20 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) |
| 10429 | It is best to say that a name designates iff there is something for it to designate [Sainsbury] |
| Full Idea: It is better to say that 'For all x ("Hesperus" stands for x iff x = Hesperus)', than to say '"Hesperus" stands for Hesperus', since then the expression can be a name with no bearer (e.g. "Vulcan"). | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.2) | |
| A reaction: In cases where it is unclear whether the name actually designates something, it seems desirable that the name is at least allowed to function semantically. |
| 10425 | Definite descriptions may not be referring expressions, since they can fail to refer [Sainsbury] |
| Full Idea: Almost everyone agrees that intelligible definite descriptions may lack a referent; this has historically been a reason for not counting them among referring expressions. | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.2) | |
| A reaction: One might compare indexicals such as 'I', which may be incapable of failing to refer when spoken. However 'look at that!' frequently fails to communicate reference. |
| 10438 | Definite descriptions are usually rigid in subject, but not in predicate, position [Sainsbury] |
| Full Idea: Definite descriptions used with referential intentions (usually in subject position) are normally rigid, ..but in predicate position they are normally not rigid, because there is no referential intention. | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.5) | |
| A reaction: 'The man in the blue suit is the President' seems to fit, but 'The President is the head of state' doesn't. Seems roughly right, but language is always too complex for philosophers. |
| 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. |
| 12695 | Epicurean atomists say body is sensible, to distinguish it from space. [Garber] |
| Full Idea: The Epicurean atomists also defined body in terms of the property of being sensible, in order to distinguish it from empty space, which is not sensible. | |
| From: Daniel Garber (Leibniz:Body,Substance,Monad [2009], 1) | |
| A reaction: This is a very illuminating bit of background, for those of us who have the knee-jerk reaction that monadology is barking mad. |
| 8983 | If 'red' is vague, then membership of the set of red things is vague, so there is no set of red things [Sainsbury] |
| Full Idea: Sets have sharp boundaries, or are sharp objects; an object either definitely belongs to a set, or it does not. But 'red' is vague; there objects which are neither definitely red nor definitely not red. Hence there is no set of red things. | |
| From: Mark Sainsbury (Concepts without Boundaries [1990], §2) | |
| A reaction: Presumably that will entail that there IS a set of things which can be described as 'definitely red'. If we describe something as 'definitely having a hint of red about it', will that put it in a set? In fact will the applicability of 'definitely' do? |
| 8986 | We should abandon classifying by pigeon-holes, and classify around paradigms [Sainsbury] |
| Full Idea: We must reject the classical picture of classification by pigeon-holes, and think in other terms: classifying can be, and often is, clustering round paradigms. | |
| From: Mark Sainsbury (Concepts without Boundaries [1990], §8) | |
| A reaction: His conclusion to a discussion of the problem of vagueness, where it is identified with concepts which have no boundaries. Pigeon-holes are a nice exemplar of the Enlightenment desire to get everything right. I prefer Aristotle's categories, Idea 3311. |
| 8982 | Vague concepts are concepts without boundaries [Sainsbury] |
| Full Idea: If a word is vague, there are or could be borderline cases, but non-vague expressions can also have borderline cases. The essence of vagueness is to be found in the idea vague concepts are concepts without boundaries. | |
| From: Mark Sainsbury (Concepts without Boundaries [1990], Intro) | |
| A reaction: He goes on to say that vague concepts are not embodied in clear cut sets, which is what gives us our notion of a boundary. So what is vague is 'membership'. You are either a member of a club or not, but when do you join the 'middle-aged'? |
| 8984 | If concepts are vague, people avoid boundaries, can't spot them, and don't want them [Sainsbury] |
| Full Idea: Vague concepts are boundaryless, ...and the manifestations are an unwillingness to draw any such boundaries, the impossibility of identifying such boundaries, and needlessness and even disutility of such boundaries. | |
| From: Mark Sainsbury (Concepts without Boundaries [1990], §5) | |
| A reaction: People have a very fine-tuned notion of whether the sharp boundary of a concept is worth discussing. The interesting exception are legal people, who are often forced to find precision where everyone else hates it. Who deserves to inherit the big house? |
| 8985 | Boundaryless concepts tend to come in pairs, such as child/adult, hot/cold [Sainsbury] |
| Full Idea: Boundaryless concepts tend to come in systems of contraries: opposed pairs like child/adult, hot/cold, weak/strong, true/false, and complex systems of colour terms. ..Only a contrast with 'adult' will show what 'child' excludes. | |
| From: Mark Sainsbury (Concepts without Boundaries [1990], §5) | |
| A reaction: This might be expected. It all comes down to the sorites problem, of when one thing turns into something else. If it won't merge into another category, then presumably the isolated concept stays applicable (until reality terminates it? End of sheep..). |
| 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. |
| 10432 | A new usage of a name could arise from a mistaken baptism of nothing [Sainsbury] |
| Full Idea: A baptism which, perhaps through some radical mistake, is the baptism of nothing, is as good a propagator of a new use as a baptism of an object. | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.3) | |
| A reaction: An obvious example might be the Loch Ness Monster. There is something intuitively wrong about saying that physical objects are actually part of linguistic meaning or reference. I am not a meaning! |
| 10434 | Even a quantifier like 'someone' can be used referentially [Sainsbury] |
| Full Idea: A large range of expressions can be used with referential intentions, including quantifier phrases (as in 'someone has once again failed to close the door properly'). | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.5) | |
| A reaction: This is the pragmatic aspect of reference, where it can be achieved by all sorts of means. But are quantifiers inherently referential in their semantic function? Some of each, it seems. |
| 10431 | Things are thought to have a function, even when they can't perform them [Sainsbury] |
| Full Idea: On one common use of the notion of a function, something can possess a function which it does not, or even cannot, perform. A malformed heart is to pump blood, even if such a heart cannot in fact pump blood. | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.2) | |
| A reaction: One might say that the heart in a dead body had the function of pumping blood, but does it still have that function? Do I have the function of breaking the world 100 metres record, even though I can't quite manage it? Not that simple. |
| 12705 | Epicurean atoms are distinguished by their extreme hardness [Garber] |
| Full Idea: In Epicurean atomism (of Cordemoy, for example) there is a world of basic things distinguished by virtue of their extreme hardness. | |
| From: Daniel Garber (Leibniz:Body,Substance,Monad [2009], 2) | |
| A reaction: Garber says that Leibniz espouses 'substantial atomism', which is different from this. Leibniz's atoms have active power, where these atoms just embody total resistance. |