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All the ideas for 'Mahaprajnaparamitashastra', 'Science of Logic' and 'What Numbers Could Not Be'

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52 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
If we start with indeterminate being, we arrive at being and nothing as a united pair [Hegel, by Houlgate]
     Full Idea: Presuppositionless thinking which begins by thinking pure, indeterminate being must therefore come to think being and nothing in terms of one another.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'From indeterminate'
     A reaction: In Houlgate's account this seems to be the key Hegelian thought. Simply by confronting nothingness he gets the idea that one concept can lead to an alternative, and that the two can then be grasped together, which is his dialectic.
Thought about being leads to a string of other concepts, like becoming, quantity, specificity, causality... [Hegel, by Houlgate]
     Full Idea: In the course of (Hegel's) logic, we come to understand that to think being is to think becoming, quality, quantity, specificity, essence and existence, substance and causality, and, ultimately, self-determining reason itself.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'The Method'
     A reaction: Extraordinary! Houlgate spells out nicely what some commentators seem to gloss over, the huge a priori ambitions of Hegel's thought. I find his entire programme utterly implausible.
We must start with absolute abstraction, with no presuppositions, so we start with pure being [Hegel]
     Full Idea: The beginning must be an absolute - an abstract beginning; and so it may not presuppose anything, must not be mediated by anything or have a ground; rather it is itself to be the ground of the entire science. ...The beginning therefore is pure being.
     From: Georg W.F.Hegel (Science of Logic [1816], p.70), quoted by Stephen Houlgate - An Introduction to Hegel 03 'Logic'
     A reaction: This is the 'presuppositionless' beginning of Hegel's metaphysics, which Houlgate emphasises. Hegel's logic is very obviously a direct descendent of Descartes' Cogito. But it is pure thought, with no mention of a Self.
2. Reason / A. Nature of Reason / 5. Objectivity
Objectivity is not by correspondence, but by the historical determined necessity of Geist [Hegel, by Pinkard]
     Full Idea: What gives objectivity to a judgment about an object is not correspondence, but the way in which a judgement is located within a pattern of reasonng that is determined by the way in which Geist is historically determined as necessarily taking the object.
     From: report of Georg W.F.Hegel (Science of Logic [1816], Intro) by Terry Pinkard - German Philosophy 1760-1860
     A reaction: I quote this, but I'm blowed if I can make sense of how objectivity could be achieved in such a way. How can a historical process create a necessary judgement? Sorry, I'm fairly new to Hegel. Pinker says it is the practice of giving reasons.
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Being and nothing are the same and not the same, which is the identity of identity and non-identity [Hegel]
     Full Idea: Pure being and pure nothing are the same, ...but on the contrary they are not the same ...they are absolutely distinct. ...This is the identity of identity and non-identity.
     From: Georg W.F.Hegel (Science of Logic [1816], I.i.i.1C p.82,74), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7
     A reaction: Even Moore, who is very patient with Hegel, gets cross at this point, describing such talk as 'shocking'. He's not wrong. Moore later says that the reason in reality tolerates contradictions, but human understanding can't.
The so-called world is filled with contradiction [Hegel]
     Full Idea: The so-called world is never and nowhere without contradiction. (...but it is unable to endure it)
     From: Georg W.F.Hegel (Science of Logic [1816], I.i.ii.2C(b)), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7
     A reaction: [Second bit in Ency I §11] To clarify this one would need to understand 'so-called'. Note that his claim is not that the world contains occasional contradictions, but that the whole of reality is contradictory. I think this idea is nonsense.
2. Reason / C. Styles of Reason / 1. Dialectic
Dialectic is the instability of thoughts generating their opposite, and then new more complex thoughts [Hegel, by Houlgate]
     Full Idea: The dialectical principle, for Hegel, is the principle whereby apparently stable thoughts reveal their inherent instability by turning into their opposites and then into new, more complex thoughts (as being turns to nothing, and then becoming).
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'The Method'
     A reaction: Houlgate says this is unique to Hegel, and is NOT the familiar thesis-antithesis-synthesis idea of dialectic, found in Kant and Engels. Hegelian idea shares the Greek idea of insights arising from oppositions.
Hegel's dialectic is not thesis-antithesis-synthesis, but usually negation of negation of the negation [Hegel, by Moore,AW]
     Full Idea: The dialectic is often described in terms of thesis, antithesis, and synthesis - though this is not a Hegelian way of speaking. Hegel himself sometimes describes it in terms of negation and negation of the negation.
     From: report of Georg W.F.Hegel (Science of Logic [1816], I.i.i.C(c) p.150) by A.W. Moore - The Evolution of Modern Metaphysics 07.4
     A reaction: A footnote says the first form of description only occurs once in Hegel's work. I am guessing that Marx is responsible for the standard misrepresentation.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
There are no such things as numbers [Benacerraf]
     Full Idea: There are no such things as numbers.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC)
     A reaction: Mill said precisely the same (Idea 9794). I think I agree. There has been a classic error of reification. An abstract pattern is not an object. If I coin a word for all the three-digit numbers in our system, I haven't created a new 'object'.
Numbers can't be sets if there is no agreement on which sets they are [Benacerraf]
     Full Idea: The fact that Zermelo and Von Neumann disagree on which particular sets the numbers are is fatal to the view that each number is some particular set.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], II)
     A reaction: I agree. A brilliantly simple argument. There is the possibility that one of the two accounts is correct (I would vote for Zermelo), but it is not actually possible to prove it.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K]
     Full Idea: Benacerraf thinks of numbers as being defined by their natural ordering.
     From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §5
     A reaction: My intuition is that cardinality is logically prior to ordinality, since that connects better with the experienced physical world of objects. Just as the fact that people have different heights must precede them being arranged in height order.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C]
     Full Idea: Benacerraf claims that the concept of a progression is in some way the fundamental arithmetical notion, essential to understanding the idea of a finite cardinal, with a grasp of progressions sufficing for grasping finite cardinals.
     From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xv
     A reaction: He cites Dedekind (and hence the Peano Axioms) as the source of this. The interest is that progression seems to be fundamental to ordianls, but this claims it is also fundamental to cardinals. Note that in the first instance they are finite.
A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf]
     Full Idea: Any set has k members if and only if it can be put into one-to-one correspondence with the set of numbers less than or equal to k.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], I)
     A reaction: This is 'Ernie's' view of things in the paper. This defines the finite cardinal numbers in terms of the finite ordinal numbers. He has already said that the set of numbers is well-ordered.
To explain numbers you must also explain cardinality, the counting of things [Benacerraf]
     Full Idea: I would disagree with Quine. The explanation of cardinality - i.e. of the use of numbers for 'transitive counting', as I have called it - is part and parcel of the explication of number.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], I n2)
     A reaction: Quine says numbers are just a progression, with transitive counting as a bonus. Interesting that Benacerraf identifies cardinality with transitive counting. I would have thought it was the possession of numerical quantity, not ascertaining it.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf]
     Full Idea: Learning number words in the right order is counting 'intransitively'; using them as measures of sets is counting 'transitively'. ..It seems possible for someone to learn the former without learning the latter.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], I)
     A reaction: Scruton's nice question (Idea 3907) is whether you could be said to understand numbers if you could only count intransitively. I would have thought such a state contained no understanding at all of numbers. Benacerraf agrees.
Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf]
     Full Idea: It seems that it is possible for someone to learn to count intransitively without learning to count transitively. But not vice versa.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], I)
     A reaction: Benacerraf favours the priority of the ordinals. It is doubtful whether you have grasped cardinality properly if you don't know how to count things. Could I understand 'he has 27 sheep', without understanding the system of natural numbers?
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
The application of a system of numbers is counting and measurement [Benacerraf]
     Full Idea: The application of a system of numbers is counting and measurement.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], I)
     A reaction: A simple point, but it needs spelling out. Counting seems prior, in experience if not in logic. Measuring is a luxury you find you can indulge in (by imagining your quantity) split into parts, once you have mastered counting.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf]
     Full Idea: Ernie's number progression is [φ],[φ,[φ]],[φ,[φ],[φ,[φ,[φ]]],..., whereas Johnny's is [φ],[[φ]],[[[φ]]],... For Ernie 3 belongs to 17, not for Johnny. For Ernie 17 has 17 members; for Johnny it has one.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], II)
     A reaction: Benacerraf's point is that there is no proof-theoretic way to choose between them, though I am willing to offer my intuition that Ernie (Zermelo) gives the right account. Seventeen pebbles 'contains' three pebbles; you must pass 3 to count to 17.
The successor of x is either x and all its members, or just the unit set of x [Benacerraf]
     Full Idea: For Ernie, the successor of a number x was the set consisting of x and all the members of x, while for Johnny the successor of x was simply [x], the unit set of x - the set whose only member is x.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], II)
     A reaction: See also Idea 9900. Benacerraf's famous point is that it doesn't seem to make any difference to arithmetic which version of set theory you choose as its basis. I take this to conclusively refute the idea that numbers ARE sets.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend]
     Full Idea: If two children were brought up knowing two different set theories, they could entirely agree on how to do arithmetic, up to the point where they discuss ontology. There is no mathematical way to tell which is the true representation of numbers.
     From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by Michèle Friend - Introducing the Philosophy of Mathematics
     A reaction: Benacerraf ends by proposing a structuralist approach. If mathematics is consistent with conflicting set theories, then those theories are not shedding light on mathematics.
No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe]
     Full Idea: Hume's Principle can't tell us what a cardinal number is (this is one lesson of Benacerraf's well-known problem). An infinity of pairs of sets could actually be the number two (not just the simplest sets).
     From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by E.J. Lowe - The Possibility of Metaphysics 10.3
     A reaction: The drift here is for numbers to end up as being basic, axiomatic, indefinable, universal entities. Since I favour patterns as the basis of numbers, I think the basis might be in a pre-verbal experience, which even a bird might have, viewing its eggs.
If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf]
     Full Idea: If a particular set-theory is in a strong sense 'reducible to' the theory of ordinal numbers... then we can still ask, but which is really which?
     From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIB)
     A reaction: A nice question about all reductions. If we reduce mind to brain, does that mean that brain is really just mind. To have a direction (up/down?), reduction must lead to explanation in a single direction only. Do numbers explain sets?
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf]
     Full Idea: If any recursive sequence whatever would do to explain ordinal numbers suggests that what is important is not the individuality of each element, but the structure which they jointly exhibit.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC)
     A reaction: This sentence launched the whole modern theory of Structuralism in mathematics. It is hard to see what properties a number-as-object could have which would entail its place in an ordinal sequence.
The job is done by the whole system of numbers, so numbers are not objects [Benacerraf]
     Full Idea: 'Objects' do not do the job of numbers singly; the whole system performs the job or nothing does. I therefore argue that numbers could not be objects at all.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC)
     A reaction: This thought is explored by structuralism - though it is a moot point where mere 'nodes' in a system (perhaps filled with old bits of furniture) will do the job either. No one ever explains the 'power' of numbers (felt when you do a sudoku). Causal?
The number 3 defines the role of being third in a progression [Benacerraf]
     Full Idea: Any object can play the role of 3; that is, any object can be the third element in some progression. What is peculiar to 3 is that it defines that role, not by being a paradigm, but by representing the relation of any third member of a progression.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC)
     A reaction: An interesting early attempt to spell out the structuralist idea. I'm thinking that the role is spelled out by the intersection of patterns which involve threes.
Number words no more have referents than do the parts of a ruler [Benacerraf]
     Full Idea: Questions of the identification of the referents of number words should be dismissed as misguided in just the way that a question about the referents of the parts of a ruler would be seen as misguided.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC)
     A reaction: What a very nice simple point. It would be very strange to insist that every single part of the continuum of a ruler should be regarded as an 'object'.
Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf]
     Full Idea: Mathematical objects have no properties other than those relating them to other 'elements' of the same structure.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], p.285), quoted by Fraser MacBride - Structuralism Reconsidered §3 n13
     A reaction: Suppose we only had one number - 13 - and we all cried with joy when we recognised it in a group of objects. Would that be a number, or just a pattern, or something hovering between the two?
How can numbers be objects if order is their only property? [Benacerraf, by Putnam]
     Full Idea: Benacerraf raises the question how numbers can be 'objects' if they have no properties except order in a particular ω-sequence.
     From: report of Paul Benacerraf (What Numbers Could Not Be [1965], p.301) by Hilary Putnam - Mathematics without Foundations
     A reaction: Frege certainly didn't think that order was their only property (see his 'borehole' metaphor in Grundlagen). It might be better to say that they are objects which only have relational properties.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Number-as-objects works wholesale, but fails utterly object by object [Benacerraf]
     Full Idea: The identification of numbers with objects works wholesale but fails utterly object by object.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC)
     A reaction: This seems to be a glaring problem for platonists. You can stare at 1728 till you are blue in the face, but it only begins to have any properties at all once you examine its place in the system. This is unusual behaviour for an object.
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Number words are not predicates, as they function very differently from adjectives [Benacerraf]
     Full Idea: The unpredicative nature of number words can be seen by noting how different they are from, say, ordinary adjectives, which do function as predicates.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], II)
     A reaction: He points out that 'x is seventeen' is a rare construction in English, unlike 'x is happy/green/interesting', and that numbers outrank all other adjectives (having to appear first in any string of them).
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf]
     Full Idea: In no consistent theory is there a class of all classes with seventeen members. The existence of the paradoxes is a good reason to deny to 'seventeen' this univocal role of designating the class of all classes with seventeen members.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], II)
     A reaction: This was Frege's disaster, and seems to block any attempt to achieve logicism by translating numbers into sets. It now seems unclear whether set theory is logic, or mathematics, or sui generis.
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
To grasp an existence, we must consider its non-existence [Hegel, by Houlgate]
     Full Idea: It is only to the extent that we can say that something is not, that we can say what it actually is.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'From indeterminate'
     A reaction: A key idea for Hegel, but it leaves me flat. Thinking about the non-being of something throws no light at all for me on the inexpressible actuality of its existence.
Nothing exists, as thinkable and expressible [Hegel]
     Full Idea: Nothing can be thought of, imagined, spoken of, and therefore it is.
     From: Georg W.F.Hegel (Science of Logic [1816], I.i.i.C.1 Rem 3 p.101), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.4
     A reaction: This sounds like Meinong on circular squares. Does this mean that the negation of every truth also somehow exists? I struggle with this idea. Lewis Carroll nailed it.
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
Thinking of nothing is not the same as simply not thinking [Hegel, by Houlgate]
     Full Idea: Thinking of nothing is not the same as simply not thinking. Thought that suspends all its presuppositions and so ends up thinking of nothing determinate still remains thought, albeit utterly indeterminate and inchoate thought.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'From indeterminate'
     A reaction: This is the very starting point of Hegel's dialectical inferences in his 'Logic'. It is hard to entirely disagree, though I wonder whether the exercise is actually possible. What are you aware of if you have a thought with no content?
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
The ground of a thing is not another thing, but the first thing's substance or rational concept [Hegel, by Houlgate]
     Full Idea: Hegel's logic reveals that the true ground of something is not something other than it is, but the substance of that thing itself, or the rational concept that makes the thing what it is.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'The Method'
     A reaction: This seems to be classic Aristotelian essentialism, though Aristotle was also interested in dependence relations.
7. Existence / D. Theories of Reality / 2. Realism
Kant's thing-in-itself is just an abstraction from our knowledge; things only exist for us [Hegel, by Bowie]
     Full Idea: For Hegel there is no thing-in-itself, because the thing only becomes a something by being for us. Kant's thing-in-itself is the result of abstracting from the thing everything we know about it.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Andrew Bowie - German Philosophy: a very short introduction 3
     A reaction: This seems to pinpoint why Hegel is an idealist philosopher. Frege objected to abstraction for similar reasons. I don't understand how the tree outside my window can only exist 'for me'. I have a much better theory about the tree.
Hegel believe that the genuine categories reveal things in themselves [Hegel, by Houlgate]
     Full Idea: Hegel believed, unlike Kant, that the categories of the understanding, when properly understood, disclose the nature of things in themselves and not just the character of things as they appear to us.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - Hegel p.101
     A reaction: 'Properly understood' sounds like 'no true Scotsman'. This is thoroughgoing idealism, because reality is determined by the activity of the mind, and not from outside. The Hegel story makes more sense if you see the categories as evolutionary.
8. Modes of Existence / A. Relations / 2. Internal Relations
The nature of each category relates itself to another [Hegel]
     Full Idea: In the categories, something through its own nature relates itself to the other.
     From: Georg W.F.Hegel (Science of Logic [1816], p.125), quoted by Stephen Houlgate - Hegel p.99
     A reaction: This is the doctrine of internal relations rejected by Moore and Russell, and also the key idea in Hegel's logic - that ideas give rise to other ideas, without contribution by the thinker.
9. Objects / F. Identity among Objects / 6. Identity between Objects
Identity statements make sense only if there are possible individuating conditions [Benacerraf]
     Full Idea: Identity statements make sense only in contexts where there exist possible individuating conditions.
     From: Paul Benacerraf (What Numbers Could Not Be [1965], III)
     A reaction: He is objecting to bizarre identifications involving numbers. An identity statement may be bizarre even if we can clearly individuate the two candidates. Winston Churchill is a Mars Bar. Identifying George Orwell with Eric Blair doesn't need a 'respect'.
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
In absolute knowing, the gap between object and oneself closes, producing certainty [Hegel]
     Full Idea: In absolute knowing ...the separation of the object from the certainty of oneself is completely eliminated: truth is now equated with certainty and this certainty with truth.
     From: Georg W.F.Hegel (Science of Logic [1816], p.49), quoted by Stephen Houlgate - An Introduction to Hegel 03 'Absolute'
     A reaction: I don't understand this, but I note it because Hegel is evidently not a fallibilist about knowledge. I take this idea to be Descartes' 'clear and distinct ideas', wearing a grand rhetorical uniform.
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
The 'absolute idea' is when all the contradictions are exhausted [Hegel, by Bowie]
     Full Idea: The point in philosophy at which the contradictions are exhausted is what Hegel means by the 'absolute idea'.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Andrew Bowie - Introduction to German Philosophy 4 'Questions'
     A reaction: {Can't think of a response to this one)
Hegel, unlike Kant, said how things appear is the same as how things are [Hegel, by Moore,AW]
     Full Idea: Hegel rejected the fundamental Kantian distinction between how things knowably appear and how they unknowably are in themselves. This was anathema to him. For Hegel how things knowably appear is how they manifestly are.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by A.W. Moore - The Evolution of Modern Metaphysics 07.2
     A reaction: We shouldn't assume that Hegel was therefore a realist, because Berkeley would agree with this idea. Hegel rejected transcendental idealism for this reason. Hegel wanted to get rid of the immanent/transcendent distinction
Hegel's non-subjective idealism is the unity of subjective and objective viewpoints [Hegel, by Pinkard]
     Full Idea: The unity of the two points of view (subjective and objective) constitutes Hegel's idealism. ...He kept emphasising that it was not 'subjective' idealism.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Terry Pinkard - German Philosophy 1760-1860 10
     A reaction: Subjective idealism denies the objective point of view. [**20th June 2019, 10:49 am. This is the 20,000th idea in the database. The project was begun in 1997, as organised notes to help with teaching. For the last ten years today has been my target**].
Hegel claimed his system was about the world, but it only mapped conceptual interdependence [Pinkard on Hegel]
     Full Idea: In the view of the later Schelling, although Hegel's system only really laid out the ways in which the senses of various concepts depended on each other, it claimed to be a system about the world itself.
     From: comment on Georg W.F.Hegel (Science of Logic [1816]) by Terry Pinkard - German Philosophy 1760-1860
     A reaction: I'm no expert, but I'm inclined to agree with Schelling. Since I am suspicious of the idea that each concept generates its own negation, I also doubt the accuracy of Hegel's map. I'm a hopeless case.
The Absolute is the primitive system of concepts which are actualised [Hegel, by Gardner]
     Full Idea: In Hegel the Absolute is the exhaustive, unconditioned and self-grounding system of concepts made concrete in actuality, the world of experience.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Sebastian Gardner - Kant and the Critique of Pure Reason 10 'Absolute'
     A reaction: If I collect multiple attempts to explain what the Absolute is, I may one day drift toward a hazy understanding of it. Right now this idea means nothing to me, but I pass it on. His notion of 'concept' seems a long way from the normal modern one.
Authentic thinking and reality have the same content [Hegel]
     Full Idea: Thinking in its immanent determination and the true nature of things form one and the same content.
     From: Georg W.F.Hegel (Science of Logic [1816], p.45), quoted by Stephen Houlgate - Hegel p.101
     A reaction: This is not much use unless we have a crystal clear idea of 'immanent determination', because we need to eliminate errors.
The absolute idea is being, imperishable life, self-knowing truth, and all truth [Hegel]
     Full Idea: The absolute idea alone is being, imperishable life, self-knowing truth, and is all truth. ....All else is error, confusion, opinion, endeavour, caprice, and transitoriness.
     From: Georg W.F.Hegel (Science of Logic [1816], II.iii.3 p.824), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.4
     A reaction: Hegel sounding a bit too much like an over-excited preacher here. The absolute idea seems to be the unified totality of all truths about reality. For Hegel human self-awareness is a big part of that. The idea is being because there is only one substance.
The absolute idea is the great unity of the infinite system of concepts [Hegel, by Moore,AW]
     Full Idea: We can think of the absolute idea roughly as the entire infinite system of interrelated concepts, in their indissoluble unity, as exercised in the self-consciousness towards which the process [of thought] leads. It is the 'telos' of the process.
     From: report of Georg W.F.Hegel (Science of Logic [1816], II.iii.3 p.825) by A.W. Moore - The Evolution of Modern Metaphysics 07.4
     A reaction: This expounds the quotation in Idea 21975. Moore emphasises concepts, where Hegel emphasises the truth. The connection is in Idea 5644.
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Hegel's 'absolute idea' is the interdependence of all truths to justify any of them [Hegel, by Bowie]
     Full Idea: Hegel's system culminates in the 'absolute idea', the explanation of why all particular truths depend on the relationship to other truths for their justification.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Andrew Bowie - German Philosophy: a very short introduction 3
     A reaction: The 'hyper-coherence' theory of justification. The normal claim is that there must be considerable local coherence to provide decent support. Hegel's picture sounds like part of the Enlightenment Dream. Is the idea of 'all truths' coherent?
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Every concept depends on the counter-concepts of what it is not [Hegel, by Bowie]
     Full Idea: Hegel relies on the claim that every concept depends for its determinacy upon its relation to other concepts which it is not (so that even the concept of being depends, for example, upon the concept of nothing).
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Andrew Bowie - Introduction to German Philosophy 4 'Questions'
     A reaction: How does he know this? A question I keep asking about continental philosophers. The negation concepts must be entirely non-conscious. Which negation concepts are relevant to the concept 'tree'?
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
When we explicate the category of being, we watch a new category emerge [Hegel, by Houlgate]
     Full Idea: For Hegel, by explicating the indeterminate category of being, we do not merely restate in different words what is obviously 'contained' in it; we watch a new category emerge.
     From: report of Georg W.F.Hegel (Science of Logic [1816]) by Stephen Houlgate - An Introduction to Hegel 02 'The Method'
     A reaction: This is obviously a response to Kant's view of analyticity, as merely explicating the contents of the subject of the sentence, without advancing knowledge or conceptual resources. A key idea of Hegel's, which I find unconvincing.
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').