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All the ideas for 'fragments/reports', 'Intuitionism and Formalism' and 'Miscellaneous Observations'

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15 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
If man sacrifices truth he sacrifices himself, by acting against his own convictions [Novalis]
     Full Idea: Man has his being in truth - if he sacrifices truth he sacrifices himself. Whoever betrays truth betrays himself. It is not a question of lying - but of acting against one's conviction.
     From: Novalis (Miscellaneous Observations [1798], 038)
     A reaction: Does he condone lying here, as long as you don't believe the lie? We would call it loss of integrity.
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
Delusion and truth differ in their life functions [Novalis]
     Full Idea: The distinction between delusion and truth lies in the difference in their life functions.
     From: Novalis (Miscellaneous Observations [1798], 008)
     A reaction: Pure pragmatism, it seems. We might expect doubts about objective truth from a leading light of the Romantic movement.
4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer]
     Full Idea: Not to the mathematician, but to the psychologist, belongs the task of explaining why ...we are averse to so-called contradictory systems in which the negative as well as the positive of certain propositions are valid.
     From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.79)
     A reaction: Was the turning point of Graham Priest's life the day he read this sentence? I don't agree. I take the principle of non-contradiction to be a highly generalised observation of how the world works (and Russell agrees with me).
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
Scientific laws largely rest on the results of counting and measuring [Brouwer]
     Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring.
     From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77)
     A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionists only accept denumerable sets [Brouwer]
     Full Idea: The intuitionist recognises only the existence of denumerable sets.
     From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80)
     A reaction: That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days.
Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
     Full Idea: Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness.
     From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80)
     A reaction: [compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals.
9. Objects / D. Essence of Objects / 3. Individual Essences
Refinement of senses increasingly distinguishes individuals [Novalis]
     Full Idea: The more our senses are refined, the more capable they become of distinguishing between individuals. The highest sense would be the highest receptivity to particularity in human nature.
     From: Novalis (Miscellaneous Observations [1798], 072)
     A reaction: I adore this idea!! It goes into the collection of support I am building for individual essences, against the absurd idea of kinds as essences (when they are actually categorisations). It also accompanies particularism in ethics.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Experiences tests reason, and reason tests experience [Novalis]
     Full Idea: Experience is the test of the rational - and vice versa.
     From: Novalis (Miscellaneous Observations [1798], 010)
     A reaction: A wonderful remark. Surely we can't ignore our need to test claims of pure logic by filling in the variables with concrete instances, to assess validity? And philosophy without examples is doomed to be abstract waffle. Coherence is the combined aim.
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
The seat of the soul is where our inner and outer worlds interpenetrate [Novalis]
     Full Idea: The seat of the soul is the point where the inner and the outer worlds touch. Wherever they penetrate each other - it is there at every point of penetration.
     From: Novalis (Miscellaneous Observations [1798], 020)
     A reaction: I surmise that Spinoza's dual-aspect monism is behind this interesting remark. See the related idea from Schopenhauer.
18. Thought / E. Abstraction / 2. Abstracta by Selection
Everything is a chaotic unity, then we abstract, then we reunify the world into a free alliance [Novalis]
     Full Idea: Before abstraction everything is one - but one as chaos is - after abstraction everything is again unified - but in a free alliance of independent, self-determined beings. A crowd has become a society - a chaos is transformed into a manifold world.
     From: Novalis (Miscellaneous Observations [1798], 094)
     A reaction: Personally I take (unfashionably) psychological abstraction to one of the key foundations of human thought, so I love this idea, which gives a huge picture of how the abstracting mind relates to reality.
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman]
     Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions.
     From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
     A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met.
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Only self-illuminated perfect individuals are beautiful [Novalis]
     Full Idea: Everything beautiful is a self-illuminated, perfect individual.
     From: Novalis (Miscellaneous Observations [1798], 101)
     A reaction: It is a commonplace to describe something beautiful as being 'perfect'. Unfinished masterpieces are interesting exceptions. Are only 'individuals' beautiful? Is unity a necessary condition of beauty? Bad art fails to be self-illuminated.
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
     Full Idea: Archelaus was the first person to say that the universe is boundless.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]
     Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
     A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Religion needs an intermediary, because none of us can connect directly to a godhead [Novalis]
     Full Idea: Nothing is more indispensable for true religious feeling than an intermediary - which connects us to the godhead. The human being is absolutely incapable of sustaining an immediate relation with this.
     From: Novalis (Miscellaneous Observations [1798], 073)
     A reaction: I take this to be a defence of priests and organised religion, and an implied attack on protestants who give centrality to private prayer and conscience.