Combining Texts

All the ideas for 'The Science of Knowing (Wissenschaftslehre) [1st ed]', 'Introduction to the Philosophy of Mathematics' and 'Friendship'

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35 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
22024 Fichte's subjectivity struggles to then give any account of objectivity [Pinkard on Fichte]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
17925 Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan]
17926 Rejecting double negation elimination undermines reductio proofs [Colyvan]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
17924 Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
22017 Normativity needs the possibility of negation, in affirmation and denial [Fichte, by Pinkard]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17929 Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17930 Axioms are 'categorical' if all of their models are isomorphic [Colyvan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17928 Ordinal numbers represent order relations [Colyvan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17923 Intuitionists only accept a few safe infinities [Colyvan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
17941 Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17922 Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17936 Transfinite induction moves from all cases, up to the limit ordinal [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17940 Most mathematical proofs are using set theory, but without saying so [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
17931 Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
17932 If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
22018 Necessary truths derive from basic assertion and negation [Fichte, by Pinkard]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
22064 Fichte's logic is much too narrow, and doesn't deduce ethics, art, society or life [Schlegel,F on Fichte]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
22032 Fichte's key claim was that the subjective-objective distinction must itself be subjective [Fichte, by Pinkard]
14. Science / C. Induction / 6. Bayes's Theorem
17943 Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
17939 Mathematics can reveal structural similarities in diverse systems [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / f. Necessity in explanations
17938 Mathematics can show why some surprising events have to occur [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
17933 Reductio proofs do not seem to be very explanatory [Colyvan]
17935 If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan]
17942 Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan]
17934 Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / a. Other minds
22020 We only see ourselves as self-conscious and rational in relation to other rationalities [Fichte]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
17937 Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
22060 The Self is the spontaneity, self-relatedness and unity needed for knowledge [Fichte, by Siep]
22066 Novalis sought a much wider concept of the ego than Fichte's proposal [Novalis on Fichte]
22016 The self is not a 'thing', but what emerges from an assertion of normativity [Fichte, by Pinkard]
16. Persons / B. Nature of the Self / 6. Self as Higher Awareness
22019 Consciousness of an object always entails awareness of the self [Fichte]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
22061 Judgement is distinguishing concepts, and seeing their relations [Fichte, by Siep]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
22023 Fichte's idea of spontaneity implied that nothing counts unless we give it status [Fichte, by Pinkard]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
23834 Friendship is partly universal - the love of a person is like the ideal of loving everyone [Weil]
26. Natural Theory / A. Speculations on Nature / 1. Nature
22065 Fichte reduces nature to a lifeless immobility [Schlegel,F on Fichte]