12 ideas
| 20768 | Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius] |
| Full Idea: He said that dialectical arguments were like spiderswebs: although they seem to indicate craftsmanlike skill, they are useless. | |
| From: report of Ariston (fragments/reports [c.250 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.161 | |
| A reaction: Useful for the spider, but useless to Ariston. |
| 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. |
| 7293 | It is legitimate to do harm if it is the unintended side-effect of an effort to achieve a good [Grayling] |
| Full Idea: The doctrine of double effect says that it is legitimate to do harm if the harm is the unintended side-effect of an effort to achieve a legitimate goal. | |
| From: A.C. Grayling (Among the Dead Cities [2006], Ch.6) | |
| A reaction: I think a key principle of morality is our duty to think about possible unnoticed consequences of our actions. To neglect concern for side-effects is wicked. Beyond that, the issue must concern the particulars of the situation. |
| 3049 | The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius] |
| Full Idea: The chief good is to live in perfect indifference to all those things which are of an intermediate character between virtue and vice. | |
| From: report of Ariston (fragments/reports [c.250 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.2.1 |
| 3549 | Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas] |
| Full Idea: Ariston says that rules are useless if you are virtuous, and useless if you are not. | |
| From: report of Ariston (fragments/reports [c.250 BCE]) by Julia Annas - The Morality of Happiness 2.4 |
| 7292 | War must also have a good chance of success, and be waged with moderation [Grayling] |
| Full Idea: To Aquinas's three conditions for war (Idea 7291) modern theorists have added two others: that to be just a war must have a reasonable chance of success, and that the means used to conduct it must be proportional to the ends sought. | |
| From: A.C. Grayling (Among the Dead Cities [2006], Ch.6) | |
| A reaction: These two principles strike me as being much more civilized and humane than Aquinas's original contribution, suggesting that in our theoretical thinking we might be making some progress. |