display all the ideas for this combination of texts
3 ideas
| 8173 | Language can violate bivalence because of non-referring terms or ill-defined predicates [Dummett] |
| Full Idea: Two features of natural languages cause them to violate bivalence: singular terms (or proper names) which have a sense but fail to denote an object ('the centre of the universe'); and predicates which are not well defined for every object. | |
| From: Michael Dummett (Thought and Reality [1997], 4) | |
| A reaction: If we switch from sentences to propositions these problems might be avoided. If there is no reference, or a vague predicate, then there is (maybe) just no proposition being expressed which could be evaluated for truth. |
| 8179 | The law of excluded middle is the logical reflection of the principle of bivalence [Dummett] |
| Full Idea: The law of excluded middle is the reflection, within logic, of the principle of bivalence. It states that 'For any statement A, the statement 'A or not-A' is true'. | |
| From: Michael Dummett (Thought and Reality [1997], 5) | |
| A reaction: True-or-not-true is an easier condition to fulfil than true-or-false. The second says that 'false' is the only alternative, but the first allows other alternatives to 'true' (such as 'undecidable'). It is hard to challenge excluded middle. Somewhat true? |
| 2669 | Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero] |
| Full Idea: It is a fundamental principle of dialectic that every statement is either true or false. So is this a true proposition or a false one: "If you say that you are lying and say it truly, you lie"? | |
| From: M. Tullius Cicero (Academica [c.45 BCE], II.xxix.95) |