display all the ideas for this combination of texts
3 ideas
| 19195 | Truth tables give prior conditions for logic, but are outside the system, and not definitions [Tarski] |
| Full Idea: Logical sentences are often assigned preliminary conditions under which they are true or false (often given as truth tables). However, these are outside the system of logic, and should not be regarded as definitions of the terms involved. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 15) | |
| A reaction: Hence, presumably, the connectives are primitives (with no nature or meaning), and the truth tables are axioms for their use? This opinion of Tarski's may have helped shift the preference towards natural deduction introduction and elimination rules. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |