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. |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
Full Idea: The terms 'set' and 'is a member of' are primitives of Zermelo's 1908 axiomatization of set theory. They are not given model-theoretic analyses or definitions. | |
From: report of Ernst Zermelo (works [1920]) by Charles Chihara - A Structural Account of Mathematics 7.5 | |
A reaction: This looks like good practice if you want to work with sets, but not so hot if you are interested in metaphysics. |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
Full Idea: For Zermelo's set theory the empty set is zero and the successor of each number is its unit set. | |
From: report of Ernst Zermelo (works [1920]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280 |
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. |
5996 | Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA] |
Full Idea: Critolaus reformulated Aristotelian theory by defining happiness as a 'fulfilment' (sumplêrôma) of psychic, physical, and external goods, where virtue vastly outweighs the rest. | |
From: report of Critolaus (fragments/reports [c.170 BCE]) by Stephen A. White - Critolaus | |
A reaction: The sounds more like an attempt at clarification than a real change of Peripatetic doctrine. Occasionally 'fulfilment' is offered as a translation for eudaimonia. Maybe we should just take up Critolaus' suggestion when we are discussing Aristotle. |