10 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. |
14280 | The probability of two events is the first probability times the second probability assuming the first [Bayes] |
Full Idea: The probability that two events will both happen is the probability of the first [multiplied by] the probability of the second on the supposition that the first happens. | |
From: Thomas Bayes (Essay on a Problem in the Doctrine of Chances [1763]), quoted by Dorothy Edgington - Conditionals (Stanf) 3.1 |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
Full Idea: Archelaus was the first person to say that the universe is boundless. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |