17 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) |
| 16659 | Relations do not add anything to reality, though they are real aspects of the world [Olivi] |
| Full Idea: It does not seem that a relation adds anything real to that on which it is founded, but only makes for another real aspect belonging to the same thing. It is real since an aspect exists in re, not solely in the intellect, but it is not another thing. | |
| From: Peter John Olivi (Summa quaestionum super Sententias [1290], II.54), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.4 |
| 16673 | Quantity just adds union and location to the extension of parts [Olivi] |
| Full Idea: Quantity or extension adds absolutely nothing really distinct to the quantified matter or to the extended and quantified form, except perhaps the union and location and position of those parts. | |
| From: Peter John Olivi (Summa quaestionum super Sententias [1290], II:58,II:440), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.1 | |
| A reaction: Other views seem to say that the Quantity provides the extension, but he seems to take that as given. |
| 12149 | Indexicals are a problem for beliefs being just subject-proposition relations [Perry] |
| Full Idea: The essential indexical is a problem for the view that belief is a relation between subjects and propositions conceived as bearers of truth and falsity. | |
| From: John Perry (The Problem of the Essential Indexical [1979], 'Intro') | |
| A reaction: My immediate reaction would be that it depends on how you conceive of 'propositions'. If they are objective, you have a problem. I take them to be subjective events in brains, and the indexical meaning to be evident within the proposition. |
| 12151 | If we replace 'I' in sentences about me, they are different beliefs and explanations of behaviour [Perry] |
| Full Idea: If I leave a trail of sugar, and realise 'that I am making a mess', ...when we replace the word 'I' with other designations of me, we no longer have an explanation of my behaviour, or an attribution of the same belief, so it is an 'essential indexical'. | |
| From: John Perry (The Problem of the Essential Indexical [1979], 'Intro') | |
| A reaction: [compressed] A famous observation of Perry's, which leads him to challenge traditional accounts of belief and of propositions. I don't think I see a problem, if we have a thoroughly non-linguistic account of essentially unambiguous propositions. |
| 18412 | Indexicals individuate certain belief states, helping in explanation and prediction [Perry] |
| Full Idea: We use sentences with indexicals or relativized propositions to individuate belief states, for the purposes of classifying believers in ways useful for explanation and prediction. | |
| From: John Perry (The Problem of the Essential Indexical [1979], 'Obvious') | |
| A reaction: He goes on to apparently connect this with some sort of moral integrity involved in 'owning up' to the fact that the person in question is you (who has spilled the sugar etc.). |
| 12150 | Indexicals reveal big problems with the traditional idea of a proposition [Perry] |
| Full Idea: The problem of the essential indexical reveals that something is badly wrong with the traditional doctrine of propositions. | |
| From: John Perry (The Problem of the Essential Indexical [1979], 'Prob') | |
| A reaction: See the reaction to 12149. The traditional view of propositions, or at least Russell's view, seems to be that they are same as facts, which strikes me as daft. I take propositions to be brain events, probably expressed in mentalese. |
| 15203 | Tense is essential for thought and action [Perry, by Le Poidevin] |
| Full Idea: Tense plays a crucial role in thought and action. | |
| From: report of John Perry (The Problem of the Essential Indexical [1979]) by Robin Le Poidevin - Past, Present and Future of Debate about Tense 3 a | |
| A reaction: This is important, because much of our metaphysics is dominated by a detached 'scientific' description of reality, which is given a rather passive character. If processes take centre stage, which they should, then our own processes are part of it. |
| 15204 | Actual tensed sentences cannot be tenseless, because they can cite their own context [Perry, by Le Poidevin] |
| Full Idea: In the new tenseless theory, no tensed token sentence can be equivalent to a tenseless token, because the former, unlike the latter, draws attention to the context in which it is tokened. | |
| From: report of John Perry (The Problem of the Essential Indexical [1979]) by Robin Le Poidevin - Past, Present and Future of Debate about Tense 3 a | |
| A reaction: So the problem about indexicals was worrying fans of the tenseless B-series view of time (and so it should). I'm inclined to translate sentences containing indexicals into their actual propositions, which tend to avoid them. 'Time/person of utterance'. |
| 16663 | Things are limited by the species to certain modes of being [Olivi] |
| Full Idea: A subject is limited by its species to certain modes of being. | |
| From: Peter John Olivi (Summa quaestionum super Sententias [1290], I:586-7), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.2 | |
| A reaction: I think this is so very the wrong way round. Species characteristics are generalisations about similar individual creatures. The 'species' doesn't do anything at all. It is a classification. See ring species, for example. |