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Ideas of JP Burgess / G Rosen, by Text

[American, fl. 1997, Both professors at Princeton University.]

1997 A Subject with No Object
I.A.1.a p.14 Abstract/concrete is a distinction of kind, not degree
     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.
I.A.1.b p.17 The old debate classified representations as abstract, not entities
     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'.
I.A.2.c p.43 'True' is only occasionally useful, as in 'everything Fermat believed was true'
     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.
II.A.1 p.102 If space is really just a force-field, then it is a physical entity
     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?
II.B.3.a p.137 We should talk about possible existence, rather than actual existence, of numbers
     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.
II.B.3.b p.141 Modal logic gives an account of metalogical possibility, not metaphysical possibility
     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...
II.C.0 p.147 Structuralism and nominalism are normally rivals, but might work together
     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.
II.C.1.a p.150 A relation is either a set of sets of sets, or a set of sets
     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.
II.C.1.b p.153 Mathematics has ascended to higher and higher levels of abstraction
     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).
II.C.1.b p.156 Mereology implies that acceptance of entities entails acceptance of conglomerates
     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.
III.A.1.d p.179 Much of what science says about concrete entities is 'abstraction-laden'
     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'.
III.B.2.c p.199 Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas
     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.
III.C.1.b p.223 The paradoxes no longer seem crucial in critiques of set theory
     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.
III.C.1.b p.224 The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set
     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).
III.C.2.a p.228 Number words became nouns around the time of Plato
     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.