27 ideas
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] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
20712 | God is 'eternal' either by being non-temporal, or by enduring forever [Davies,B] |
20701 | Can God be good, if he has not maximised goodness? [Davies,B] |
20702 | The goodness of God may be a higher form than the goodness of moral agents [Davies,B] |
20703 | How could God have obligations? What law could possibly impose them? [Davies,B] |
20694 | 'Natural theology' aims to prove God to anyone (not just believers) by reason or argument [Davies,B] |
20706 | A distinct cause of the universe can't be material (which would be part of the universe) [Davies,B] |
20707 | The universe exhibits design either in its sense of purpose, or in its regularity [Davies,B] |
20708 | If God is an orderly being, he cannot be the explanation of order [Davies,B] |
20710 | Maybe an abnormal state of mind is needed to experience God? [Davies,B] |
20711 | A believer can experience the world as infused with God [Davies,B] |
20709 | The experiences of God are inconsistent, not universal, and untestable [Davies,B] |
20697 | One does not need a full understanding of God in order to speak of God [Davies,B] |
20699 | Paradise would not contain some virtues, such as courage [Davies,B] |