16 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) |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 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) |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 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. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 22709 | We should first decide what are the great works of art, with aesthetic theory following from that [Murdoch] |
| Full Idea: Our aesthetic must stand to be judged by great works of art which we know to be such independently. …So let us start by saying that Shakespeare is the greatest of all artists, and let our aesthetic be the philosophical justification of this judgement. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.205) | |
| A reaction: She offers this view in specific contradiction of Tolstoy, which says we should first have a theory, and then judge accordingly. I take Murdoch to be entirely right, but it means that our aesthetic theory will shift over time. |
| 22715 | Great art proves the absurdity of art for art's sake [Murdoch] |
| Full Idea: The work of the great artists shows up 'art-for-art's-sake' as a flimsy frivolous doctrine. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.218) | |
| A reaction: She keeps referring to tragedy (as the greatest art), but it is hard to see how we learn love and morality from a great pot or a great abstract painting. Wilde makes the doctrine frivolous, but I think it contains a degree of truth. Music. |
| 22714 | Because art is love, it improves us morally [Murdoch] |
| Full Idea: It is of course a fact that if art is love then art improves us morally, but this is, as it were, accidental. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.218) | |
| A reaction: Is an enhancement of one's love necessarily a moral improvement? Love is a fine feeling, but how does it motivate? Has no wickedness ever been perpetrated in the name of love? 'All's fair in love and war'. |
| 22712 | Art and morals are essentially the same, and are both identical with love [Murdoch] |
| Full Idea: Art and morals are (with certain provisos) one. Their essence is the same. The essence of both of them is love. Love is the perception of individuals. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.215) | |
| A reaction: The idea that art, morals and love are all just a single thing seems unhelpful. What about satire? What about duty without love? What about pure abstract painting? What about Stravinsky's highly formal view of his music? |
| 22713 | Love is realising something other than oneself is real [Murdoch] |
| Full Idea: Love is the extremely difficult realisation that something other than oneself is real. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.215) | |
| A reaction: I suspect that this is a necessary condition for love, but not the thing itself. The realisation she describes may not be love. You would attain her realisation if you shared a prison cell with a terrifying psychopath. |