24 ideas
| 15557 | Verisimilitude has proved hard to analyse, and seems to have several components [Lewis] |
| Full Idea: The analysis of verisimilitude has been much debated. Some plausible analyses have failed disastrously, others conflict with one another. One conclusion is that verisimilitude seems to consist of several distinguishable virtues. | |
| From: David Lewis (Causal Explanation [1986], V n7) | |
| A reaction: Presumably if it is complex, you can approach truth in one respect while receding from it in another. It seems clear enough if you are calculating pi by some iterative process. |
| 10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
| Full Idea: Second-order logic raises doubts because of its ontological commitment to the set-theoretic hierarchy, and the allegedly problematic epistemic status of the second-order consequence relation. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §1) | |
| A reaction: The 'epistemic' problem is whether you can know the truths, given that the logic is incomplete, and so they cannot all be proved. Rossberg defends second-order logic against the second problem. A third problem is that it may be mathematics. |
| 10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
| Full Idea: Henkin semantics (for second-order logic) specifies a second domain of predicates and relations for the upper case constants and variables. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This second domain is restricted to predicates and relations which are actually instantiated in the model. Second-order logic is complete with this semantics. Cf. Idea 10756. |
| 10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
| Full Idea: In addition to standard and Henkin semantics for second-order logic, one might also employ substitutional or game-theoretical or topological semantics, or Boolos's plural interpretation, or even a semantics inspired by Lesniewski. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This is helpful in seeing the full picture of what is going on in these logical systems. |
| 10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
| Full Idea: Logical consequence is intuitively taken to be a semantic notion, ...and it is therefore the formal semantics, i.e. the model theory, that captures logical consequence. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: If you come at the issue from normal speech, this seems right, but if you start thinking about the necessity of logical consequence, that formal rules and proof-theory seem to be the foundation. |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| Full Idea: Deductive consequence, written Γ|-S, is loosely read as 'the sentence S can be deduced from the sentences Γ', and semantic consequence Γ|=S says 'all models that make Γ true make S true as well'. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: We might read |= as 'true in the same model as'. What is the relation, though, between the LHS and the RHS? They seem to be mutually related to some model, but not directly to one another. |
| 10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
| Full Idea: A proof-theorist could insist that the logical form of a sentence is exhibited by the logical constants that it contains. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: You have to first get to the formal logical constants, rather than the natural language ones. E.g. what is the truth table for 'but'? There is also the matter of the quantifiers and the domain, and distinguishing real objects and predicates from bogus. |
| 10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
| Full Idea: A standard model is a set of objects called the 'domain', and an interpretation function, assigning objects in the domain to names, subsets to predicate letters, subsets of the Cartesian product of the domain with itself to binary relation symbols etc. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: The model actually specifies which objects have which predicates, and which objects are in which relations. Tarski's account of truth in terms of 'satisfaction' seems to be just a description of those pre-decided facts. |
| 10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
| Full Idea: A mathematical theory is 'categorical' if, and only if, all of its models are isomorphic. Such a theory then essentially has just one model, the standard one. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: So the term 'categorical' is gradually replacing the much-used phrase 'up to isomorphism'. |
| 10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
| Full Idea: All that should be required to get a semantics relative to which a given deductive system is complete is a sufficiently cunning model-theorist. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §5) |
| 10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
| Full Idea: No deductive system is semantically incomplete in and of itself; rather a deductive system is incomplete with respect to a specified formal semantics. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This important point indicates that a system might be complete with one semantics and incomplete with another. E.g. second-order logic can be made complete by employing a 'Henkin semantics'. |
| 15554 | A disposition needs a causal basis, a property in a certain causal role. Could the disposition be the property? [Lewis] |
| Full Idea: I take for granted that a disposition requires a causal basis: one has the disposition iff one has a property that occupies a certain causal role. Shall we then identify the disposition with its basis? That makes the disposition cause its manifestations. | |
| From: David Lewis (Causal Explanation [1986], III) | |
| A reaction: Introduce the concept of a 'power' and I see no problem with his proposal. Fundamental dispositions are powerful, and provide the causal basis for complex dispositions. Something had better be powerful. |
| 15560 | We can explain a chance event, but can never show why some other outcome did not occur [Lewis] |
| Full Idea: I think we are right to explain chance events, yet we are right also to deny that we can ever explain why a chance process yields one outcome rather than another. We cannot explain why one event happened rather than the other. | |
| From: David Lewis (Causal Explanation [1986], VI) | |
| A reaction: This misses out an investigation which slowly reveals that a 'chance' event wasn't so chancey after all. Failure to explain confirms chance, so the judgement of chance shouldn't block attempts to explain. |
| 15559 | Does a good explanation produce understanding? That claim is just empty [Lewis] |
| Full Idea: It is said that a good explanation ought to produce understanding, ...but this just says that a good explanation produces possession of that which it provide, so this desideratum is empty. It adds nothing to our understanding of explanation. | |
| From: David Lewis (Causal Explanation [1986], V) | |
| A reaction: I am not convinced by this dismissal. If you are looking for a test of whether an explanation is good, the announcement that the participants feel they have achieved a good understanding sounds like success. |
| 15556 | Science may well pursue generalised explanation, rather than laws [Lewis] |
| Full Idea: The pursuit of general explanations may be very much more widespread in science than the pursuit of general laws. | |
| From: David Lewis (Causal Explanation [1986], IV) | |
| A reaction: Nice. I increasingly think that the main target of all enquiry is ever-widening generality, with no need to aspire to universality. |
| 15558 | A good explanation is supposed to show that the event had to happen [Lewis] |
| Full Idea: It is said that a good explanation ought to show that the explanandum event had to happen, given the laws and circumstances. | |
| From: David Lewis (Causal Explanation [1986], V) | |
| A reaction: I cautiously go along with this view. Given that there are necessities in nature (a long story), we should aim to reveal them. There is no higher aspiration open to us than successful explanation. Lewis says good explanations can reveal falsehoods. |
| 4809 | Lewis endorses the thesis that all explanation of singular events is causal explanation [Lewis, by Psillos] |
| Full Idea: Lewis endorses the thesis that all explanation of singular events is causal explanation. | |
| From: report of David Lewis (Causal Explanation [1986]) by Stathis Psillos - Causation and Explanation p.237 | |
| A reaction: It is hard to challenge this. The assumption is that only nomological and causal explanations are possible, and the former are unobtainable for singular events. |
| 14321 | To explain an event is to provide some information about its causal history [Lewis] |
| Full Idea: Here is my main thesis: to explain an event is to provide some information about its causal history. | |
| From: David Lewis (Causal Explanation [1986], II) | |
| A reaction: The obvious thought is that you might provide some tiny and barely relevant part of that causal history, such as a bird perched on the Titanic's iceberg. So how do we distinguish the 'important' causal information? |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 15555 | Explaining match lighting in general is like explaining one lighting of a match [Lewis] |
| Full Idea: Explaining why struck matches light in general is not so very different from explaining why some particular struck match lit. ...We may generalize modestly, without laying claim to universality. | |
| From: David Lewis (Causal Explanation [1986], IV) | |
| A reaction: A suggestive remark, since particular causation and general causation seem far apart, but Lewis suggests that the needs of explanation bring them together. Lawlike and unlawlike explanations? |
| 15551 | Ways of carving causes may be natural, but never 'right' [Lewis] |
| Full Idea: There is no one right way - though there may be more or less natural ways - of carving up a causal history. | |
| From: David Lewis (Causal Explanation [1986], I) | |
| A reaction: This invites a distinction between the 'natural' causes and the 'real' causes. Presumably if any causes were 'real', they would have a better claim to be 'right'. Is an earthquake the 'real' (correct?) cause of a tsunami? |
| 15552 | We only pick 'the' cause for the purposes of some particular enquiry. [Lewis] |
| Full Idea: Disagreement about 'the' cause is only disagreement about which part of the causal history is most salient for the purposes of some particular inquiry. | |
| From: David Lewis (Causal Explanation [1986], I) | |
| A reaction: I don't believe this. In the majority of cases I see the cause of an event, without having any interest in any particular enquiry. It is just so obvious that there isn't even a disagreement. Maybe there is only one sensible enquiry. |
| 15553 | Causal dependence is counterfactual dependence between events [Lewis] |
| Full Idea: I take causal dependence to be counterfactual dependence, of a suitably back-tracking sort, between distinct events. | |
| From: David Lewis (Causal Explanation [1986], I) | |
| A reaction: He quotes Hume in support. 'Counterfactual dependence' strikes me as too vague, or merely descriptive, for the job of explanation. 'If...then' is a logical relationship; what is it in nature that justifies the dependency? |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |