16 ideas
| 17596 | Coherence problems have positive and negative restraints; solutions maximise constraint satisfaction [Thagard] |
| Full Idea: A coherence problem is a set of elements connected by positive and negative restraints, and a solution consists of partitioning the elements into two sets (accepted and rejected) in a way that maximises satisfaction of the constraints. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.42) | |
| A reaction: I'm enthusiastic about this, as it begins to clarify the central activity of epistemology, which is the quest for best explanations. |
| 17597 | Coherence is explanatory, deductive, conceptual, analogical, perceptual, and deliberative [Thagard] |
| Full Idea: I propose that there are six main kinds of coherence: explanatory, deductive, conceptual, analogical, perceptual, and deliberative. ...Epistemic coherence is a combination of the first five kinds, and ethics adds the sixth. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.43) | |
| A reaction: Wonderful. Someone is getting to grips with the concept of coherence, instead of just whingeing about how vague it is. |
| 17598 | Explanatory coherence needs symmetry,explanation,analogy,data priority, contradiction,competition,acceptance [Thagard] |
| Full Idea: Informally, a theory of explanatory coherence has the principles of symmetry, explanation, analogy, data priority, contradiction, competition and acceptance. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.44) | |
| A reaction: [Thagard give a concise summary of his theory here] Again Thagard makes a wonderful contribution in an area where most thinkers are pessimistic about making any progress. His principles are very plausible. |
| 17602 | Verisimilitude comes from including more phenomena, and revealing what underlies [Thagard] |
| Full Idea: A scientific theory is progressively approximating the truth if it increases its explanatory coherence by broadening to more phenomena and deepening by investigating layers of mechanisms. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.46) |
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion. | |
| From: JC Beall / G Restall (Logical Consequence [2005], Intro) |
| 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) |
| 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) |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 17601 | Neither a priori rationalism nor sense data empiricism account for scientific knowledge [Thagard] |
| Full Idea: Both rationalists (who start with a priori truths and make deductions) and empiricists (starting with indubitable sense data and what follows) would guarantee truth, but neither even begins to account for scientific knowledge. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.46) | |
| A reaction: Thagard's answer, and mine, is inference to the best explanation, but goes beyond both the a priori truths and the perceptions. |
| 17600 | Bayesian inference is forced to rely on approximations [Thagard] |
| Full Idea: It is well known that the general problem with Bayesian inference is that it is computationally intractable, so the algorithms used for computing posterior probabilities have to be approximations. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.45) | |
| A reaction: Thagard makes this sound devastating, but then concedes that all theories have to rely on approximations, so I haven't quite grasped this idea. He gives references. |
| 17599 | The best theory has the highest subjective (Bayesian) probability? [Thagard] |
| Full Idea: On the Bayesian view, the best theory is the one with the highest subjective probability, given the evidence as calculated by Bayes's theorem. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.45) |
| 9141 | Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert] |
| Full Idea: A theory of abstraction is any account that reconstructs mathematical theories using second-order abstraction principles of the form: §xFx = §xGx iff E(F,G). We ignore first-order abstraction principles such as Frege's direction abstraction. | |
| From: R Cook / P Ebert (Notice of Fine's 'Limits of Abstraction' [2004], 1) | |
| A reaction: Presumably part of the neo-logicist programme, which also uses such principles. The function § (extension operator) 'provides objects corresponding to the argument concepts'. The aim is to build mathematics, rather than the concept of a 'rabbit'. |