18 ideas
6222 | If a decision is in accord with right reason, everyone can agree with it [Cumberland] |
Full Idea: No decision can be in accord with right reason unless all can agree on it. | |
From: Richard Cumberland (De Legibus Naturae [1672], Ch.V.XLVI) | |
A reaction: Personally I think anyone who disagrees with this should get out of philosophy (and into sociology, fantasy fiction, ironic game-playing, crime…). Of course 'can' agree is not the same as 'will' agree. You must have faith that good reasons are persuasive. |
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) |
12732 | Some necessary truths are brute, and others derive from final causes [Leibniz] |
Full Idea: There is a difference between truths whose necessity is brute and geometric and those truths which have their source in fitness and final causes. | |
From: Gottfried Leibniz (Letters to Remond de Montmort [1715], 1715.06.22/G III 645), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 6 | |
A reaction: The second one is a necessity deriving from God's wisdom. Strictly it could have been otherwise, unlike 'geometrical' necessity, which is utterly fixed. |
19438 | Our large perceptions and appetites are made up tiny unconscious fragments [Leibniz] |
Full Idea: Our great perceptions and our great appetites of which we are conscious, are composed of innumerable little perceptions and little inclinations of which we cannot be conscious. | |
From: Gottfried Leibniz (Letters to Remond de Montmort [1715], 1715 §2) | |
A reaction: I think this is a wonderfully accurate report of how the mind is, in comparison with the much more simplistic views presented by most philosophers of that era. And so much understanding flows from Leibniz's account. |
19415 | Passions reside in confused perceptions [Leibniz] |
Full Idea: The passions of monads reside in their confused perceptions. | |
From: Gottfried Leibniz (Letters to Remond de Montmort [1715], 1715) | |
A reaction: He thinks perceptions come in degrees of confusion, all the way up to God, who alone has fully clear perceptions. He blames in on these confused perceptions. |
6217 | Natural law is supplied to the human mind by reality and human nature [Cumberland] |
Full Idea: Some truths of natural law, concerning guides to moral good and evil, and duties not laid down by civil law and government, are necessarily supplied ot the human mind by the nature of things and of men. | |
From: Richard Cumberland (De Legibus Naturae [1672], Ch.I.I) | |
A reaction: I agree that some moral truths have the power of self-evidence. If you say they are built into the mind, we now ask what did the building, and evolution is the only answer, and hence we distance ourselves from the truths, seeing them as strategies. |
6221 | If there are different ultimate goods, there will be conflicting good actions, which is impossible [Cumberland] |
Full Idea: If there be posited different ultimate ends, whose causes are opposed to each other, then there will be truly good actions likewise opposed to each other, which is impossible. | |
From: Richard Cumberland (De Legibus Naturae [1672], Ch.V.XVI) | |
A reaction: A very interesting argument for there being one good rather than many, and an argument which I don't recall in any surviving Greek text. A response might be to distinguish between what is 'right' and what is 'good'. See David Ross. |
6218 | The happiness of individuals is linked to the happiness of everyone (which is individuals taken together) [Cumberland] |
Full Idea: The happiness of each person cannot be separated from the happiness of all, because the whole is no different from the parts taken together. | |
From: Richard Cumberland (De Legibus Naturae [1672], Ch.I.VI) | |
A reaction: Sounds suspiciously like the fallacy of composition (Idea 6219). An objection to utilitarianism is its assumption that a group of people have a 'total happiness' that is different from their individual states. Still, Cumberland is on to utilitarianism. |
6220 | The happiness of all contains the happiness of each, and promotes it [Cumberland] |
Full Idea: The common happiness of all contains the greatest happiness for each, and most effectively promotes it. …There is no path leading anyone to his own happiness, other than the path which leads all to the common happiness. | |
From: Richard Cumberland (De Legibus Naturae [1672], Ch.I.VI) | |
A reaction: I take this as a revolutionary idea, which leads to utilitarianism. It is doing what seemed to the Greeks unthinkable, which is combining hedonism with altruism. There is no proof for it, but it is a wonderful clarion call for building a civil society. |
6216 | Natural law is immutable truth giving moral truths and duties independent of society [Cumberland] |
Full Idea: Natural law is certain propositions of immutable truth, which guide voluntary actions about the choice of good and avoidance of evil, and which impose an obligation to act, even without regard to civil laws, and ignoring compacts of governments. | |
From: Richard Cumberland (De Legibus Naturae [1672], Ch.I.I) | |
A reaction: Not a popular view, but I am sympathetic. If you are in a foreign country and find a person lying in pain, there is a terrible moral deficiency in anyone who just ignores such a thing. No legislation can take away a person's right of self-defence. |
19439 | God produces possibilities, and thus ideas [Leibniz] |
Full Idea: God is the source of possibilities and consequently of ideas. | |
From: Gottfried Leibniz (Letters to Remond de Montmort [1715], 1715 §8) | |
A reaction: A wonderfully individual conception of the nature of God. He produces the possibilities from which creation is chosen, and ideas and concepts are of everything which is non-contradictory, and thus possible. It all makes lovely sense! |