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] |
| 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
| 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] |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| 8526 | We might treat both tropes and substances as fundamental, so we can't presume it is just tropes [Daly] |
| 8527 | More than one trope (even identical ones!) can occupy the same location [Daly] |
| 8528 | If tropes are linked by the existence of concurrence, a special relation is needed to link them all [Daly] |