12 ideas
| 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) |
| 19727 | Reliabilist knowledge is evidence based belief, with high conditional probability [Comesaņa] |
| Full Idea: The best definition of reliabilism seems to be: the agent has evidence, and bases the belief on the evidence, and the actual conditional reliability of the belief on the evidence is high enough. | |
| From: Juan Comesaņa (Reliabilism [2011], 4.4) | |
| A reaction: This is Comesaņa's own theory, derived from Alston 1998, and based on conditional probabilities. |
| 19725 | In a sceptical scenario belief formation is unreliable, so no beliefs at all are justified? [Comesaņa] |
| Full Idea: If the processes of belief-formation are unreliable (perhaps in a sceptical scenario), then reliabilism has the consequence that those victims can never have justified beliefs (which Sosa calls the 'new evil demon problem'). | |
| From: Juan Comesaņa (Reliabilism [2011], 4.1) | |
| A reaction: That may be the right outcome. Could you have mathematical knowledge in a sceptical scenario? But that would be different processes. If I might be a brain in a vat, then it's true that I have no perceptual knowledge. |
| 19726 | How do we decide which exact process is the one that needs to be reliable? [Comesaņa] |
| Full Idea: The reliabilist has the problem of finding a principled way of selecting, for each token-process of belief formation, the type whose reliability ratio must be high enough for the belief to be justified. | |
| From: Juan Comesaņa (Reliabilism [2011], 4.3) | |
| A reaction: The question is which exact process I am employing for some visual knowledge (and how the process should be described). Seeing, staring, squinting, glancing.... This seems to be called the 'generality problem'. |
| 20956 | Ultimately, all being is willing. The nature of primal being is the same as the nature of willing [Schelling] |
| Full Idea: In the last and highest instance there is no other being but willing. Willing is primal being, and all the predicates of primal being only fit willing: groundlessness, eternity, being independent of time, self-affirmation. | |
| From: Friedrich Schelling (On the Essence of Human Freedom [1809], I.7.350), quoted by Andrew Bowie - Introduction to German Philosophy 5 'Reason' | |
| A reaction: Insofar as this says that 'primal being' must be active in character, I love this idea. Not the rest of the idea though! Bowie says this essay clearly influenced Schopenhauer. It looks as if Nietzsche must be read it too. |