31 ideas
| 9921 | 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen] |
| Full Idea: In the disquotational view of truth, what saves truth from being wholly redundant and so wholly useless, is mainly that it provides an ability to state generalisations like 'Everything Fermat believed was true'. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], I.A.2.c) | |
| A reaction: Sounds like the thin end of the wedge. Presumably we can infer that the first thing Fermat believed on his last Christmas Day was true. |
| 9924 | Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen] |
| Full Idea: If you want a logic of metaphysical possibility, the existing literature was originally developed to supply a logic of metalogical possibility, and still reflects its origins. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], II.B.3.b) | |
| A reaction: This is a warning shot (which I don't fully understand) to people like me, who were beginning to think they could fill their ontology with possibilia, which could then be incorporated into the wider account of logical thinking. Ah well... |
| 9933 | The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen] |
| Full Idea: The paradoxes only seem to arise in connection with Frege's logical notion of extension or class, not Cantor's mathematical notion of set. Cantor never assumed that every condition determines a set. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], III.C.1.b) | |
| A reaction: This makes the whole issue a parochial episode in the history of philosophy, not a central question. Cantor favoured some sort of abstractionism (see Kit Fine on the subject). |
| 9928 | Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen] |
| Full Idea: Mereology has ontological implications. The acceptance of some initial entities involves the acceptance of many further entities, arbitrary wholes having the entities as parts. It must accept conglomerates. Geometric points imply geometric regions. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], II.C.1.b) | |
| A reaction: Presumably without the wholes being entailed by the parts, there is no subject called 'mereology'. But if the conglomeration is unrestricted, there is not much left to be said. 'Restricted' composition (by nature?) sounds a nice line. |
| 9926 | A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen] |
| Full Idea: While in general a relation is taken to be a set of ordered pairs <u, v> = {{u}, {u, v}}, and hence a set of sets of sets, in special cases a relation can be represented by a set of sets. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], II.C.1.a) | |
| A reaction: [See book for their examples, which are <, symmetric, and arbitrary] The fact that a relation (or anything else) can be represented in a certain way should never ever be taken to mean that you now know what the thing IS. |
| 17743 | De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki] |
| Full Idea: In 1846 De Morgan introduced the enormously influential notion of a possibly arbitrary and stipulated 'universe of discourse'. It replaced Boole's original - and metaphysically a bit suspect - universe of 'all things'. | |
| From: report of Augustus De Morgan (works [1846]) by Michal Walicki - Introduction to Mathematical Logic History D.1.1 | |
| A reaction: This not only brings formal logic under control, but also reflects normal talk, because there is always an explicit or implicit domain of discourse when we talk. Of virtually any conversation, you can say what it is 'about'. |
| 9932 | The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen] |
| Full Idea: Recent commentators have de-emphasised the set paradoxes because they play no prominent part in motivating the most articulate and active opponents of set theory, such as Kronecker (constructivism) or Brouwer (intuitionism), or Weyl (predicativism). | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], III.C.1.b) | |
| A reaction: This seems to be a sad illustration of the way most analytical philosophers have to limp along behind the logicians and mathematicians, arguing furiously about problems that have largely been abandoned. |
| 9923 | We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen] |
| Full Idea: The modal strategy for numbers is to replace assumptions about the actual existence of numbers by assumptions about the possible existence of numbers | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], II.B.3.a) | |
| A reaction: This seems to be quite a good way of dealing with very large numbers and infinities. It is not clear whether 5 is so regularly actualised that we must consider it as permanent, or whether it is just a prominent permanent possibility. |
| 9925 | Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen] |
| Full Idea: Usually structuralism and nominalism are considered rivals. But structuralism can also be the first step in a strategy of nominalist reconstrual or paraphrase. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], II.C.0) | |
| A reaction: Hellman and later Chihara seem to be the main proponents of nominalist structuralism. My sympathies lie with this strategy. Are there objects at the nodes of the structure, or is the structure itself platonic? Mill offers a route. |
| 9934 | Number words became nouns around the time of Plato [Burgess/Rosen] |
| Full Idea: The transition from using number words purely as adjectives to using them extensively as nouns has been traced to 'around the time of Plato'. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], III.C.2.a) | |
| A reaction: [The cite Kneale and Kneale VI,§2 for this] It is just too tempting to think that in fact Plato (and early Platonists) were totally responsible for this shift, since the whole reification of numbers seems to be inherently platonist. |
| 9918 | Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen] |
| Full Idea: The distinction of abstract and concrete is one of kind and not degree. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], I.A.1.a) | |
| A reaction: I think I must agree with this. If there is a borderline, it would be in particulars that seem to have an abstract aspect to them. A horse involves the abstraction of being a horse, and it involves be one horse. |
| 9929 | Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen] |
| Full Idea: Much of what science says about concrete entities is 'abstraction-laden'. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], III.A.1.d) | |
| A reaction: Not just science. In ordinary conversation we continually refer to particulars using so-called 'universal' predicates and object-terms, which are presumably abstractions. 'I've just seen an elephant'. |
| 9927 | Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen] |
| Full Idea: In mathematics, since the beginning of the nineteenth century, there has been an ascent to higher and higher levels of abstraction. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], II.C.1.b) | |
| A reaction: I am interested in clarifying what this means, which might involve the common sense and psychological view of the matter, as well as some sort of formal definition in terms of equivalence (or whatever). |
| 9930 | Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen] |
| Full Idea: There is a scale of abstractness that leads downwards from sets through attributes to formulas as abstract types and on to formulas as abstract tokens. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], III.B.2.c) | |
| A reaction: Presumably the 'abstract tokens' at the bottom must have some interpretation, to support the system. Presumably one can keep going upwards, through sets of sets of sets. |
| 23708 | Humeans see properties as having no more essential features and relations than their distinctness [Friend/Kimpton-Nye, by PG] |
| Full Idea: The Humean view says properties are 'quiddities', which individuates properties by nothing more than their distinctness from one another, so that dispositions are not essential to them, and there is no limit to possible property recombination. | |
| From: report of Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.3.1) by PG - Db (ideas) | |
| A reaction: [my summary] All of this is implied by Hume, rather than stated. David Lewis supports this view. The theory of basic powers is the view's main opponent. This quidditist view is not found in physics, where a property's modal profile matters. |
| 23709 | Dispositions are what individuate properties, and they constitute their essence [Friend/Kimpton-Nye] |
| Full Idea: Dispositions constitute the essences of properties, and hence the identity of a property is not primitive ('quidditism'), but is given in terms of its dispositional relations to other properties. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.3.1) | |
| A reaction: I like the picture that powers are basic, giving rise to dispositions, which combine to produce qualitative and active properties. Powers are precise and relatively few, and properties are ill-defined and very numerous. Being 'influential', for example. |
| 23707 | Powers are properties which necessitate dispositions [Friend/Kimpton-Nye] |
| Full Idea: In broad terms: powers are properties that necessitate dispositions. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.2) | |
| A reaction: If powers are properties then they must be properties 'of' something, which then seems to be more fundamental than the powers. Maybe our concept of an electron helps, which seems to be a bundle of a few properties, but no one even asks 'of' what. |
| 23714 | Dispositional essentialism (unlike the grounding view) says only fundamental properties are powers [Friend/Kimpton-Nye] |
| Full Idea: Dispositional essentialism yields the view that just fundamental properties and some evolved macro properties are powers. The grounding view, by contrast, seems to yield the result that all properties are powers. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.7) | |
| A reaction: For the second view, Mumford (for example) claims that the sphericity of a ball is a power, but that seems to miss the whole motivation for the powers ontology, which offers a fairly fundamental explanation of laws and modality. |
| 23711 | A power is a property which consists entirely of dispositions [Friend/Kimpton-Nye] |
| Full Idea: In the 'dispositional essentialist' account (the main view) …what it is to be a power is to be a property whose essence is exhaustively constituted by dispositions. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.4) | |
| A reaction: [compressed] Sounds wrong to me. A very complex property (such as 'stormy' weather) could be nothing more than a large bundle of dispositions, but that wouldn't make it a 'power', which has to be simpler and more basic. |
| 23712 | Powers are qualitative properties which fully ground dispositions [Friend/Kimpton-Nye] |
| Full Idea: In the 'grounding' view of powers …powers are qualitative, because their essence can be specified independently of any dispositions or relations, but they fully ground dispositions. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.4) | |
| A reaction: [compressed] They give this as the rival view to dispositional essentialism. It may be a mistake to call a power a property (which needs to be 'of' something). Not sure how powers can be both fundamental and qualitative. Don't they also ground qualities? |
| 23698 | Dispositions have directed behaviour which occurs if triggered [Friend/Kimpton-Nye] |
| Full Idea: The three platitudes about dispositions are that 1) they are directed towards some specific behaviour, 2) they can be triggered under specific conditions, and 3) their directedness is modal, meaning not 'when it is triggered' but 'it it were triggered'. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.1.1) | |
| A reaction: [PG summary] This is the preliminary to an attempt at a precise formal analysis, covering a number of hypothetical problem cases. 3) is the counterfactual rather than material conditional. Seems accurate. |
| 23699 | 'Masked' dispositions fail to react because something intervenes [Friend/Kimpton-Nye] |
| Full Idea: A disposition is 'masked' when it fails to manifest due to interference, such as a fragile vase packed in bubble wrap, or an antidote taken after some poison. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.1) | |
| A reaction: [compressed] The easiest account of these would be to say that the stimulus or trigger of the disposition never completely occurs. Poisons are only disposed to kill when they are fully ingested. Bubble wrapped vases can't be properly struck. |
| 23700 | A disposition is 'altered' when the stimulus reverses the disposition [Friend/Kimpton-Nye] |
| Full Idea: A disposition is subject to 'altering' when the stimulus of the disposition influences whether (and to what degree) an object has that disposition. Either a live wire goes dead when it is touched, or a dead wire has a sensor making it live when touched. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.2) | |
| A reaction: The word 'fink' is used of such interference. Not much of a problem, I would say, because at the moment when the stimulus comes to do its job, there is no longer a disposition for it to trigger. No different from switching off a light. |
| 23701 | A disposition is 'mimicked' if a different cause produces that effect from that stimulus [Friend/Kimpton-Nye] |
| Full Idea: A disposition is 'mimicked' by objects without that disposition which behave as though they do have it. Styrofoam plates are not fragile, but make a horrible sound when stressed, causing some annoyed person to break them. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.3) | |
| A reaction: A rather strained example! It shouldn't be a problem if the same cause (stress) leads to the same effect (breaking), but by a different path which is not the same as fragility. A formal analysis must obviously cover this case. |
| 23702 | A 'trick' can look like a stimulus for a disposition which will happen without it [Friend/Kimpton-Nye] |
| Full Idea: A 'trick' can behave like a disposition, as when someone says 'abracadabra' over a hot cup of coffee, stimulating it (?) to gradually cool down. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.4) | |
| A reaction: This is like Humean constant conjunction which is obviously not a cause, such as night following day. Only a problem is this cup of coffee is seen in isolation from all other cups of coffee. Post hoc propter hoc does not apply to all stimuli! |
| 23703 | Some dispositions manifest themselves without a stimulus [Friend/Kimpton-Nye] |
| Full Idea: Some dispositions, such as loquaciousness or irascibility, are disposed to manifest whether they are provoked to do so. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.3.3) | |
| A reaction: We might surmise that such people have internal triggers that get them going, rather than overt ones. The Sun has a disposition to shine, without an external stimulus. The theory of powers says nature is active, rather than being disposed to activity. |
| 23704 | We could analyse dispositions as 'possibilities', with no mention of a stimulus [Friend/Kimpton-Nye] |
| Full Idea: We might abandon the relational analysis of dispositions (as stimulus-effect), and just say a disposition is a 'possibility', which simply can manifest, however that manifestation comes about. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.3.5) | |
| A reaction: [Compressed. He particularly cites Barbara Vetter] A mere 'possibility' seems to cover passive states as well as potentially active ones. A cushion can be dented, but I wouldn't say it was 'disposed' to dent. Radioactive decay is a disposition, though. |
| 23710 | Dispositionalism says modality is in the powers of this world, not outsourced to possible worlds [Friend/Kimpton-Nye] |
| Full Idea: Dispositionalism does not 'outsource' modality to other possible worlds, it roots modality in the powers of concrete individuals in this world. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.3.3) | |
| A reaction: Possible worlds are to abolish modality, by treating it as the non-modal facts of different worlds. I see the dispositional view as vastly superior, because the world is awash with vivid and undeniable potentialities, and one world is better ontology. |
| 9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
| Full Idea: The original debate was over abstract ideas; thus it was mental (or linguistic) representations that were classified as abstract or otherwise, and not the entities represented. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], I.A.1.b) | |
| A reaction: This seems to beg the question of whether there are any such entities. It is equally plausible to talk of the entities that are 'constructed', rather than 'represented'. |
| 23706 | Hume's Dictum says no connections are necessary - so mass and spacetime warping could separate [Friend/Kimpton-Nye] |
| Full Idea: Hume's Dictum says there are no necessary connections between existences, …and also between the distinct properties that individuals instantiate. …It follows that an object's property of mass and its disposition to warp space-time could come apart. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.2) | |
| A reaction: [compressed] This nicely pinpoints the heart of the Humean view, to which scientific essentialists and fans of powers in nature object. The objectors include me. |
| 9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |
| Full Idea: According to many philosophical commentators, a force-field must be considered to be a physical entity, and as the distinction between space and the force-field may be considered to be merely verbal, space itself may be considered to be a physical entity. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], II.A.1) | |
| A reaction: The ontology becomes a bit odd if we cheerfully accept that space is physical, but then we can't give the same account of time. I'm not sure how time could be physical. What's it made of? |