81 ideas
| 19073 | True philosophy aims at absolute unity, while our understanding sees only separation [Hegel] |
| Full Idea: Everything deserving the name of philosophy has constantly been based on the consciousness of an absolute unity, where the understanding sees and accepts only separation. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §213) | |
| A reaction: Puzzled by the role of 'understanding' here. I tend to cite that as the highest aspiration of philosophy. Hegel seems to offer a higher understanding of unity, and a weaker analytic understanding, which is part of our limited psychology. |
| 15624 | Free thinking has no presuppositions [Hegel] |
| Full Idea: Thinking that is free is without presuppositions. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §41 Add1) | |
| A reaction: Fat chance, I would have thought. Hegel's project was indeed to try to get right to the bottom of the presuppositions. My picture is always of holding one thing presupposed while you examine another, and then switching to other presuppositions. |
| 15631 | The ideal of reason is the unification of abstract identity (or 'concept') and being [Hegel] |
| Full Idea: Abstract identity (which is what here is also called 'concept') and being are the two moments that reason seeks to unify; this unification is the Ideal of reason. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §49) | |
| A reaction: Not sure I understand this, but I connect it to Aristotle's approach to the problem of being, which was to abandon the head-on approach, and aim to understand the identities of particulars and kinds. |
| 15612 | Older metaphysics naively assumed that thought grasped things in themselves [Hegel] |
| Full Idea: The older metaphysics has the naïve presupposition that thinking grasps what things are in-themselves, that things only are what they genuinely are when they are captured in thought. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §28 Add) | |
| A reaction: His 'older' metaphysics is prior to Kant's critique. The less naïve version is more aware of antinomies and dialectical conflicts within thought. |
| 21768 | Logic is metaphysics, the science of things grasped in thoughts [Hegel] |
| Full Idea: Logic coincides with metaphysics, with the science of things grasped in thoughts. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §24), quoted by Stephen Houlgate - An Introduction to Hegel 02 'Logic' | |
| A reaction: Not a very clear definition, given that thinking about a table appears to be a 'thing grasped in thought'. Presumably it refers to things which can only be grasped in thought, which seems to make it entirely a priori. |
| 21984 | We must break up the rigidity that our understanding has imposed [Hegel] |
| Full Idea: The battle of reason is the struggle to break up the rigidity to which the understanding has reduced everything. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], I §80Z p.115), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: This sounds like a combination of Nietzsche and later Wittgenstein, and may be one of the ideas that launches 'continental' philosophy. Recent French thinkers talk continually of 'liberation'. |
| 22081 | Let thought follow its own course, and don't interfere [Hegel] |
| Full Idea: Let thought follow its own course; and I think badly whenever I add something of my own. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §24 Add 2), quoted by Stephen Houlgate - Hegel p.100 | |
| A reaction: The idea that reason has a course of its own is a mega-assumption, which I would only accept after a lot of persuasion, which I doubt that Hegel can provide. The modern analytic idea of metaphysics as logic has a similar basis. |
| 15626 | Categories create objective experience, but are too conditioned by things to actually grasp them [Hegel] |
| Full Idea: It is the categories that elevate mere perception into objectivity, into experience; but these concepts ...are conditioned by the given material. ...Hence the understanding, or cognition through categories, cannot become cognizant of things-in-themselves. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §43-4) | |
| A reaction: As one often fears with Hegel, this sounds like a deep insight, but is less persuasive when translated into simpler English (if I've got it right!). Being 'conditioned by the material' strikes me as just what is needed for good categories. |
| 15616 | If truth is just non-contradiction, we must take care that our basic concepts aren't contradictory [Hegel] |
| Full Idea: If truth were nothing more than lack of contradiction, one would have to examine first of all, with regard to each concept, whether it does not on its own account, contain an inner contradiction. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §33 Rem) | |
| A reaction: This is a very nice thought, which modern analytic philosophers, steeped in logic, should think about. It is always presumed that a contradiction is between a proposition and its negation, not some inner feature. |
| 15615 | Older metaphysics became dogmatic, by assuming opposed assertions must be true and false [Hegel] |
| Full Idea: The older metaphysics became dogmatism because, given the nature of finite determinations, it had to assume that of two opposed assertions (of the kind that those propositions were) one must be true and the other false. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §32) | |
| A reaction: While dialethism in logic looks very dubious to me, I have every sympathy with Hegel when it comes to the reasonings of ordinary language. There it is much harder to know whether you are addressing truly opposed assertions. |
| 21767 | Dialectic is seen in popular proverbs like 'pride comes before a fall' [Hegel] |
| Full Idea: In the domain of individual ethics, we find the consciousness of dialectic in those universally familiar proverbs 'pride goes before a fall' and 'too much wit outwits itself'. ...Joy relieves itself in tears, and melancholy can be revealed in a smile. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §81), quoted by Stephen Houlgate - An Introduction to Hegel 02 'The Method' | |
| A reaction: 'Too clever by half' is the English version. Hegel's dialectic suggests that each concept somehow implies its opposite, rather than a mere mercurial drift from one extreme to the other. Most pride doesn't lead to a fall. |
| 15639 | Socratic dialectic is subjective, but Plato made it freely scientific and objective [Hegel] |
| Full Idea: It is in the Platonic philosophy that dialectic first occurs in a form which is freely scientific, and hence also objective. With Socrates, dialectical thinking still has a predominantly subjective shape, consistent with his irony. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §81 Add1) | |
| A reaction: I don't understand how dialectic can be 'objective', given that it is a method rather than a belief. Plato certainly seems to elevate dialectic into something almost mystical, because of what is said to be within its power. |
| 15638 | Dialectic is the moving soul of scientific progression, the principle which binds science together [Hegel] |
| Full Idea: The dialectical constitutes the moving soul of scientific progression, and it is the principle through which alone immanent coherence and necessity enter into the content of science. ..[Add 1] It is the principle of all motion, of all life. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §81) |
| 19070 | Superficial truth is knowing how something is, which is consciousness of bare correctness [Hegel] |
| Full Idea: Truth is at first taken to mean that I know how something is. This is truth, however, only in reference to consciousness; it is formal truth, bare correctness. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §213) | |
| A reaction: I would translate this idea as saying that bare correctness is conscious awareness of the truthmaker for some statement. Hegel then offers a 'deeper' account of the nature of truth. I would say awareness is quite separate from the concept of truth. |
| 5644 | In Hegel's logic it is concepts (rather than judgements or propositions) which are true or false [Hegel, by Scruton] |
| Full Idea: The terms of Hegel's logic are not judgements or propositions, but rather concepts: and it is concepts, in this view, that are true or false. | |
| From: report of Georg W.F.Hegel (Logic (Encyclopedia I) [1817]) by Roger Scruton - Short History of Modern Philosophy Ch.12 | |
| A reaction: Quite alien to normal studies of logic, but I can make sense of a correspondence theory of truth for concepts, which might be more interesting than normal propositional or predicate logic. Does the concept of, say, a 'natural law' correspond to anything? |
| 19072 | In the deeper sense of truth, to be untrue resembles being bad; badness is untrue to a thing's nature [Hegel] |
| Full Idea: When truth is viewed in the deeper sense, to be untrue means much the same as to be bad. A bad man is an untrue man, and man who does not behave as his notion or his vocation requires. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §213) | |
| A reaction: See Idea 19071 for the 'deeper sense'. This seems to confirm that Hegel's deeper concept of truth resembles authenticity. I guess it will be something fulfilling the essence of the thing. Doctors must be proper doctors. Gold must be true gold? |
| 19071 | The deeper sense of truth is a thing matching the idea of what it ought to be [Hegel] |
| Full Idea: Truth in the deeper sense is the identity between objectivity and the notion. It is in this deeper sense of truth that we speak of a true state or work of art. These are true if they are as they ought to be (their reality corresponds to their notion). | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §213) | |
| A reaction: This seems to be a correspondence theory, but not as we know it, Jim. He seems to have a value built into truth, which sounds to me like existentialist 'authenticity'. I like what he is saying, but I would analyse it into two or more components. |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| Full Idea: Though it may appear that the intuitionist is providing an account of the connectives couched in terms of assertability conditions, the notion of assertability is a derivative one, ultimately cashed out by appealing to the concept of truth. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: I have quite a strong conviction that Kitcher is right. All attempts to eliminate truth, as some sort of ideal at the heart of ordinary talk and of reasoning, seems to me to be doomed. |
| 21595 | Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel] |
| Full Idea: The law of excluded middle is ...the maxim of the definite understanding, which would fain avoid contradiction, but in doing so falls into it. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], p.172), quoted by Timothy Williamson - Vagueness 1.5 | |
| A reaction: Not sure how this works, but he would say this, wouldn't he? |
| 15628 | The idea that contradiction is essential to rational understanding is a key modern idea [Hegel] |
| Full Idea: The thought that the contradiction which is posited by the determinations of the understanding in what is rational is essential and necessary, has to be considered one of the most important and profound advances of the philosophy of modern times. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48) | |
| A reaction: This is the aspect of Kant's philosophy which launched the whole career of Hegel. Hegel is the philosopher of the antinomies. Graham Priest is his current representative on earth. |
| 15629 | Tenderness for the world solves the antinomies; contradiction is in our reason, not in the essence of the world [Hegel] |
| Full Idea: The solution to the antinomies is as trivial as they are profound; it consists merely in a tenderness for the things of this world. The stain of contradiction ought not to be in the essence of what is in the world; it must belong only to thinking reason. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48 Rem) | |
| A reaction: A rather Wittgensteinian remark. I love his 'tenderness for the things of this world'! I'm not clear why our thinking should be considered to be inescapably riddled with basic contradictions, as Hegel seems to imply. Just make more effort. |
| 15630 | Antinomies are not just in four objects, but in all objects, all representations, all objects and all ideas [Hegel] |
| Full Idea: The main point that has to be made is that antinomy is found not only in Kant's four particular objects taken from cosmology, but rather in all objects of all kinds, in all representations, concepts and ideas. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48 Rem) | |
| A reaction: I suppose Heraclitus and Empedocles, with their oppositional accounts of reality, are the ancestors of this worldview. I just don't feel that sudden flood of insight from this idea of Hegel that comes from some of the other great philsophical theories. |
| 6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik] |
| Full Idea: Kitcher says maths is an 'idealising theory', like some in physics; maths idealises features of the world, and practical operations, such as segregating and matching (numbering), measuring, cutting, moving, assembling (geometry), and collecting (sets). | |
| From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984]) by Michael D. Resnik - Maths as a Science of Patterns One.4.2.2 | |
| A reaction: This seems to be an interesting line, which is trying to be fairly empirical, and avoid basing mathematics on purely a priori understanding. Nevertheless, we do not learn idealisation from experience. Resnik labels Kitcher an anti-realist. |
| 12392 | Mathematical a priorism is conceptualist, constructivist or realist [Kitcher] |
| Full Idea: Proposals for a priori mathematical knowledge have three main types: conceptualist (true in virtue of concepts), constructivist (a construct of the human mind) and realist (in virtue of mathematical facts). | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.3) | |
| A reaction: Realism is pure platonism. I think I currently vote for conceptualism, with the concepts deriving from the concrete world, and then being extended by fictional additions, and shifts in the notion of what 'number' means. |
| 18078 | The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher] |
| Full Idea: What makes a question interesting or gives it aesthetic appeal is its focussing of the project of advancing mathematical understanding, in light of the concepts and systems of beliefs already achieved. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.3) | |
| A reaction: Kitcher defends explanation (the source of understanding, presumably) in terms of unification with previous theories (the 'concepts and systems'). I always have the impression that mathematicians speak of 'beauty' when they see economy of means. |
| 12426 | The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher] |
| Full Idea: Insofar as we can honor claims about the aesthetic qualities or the interest of mathematical inquiries, we should do so by pointing to their explanatory power. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.4) | |
| A reaction: I think this is a good enough account for me (but probably not for my friend Carl!). Beautiful cars are particularly streamlined. Beautiful people look particularly healthy. A beautiful idea is usually wide-ranging. |
| 12395 | Real numbers stand to measurement as natural numbers stand to counting [Kitcher] |
| Full Idea: The real numbers stand to measurement as the natural numbers stand to counting. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.4) |
| 12425 | Complex numbers were only accepted when a geometrical model for them was found [Kitcher] |
| Full Idea: An important episode in the acceptance of complex numbers was the development by Wessel, Argand, and Gauss, of a geometrical model of the numbers. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5) | |
| A reaction: The model was in terms of vectors and rotation. New types of number are spurned until they can be shown to integrate into a range of mathematical practice, at which point mathematicians change the meaning of 'number' (without consulting us). |
| 18071 | A one-operation is the segregation of a single object [Kitcher] |
| Full Idea: We perform a one-operation when we perform a segregative operation in which a single object is segregated. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.3) | |
| A reaction: This is part of Kitcher's empirical but constructive account of arithmetic, which I find very congenial. He avoids the word 'unit', and goes straight to the concept of 'one' (which he treats as more primitive than zero). |
| 18066 | The old view is that mathematics is useful in the world because it describes the world [Kitcher] |
| Full Idea: There is an old explanation of the utility of mathematics. Mathematics describes the structural features of our world, features which are manifested in the behaviour of all the world's inhabitants. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1) | |
| A reaction: He only cites Russell in modern times as sympathising with this view, but Kitcher gives it some backing. I think the view is totally correct. The digression produced by Cantorian infinities has misled us. |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| Full Idea: The method of infinitesimals is that you divide by the time, and then set the time to zero. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 10.2) |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher] |
| Full Idea: The process of pure intuition does not measure up to the standards required of a priori warrants not because it is sensuous but because it is fallible. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.2) |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| Full Idea: If mathematical statements are don't merely report features of transient and private mental entities, it is unclear how pure intuition generates mathematical knowledge. But if they are, they express different propositions for different people and times. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.1) | |
| A reaction: This seems to be the key dilemma which makes Kitcher reject intuition as an a priori route to mathematics. We do, though, just seem to 'see' truths sometimes, and are unable to explain how we do it. |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| Full Idea: The intuitions of which mathematicians speak are not those which Platonism requires. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.3) | |
| A reaction: The point is that it is not taken to be a 'special' ability, but rather a general insight arising from knowledge of mathematics. I take that to be a good account of intuition, which I define as 'inarticulate rationality'. |
| 12387 | Mathematical knowledge arises from basic perception [Kitcher] |
| Full Idea: Mathematical knowledge arises from rudimentary knowledge acquired by perception. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro) | |
| A reaction: This is an empiricist manifesto, which asserts his allegiance to Mill, and he gives a sophisticated account of how higher mathematics can be accounted for in this way. Well, he tries to. |
| 12412 | My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher] |
| Full Idea: The constructivist position I defend claims that mathematics is an idealized science of operations which can be performed on objects in our environment. It offers an idealized description of operations of collecting and ordering. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro) | |
| A reaction: I think this is right. What is missing from Kitcher's account (and every other account I've met) is what is meant by 'idealization'. How do you go about idealising something? Hence my interest in the psychology of abstraction. |
| 18065 | We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher] |
| Full Idea: I propose that a very limited amount of our mathematical knowledge can be obtained by observations and manipulations of ordinary things. Upon this small base we erect the powerful general theories of modern mathematics. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 05.2) | |
| A reaction: I agree. The three related processes that take us from the experiential base of mathematics to its lofty heights are generalisation, idealisation and abstraction. |
| 18077 | The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher] |
| Full Idea: Proponents of complex numbers had ultimately to argue that the new operations shared with the original paradigms a susceptibility to construal in physical terms. The geometrical models of complex numbers answered to this need. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5) | |
| A reaction: [A nice example of the verbose ideas which this website aims to express in plain English!] The interest is not that they had to be described physically (which may pander to an uninformed audience), but that they could be so described. |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| Full Idea: Philosophers who hope to avoid commitment to abstract entities by claiming that mathematical statements are analytic must show how analyticity is, or provides a species of, truth not requiring reference. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.I) | |
| A reaction: [the last part is a quotation from W.D. Hart] Kitcher notes that Frege has a better account, because he provides objects to which reference can be made. I like this idea, which seems to raise a very large question, connected to truthmakers. |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| Full Idea: I construe arithmetic as an idealizing theory. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: I find 'generalising' the most helpful word, because everyone seems to understand and accept the idea. 'Idealisation' invokes 'ideals', which lots of people dislike, and lots of philosophers seem to have trouble with 'abstraction'. |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| Full Idea: I want to suggest both that arithmetic owes its truth to the structure of the world and that arithmetic is true in virtue of our constructive activity. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: Well said, but the problem seems no more mysterious to me than the fact that trees grow in the woods and we build houses out of them. I think I will declare myself to be an 'empirical constructivist' about mathematics. |
| 18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
| Full Idea: The development of a language for describing our correlational activity itself enables us to perform higher level operations. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: This is because all language itself (apart from proper names) is inherently general, idealised and abstracted. He sees the correlations as the nested collections expressed by set theory. |
| 18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
| Full Idea: The constructivist ontological thesis is that mathematics owes its truth to the activity of an actual or ideal subject. The epistemological thesis is that we can have a priori knowledge of this activity, and so recognise its limits. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: The mention of an 'ideal' is Kitcher's personal view. Kitcher embraces the first view, and rejects the second. |
| 18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher] |
| Full Idea: Conceptualists claim that we have basic a priori knowledge of mathematical axioms in virtue of our possession of mathematical concepts. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.1) | |
| A reaction: I sympathise with this view. If concepts are reasonably clear, they will relate to one another in certain ways. How could they not? And how else would you work out those relations other than by thinking about them? |
| 18064 | If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher] |
| Full Idea: Someone who believes that basic truths of mathematics are true in virtue of meaning is not absolved from the task of saying what the referents of mathematical terms are, or ...what mathematical reality is like. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.6) | |
| A reaction: Nice question! He's a fan of getting at the explanatory in mathematics. |
| 19400 | Possibles demand existence, so as many of them as possible must actually exist [Leibniz] |
| Full Idea: From the conflict of all the possibles demanding existence, this at once follows, that there exists that series of things by which as many of them as possible exist. | |
| From: Gottfried Leibniz (Exigency to Exist in Essences [1690], p.91) | |
| A reaction: I'm in tune with a lot of Leibniz, but my head swims with this one. He seems to be a Lewisian about possible worlds - that they are concrete existing entities (with appetites!). Could Lewis include Leibniz's idea in his system? |
| 19401 | God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz] |
| Full Idea: The sufficient reason for God's choice can be found only in the fitness (convenance) or in the degree of perfection that the several worlds possess. | |
| From: Gottfried Leibniz (Exigency to Exist in Essences [1690], p.92) | |
| A reaction: The 'fitness' of a world and its 'perfection' seem very different things. A piece of a jigsaw can have wonderful fitness, without perfection. Occasionally you get that sinking feeling with metaphysicians that they just make it up. |
| 22078 | Even simple propositions about sensations are filled with categories [Hegel] |
| Full Idea: Categories, like 'being', or 'individuality', are already mingled into every proposition, even when it has a completely sensible content, such as "this leaf is green". | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §246 Add), quoted by Stephen Houlgate - Hegel p.95 | |
| A reaction: This is the source of the idea that observation is theory-laden (which tracks back to Kant). Not Duhem, who gets the credit among analytic philosophers. Quine obviously never read Hegel. But the idea is overrated. |
| 15634 | Thought about particulars is done entirely through categories [Hegel] |
| Full Idea: As an activity of the particular, thinking has the categories as its only product and content. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §62) | |
| A reaction: There seems to be an interesting implication in this remark (taken in isolation!) that one can somehow transcend the categories when one begins to think about the universal. Are the universal and the categories not connected? |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| Full Idea: The original introduction of abstract objects was a bad way of doing justice to the insight that mathematics is concerned with structure. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1) | |
| A reaction: I'm a fan of explanations in metaphysics, and hence find the concept of 'bad' explanations in metaphysics particularly intriguing. |
| 21981 | The one substance is formless without the mediation of dialectical concepts [Hegel] |
| Full Idea: As intuitively accepted by Spinoza without a previous mediation by dialectic, substance is as it were a dark shapeless abyss which engulfs all definite content as radically null, and produces from itself nothing that has a positive substance of its own. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], I §151Z p.215), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.6 | |
| A reaction: This seems to be an expression of idealism, since only what is conceptualised can exist. |
| 15637 | Essence is the essential self-positing unity of immediacy and mediation [Hegel] |
| Full Idea: The entire second part of the 'Logic', the doctrine of Essence, deals with the essential self-positing unity of immediacy and mediation. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §65) | |
| A reaction: He is referring to his book 'Science of Logic'. I don't really understand this, but that essence 'posits' the unity of a thing catches my attention. |
| 15613 | Real cognition grasps a thing from within itself, and is not satisfied with mere predicates [Hegel] |
| Full Idea: In genuine cognition ...an object determines itself from within itself, and does not acquire its predicates in an external way. If we proceed by way of predication, the spirit gets the feeling that the predicates cannot exhaust what they are attached to. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §28 Add) | |
| A reaction: I take this to be a glimpse of Hegel's notoriously difficult account of essence. Place this alongside Locke's distinction between Nominal and Real essences. Once we have the predicates, we want to grasp their source. |
| 19402 | The actual universe is the richest composite of what is possible [Leibniz] |
| Full Idea: The actual universe is the collection of the possibles which forms the richest composite. | |
| From: Gottfried Leibniz (Exigency to Exist in Essences [1690], p.92) | |
| A reaction: 'Richest' for Leibniz means a maximum combination of existence, order and variety. It's rather like picking the best starting team from a squad of footballers. |
| 15636 | The Cogito is at the very centre of the entire concern of modern philosophy [Hegel] |
| Full Idea: The proposition 'Cogito Ergo Sum' stands at the very centre, so to speak, of the entire concern of modern philosophy. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §64 Rem) | |
| A reaction: I distinguish two approaches to philosophy: the Parmenidean (which starts from the nature of being), and the Cartesian (which starts from the fact of consciousness). This remark confirms that Hegel is firmly in the latter school. |
| 22300 | Existence is just a set of relationships [Hegel] |
| Full Idea: Everything that exists stands in correlation, and this correlation is the veritable nature of existence. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], p.235 (1892)), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 23 'Abs' |
| 12390 | A priori knowledge comes from available a priori warrants that produce truth [Kitcher] |
| Full Idea: X knows a priori that p iff the belief was produced with an a priori warrant, which is a process which is available to X, and this process is a warrant, and it makes p true. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.4) | |
| A reaction: [compression of a formal spelling-out] This is a modified version of Goldman's reliabilism, for a priori knowledge. It sounds a bit circular and uninformative, but it's a start. |
| 12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
| Full Idea: When we follow long mathematical proofs we lose our a priori warrants for their beginnings. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.2) | |
| A reaction: Kitcher says Descartes complains about this problem several times in his 'Regulae'. The problem runs even deeper into all reasoning, if you become sceptical about memory. You have to remember step 1 when you do step 2. |
| 12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher] |
| Full Idea: Knowledge is independent of experience if any experience which would enable us to acquire the concepts involved would enable us to have the knowledge. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.3) | |
| A reaction: This is the 'conceptualist' view of a priori knowledge, which Kitcher goes on to attack, preferring a 'constructivist' view. The formula here shows that we can't divorce experience entirely from a priori thought. I find conceptualism a congenial view. |
| 12416 | We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher] |
| Full Idea: One can make a powerful case for supposing that some self-knowledge is a priori. At most, if not all, of our waking moments, each of us knows of herself that she exists. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.6) | |
| A reaction: This is a begrudging concession from a strong opponent to the whole notion of a priori knowledge. I suppose if you ask 'what can be known by thought alone?' then truths about thought ought to be fairly good initial candidates. |
| 15609 | The sensible is distinguished from thought by being about singular things [Hegel] |
| Full Idea: The distinction of the sensible from thought is to be located in that fact that the determination of the sensible is singularity. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §20 Rem) | |
| A reaction: Compare Idea 15608, where we find that thought concerns universals. What a very clear thinker Hegel was! |
| 15625 | Sense perception is secondary and dependent, while thought is independent and primitive [Hegel] |
| Full Idea: What can be perceived by the senses is really secondary and not self-standing, while thoughts, on the contrary, are what is genuinely independent and primitive. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §41 Add2) | |
| A reaction: Although this is post-Kant, it strikes me as a perfect slogan for rationalism. Personally I would say that such a dichotomy is becoming a historical relic, in the light of modern understanding of the brain. Experience and thought are inextricable. |
| 15620 | Empiricism contains the important idea that we should see knowledge for ourselves, and be part of it [Hegel] |
| Full Idea: We must recognise the important principle of freedom that lies in Empiricism; namely, that what ought to count in our human knowing, we ought to see for ourselves, and to know ourselves as present in it. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §38 Rem) | |
| A reaction: Like Idea 15619, this is an interesting and perceptive remark, from a philosopher who seems a long way from empiricism. I presume he will be thinking mainly of Hume, via Kant. Personally I prefer Locke. |
| 15619 | Empiricism made particular knowledge possible, and blocked wild claims [Hegel] |
| Full Idea: Empiricism resulted from a need for concrete content, as opposed to abstract theories that cannot advance from universal generalizations to the particular, and for a firm hold against the possibility of proving any claim at all in the field. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §37) | |
| A reaction: That sounds about right, and makes you wonder why Hegel wasn't an empiricist. |
| 15622 | Empiricism unknowingly contains and uses a metaphysic, which underlies its categories [Hegel] |
| Full Idea: Empiricism operates without knowing that it contains a metaphysics and is engaged in it, and that it is using categories and their connections in a totally uncritical and unconscious manner. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §38 Rem) | |
| A reaction: I doubt whether this is true of modern empiricists, who have been challenged so often from within their own ranks on so many things. I'm not even sure that it is true of Locke and Hume, apart from the way in which all philosophers are unaware of things. |
| 15621 | Empiricism of the finite denies the supersensible, and can only think with formal abstraction [Hegel] |
| Full Idea: Inasmuch as Empiricism restricts itself to what is finite, the consistent carrying through of its programme denies the supersensible altogether, ..and it leaves thinking with abstraction only, [i.e.] with formal universality and identity. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §38 Rem) | |
| A reaction: I'm not clear how a denial of empiricism allows you (with intellectual integrity) to embrace 'the supersensible'. The set theoretic account of higher levels of infinity looks like a nice test case. |
| 15632 | The Humean view stops us thinking about perception, and finding universals and necessities in it [Hegel] |
| Full Idea: The Humean standpoint proclaims the thinking of our perceptions to be inadmissible; i.e. the eliciting of the universal and necessary out of those perceptions. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §50) | |
| A reaction: Obviously Hume permits 'relations of ideas', but presumably the point is that his approach only legitimates a rather passive abstraction from experience, rather than an active application of a priori concepts to it. A fair criticism. See Bonjour. |
| 12413 | A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher] |
| Full Idea: A 'warrant' refers to those processes which produce belief 'in the right way': X knows that p iff p, and X believes that p, and X's belief that p was produced by a process which is a warrant for it. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.2) | |
| A reaction: That is, a 'warrant' is a justification which makes a belief acceptable as knowledge. Traditionally, warrants give you certainty (and are, consequently, rather hard to find). I would say, in the modern way, that warrants are agreed by social convention. |
| 20473 | If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo] |
| Full Idea: According to Kitcher, if experiential evidence can defeat someone's justification for a belief, then their justification depends on the absence of that experiential evidence. | |
| From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984], p.89) by Albert Casullo - A Priori Knowledge 2.3 | |
| A reaction: Sounds implausible. There are trillions of possible defeaters for most beliefs, but to say they literally depend on trillions of absences seems a very odd way of seeing the situation |
| 15623 | Humean scepticism, unlike ancient Greek scepticism, accepts the truth of experience as basic [Hegel] |
| Full Idea: Humean scepticism should be very carefully distinguished from Greek scepticism. In Humean scepticism, the truth of the empirical, the truth of feeling and intuition is taken as basic. ..Greek scepticism turned itself against the sensible. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §39 Rem) | |
| A reaction: This seems right, and Hume himself was quite contemptuous of the sort of scepticism found in the ideas of Sextus Empiricus. |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| Full Idea: To idealize is to trade accuracy in describing the actual for simplicity of description, and the compromise can sometimes be struck in different ways. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: There is clearly rather more to idealisation than mere simplicity. A matchstick man is not an ideal man. |
| 15617 | In abstraction, beyond finitude, freedom and necessity must exist together [Hegel] |
| Full Idea: Considered as abstractly confronting one another, freedom and necessity pertain to finitude only and are valid only on its soil. A freedom with no necessity in it, and a mere necessity without freedom, are determinations that are abstract and thus untrue. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §35 Add) | |
| A reaction: This is, presumably, the Hegelian dialectical nature of things, that contradictories are bound together. We must struggle hard to undestand a freedom bound by necessity, and a necessity which contains freedom. (Good luck). |
| 15608 | The act of thinking is the bringing forth of universals [Hegel] |
| Full Idea: Thinking as an activity is the active universal, and indeed the self-actuating universal, since the act, or what is brought forth, is precisely the universal. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §20) | |
| A reaction: One should contemplate animal thought in the light of this remark. Thought requires the recognition of types of things, and resemblances, and repetitions, and patterns. Language consists almost entirely of universals. |
| 21986 | Hegel's system has a vast number of basic concepts [Hegel, by Moore,AW] |
| Full Idea: For Hegel the full system of concepts ...contains many more than Kant's twelve. | |
| From: report of Georg W.F.Hegel (Logic (Encyclopedia I) [1817], I §60Z) by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: This offers some sort of conceptual scheme, but not the structured one that Kant proposes. The sequence of dialectical mediation imposes some sort of shape on the concepts. |
| 15607 | We don't think with concepts - we think the concepts [Hegel] |
| Full Idea: There is a saying that, when we have grasped a concept, we still do not know what to think with it. But there is nothing to be thought with a concept save the concept itself. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §03 Rem) | |
| A reaction: Analytic philosophers should read Hegel on concepts, because he approaches the matter so very differently, and seems to be the root of the continental approach to such things. He seems to me to talk more sense than Frege on the subject. |
| 15610 | Active thought about objects produces the universal, which is what is true and essential of it [Hegel] |
| Full Idea: When thinking is taken as active with regard to ob-jects, as the thinking-over of something, then the universal - as the product of the activity - contains the value of the matter, what is essential, inner, true. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §21) | |
| A reaction: I prefer to talk of 'general terms' rather than 'universals'. If 'tiger' is coined for the first one, but must be applicable to subsequent tigers, it has to generalise what they all have in common. Locke's 'nominal' essence, I would say. |
| 15614 | Old metaphysics tried to grasp eternal truths through causal events, which is impossible [Hegel] |
| Full Idea: When finite things are grasped according to the determinations of cause and effect they are known in their finitude. But objects of reason cannot be determined through such finite predicates, and the attempt to do this was the defect of older metaphysics. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §28 Add) | |
| A reaction: This sounds the launching point for a grand philosophical system which makes scientifically inclined philosophers feel very nervous indeed. I think I prefer the old (pre-Kantian) metaphysics. |
| 15635 | The older conception of God was emptied of human features, to make it worthy of the Infinite [Hegel] |
| Full Idea: In earlier times, every type of so-called anthropomorphic representation was banished from God as finite, and hence unworthy of the Infinite; and as a result he had already grown into something remarkably empty. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §62 Rem) | |
| A reaction: Hegel favoured Christianity, because of its human aspect. His description fits Islam, where indeed the concept of God seems so drain of particularity that there is little in it to doubt, which might explain the durability of that religion. |
| 21980 | God is the absolute thing, and also the absolute person [Hegel] |
| Full Idea: It is true that God ...is the absolute thing: he is however no less the absolute person. That he is the absolute person however is a point which the philosophy of Spinoza never reached. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], I §151Z p.214), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.6 | |
| A reaction: Moore says Hegel was a Spinozist, in his commitment to a single substance, but his idea of God is very different, presumably because consciousness and concepts are so important to Hegel. Hegel needs a Lockean abstract notion of 'person' here. |
| 15618 | If God is the abstract of Supremely Real Essence, then God is a mere Beyond, and unknowable [Hegel] |
| Full Idea: When the concept of God is apprehended merely as that of the abstract of Supremely Real Essence, then God becomes for us a mere Beyond, and there can be no further talk of the cognition of God. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §36 Add) |
| 15633 | We establish unification of the Ideal by the ontological proof, deriving being from abstraction of thinking [Hegel] |
| Full Idea: One unification through which the Ideal is to be established starts from the abstraction of thinking and goes on to the determination for which being alone remains; this is the ontological proof that God is there. | |
| From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §51) | |
| A reaction: It should come as no surprise that a philosopher who so passionately endorses pure thinking, in opposition to empiricism, should end up endorsing the highly implausible ontological argument for God's existence. Jacquette gets existence from reason. |