13 ideas
| 22752 | Reasoning is impossible without a preconception [Sext.Empiricus] |
| Full Idea: It is not possible either to seek or to doubt without a preconception. | |
| From: Sextus Empiricus (Against the Ethicists (one book) [c.180], II.22) | |
| A reaction: [Sextus quotes this from 'the sapient Epicurus'] I think this may be a message across the centuries to Hegel, who attempted this impossible feat. My picture of philosophy is a continual shift of the preconceptions, to explore thoroughly. |
| 22304 | Truth is conceivability, or the systematic coherence of a significant whole [Joachim] |
| Full Idea: Truth is in its essence conceivability or systematic coherence. ...[p.78] It is the systematic coherence which characterises a significant whole. | |
| From: Harold Joachim (The Nature of Truth [1906], p.68), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 35 'coh' | |
| A reaction: We obviously need to know when a whole becomes 'significant'. Potter says mystical idealists liked this because it contributed to their teleological view of the whole of reality. Presumably its roots are in Hegel. |
| 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) |
| 22754 | Saying the good is useful or choiceworth or happiness-creating is not the good, but a feature of it [Sext.Empiricus] |
| Full Idea: Asserting that the good is 'the useful', or 'what is choiceworthy for its own sake', or 'that which contributes to happiness', does not teach us what good is but states its accidental property. | |
| From: Sextus Empiricus (Against the Ethicists (one book) [c.180], II.35) | |
| A reaction: This seems to be a pretty accurate statement of Moore's famous Open Question argument. I read it in an Aristotelian way - that that quest is always for the essential nature of the thing itself, not for its role or function or use. |
| 22755 | Like a warming fire, what is good by nature should be good for everyone [Sext.Empiricus] |
| Full Idea: Just as fire which is warmth-giving by nature warms all men, and does not chill some of them, so what is good by nature ought to be good for all, and not good for some but not good for others. | |
| From: Sextus Empiricus (Against the Ethicists (one book) [c.180], II.69) | |
| A reaction: This is going to confine the naturally good to the basics of life, which we all share. Is a love of chess a natural good? It seems to capture an aspect of human nature, without appealing to everyone. Sextus says nothing is good for everyone. |
| 22756 | If a desire is itself desirable, then we shouldn't desire it, as achieving it destroys it [Sext.Empiricus] |
| Full Idea: If the desire for wealth or health is desirable, we ought not to purse wealth or health, lest by acquiring them we cease to desire them any longer. | |
| From: Sextus Empiricus (Against the Ethicists (one book) [c.180], II.81) | |
| A reaction: He is investigating whether desires can be desirable, and if so which ones. Roots of this are in Plato's 'Gorgias' on drinking water. Similar to 'if compassion is the highest good then we need lots of suffering'. Desire must be a means, not an end. |