Combining Texts

All the ideas for 'Roman Law', 'Letters to Queen Charlotte' and 'A Subject with No Object'

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21 ideas

3. Truth / H. Deflationary Truth / 2. Deflationary Truth
'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.
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
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...
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
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).
4. Formal Logic / G. Formal Mereology / 1. Mereology
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.
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
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.
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
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.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz]
     Full Idea: It is by the natural light that the axioms of mathematics are recognised. If we take away the same quantity from two equal things, …a thing we can easily predict without having experienced it.
     From: Gottfried Leibniz (Letters to Queen Charlotte [1702], p.189)
     A reaction: He also says two equal weights will keep a balance level. Plato thinks his slave boy understands halving an area by the natural light, but that is just as likely to be experience. It is too easy to attribut thoughts to a 'natural light'.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
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.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
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.
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'.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
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).
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.
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz]
     Full Idea: That which is necessary for something does not constitute its essence. Air is necessary for our life, but our life is something other than air.
     From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702)
     A reaction: Bravo. Why can't modern philosophers hang on to this distinction? They seem to think that because they don't believe in traditional essences they can purloin the word for something else. Same with the word 'abstraction'.
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
Intelligible truth is independent of any external things or experiences [Leibniz]
     Full Idea: Intelligible truth is independent of the truth or of the existence outside us of sensible and material things. ....It is generally true that we only know necessary truths by the natural light [of reason]
     From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702)
     A reaction: A nice quotation summarising a view for which Leibniz is famous - that there is a tight correlation between necessary truths and our a priori knowledge of them. The obvious challenge comes from Kripke's claim that scientists can discover necessities.
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz]
     Full Idea: We use the external senses ...to make us know their particular objects ...but they do not make us know what those sensible qualities are ...whether red is small revolving globules causing light, heat a whirling of dust, or sound is waves in air.
     From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702)
     A reaction: These seems to be exactly the concept of secondary qualities which Locke was promoting. They are unreliable information about the objects we perceive. Primary qualities are reliable information. I like that distinction.
12. Knowledge Sources / D. Empiricism / 1. Empiricism
There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz]
     Full Idea: It can be said that there is nothing in the understanding which does not come from the senses, except the understanding itself, or that which understands.
     From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702)
     A reaction: Given that Leibniz is labelled as a 'rationalist', this is awfully close to empiricism. Not Locke's 'tabula rasa' perhaps, but Hume's experiences plus associations. Leibniz has a much loftier notion of understanding and reason than Hume does.
18. Thought / E. Abstraction / 2. Abstracta by Selection
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'.
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
No crime and no punishment without a law [Roman law]
     Full Idea: An ancient principle of Roman law states, nullum crimen et nulla poene sine lege, - there is no crime and no punishment without a law.
     From: [Roman law] (Roman Law [c.100]), quoted by A.C. Grayling - Among the Dead Cities Ch.6
     A reaction: That there is no 'punishment' without law seems the basis of civilization. Suppose a strong person imposed firm punishment in order to forestall more brutal revenge by others? What motivates the creation of criminal laws?
27. Natural Reality / C. Space / 2. Space
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?