15 ideas
1749 | If all laws were abolished, philosophers would still live as they do now [Aristippus elder] |
Full Idea: If all laws were abolished, philosophers would still live as they do now. | |
From: Aristippus the elder (fragments/reports [c.395 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.4 | |
A reaction: Presumably philosophers develop inner laws which other people lack. |
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) |
15793 | We can take 'ways things might have been' as irreducible elements in our ontology [Stalnaker, by Lycan] |
Full Idea: Stalnaker suggests talking 'ways things might have been' as sui generis elements of our ontology - actual abstract entities in their own right, not to be reduced to more familiar items. | |
From: report of Robert C. Stalnaker (Possible Worlds [1976]) by William Lycan - The Trouble with Possible Worlds 09 | |
A reaction: This seems to rest on an ontology of 'states of affairs', favoured by Armstrong, and implied in the Tractatus. How big is a state of affairs? How manys states of affairs can be co-present? |
3558 | Only the Cyrenaics reject the idea of a final moral end [Aristippus elder, by Annas] |
Full Idea: The Cyrenaics are the most radical ancient moral philosophers, since they are the only school explicitly to reject the importance of achieving an overall final end. | |
From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Julia Annas - The Morality of Happiness 11.1 | |
A reaction: This looks like dropping out, but it could also be Keats's 'negative capability', of simply participating in existence without needing to do anything about it. |
5835 | The road of freedom is the surest route to happiness [Aristippus elder, by Xenophon] |
Full Idea: The surest road to happiness is not the path through rule nor through servitude, but through liberty. | |
From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Xenophon - Memorabilia of Socrates 2.1.9 | |
A reaction: The great anarchist slogan. Personally I don't believe it, because I agree a little with Hobbes that authority is required to make cooperation flourish, and that is essential for full happiness. If I were a slave, I would agree with Aristippus. |
3018 | People who object to extravagant pleasures just love money [Aristippus elder, by Diog. Laertius] |
Full Idea: When blamed for buying expensive food he asked "Would you have bought it for just three obols?" When the person said yes, he said,"Then it is not that I am fond of pleasure, but that you are fond of money". | |
From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.4 |
1751 | Pleasure is the good, because we always seek it, it satisfies us, and its opposite is the most avoidable thing [Aristippus elder, by Diog. Laertius] |
Full Idea: Pleasure is the good because we desire it from childhood, when we have it we seek nothing further, and the most avoidable thing is its opposite, pain. | |
From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.8 |
1755 | Errors result from external influence, and should be corrected, not hated [Aristippus elder, by Diog. Laertius] |
Full Idea: Errors ought to meet with pardon, for a man does not err intentionally, but influenced by some external circumstances. We should not hate someone who has erred, but teach him better. | |
From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.9 |