40 ideas
| 1642 | We must fight fiercely for knowledge, understanding and intelligence [Plato] |
| 13734 | Modern Quinean metaphysics is about what exists, but Aristotelian metaphysics asks about grounding [Schaffer,J] |
| 13751 | If you tore the metaphysics out of philosophy, the whole enterprise would collapse [Schaffer,J] |
| 1645 | The desire to split everything into its parts is unpleasant and unphilosophical [Plato] |
| 13743 | We should not multiply basic entities, but we can have as many derivative entities as we like [Schaffer,J] |
| 287 | Good analysis involves dividing things into appropriate forms without confusion [Plato] |
| 1644 | Dialectic should only be taught to those who already philosophise well [Plato] |
| 20478 | In discussion a person's opinions are shown to be in conflict, leading to calm self-criticism [Plato] |
| 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] |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [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] |
| 13741 | If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J] |
| 11278 | What does 'that which is not' refer to? [Plato] |
| 1643 | If statements about non-existence are logically puzzling, so are statements about existence [Plato] |
| 7022 | To be is to have a capacity, to act on other things, or to receive actions [Plato] |
| 13748 | Grounding is unanalysable and primitive, and is the basic structuring concept in metaphysics [Schaffer,J] |
| 13747 | Supervenience is just modal correlation [Schaffer,J] |
| 13744 | The cosmos is the only fundamental entity, from which all else exists by abstraction [Schaffer,J] |
| 1641 | Some alarming thinkers think that only things which you can touch exist [Plato] |
| 10784 | Whenever there's speech it has to be about something [Plato] |
| 13739 | Maybe categories are just the different ways that things depend on basic substances [Schaffer,J] |
| 16122 | Good thinkers spot forms spread through things, or included within some larger form [Plato] |
| 10422 | The not-beautiful is part of the beautiful, though opposed to it, and is just as real [Plato] |
| 15855 | If we see everything as separate, we can then give no account of it [Plato] |
| 13742 | There exist heaps with no integral unity, so we should accept arbitrary composites in the same way [Schaffer,J] |
| 13752 | The notion of 'grounding' can explain integrated wholes in a way that mere aggregates can't [Schaffer,J] |
| 13749 | Belief in impossible worlds may require dialetheism [Schaffer,J] |
| 13740 | 'Moorean certainties' are more credible than any sceptical argument [Schaffer,J] |
| 1637 | A soul without understanding is ugly [Plato] |
| 1636 | Wickedness is an illness of the soul [Plato] |
| 1638 | Didactic education is hard work and achieves little [Plato] |