28 ideas
7578 | I conceived it my task to create difficulties everywhere [Kierkegaard] |
22047 | Wherever there is painless contradiction there is also comedy [Kierkegaard] |
22092 | Kierkegaard's truth draws on authenticity, fidelity and honesty [Kierkegaard, by Carlisle] |
15999 | Pure truth is for infinite beings only; I prefer endless striving for truth [Kierkegaard] |
20313 | The highest truth we can get is uncertainty held fast by an inward passion [Kierkegaard] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
20742 | The real subject is ethical, not cognitive [Kierkegaard] |
11127 | If concepts just are mental representations, what of concepts we may never acquire? [Peacocke] |
7579 | While big metaphysics is complete without ethics, personal philosophy emphasises ethics [Kierkegaard] |
7581 | Speculative philosophy loses the individual in a vast vision of humanity [Kierkegaard] |
20314 | People want to lose themselves in movements and history, instead of being individuals [Kierkegaard] |
7582 | Becoming what one is is a huge difficulty, because we strongly aspire to be something else [Kierkegaard] |
7586 | God does not think or exist; God creates, and is eternal [Kierkegaard] |
20312 | God cannot be demonstrated objectively, because God is a subject, only existing inwardly [Kierkegaard] |
7580 | Pantheism destroys the distinction between good and evil [Kierkegaard] |
7583 | Faith is the highest passion in the sphere of human subjectivity [Kierkegaard] |
7584 | Without risk there is no faith [Kierkegaard] |