Combining Texts

All the ideas for 'The Runabout Inference Ticket', 'Miscellaneous Observations' and 'The Architecture of Mathematics'

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13 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.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
We need to know the meaning of 'and', prior to its role in reasoning [Prior,AN, by Belnap]
     Full Idea: For Prior, so the moral goes, we must first have a notion of what 'and' means, independently of the role it plays as premise and as conclusion.
     From: report of Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.132
     A reaction: The meaning would be given by the truth tables (the truth-conditions), whereas the role would be given by the natural deduction introduction and elimination rules. This seems to be the basic debate about logical connectives.
Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B [Belnap on Prior,AN]
     Full Idea: Prior's definition of 'tonk' is inconsistent. It gives us an extension of our original characterisation of deducibility which is not conservative, since in the extension (but not the original) we have, for arbitrary A and B, A |- B.
     From: comment on Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.135
     A reaction: Belnap's idea is that connectives don't just rest on their rules, but also on the going concern of normal deduction.
Prior rejected accounts of logical connectives by inference pattern, with 'tonk' his absurd example [Prior,AN, by Read]
     Full Idea: Prior dislike the holism inherent in the claim that the meaning of a logical connective was determined by the inference patterns into which it validly fitted. ...His notorious example of 'tonk' (A → A-tonk-B → B) was a reductio of the view.
     From: report of Arthur N. Prior (The Runabout Inference Ticket [1960]) by Stephen Read - Thinking About Logic Ch.8
     A reaction: [The view being attacked was attributed to Gentzen]
Maybe introducing or defining logical connectives by rules of inference leads to absurdity [Prior,AN, by Hacking]
     Full Idea: Prior intended 'tonk' (a connective which leads to absurdity) as a criticism of the very idea of introducing or defining logical connectives by rules of inference.
     From: report of Arthur N. Prior (The Runabout Inference Ticket [1960], §09) by Ian Hacking - What is Logic?
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]
     Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures.
     From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79
     A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s.
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.
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.
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.