43 ideas
21761 | 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. |
21764 | 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. |
21769 | 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. |
22037 | 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. |
21983 | 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. |
21985 | 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. |
21766 | 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. |
21978 | 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. |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
Full Idea: On Zermelo's view, predicative definitions are not only indispensable to mathematics, but they are unobjectionable since they do not create the objects they define, but merely distinguish them from other objects. | |
From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Shaughan Lavine - Understanding the Infinite V.1 | |
A reaction: This seems to have an underlying platonism, that there are hitherto undefined 'objects' lying around awaiting the honour of being defined. Hm. |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
Full Idea: Starting from set theory as it is historically given ...we must, on the one hand, restrict these principles sufficiently to exclude as contradiction and, on the other, take them sufficiently wide to retain all that is valuable in this theory. | |
From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro) | |
A reaction: Maddy calls this the one-step-back-from-disaster rule of thumb. Zermelo explicitly mentions the 'Russell antinomy' that blocked Frege's approach to sets. |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
Full Idea: Set theory is that branch whose task is to investigate mathematically the fundamental notions 'number', 'order', and 'function', taking them in their pristine, simple form, and to develop thereby the logical foundations of all of arithmetic and analysis. | |
From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro) | |
A reaction: At this point Zermelo seems to be a logicist. Right from the start set theory was meant to be foundational to mathematics, and not just a study of the logic of collections. |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
Full Idea: Zermelo-Fraenkel axioms: Existence (at least one set); Extension (same elements, same set); Specification (a condition creates a new set); Pairing (two sets make a set); Unions; Powers (all subsets make a set); Infinity (set of successors); Choice | |
From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15 |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
Full Idea: Zermelo proposed his listed of assumptions (including the controversial Axiom of Choice) in 1908, in order to secure his controversial proof of Cantor's claim that ' we can always bring any well-defined set into the form of a well-ordered set'. | |
From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1 | |
A reaction: This is interesting because it sometimes looks as if axiom systems are just a way of tidying things up. Presumably it is essential to get people to accept the axioms in their own right, the 'old-fashioned' approach that they be self-evident. |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
Full Idea: I intend to show how the entire theory created by Cantor and Dedekind can be reduced to a few definitions and seven principles, or axioms, which appear to be mutually independent. | |
From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro) | |
A reaction: The number of axioms crept up to nine or ten in subsequent years. The point of axioms is maximum reduction and independence from one another. He says nothing about self-evidence (though Boolos claimed a degree of that). |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
Full Idea: Zermelo's Pairing Axiom superseded (in 1930) his original 1908 Axiom of Elementary Sets. Like Union, its only justification seems to rest on 'limitations of size' and on the 'iterative conception'. | |
From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.3 | |
A reaction: Maddy says of this and Union, that they seem fairly obvious, but that their justification is of prime importance, if we are to understand what the axioms should be. |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
Full Idea: Zermelo used a weak form of the Axiom of Foundation to block Russell's paradox in 1906, but in 1908 felt that the form of his Separation Axiom was enough by itself, and left the earlier axiom off his published list. | |
From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.2 | |
A reaction: Foundation turns out to be fairly controversial. Barwise actually proposes Anti-Foundation as an axiom. Foundation seems to be the rock upon which the iterative view of sets is built. Foundation blocks infinite descending chains of sets, and circularity. |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
Full Idea: Zermelo assumes that not every predicate has an extension but rather that given a set we may separate out from it those of its members satisfying the predicate. This is called 'separation' (Aussonderung). | |
From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by William D. Hart - The Evolution of Logic 3 |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
Full Idea: The most characteristic Zermelo axiom is Separation, guided by a new rule of thumb: 'one step back from disaster' - principles of set generation should be as strong as possible short of contradiction. | |
From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.4 | |
A reaction: Why is there an underlying assumption that we must have as many sets as possible? We are then tempted to abolish axioms like Foundation, so that we can have even more sets! |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
Full Idea: In Zermelo's set theory, the Burali-Forti Paradox becomes a proof that there is no set of all ordinals (so 'is an ordinal' has no extension). | |
From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by William D. Hart - The Evolution of Logic 3 |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
Full Idea: For Zermelo the successor of n is {n} (rather than Von Neumann's successor, which is n U {n}). | |
From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Naturalism in Mathematics I.2 n8 | |
A reaction: I could ask some naive questions about the comparison of these two, but I am too shy about revealing my ignorance. |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
Full Idea: Zermelo was a reductionist, and believed that theorems purportedly about numbers (cardinal or ordinal) are really about sets, and since Von Neumann's definitions of ordinals and cardinals as sets, this has become common doctrine. | |
From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.8 | |
A reaction: Frege has a more sophisticated take on this approach. It may just be an updating of the Greek idea that arithmetic is about treating many things as a unit. A set bestows an identity on a group, and that is all that is needed. |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
Full Idea: In Zermelo's set-theoretic definition of number, 2 is a member of 3, but not a member of 4; in Von Neumann's definition every number is a member of every larger number. This means they have two different structures. | |
From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by James Robert Brown - Philosophy of Mathematics Ch. 4 | |
A reaction: This refers back to the dilemma highlighted by Benacerraf, which was supposed to be the motivation for structuralism. My intuition says that the best answer is that they are both wrong. In a pattern, the nodes aren't 'members' of one another. |
21762 | 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. |
21977 | 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. |
21760 | 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? |
21765 | 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. |
22059 | 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. |
22083 | 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. |
22080 | 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. |
21772 | 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. |
21972 | 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 |
22038 | 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**]. |
22044 | 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. |
21464 | 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. |
21975 | 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. |
21976 | 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. |
22084 | 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. |
20954 | 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) |
22058 | 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? |
20953 | 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'? |
21763 | 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. |
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. |
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. |