14 ideas
12036 | Xenophanes began the concern with knowledge [Annas] |
Full Idea: Xenophanes begins a long concern with knowledge and its grounds. | |
From: Julia Annas (Ancient Philosophy: very short introduction [2000], Intro) | |
A reaction: Having that on his cv ought to make Xenophanes more famous than he is. |
12046 | Plato was the first philosopher who was concerned to systematize his ideas [Annas] |
Full Idea: In the ancient world Plato was seen as a pivotal figure, the first philosopher who was concerned to systematize his ideas. | |
From: Julia Annas (Ancient Philosophy: very short introduction [2000], Ch.6) |
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) |
1757 | The Electra: she knows this man, but not that he is her brother [Eucleides, by Diog. Laertius] |
Full Idea: The 'Electra': Electra knows that Orestes is her brother, but not that this man is Orestes, so she knows and does not know her brother simultaneously. | |
From: report of Eucleides (fragments/reports [c.410 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Eu.4 | |
A reaction: Hence we distinguish 'know of', 'know that' and 'know how'. Hence Russell makes 'knowledge by acquaintance' fundamental, and descriptions come later. |
12037 | Euripides's Medea is a key case of reason versus the passions [Annas] |
Full Idea: Euripides's Medea has remained a key case for discussion of reason and the passions. | |
From: Julia Annas (Ancient Philosophy: very short introduction [2000], Ch.1) |
3028 | The chief good is unity, sometimes seen as prudence, or God, or intellect [Eucleides] |
Full Idea: The chief good is unity, which is known by several names, for at one time people call it prudence, at another time God, at another intellect, and so on. | |
From: Eucleides (fragments/reports [c.410 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 02.9.2 | |
A reaction: So the chief good is what unites and focuses our moral actions. Kant calls that 'the will'. |
12040 | Virtue is a kind of understanding of moral value [Annas] |
Full Idea: There is a widespread view in ancient ethics that virtue is a kind of understanding of moral value. | |
From: Julia Annas (Ancient Philosophy: very short introduction [2000], Ch.3) | |
A reaction: In Aristotle's case, this coincides with his apparent view that 'understanding' is the aim of all areas of human thought. See Idea 12038. |