Combining Texts

All the ideas for 'Cours d'Analyse', 'Theology and Verification' and 'The Concept of Dread (/Anxiety)'

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10 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
     Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit.
     From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
     A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
     Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others.
     From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
     A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction?
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
Socrates neglects the gap between knowing what is good and doing good [Kierkegaard, by Carlisle]
     Full Idea: There is a fundamental weakness in Socrates, that he does not take into account the gap between knowing what is good and actually putting this into action.
     From: report of Søren Kierkegaard (The Concept of Dread (/Anxiety) [1844]) by Clare Carlisle - Kierkegaard: a guide for the perplexed 5
     A reaction: This rejects Socrates's intellectualism about weakness of will. It is perhaps a better criticism that Aristotle's view that desires sometimes overcome the will. It is also the problem of motivation in Kantian deontology. Or utilitarianism.
23. Ethics / F. Existentialism / 3. Angst
Anxiety is not a passing mood, but a response to human freedom [Kierkegaard, by Carlisle]
     Full Idea: For Kierkegaard anxiety is not simply a mood or an emotion that certain people experience at certain times, but a basic response to freedom that is part of the human condition.
     From: report of Søren Kierkegaard (The Concept of Dread (/Anxiety) [1844]) by Clare Carlisle - Kierkegaard: a guide for the perplexed 5
     A reaction: Outside of Christianity, this may be Kierkegaard's most influential idea - since existential individualism is floating around in the romantic movement. But the Byronic hero experiences a sort of anxiety. If you can't face anxiety, become a monk or nun.
The ultimate in life is learning to be anxious in the right way [Kierkegaard]
     Full Idea: Every human being must learn to be anxious in order that he might not perish either by never having been in anxiety or by succumbing in anxiety. Whoever has learned to be anxious in the right way has learnt the ultimate.
     From: Søren Kierkegaard (The Concept of Dread (/Anxiety) [1844], p.154), quoted by Clare Carlisle - Kierkegaard: a guide for the perplexed 5
     A reaction: I think this is the most existentialist quotation I have found in Kierkegaard. It sounds circular. You must be in anxiety because otherwise you won't be able to cope with anxiety? I suppose anxiety is facing up to his concept of truth.
Ultimate knowledge is being anxious in the right way [Kierkegaard]
     Full Idea: Whoever learns to be anxious in the right way has learned the ultimate.
     From: Søren Kierkegaard (The Concept of Dread (/Anxiety) [1844], p.187), quoted by Alastair Hannay - Kierkegaard 06
     A reaction: This shows us that Kierkegaard had a rather bizarre mental life which the rest of us have little chance of penetrating. I'll have a go at cataloguing my types of anxiety, but I'm not hopeful.
Anxiety is staring into the yawning abyss of freedom [Kierkegaard]
     Full Idea: One may liken anxiety to dizziness. He whose eyes chance to look down into a yawning abyss becomes dizzy. Anxiety is the dizziness of freedom which is when freedom gazes down into its own possibility, grasping at finiteness to sustain itself.
     From: Søren Kierkegaard (The Concept of Dread (/Anxiety) [1844], p.55), quoted by Kevin Aho - Existentialism: an introduction 6 'Moods'
     A reaction: Most of us rapidly retreat from the thought of the infinity of things we might choose. Choosing bizarrely merely to assert one's freedom is simple stupidity.
29. Religion / D. Religious Issues / 1. Religious Commitment / c. Religious Verification
Belief in an afterlife may be unverifiable in this life, but it will be verifiable after death [Hick, by PG]
     Full Idea: Religion is capable of 'eschatological verification', by reaching evidence at the end of life, even though falsification of its claims is never found in this life; a prediction of coming to a Celestial City must await the end of the journey.
     From: report of John Hick (Theology and Verification [1960], III) by PG - Db (ideas)
It may be hard to verify that we have become immortal, but we could still then verify religious claims [Hick, by PG]
     Full Idea: Verification of religious claims after death is only possible if the concept of surviving death is intelligible, and we can understand the concept of immortality, despite difficulties in being certain that we had reached it.
     From: report of John Hick (Theology and Verification [1960], IV) by PG - Db (ideas)
29. Religion / D. Religious Issues / 1. Religious Commitment / d. Religious Falsification
Some things (e.g. a section of the expansion of PI) can be verified but not falsified [Hick, by PG]
     Full Idea: Falsification and verification are not logically equivalent. For example, you might verify the claim that there will be three consecutive sevens in the infinite expansion of PI, but you could never falsify such a claim.
     From: report of John Hick (Theology and Verification [1960], §II) by PG - Db (ideas)