13 ideas
| 4748 | Anselm of Canterbury identified truth with God [Anselm, by Engel] |
| Full Idea: Anselm of Canterbury identified truth with God. | |
| From: report of Anselm (De Veritate (On Truth) [1095]) by Pascal Engel - Truth §1.6 | |
| A reaction: An interesting claim, perhaps, depending on what it means. God decrees truth, God knows all truth, God makes truth possible, God connects us to the world, God is the world…? |
| 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) |
| 18239 | What is contemplated must have a higher value than contemplation [Kant, by Korsgaard] |
| Full Idea: Kant objects that the world must have a final purpose in order to be worth contemplating, so contemplation cannot be that final purpose. | |
| From: report of Immanuel Kant (Critique of Judgement II: Teleological [1790]) by Christine M. Korsgaard - Aristotle and Kant on the Source of Value 8 'Arist and' | |
| A reaction: That is a very good objection. If we contemplate the ordered heavens, the ordering of the heavens seems to have a greater value than our contemplation of them. The reply is that the contemplation is the final purpose being contemplated! |
| 18238 | Only a good will can give man's being, and hence the world, a final purpose [Kant] |
| Full Idea: A good will is that whereby alone [man's] being can have an absolute worth and in reference to which the being of the world can have a final purpose. | |
| From: Immanuel Kant (Critique of Judgement II: Teleological [1790], C3 443), quoted by Christine M. Korsgaard - Aristotle and Kant on the Source of Value 8 'Kant' | |
| A reaction: I wish Kant gave a better account of what a 'good' will consists of. This is an awful burden to bear when you are making decisions. |
| 22053 | The Critique of Judgement aims for a principle that unities humanity and nature [Kant, by Bowie] |
| Full Idea: The Critique of Judgement aims to show how judgement functions 'according to the principle of the appropriateness of nature to our capacity for cognition'. It is meant to provide a principle of the unity of humankind and nature. | |
| From: report of Immanuel Kant (Critique of Judgement II: Teleological [1790]) by Andrew Bowie - German Philosophy: a very short introduction 1 | |
| A reaction: Hence this work is often overlooked as a key part of Kant's 'system'. At first he probably didn't realise he was creating a system. Kant set an agenda for the philosophy of the ensuing thirty years. |
| 18237 | Without men creation would be in vain, and without final purpose [Kant] |
| Full Idea: Without men the whole creation would be mere waste, in vain, and without final purpose. | |
| From: Immanuel Kant (Critique of Judgement II: Teleological [1790], C3 442), quoted by Christine M. Korsgaard - Aristotle and Kant on the Source of Value 8 'Kant' | |
| A reaction: The standard early twenty-first century response to that is 'get over it'! The remark shows how deep religion runs in Kant, despite his great caution about the existence of God. His notion of 'duty' is similarly religious. |