16 ideas
| 13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
| 13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 5987 | Alcmaeon was the first to say the brain is central to thinking [Alcmaeon, by Staden, von] |
| 24043 | Soul must be immortal, since it continually moves, like the heavens [Alcmaeon, by Aristotle] |