15 ideas
| 19336 | Wisdom involves the desire to achieve perfection [Leibniz] |
| Full Idea: The wiser one is, the more one is determined to do that which is most perfect. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.151) | |
| A reaction: Debatable. 'Perfectionism' is a well-known vice in many areas of life. Life is short, and the demands on us are many. Skilled shortcuts and compromises are one hallmark of genius, and presumably also of wisdom. |
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3) | |
| A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough. |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.3) |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) | |
| A reaction: [He cites Fagin and Halpern 1988 for this] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
| From: Melvin Fitting (Intensional Logic [2007], §1) |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
| From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
| A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
| 21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
| Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people." | |
| From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork. |
| 7696 | Leibniz first asked 'why is there something rather than nothing?' [Leibniz, by Jacquette] |
| Full Idea: The historical honour of having first raised the question "Why is there something rather than nothing?" belongs to Leibniz. | |
| From: report of Gottfried Leibniz (On the Ultimate Origination of Things [1697]) by Dale Jacquette - Ontology Ch.3 | |
| A reaction: I presume that people before Leibniz may well have had the thought, but not bothered to even articulate it, because there seemed nothing to say by way of answer, other than some reference to the inscrutable will of God. |
| 19341 | There must be a straining towards existence in the essence of all possible things [Leibniz] |
| Full Idea: Since something rather than nothing exists, there is a certain urge for existence, or (so to speak) a straining toward existence in possible things or in possibility or essence itself; in a word, essence in and of itself strives for existence. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.150) | |
| A reaction: Thus 'essence precedes existence'. Not sure I understand this, but at least it places an active power at the root of everything (though Leibniz probably sees that as divine). The Big Bang triggered by a 'quantum fluctuation'? |
| 19428 | Because something does exist, there must be a drive in possible things towards existence [Leibniz] |
| Full Idea: From the very fact that something exists rather than nothing, we recognise that there is in possible things, that is, in the very possibility or essence, a certain exigent need of existence, and, so to speak, some claim to existence. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.347) | |
| A reaction: I love the fact that Leibniz tried to explain why there is something rather than nothing. Bede Rundle and Dale Jacquette are similar heroes. As Leibniz tells us, contradictions have no claim to existence, but non-contradictions do. |
| 5047 | The world is physically necessary, as its contrary would imply imperfection or moral absurdity [Leibniz] |
| Full Idea: Although the world is not metaphysically necessary, such that its contrary would imply a contradiction or logical absurdity, it is necessary physically, that is, determined in such a way that its contrary would imply imperfection or moral absurdity. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.139) | |
| A reaction: How does Leibniz know things like this? The distinction between 'metaphysical' necessity and 'natural' (what he calls 'physical') necessity is a key idea. But natural necessity is controversial. See 'Essentialism'. |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
| Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.4) | |
| A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others. |
| 19343 | We follow the practical rule which always seeks maximum effect for minimum cost [Leibniz] |
| Full Idea: In practical affairs one always follows the decision rule in accordance with which one ought to seek the maximum or the minimum: namely, one prefers the maximum effect at the minimum cost, so to speak. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.150) | |
| A reaction: Animals probably do that too, and even water sort of obeys the rule when it runs downhill. |
| 19429 | The principle of determination in things obtains the greatest effect with the least effort [Leibniz] |
| Full Idea: There is always in things a principle of determination which is based on consideration of maximum and minimum, such that the greatest effect is obtained with the least, so to speak, expenditure. | |
| From: Gottfried Leibniz (On the Ultimate Origination of Things [1697], p.347) | |
| A reaction: This is obvious in human endeavours. Leibniz applied it to physics, producing a principle that shortest paths are always employed. It has a different formal name in modern physics, I think. He says if you make an unrestricted triangle, it is equilateral. |