Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Appearance and Reality' and 'Remarks on axiomatised set theory'

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14 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Claims about 'the Absolute' are not even verifiable in principle [Ayer on Bradley]
     Full Idea: Such a metaphysical pseudo-proposition as 'the Absolute enters into, but is itself incapable of, evolution and progress' (F.H.Bradley) is not even in principle verifiable.
     From: comment on F.H. Bradley (Appearance and Reality [1893]) by A.J. Ayer - Language,Truth and Logic Ch.1
     A reaction: One may jeer at the Verification Principle for either failing to be precise, or for failing to pass its own test, but Ayer still has a point here. When we drift off into sustained abstractions, we must keeping asking if we are still saying anything real.
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
Metaphysics is finding bad reasons for instinctive beliefs [Bradley]
     Full Idea: Metaphysics is the finding of bad reasons for what we believe upon instinct; but to find these reasons is no less an instinct.
     From: F.H. Bradley (Appearance and Reality [1893]), quoted by Robin Le Poidevin - Interview with Baggini and Stangroom p.165
     A reaction: A famous and very nice remark. The idea of believing things on instinct sounds more like David Hume than an idealist. Personally I am not so pessimistic about the enterprise. I think metaphysics is capable of changing what we believe.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Axiomatising set theory makes it all relative [Skolem]
     Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation.
     From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296)
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Names need a means of reidentifying their referents [Bradley, by Read]
     Full Idea: Unless a name has associated with it a means of reidentifying its referent, we cannot use it.
     From: report of F.H. Bradley (Appearance and Reality [1893]) by Stephen Read - Thinking About Logic Ch.4
     A reaction: Brilliant! This point is totally undeniable. It is not enough that someone be 'baptised'. We need to hang onto both the name and what it refers to, and how are we going to do that?
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]
     Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain.
     From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293)
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
     Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind.
     From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299)
     A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Mathematician want performable operations, not propositions about objects [Skolem]
     Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that.
     From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300)
8. Modes of Existence / A. Relations / 2. Internal Relations
Internal relations are said to be intrinsic properties of two terms, and of the whole they compose [Bradley, by Russell]
     Full Idea: The doctrine of internal relations held that every relation between two terms expresses, primarily, intrinsic properties of the two terms and, in ultimate analysis, a property of the whole which the two compose.
     From: report of F.H. Bradley (Appearance and Reality [1893]) by Bertrand Russell - My Philosophical Development Ch.5
     A reaction: Russell's first big campaign was to reject this view, and his ontology from then on included relations among the catalogue of universals. The coherence theory of truth also gets thrown out at the same time. Russell seems right.
Relations must be linked to their qualities, but that implies an infinite regress of relations [Bradley]
     Full Idea: If a relation between qualities is to be something, then clearly we will now require a new connecting relation. The links are united by a link, and this link has two ends, which require a fresh link to connect them to the old.
     From: F.H. Bradley (Appearance and Reality [1893], p.28), quoted by Cynthia Macdonald - Varieties of Things Ch.6
     A reaction: That is: external relations generates an infinite regress, so relations must be internal. Russell launched his own philosophy with an attack on Bradley's idea. Personally I take how two things 'relate' to one another as one of the deepest of mysteries.
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
British Idealists said reality is a single Mind which experiences itself [Bradley, by Grayling]
     Full Idea: The idealism of Green and Bradley, both of whom were much influenced by the German Idealists, espoused the thesis that the universe ultimately consists of a single Mind which, so to speak, experiences itself.
     From: report of F.H. Bradley (Appearance and Reality [1893]) by A.C. Grayling - Russell Ch.2
     A reaction: This looks now like the last (extreme) throw by the religious view of the world, which collapsed in the face of the empirical realism of Russell and Moore. It is all Kant's fault, for cutting us off from his 'noumenon'.
Bradley's objective idealism accepts reality (the Absolute), but says we can't fully describe it [Bradley, by Potter]
     Full Idea: Objective idealists such as Bradley (rather than Berkeley's subjective view) accepted the substantial existence of reality (which they called the 'Absolute') but held that thought cannot fully describe it.
     From: report of F.H. Bradley (Appearance and Reality [1893]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 23 'Abs'
     A reaction: That thought can't 'fully' describe it seems obvious, so I suspect Bradley's view are stronger than that. This sounds like modern strong and weak anti-realists; strong ones deny reality, but weak ones just deny we know where the joints are.
Qualities and relations are mere appearance; the Absolute is a single undifferentiated substance [Bradley, by Heil]
     Full Idea: In Bradley's view, qualities and relations belong to the realm of appearance. We are left with a single, undifferentiated substance: the Absolute.
     From: report of F.H. Bradley (Appearance and Reality [1893]) by John Heil - Relations 'Internal'
     A reaction: I've not read Bradley, but I can't distinguish this proposal from Parmenides's belief in The One. Or maybe Spinoza's monist view of God and Nature (but that is 'differentiated'). It doesn't sound like Hegel.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
Reality is one, because plurality implies relations, and they assert a superior unity [Bradley]
     Full Idea: Reality is one. It must be simple because plurality, taken as real, contradicts itself. Plurality implies relations, and, through its relations it unwillingly asserts always a superior unity.
     From: F.H. Bradley (Appearance and Reality [1893], p.519), quoted by A.C. Grayling - Russell Ch.2
     A reaction: This argument depends on a belief in 'internal' relations, which Russell famously attacked. If an internal feature of every separate item was its relation to other things, then I suppose Bradley would be right. But it isn't, and he isn't.