21 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. |
| 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. |
| 16641 | Whiteness does not exist, but by it something can exist-as-white [Aquinas] |
| Full Idea: Whiteness is said to exist not because it subsists in itself, but because by it something has existence-as-white. | |
| From: Thomas Aquinas (Quodlibeta [1267], IX.2.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 10.2 | |
| A reaction: It seems unavoidable to refer to the whiteness as 'it'. It might be called the 'adverbial' theory of properties, as ways of doing something. |
| 22170 | Senses grasp external properties, but the understanding grasps the essential natures of things [Aquinas] |
| Full Idea: Our imagination and senses grasp only the outer properties of things, not their natures. ...Understanding, however, grasps the very substance and nature of things, so that what is represented in understanding is a likeness of thing's very essence. | |
| From: Thomas Aquinas (Quodlibeta [1267], 8.2.2) | |
| A reaction: This is exactly the picture I endorse for modern science. Explanation is the path to understanding, and that must venture beyond immediate experience. |
| 22169 | Initial universal truths are present within us as potential, to be drawn out by reason [Aquinas] |
| Full Idea: For present in us by nature are certain initial truths everyone knows, in which lie potentially known conclusions our reasons can draw out and make actually known. | |
| From: Thomas Aquinas (Quodlibeta [1267], 8.2.2) | |
| A reaction: Note that these are truths rather than concepts, but that they have to be 'drawn out' by reason. This is Descartes' view of the matter, where the 'natural light' of reason is needed to articulate what is innate, such as geometry. |
| 22168 | Minds take in a likeness of things, which activates an awaiting potential [Aquinas] |
| Full Idea: What the mind takes in is not some material element of the agent, but a likeness of the agent actualising some potential the patient already has. This, for example, is the way our seeing takes in the colour of a coloured body. | |
| From: Thomas Aquinas (Quodlibeta [1267], 8.2.1) | |
| A reaction: This is exactly right. Descartes agreed. It works for colour, but not (obviously) for cheese graters. |
| 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'. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 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? |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |