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All the ideas for 'works', 'Continuity and Irrational Numbers' and 'Five Milestones of Empiricism'

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13 ideas

2. Reason / D. Definition / 7. Contextual Definition
Contextual definition shifted the emphasis from words to whole sentences [Quine]
     Full Idea: Contextual definition precipitated a revolution in semantics. The primary vehicle of meaning is seen no longer as the word, but as the sentence.
     From: Willard Quine (Five Milestones of Empiricism [1975], p.69)
     A reaction: I think the idea is that the term is now supported entirely by its surrounding language, and not by its denotation of something in the world.
Bentham's contextual definitions preserved terms after their denotation became doubtful [Quine]
     Full Idea: If Bentham found some term convenient but ontologically embarrassing, contextual definition enabled him in some cases to continue to enjoy the services of the term while disclaiming its denotation.
     From: Willard Quine (Five Milestones of Empiricism [1975], p.68)
     A reaction: In Quine's terms this would be to withdraw the term from the periphery of the theory, where it has to meet the world, and make it part of the inner connections of the theory. He suggests that Bentham invented this technique.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
     Full Idea: It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], Intro)
     A reaction: [He seeks the origin of the theorem that differential calculus deals with continuous magnitude, and he wants an arithmetical rather than geometrical demonstration; the result is his famous 'cut'].
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A cut between rational numbers creates and defines an irrational number [Dedekind]
     Full Idea: Whenever we have to do a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], §4)
     A reaction: Fine quotes this to show that the Dedekind Cut creates the irrational numbers, rather than hitting them. A consequence is that the irrational numbers depend on the rational numbers, and so can never be identical with any of them. See Idea 10573.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
     Full Idea: I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself is nothing else than the successive creation of the infinite series of positive integers.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], §1)
     A reaction: Thus counting roots arithmetic in the world, the successor operation is the essence of counting, and the Dedekind-Peano axioms are built around successors, and give the essence of arithmetic. Unfashionable now, but I love it. Intransitive counting?
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
If x changes by less and less, it must approach a limit [Dedekind]
     Full Idea: If in the variation of a magnitude x we can for every positive magnitude δ assign a corresponding position from and after which x changes by less than δ then x approaches a limiting value.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], p.27), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.7
     A reaction: [Kitcher says he 'showed' this, rather than just stating it]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
In scientific theories sentences are too brief to be independent vehicles of empirical meaning [Quine]
     Full Idea: We have come to recognise that in a scientific theory even a whole sentence is ordinarily too short a text to serve as an independent vehicle of empirical meaning.
     From: Willard Quine (Five Milestones of Empiricism [1975], p.70)
Empiricism improvements: words for ideas, then sentences, then systems, then no analytic, then naturalism [Quine]
     Full Idea: Since 1750 empiricism shows five turns for the better. First was a shift from ideas to words. Second a shift from terms to sentences. Third the shift to systems of sentences. Fourth the abandonment of analytic-synthetic dualism. Fifth was naturalism.
     From: Willard Quine (Five Milestones of Empiricism [1975], p.67)
     A reaction: [compressed] Quine must be largely credited with the last two. The first four are almost entirely linguistic in character, which is characteristic of mid-twentieth-century empiricism. I would offer the recognition of explanation as central for the sixth.
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
Freud treats the unconscious as intentional and hence mental [Freud, by Searle]
     Full Idea: Freud thinks that our unconscious mental states exist as occurrent intrinsic intentional states even when unconscious. Their ontology is that of the mental, even when they are unconscious.
     From: report of Sigmund Freud (works [1900]) by John Searle - The Rediscovery of the Mind Ch. 7.V
     A reaction: Searle states this view in order to attack it. Whether such states are labelled as 'mental' seems uninteresting. Whether unconscious states can be intentional is crucial, and modern scientific understanding of the brain strongly suggest they can.
16. Persons / C. Self-Awareness / 3. Limits of Introspection
Freud and others have shown that we don't know our own beliefs, feelings, motive and attitudes [Freud, by Shoemaker]
     Full Idea: Freud persuaded many that beliefs, wishes and feelings are sometimes unconscious, and even sceptics about Freud acknowledge that there is self-deception about motive and attitudes.
     From: report of Sigmund Freud (works [1900]) by Sydney Shoemaker - Introspection p.396
     A reaction: This seems to me obviously correct. The traditional notion is that the consciousness is the mind, but now it seems obvious that consciousness is only one part of the mind, and maybe even a peripheral (epiphenomenal) part of it.
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
Freud said passions are pressures of some flowing hydraulic quantity [Freud, by Solomon]
     Full Idea: Freud argued that the passions in general …were the pressures of a yet unknown 'quantity' (which he simply designated 'Q'). He first thought this flowed through neurones, …and always couched the idea in the language of hydraulics.
     From: report of Sigmund Freud (works [1900]) by Robert C. Solomon - The Passions 3.4
     A reaction: This is the main target of Solomon's criticism, because its imagery has become so widespread. It leads to talk of suppressing emotions, or sublimating them. However, it is not too different from Nietzsche's 'drives' or 'will to power'.
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
Holism in language blurs empirical synthetic and empty analytic sentences [Quine]
     Full Idea: Holism blurs the supposed contrast beween the synthetic sentence, with its empirical content, and the analytic sentence, with its null content.
     From: Willard Quine (Five Milestones of Empiricism [1975], p.71)
     A reaction: This spells out nicely that Quine's rejection of the distinction is completely tied to his holistic view of language. The obvious phenomenon of compositionality (building sentence meaning in steps) counts against holism.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Freud is pessimistic about human nature; it is ambivalent motive and fantasy, rather than reason [Freud, by Murdoch]
     Full Idea: Freud takes a thoroughly pessimistic view of human nature. ...Introspection reveals only the deep tissue of ambivalent motive, and fantasy is a stronger force than reason. Objectivity and unselfishness are not natural to human beings.
     From: report of Sigmund Freud (works [1900], II) by Iris Murdoch - The Sovereignty of Good II
     A reaction: Interesting. His view seems to have coloured the whole of modern culture, reinforced by the hideous irrationality of the Nazis. Adorno and Horkheimer attacking the Enlightenment was the last step in that process.