7 ideas
| 14965 | Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta] |
| Full Idea: The basic principles governing truth are Truth Elimination (sentence A follows from ''A' is true') and the converse Truth Introduction (''A' is true' follows from A), which combine into Tarski's T-schema - 'A' is true if and only if A. | |
| From: Anil Gupta (Truth [2001], 5.1) | |
| A reaction: Introduction and Elimination rules are the basic components of natural deduction systems, so 'true' now works in the same way as 'and', 'or' etc. This is the logician's route into truth. |
| 14968 | A weakened classical language can contain its own truth predicate [Gupta] |
| Full Idea: If a classical language is expressively weakened - for example, by dispensing with negation - then it can contain its own truth predicate. | |
| From: Anil Gupta (Truth [2001], 5.2) | |
| A reaction: Thus the Tarskian requirement to move to a metalanguage for truth is only a requirement of a reasonably strong language. Gupta uses this to criticise theories that dispense with the metalanguage. |
| 19053 | Logic would be more natural if negation only referred to predicates [Dummett] |
| Full Idea: A better proposal for a formal logic closer to natural language would be one that had a negation-operator only for (simple) predicates. | |
| From: Michael Dummett (Presupposition [1960], p.27) | |
| A reaction: Dummett observes that classical formal logic was never intended to be close to natural language. Term logic does have that aim, but the meta-question is whether that end is desirable, and why. |
| 19052 | Natural language 'not' doesn't apply to sentences [Dummett] |
| Full Idea: Natural language does not possess a sentential negation-operator. | |
| From: Michael Dummett (Presupposition [1960], p.27) | |
| A reaction: This is a criticism of Strawson, who criticises logic for not following natural language, but does it himself with negation. In the question of how language and logic connect, this idea seems important. Term Logic aims to get closer to natural language. |
| 14964 | The Liar reappears, even if one insists on propositions instead of sentences [Gupta] |
| Full Idea: There is the idea that the Liar paradox is solved simply by noting that truth is a property of propositions (not of sentences), and the Liar sentence does not express a proposition. But we then say 'I am not now expressing a true proposition'! | |
| From: Anil Gupta (Truth [2001], 5.1) | |
| A reaction: Disappointed to learn this, since I think focusing on propositions (which are unambiguous) rather than sentences solves a huge number of philosophical problems. |
| 14969 | Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta] |
| Full Idea: An example of the Strengthened Liar is the following statement SL: 'Either SL is neither-true-nor-false or it is not true'. This raises a serious problem for any theory that assesses the paradoxes to be neither true nor false. | |
| From: Anil Gupta (Truth [2001], 5.4.2) | |
| A reaction: If the sentence is either true or false it reduces to the ordinary Liar. If it is neither true nor false, then it is true. |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |