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) |
| 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. |
| 17292 | Avoid 'in virtue of' for grounding, since it might imply a reflexive relation such as identity [Audi,P] |
| Full Idea: We should not use 'in virtue of' where it might express a reflexive relation, such as identity. Since grounding is a relation of determination, and closely linked to the concept of explanation, it is irreflexive and asymmetric. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.2) | |
| A reaction: E.g. he says someone isn't a bachelor in virtue of being an unmarried man, since a bachelor just is an unmarried man. I can't disagree. 'Determination' looks like the magic word, even if we don't know how it cashes out. |
| 17295 | Ground relations depend on the properties [Audi,P] |
| Full Idea: On my view, grounding relations depend on the natures of the properties involved in them. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.2) | |
| A reaction: I'm cautious about this if we don't find out more exactly what properties are (and they had better not just be predicates). Maybe properties are the only apparatus we have here, though I prefer 'powers' for the fundamentals. |
| 17297 | A ball's being spherical non-causally determines its power to roll [Audi,P] |
| Full Idea: The fact that a given thing is spherical non-causally determines the fact that it has the power to roll. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.3) | |
| A reaction: Quine won't accept this, because you have added something called a 'power' to the ball (intrinsically, it seems), over and above its observable sphericity. Does being a ball 'determine' that it can't be in two places at once? Order of explanation? |
| 17302 | Ground is irreflexive, asymmetric, transitive, non-monotonic etc. [Audi,P] |
| Full Idea: The logical principles about grounding include irreflexivity, asymmetry, transitivity, non-monotonicity, and so forth. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.8) | |
| A reaction: [It can't ground itself, there is no mutual grounding, grounds of grounds ground, and grounding judgements are not fixed] |
| 17303 | The best critique of grounding says it is actually either identity or elimination [Audi,P] |
| Full Idea: I think the most promising skeptical strategy is to insist on either identity or elimination wherever grounding is alleged to hold. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.9) | |
| A reaction: This comes after an assessment of the critiques of grounding by Oliver, Hofweber and Daly. So we don't say chemistry grounds biology, we either say biology is chemistry, or that there is no biology. Everything is just simples. Not for me. |
| 17294 | Grounding is a singular relation between worldly facts [Audi,P] |
| Full Idea: On my view, grounding is a singular relation between facts. ...Facts, on this view, are obtaining states of affairs. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.2) | |
| A reaction: He rest this claim on his 'worldly' view of facts, Idea 17293. I seem to be agreeing with him. Note that it is not between types of fact, even if there are such general truths, such as in chemistry. |
| 17300 | If grounding relates facts, properties must be included, as well as objects [Audi,P] |
| Full Idea: Taking facts to be the relata of grounding has the interesting consequence that it does not relate ordinary particulars, objects, considered apart from their properties. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.4) | |
| A reaction: It will depend on what you mean by properties, and it seems to me that something like 'powers' must be invoked, to get the active character that seems to be involved in grounding. |
| 17296 | We must accept grounding, for our important explanations [Audi,P] |
| Full Idea: The reason we must countenance grounding is that it is indispensible to certain important explanations. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.3) | |
| A reaction: I like this a lot. The first given of all philosophy is the drive to exlain. However, we mustn't go inventing features of the world, simply to give us the possibility of explaining it. The objective fact seems to be the without-which-not relation. |
| 17301 | Reduction is just identity, so the two things are the same fact, so reduction isn't grounding [Audi,P] |
| Full Idea: I deny that when p grounds q, q thereby reduces to p, and I deny that if q reduces to p, then p grounds q. ...On my view, reduction is nothing other than identity, so p is the same fact as q. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.5) | |
| A reaction: Very good. I can't disagree with any of it, and it is crystal clear. Philosophical heaven. |
| 17293 | Worldly facts are obtaining states of affairs, with constituents; conceptual facts also depend on concepts [Audi,P] |
| Full Idea: The 'worldly' view of facts says they are obtaining states of affairs, individuated by their constituents and their combination. On the 'conceptual' view, facts will differ if they pick out an object or property via different concepts. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.2) | |
| A reaction: Might it be that conceptual differences between facts are supervenient on worldly differences (with the worldly facts in charge)? |
| 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. |
| 17298 | Two things being identical (like water and H2O) is not an explanation [Audi,P] |
| Full Idea: If there is identity between water and H2O, we have neither the asymmetry nor the irreflexivity that explanations require. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.3) | |
| A reaction: Once you realise it is H2O, you understand its deeper features, which will open up new explanations. He's right, though. |
| 17299 | There are plenty of examples of non-causal explanation [Audi,P] |
| Full Idea: There are a number of explanations where it seems clear that causation is not involved at all: normative grounded in non-normative, disposition grounded in categorical, aesthetic grounded in non-aesthetic, semantic in social and psychological. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.3) | |
| A reaction: Apart from dispositions, perhaps, these all seem to be experienced phenomena grounded in the physical world. 'Determination' is the preferred term for non-causal grounding. |
| 21125 | Liberals must respect family freedom - but families are the great oppressors of women [Nussbaum] |
| Full Idea: A liberal society should give people considerable latitude to form families as they choose. …On the other hand the family …is one of the most notorious homes of sex hierarchy, denial of sexual opportunity, and sex-based violence and humiliation. | |
| From: Martha Nussbaum (Rawls and Feminism [2003], 03), quoted by Andrew Shorten - Contemporary Political Theory | |
| A reaction: The question of how the state might intervene in the family rarely seems to turn up in standard political theory. This idea shows why that is a mistake. |