14 ideas
| 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. |
| 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. |
| 2798 | Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich] |
| Full Idea: Bayesianism says ideally rational people should have degrees of belief (not all-or-nothing beliefs), corresponding with probability theory. Probability of H, given evidence E, is prob(H) X prob(E given H) / prob(E). | |
| From: Paul Horwich (Bayesianism [1992], p.41) |
| 2799 | Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich] |
| Full Idea: Bayesianism can explain the fact that in science surprising predictions have greater evidential value, as the equation produces a higher degree of confirmation. | |
| From: Paul Horwich (Bayesianism [1992], p.42) |
| 20180 | A happy and joyous life must largely be a quiet life [Russell] |
| Full Idea: A happy life must to a great extent be a quiet life, for it is only in an atmosphere of quiet that true joy can live. | |
| From: Bertrand Russell (The Conquest of Happiness [1930], 4) | |
| A reaction: Most people's image of happiness is absorption in an interesting task, or relaxing in good company. The idea that happiness is wild excitement exists, but is a minority view. |
| 20177 | Boredom always involves not being fully occupied [Russell] |
| Full Idea: It is one of the essentials of boredom that one's faculties must not be fully occupied. | |
| From: Bertrand Russell (The Conquest of Happiness [1930], 4) | |
| A reaction: He gives running for your life as an example of non-boredom. I suspect that this is only the sort of boredom that troubled Russell, and not the sort of profound boredom that led the actor George Sanders to suicide (according to his last note). |
| 20179 | Happiness involves enduring boredom, and the young should be taught this [Russell] |
| Full Idea: A certain power of enduring boredom is essential to a happy life, and is one of the things that ought to be taught to the young. | |
| From: Bertrand Russell (The Conquest of Happiness [1930], 4) | |
| A reaction: As an example he suggests that Wordsworth would never have written 'The Prelude' is he had never been bored when young. Which suggests that Russell doesn't really get boredom, seeing it merely as a stimulus to work. |
| 20176 | Boredom is an increasingly strong motivating power [Russell] |
| Full Idea: Boredom has been, I believe, one of the great motive powers throughout the historical epoch, and is so at the present day more than ever. | |
| From: Bertrand Russell (The Conquest of Happiness [1930], 4) | |
| A reaction: Most of his essay tells us how to avoid boredom, rather than how it motivates. |
| 20178 | Life is now more interesting, but boredom is more frightening [Russell] |
| Full Idea: We are less bored than our ancestors were, but we are more afraid of boredom | |
| From: Bertrand Russell (The Conquest of Happiness [1930], 4) | |
| A reaction: I get the impression that the invention of the powerful mobile phone has largely banished boredom from human life, except when you are obliged to switch it off. The fear of boredom may hence be even greater now. |