display all the ideas for this combination of texts
9 ideas
10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
Full Idea: Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought. | |
From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
A reaction: [compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski. |
10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
Full Idea: Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples. | |
From: JC Beall / G Restall (Logical Consequence [2005], 3) |
10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
Full Idea: Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists). | |
From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
A reaction: Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one. |
10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
Full Idea: A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form. | |
From: JC Beall / G Restall (Logical Consequence [2005], 2) |
9148 | I think of variables as objects rather than as signs [Fine,K] |
Full Idea: It is natural nowadays to think of variables as a certain kind of sign, but I wish to think of them as a certain kind of object. | |
From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §2) | |
A reaction: Fine has a theory based on 'arbitrary objects', which is a rather charming idea. The cell of a spreadsheet is a kind of object, I suppose. A variable might be analogous to a point in space, where objects can locate themselves. |
10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'. | |
From: JC Beall / G Restall (Logical Consequence [2005], 4) | |
A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules. |
10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
Full Idea: Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language. | |
From: JC Beall / G Restall (Logical Consequence [2005], 3) |
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. |