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Ideas for 'works', 'On the Nature of Mathematical Reasoning' and 'Logic (Encyclopedia I)'

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11 ideas

2. Reason / A. Nature of Reason / 2. Logos
For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle]
     Full Idea: For Aristotle logos is the ability to speak rationally about, with the hope of attaining knowledge, questions of value.
     From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.26
2. Reason / A. Nature of Reason / 3. Pure Reason
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.
2. Reason / A. Nature of Reason / 4. Aims of Reason
Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle]
     Full Idea: Aristotle is the great theoretician who articulates a vision of a world in which natural and stable structures can be rationally discovered. His is the most optimistic and richest view of the possibilities of logos
     From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.95
2. Reason / A. Nature of Reason / 5. Objectivity
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.
2. Reason / B. Laws of Thought / 3. Non-Contradiction
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.
2. Reason / C. Styles of Reason / 1. Dialectic
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.
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.
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)
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.
2. Reason / D. Definition / 4. Real Definition
Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine]
     Full Idea: A real definition, according to the Aristotelian tradition, gives the essence of the kind of thing defined. Man is defined as a rational animal, and thus rationality and animality are of the essence of each of us.
     From: report of Aristotle (works [c.330 BCE]) by Willard Quine - Vagaries of Definition p.51
     A reaction: Compare Idea 4385. Personally I prefer the Aristotelian approach, but we may have to say 'We cannot identify the essence of x, and so x cannot be defined'. Compare 'his mood was hard to define' with 'his mood was hostile'.
2. Reason / D. Definition / 5. Genus and Differentia
Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson]
     Full Idea: For Aristotle, to give a definition one must first state the genus and then the differentia of the kind of thing to be defined.
     From: report of Aristotle (works [c.330 BCE]) by J.O. Urmson - Aristotle's Doctrine of the Mean p.157
     A reaction: Presumably a modern definition would just be a list of properties, but Aristotle seeks the substance. How does he define a genus? - by placing it in a further genus?