Combining Texts

All the ideas for 'Logical Consequence', 'Queries to the 'Opticks'' and 'Beyond Individualism'

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12 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
'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)
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
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.
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
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)
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
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.
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
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)
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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.
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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)
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
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)
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
Passion for progress is always short-lived [Sandel]
     Full Idea: Progress demands passions that cannot last for long.
     From: Michael J. Sandel (Beyond Individualism [1988], p.35)
     A reaction: The obvious example, for me, is the Labour Government in the UK, 1945-51. This is the kind of realism which progressive politicians must face up to. Unfortunately it is the logic of very ruthless revolutionaries.
24. Political Theory / D. Ideologies / 3. Conservatism
Conservatives are either individualistic, or communal [Sandel]
     Full Idea: Individualist conservatives believe people should be free to do as they please so long as they do not harm others. ...Communal conservatives, by contrast, believe government should affirm moral and religious values.
     From: Michael J. Sandel (Beyond Individualism [1988], p.38)
     A reaction: Nozick represents the first group (as does J.S.Mill, usually seen as epitomising liberalism). He says the first group like volunteer armies and oppose welfare; the second group favour conscription and conservative welfare.
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Modern liberalism fails to articulate a vision of the common good [Sandel]
     Full Idea: In recent years liberalism has faltered because of its failure to argue for a vision of the common good.
     From: Michael J. Sandel (Beyond Individualism [1988], p.45)
     A reaction: This is Sandel's main theme. He derives his concept of the common good from the essential natures of persons and institutions. I greatly admire this.
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Principles of things are not hidden features of forms, but the laws by which they were formed [Newton]
     Full Idea: The (active) principles I consider not as occult qualities, supposed to result from the specific forms of things, but as general laws of nature, by which the things themselves are formed.
     From: Isaac Newton (Queries to the 'Opticks' [1721], q 31), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 23.6
     A reaction: This is the external, 'imposed' view of laws (with the matter passive) at its most persuasive. If laws arise out the stuff (as I prefer to think), what principles went into the formulation of the stuff?