55 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. |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| Full Idea: Cohen's method of 'forcing' produces a new model of ZFC from an old model by appending a carefully chosen 'generic' set. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.4) |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| Full Idea: A possible axiom is the Large Cardinal Axiom, which asserts that there are more and more stages in the cumulative hierarchy. Infinity can be seen as the first of these stages, and Replacement pushes further in this direction. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.5) |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| Full Idea: The axiom of infinity: that there are infinite sets is to claim that completed infinite collections can be treated mathematically. In its standard contemporary form, the axioms assert the existence of the set of all finite ordinals. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.3) |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| Full Idea: In the presence of other axioms, the Axiom of Foundation is equivalent to the claim that every set is a member of some Vα. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.3) |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| Full Idea: The Axiom of Reducibility states that every propositional function is extensionally equivalent to some predicative proposition function. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| Full Idea: A 'propositional function' is generated when one of the terms of the proposition is replaced by a variable, as in 'x is wise' or 'Socrates'. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: This implies that you can only have a propositional function if it is derived from a complete proposition. Note that the variable can be in either subject or in predicate position. It extends Frege's account of a concept as 'x is F'. |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| Full Idea: The line of development that finally led to a coherent foundation for the calculus also led to the explicit introduction of completed infinities: each real number is identified with an infinite collection of rationals. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.3) | |
| A reaction: Effectively, completed infinities just are the real numbers. |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| Full Idea: Both Cantor's real number (Cauchy sequences of rationals) and Dedekind's cuts involved regarding infinite items (sequences or sets) as completed and subject to further manipulation, bringing the completed infinite into mathematics unambiguously. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1 n39) | |
| A reaction: So it is the arrival of the real numbers which is the culprit for lumbering us with weird completed infinites, which can then be the subject of addition, multiplication and exponentiation. Maybe this was a silly mistake? |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| Full Idea: The stunning discovery that infinity comes in different degrees led to the theory of infinite cardinal numbers, the heart of contemporary set theory. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: It occurs to me that these huge cardinals only exist in set theory. If you took away that prop, they would vanish in a puff. |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| Full Idea: By the mid 1890s Cantor was aware that there could be no set of all sets, as its cardinal number would have to be the largest cardinal number, while his own theorem shows that for any cardinal there is a larger. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: There is always a larger cardinal because of the power set axiom. Some people regard that with suspicion. |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| Full Idea: An 'inaccessible' cardinal is one that cannot be reached by taking unions of small collections of smaller sets or by taking power sets. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.5) | |
| A reaction: They were introduced by Hausdorff in 1908. |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| Full Idea: Even the fundamental theorems about limits could not [at first] be proved because the reals themselves were not well understood. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: This refers to the period of about 1850 (Weierstrass) to 1880 (Dedekind and Cantor). |
| 18182 | The extension of concepts is not important to me [Maddy] |
| Full Idea: I attach no decisive importance even to bringing in the extension of the concepts at all. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], §107) | |
| A reaction: He almost seems to equate the concept with its extension, but that seems to raise all sorts of questions, about indeterminate and fluctuating extensions. |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| Full Idea: In the ZFC cumulative hierarchy, Frege's candidates for numbers do not exist. For example, new three-element sets are formed at every stage, so there is no stage at which the set of all three-element sets could he formed. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: Ah. This is a very important fact indeed if you are trying to understand contemporary discussions in philosophy of mathematics. |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| Full Idea: To solve the Julius Caesar problem, Frege requires explicit definitions of the numbers, and he proposes his well-known solution: the number of Fs = the extension of the concept 'equinumerous with F' (based on one-one correspondence). | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: Why do there have to be Fs before there can be the corresponding number? If there were no F for 523, would that mean that '523' didn't exist (even if 522 and 524 did exist)? |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| Full Idea: The set theory axioms developed in producing foundations for mathematics also have strong consequences for existing fields, and produce a theory that is immensely fruitful in its own right. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: [compressed] Second of Maddy's three benefits of set theory. This benefit is more questionable than the first, because the axioms may be invented because of their nice fruit, instead of their accurate account of foundations. |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| Full Idea: The single unified area of set theory provides a court of final appeal for questions of mathematical existence and proof. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: Maddy's third benefit of set theory. 'Existence' means being modellable in sets, and 'proof' means being derivable from the axioms. The slightly ad hoc character of the axioms makes this a weaker defence. |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| Full Idea: Set theoretic foundations bring all mathematical objects and structures into one arena, allowing relations and interactions between them to be clearly displayed and investigated. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: The first of three benefits of set theory which Maddy lists. The advantages of the one arena seem to be indisputable. |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| Full Idea: The identification of geometric points with real numbers was among the first and most dramatic examples of the power of set theoretic foundations. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: Hence the clear definition of the reals by Dedekind and Cantor was the real trigger for launching set theory. |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| Full Idea: The structure of a geometric line by rational points left gaps, which were inconsistent with a continuous line. Set theory provided an ordering that contained no gaps. These reals are constructed from rationals, which come from integers and naturals. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: This completes the reduction of geometry to arithmetic and algebra, which was launch 250 years earlier by Descartes. |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| Full Idea: Our much loved mathematical knowledge rests on two supports: inexorable deductive logic (the stuff of proof), and the set theoretic axioms. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I Intro) |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| Full Idea: It could turn out that all applications of continuum mathematics in natural sciences are actually instances of idealisation. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.6) |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| Full Idea: Crudely, the scientist posits only those entities without which she cannot account for observations, while the set theorist posits as many entities as she can, short of inconsistency. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.5) |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| Full Idea: Recent commentators have noted that Frege's versions of the basic propositions of arithmetic can be derived from Hume's Principle alone, that the fatal Law V is only needed to derive Hume's Principle itself from the definition of number. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: Crispin Wright is the famous exponent of this modern view. Apparently Charles Parsons (1965) first floated the idea. |
| 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. |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| Full Idea: The case of atoms makes it clear that the indispensable appearance of an entity in our best scientific theory is not generally enough to convince scientists that it is real. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.6) | |
| A reaction: She refers to the period between Dalton and Einstein, when theories were full of atoms, but there was strong reluctance to actually say that they existed, until the direct evidence was incontrovertable. Nice point. |
| 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. |
| 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) |
| 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. |
| 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. |
| 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. |
| 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? |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| Full Idea: In science we treat the earth's surface as flat, we assume the ocean to be infinitely deep, we use continuous functions for what we know to be quantised, and we take liquids to be continuous despite atomic theory. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.6) | |
| A reaction: If fussy people like scientists do this all the time, how much more so must the confused multitude be doing the same thing all day? |
| 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. |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |