Ideas from 'Truth' by Anil Gupta [2001], by Theme Structure

[found in 'Blackwell Guide to Philosophical Logic' (ed/tr Goble,Lou) [Blackwell 2001,0-631-20693-0]].

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3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true)
                        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.
3. Truth / F. Semantic Truth / 2. Semantic Truth
A weakened classical language can contain its own truth predicate
                        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.
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The Liar reappears, even if one insists on propositions instead of sentences
                        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.
Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true
                        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.