction: [The cite Eklund] They observe that maximalism denies contingent non-existence (of the £20 note I haven't got). There seems to be the related problem of 'hyperinflation', that if abstract objects are generated logically, the process is unstoppable. |
| 12226 | The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright] |
| Full Idea: Identity is sometimes read so that 'Pegasus is Pegasus' expresses a truth, the non-existence of any winged horse notwithstanding. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §5) | |
| A reaction: This would give you ontological commitment to truth, without commitment to existence. It undercuts the use of identity statements as the basis of existence claims, which was Frege's strategy. |
| 12229 | Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright] |
| Full Idea: There is a compatibilist view which says that it is for the abundant properties to play the role of 'bedeutungen' in semantic theory, and the sparse ones to address certain metaphysical concerns. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: Only a philosopher could live with the word 'property' having utterly different extensions in different areas of discourse. They similarly bifurcate words like 'object' and 'exist'. Call properties 'quasi-properties' and I might join in. |
| 18443 | A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright] |
| Full Idea: The good standing of a predicate is already trivially sufficient to ensure the existence of an associated property, a (perhaps complex) way of being which the predicate serves to express. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: 'Way of being' is interesting. Is 'being near Trafalgar Sq' a way of being? I take properties to be 'features', which seems to give a clearer way of demarcating them. They say they are talking about 'abundant' (rather than 'sparse') properties. |
| 10626 | Objects just are what singular terms refer to [Hale/Wright] |
| Full Idea: Objects, as distinct from entities of other types (properties, relations or, more generally, functions of different types and levels), just are what (actual or possible) singular terms refer to. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.1) | |
| A reaction: I find this view very bizarre and hard to cope with. It seems either to preposterously accept the implications of the way we speak into our ontology ('sakes'?), or preposterously bend the word 'object' away from its normal meaning. |
| 14703 | Superficial necessity is true in all worlds; deep necessity is thus true, no matter which world is actual [Schroeter] |
| Full Idea: If we have a 'fixedly' operator F, then a sentence is fixedly actually true if it is true no matter which world is designated as actual (which 'he actually won in 2008' fails to be). Maybe '□' is superficial necessity, and FA is 'deep' necessity. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.2.2) | |
| A reaction: Gareth Evans distinguishes 'deep' from 'superficial' necessity. Humberstone and others introduced 'F'. Presumably FA is deeper because it has to pass a tougher test. |
| 14714 | Contradictory claims about a necessary god both seem apriori coherent [Schroeter] |
| Full Idea: It seems apriori coherent that there could be a necessarily existing god, and that there could be no such god - but they can't both be true. Other examples include unprovable mathematical necessities | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.4) |
| 14704 | 2D semantics gives us apriori knowledge of our own meanings [Schroeter] |
| Full Idea: Generalized 2D semantics is meant to vindicate the traditional idea that we have apriori access to our own meanings through armchair reflection. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.1) | |
| A reaction: The idea is to split meaning in two, so that we know one part of it a priori. It is an unfashionably internalist view of meaning (which doesn't make it wrong!). |
| 14706 | Your view of water depends on whether you start from the actual Earth or its counterfactual Twin [Schroeter] |
| Full Idea: Your verdicts about whether the stuff on Twin Earth counts as water depends on whether you think of Twin Earth as a hypothesis about your actual environment or as a purely counterfactual possibility. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.2.3) | |
| A reaction: This is the 'two-dimensional semantics' approach to the Twin Earth problem, which splits meaning into two components. Whether you start from the actual world or from Twin Earth, you will rigidly designate the local wet stuff as 'water'. |
| 14711 | Rationalists say knowing an expression is identifying its extension using an internal cognitive state [Schroeter] |
| Full Idea: In rationalist views of meaning, based on the 'golden triangle', to be competent with an expression is to be in an internal cognitive state that puts one in a position to identify its extension in any possible world based only on apriori reflection. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.1) | |
| A reaction: This looks like a proper fight-back against modern rampant externalism about meaning. All my intuitions are with internalism, which I think points to a more coherent overall philosophy. Well done, David Chalmers! Even if he is wrong. |
| 10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
| Full Idea: The new kind of abstract objects are not creations of the human mind. ...The existence of such objects depends upon whether or not the relevant equivalence relation holds among the entities of the presupposed kind. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) | |
| A reaction: It seems odd that we no longer have any choice about what abstract objects we use, and that we can't evade them if the objects exist, and can't have them if the objects don't exist - and presumably destruction of the objects kills the concept? |
| 8786 | One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright] |
| Full Idea: An example of a first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines; a higher-order example (which refers to first-order predicates) defines 'equinumeral' in terms of one-to-one correlation (Hume's Principle). | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1) | |
| A reaction: [compressed] This is the way modern logicians now treat abstraction, but abstraction principles include the elusive concept of 'equivalence' of entities, which may be no more than that the same adjective ('parallel') can be applied to them. |
| 12227 | Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright] |
| Full Idea: Abstractionism needs a face-value, existentially committed reading of the terms occurring on the left-hand sides together with sameness of truth-conditions across the biconditional. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §5) | |
| A reaction: They employ 'abstractionism' to mean their logical Fregean strategy for defining abstractions, not to mean the older psychological account. Thus the truth-conditions for being 'parallel' and for having the 'same direction' must be consistent. |
| 12228 | Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright] |
| Full Idea: Abstraction principles purport to introduce fundamental means of reference to a range of objects, to which there is accordingly no presumption that we have any prior or independent means of reference. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §8) | |
| A reaction: There's the rub! They make it sound like a virtue, that we open up yet another heaven of abstract toys to play with. As fictions, they are indeed exciting new fun. As platonic discoveries they strike me as Cloud-Cuckoo Land. |
| 14717 | Internalist meaning is about understanding; externalist meaning is about embedding in a situation [Schroeter] |
| Full Idea: Internalists take the notion of meaning to capture an aspect of an individual's current state of understanding, while externalists take the notion of meaning to reflect how an individual is embedded within her social and physical environment. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.4.3) | |
| A reaction: This idea also occurs in discussions of concepts (filed here under 'Thought'). |
| 12231 | Reference needs truth as well as sense [Hale/Wright] |
| Full Idea: It takes, over and above the possession of sense, the truth of relevant contexts to ensure reference. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: Reference purely through sense was discredited by Kripke. The present idea challenges Kripke's baptismal realist approach. How do you 'baptise' an abstract object? But isn't reference needed prior to the establishment of truth? |
| 14720 | Semantic theory assigns meanings to expressions, and metasemantics explains how this works [Schroeter] |
| Full Idea: A semantic theory assigns semantic values (meanings) to particular expressions of the language. In contrast, a metasemantic theory explains why expressions have those semantic values, appealing to facts about speakers and communities. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 3.4) | |
| A reaction: Presumably some people only want the metasemantic version. I assume that the two are entangled, but I would vote for both. |
| 14695 | Semantic theories show how truth of sentences depends on rules for interpreting and joining their parts [Schroeter] |
| Full Idea: Semantic theories explain how the truth or falsity of whole sentences depends on the meanings of their parts by stating rules governing the interpretation of subsentential expressions and their modes of combination. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: Somehow it looks as if the mystery of the whole business will still be missing if this project is ever successfully completed. Also one suspects that such a theory would be a fiction, rather than a description of actuality, which is too complex. |
| 14696 | Simple semantics assigns extensions to names and to predicates [Schroeter] |
| Full Idea: The simplest semantic frameworks assign extensions as semantic values of particular expressions. The extension of a name is the thing, of 'cool' is the set of cool things, and sets of ordered pairs for 2-place predicates. The sentence has T or F. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: The immediate well-known problem is different predicates with the same extensions, such as 'renate' and 'cordate'. Possible worlds semantics is supposed to be an improvement to cover this, and to give a semantics for modal talk as well. Sounds good. |
| 14697 | 'Federer' and 'best tennis player' can't mean the same, despite having the same extension [Schroeter] |
| Full Idea: A simple extensional semantics will assign the same semantic value to 'Roger Federer' and 'world's best tennis player', but they clearly differ in meaning, and if events had unfolded differently they would pick out different people. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: You would think that this would be too obvious to need pointing out, but it is clearly a view that had a lot of popularity before the arrival of possible worlds. |
| 14698 | Possible worlds semantics uses 'intensions' - functions which assign extensions at each world [Schroeter] |
| Full Idea: In standard possible worlds semantics, the semantic value of an expression is an 'intension', a function that assigns an extension to the expression 'at' every possible world. ...It keeps track of the 'modal profiles' of objects, kinds and properties. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: Personally I just don't buy a semantics which is entirely based on extensions, even if this has sorted out some more obvious problems of extensionality. When I say someone is 'my hero', I don't just mean to pick out a particular person. |
| 14699 | Possible worlds make 'I' and that person's name synonymous, but they have different meanings [Schroeter] |
| Full Idea: In standard possible worlds semantics the semantic value of Hllary Clinton's utterance of 'I' will be the same as her utterance of 'Hillary Clinton'. But clearly the English word 'I' is not synonymous with the name 'Hillary Clinton'. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: This problem was spotted by Kaplan, and it has been a chief motivator for the creation of two-dimensional semantics, which some people have then extended into a complete semantic theory. No purely extensional semantics can be right. |
| 14709 | Possible worlds semantics implies a constitutive connection between meanings and modal claims [Schroeter] |
| Full Idea: In standard possible world semantics an expression's intension reflects the modal profile of an object, kind or property, which would establish an important constitutive connection between meanings and modal claims. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.1) | |
| A reaction: The central question becomes 'do you need to know a thing's modal profile in order to have a decent understanding of it?', but if you express it that way (my way), then what counts as 'decent' will be relative to all sorts of things. |
| 14719 | In the possible worlds account all necessary truths are same (because they all map to the True) [Schroeter] |
| Full Idea: A problem for a standard possible worlds analysis is that all necessary truths have precisely the same content (the function mapping every world to the True). Hesperus=Phosphorus has the same content as Hesperus=Hesperus-and-2+2=4. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 3.3) | |
| A reaction: If this is supposed to be a theory of meaning then it has gone very badly wrong indeed. Has modern semantics taken a wrong turning somewhere? Two-dimensionalism is meant to address some of these problems. |
| 14701 | Array worlds along the horizontal, and contexts (world,person,time) along the vertical [Schroeter] |
| Full Idea: In a two-dimensional matrix we array possible circumstances of evaluation (worlds) along the horizontal axis, and possible contexts of utterance (world, person, time) along the vertical axis. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.2) | |
| A reaction: This is due to Stalnaker 1978, and is clearest in operation when applied to an indexical such as 'I' in 'I am President'. 'I' is a rigid designator, but depends on context. The grid is filled in with T or F for each utterance in each world. |
| 14702 | If we introduce 'actually' into modal talk, we need possible worlds twice to express this [Schroeter] |
| Full Idea: At first glance necessity and possibility can be fully expressed by quantifying over all possible worlds, but this cannot capture 'Possibly everything actually red is also shiny'. This needs a double-indexed framework, with worlds playing two roles. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.2.1) | |
| A reaction: She points out that this also applies to tense logic, for the notion of 'now'. The point is that we not only need a set of possible worlds, but we also need a procedure (the 'Actuality' operator A or @) for picking out one of the worlds as special. |
| 14705 | Do we know apriori how we refer to names and natural kinds, but their modal profiles only a posteriori? [Schroeter] |
| Full Idea: Perhaps our best way of understanding names and natural kind terms is that we have apriori access to currently associated reference-fixing criterion, but only a posteriori access to the associated modal profile. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.1) | |
| A reaction: This is the 'generalized' view of 2D semantics (covering everything, not just modals and indexicals). I know apriori what something is, but only study will reveal its possibilities. The actual world is easy to talk about, but possible worlds are harder. |
| 14715 | 2D fans defend it for conceptual analysis, for meaning, and for internalist reference [Schroeter] |
| Full Idea: Supporters of generalized two-dimensional semantics agree to defend apriori conceptual analysis in metaphysics, and that 2D captures meaning and not just belief-patterns, and it gives a broadly internalist approach to reference determination. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.4) | |
| A reaction: I'm not sure I can evaluate this, but I sort of like conceptual analysis, and the concept of meaning, and fairly internalist views of reference, so I am ripe for the picking. |
| 14716 | 2D semantics can't respond to contingent apriori claims, since there is no single proposition involved [Schroeter] |
| Full Idea: It is objected to 2D semantics that it cannot explain Kripke's cases of contingent apriori truths, for there is no single proposition (construed as a set of possible worlds) that is both apriori and contingent. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.4.2) | |
| A reaction: This sounds like a rather large objection to the whole 2D plan, if it implies that when we say something there is no single proposition that is being expressed. |
| 10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
| Full Idea: There are many statements which are plausibly viewed as conceptual truths (such as 'what is yellow is extended') which do not qualify as analytic under Frege's definition (as provable using only logical laws and definitions). | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) | |
| A reaction: Presumably this is because the early assumptions of Frege were mathematical and logical, and he was trying to get away from Kant. That yellow is extended is a truth for non-linguistic beings. |
| 20646 | Helmholtz used 'energy' to mathematically link heat, light, electricity and magnetism [Helmholtz, by Watson] |
| Full Idea: Helmholtz provided the requisite mathematical formulation linking heat, light, electricity and magnetism, by treating these phenomena as different manifestations of 'energy'. | |
| From: report of Hermann von Helmholtz (On the Conservation of Force [1847]) by Peter Watson - Convergence 01 'Human' | |
| A reaction: I'm increasingly struck by the neglect by philosophers of nature of these amazing developments in 19th century physics, because they prefer the excitement of the latest nuclear physics. There is more philosophical interest in the earlier stages. |
| 20973 | All forces conserve the sum of kinetic and potential energy [Helmholtz, by Papineau] |
| Full Idea: Helmholtz crucially asserted that all forces conserve the sum of kinetic and potential energy; superficially non-conservative forces like friction are simply macroscopic manifestations of more fundamental forces conserving energy at the micro-level. | |
| From: report of Hermann von Helmholtz (On the Conservation of Force [1847]) by David Papineau - Thinking about Consciousness App 4.3 | |
| A reaction: Friction had been a problem case, because it appeared not to conserve energy when it slowed movement down. |