13 ideas
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 8329 | Either causal relations are given in experience, or they are unobserved and theoretical [Sosa/Tooley] |
| Full Idea: There is a fundamental choice between the realist approach to causation which says that the relation is immediately given in experience, and the view that causation is a theoretical relation, and so not directly observable. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §1) | |
| A reaction: Even if immediate experience is involved, there is a step of abstraction in calling it a cause, and picking out events. A 'theoretical relation' is not of much interest there if no observations are involved. I don't think a choice is required here. |
| 8324 | The problem is to explain how causal laws and relations connect, and how they link to the world [Sosa/Tooley] |
| Full Idea: Causal states of affairs encompass causal laws, and causal relations between events or states of affairs; two key questions concern the relation between causal laws and causal relations, and the relation between these and non-causal affairs. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §1) | |
| A reaction: This is the agenda for modern analytical philosophy. I'm not quite clear what would count as an answer. When have you 'explained' a relation? Does calling it 'gravity', or finding an equation, explain that relation? Do gravitinos explain it? |
| 8328 | Causation isn't energy transfer, because an electron is caused by previous temporal parts [Sosa/Tooley] |
| Full Idea: The temporal parts of an electron (for example) are causally related, but this relation does not involve any transfer of energy or momentum. Causation cannot be identified with physical energy relations, and physicalist reductions look unpromising. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §1) | |
| A reaction: This idea, plus Idea 8327, are their grounds for rejecting Fair's proposal (Idea 8326). It feels like a different use of 'cause' when we say 'the existence of x was caused by its existence yesterday'. It is more like inertia. Destruction needs energy. |
| 8327 | If direction of causation is just direction of energy transfer, that seems to involve causation [Sosa/Tooley] |
| Full Idea: The objection to Fair's view that the direction of causation is the direction of the transference of energy and/or momentum is that the concept of transference itself involves the idea of causation. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §1) | |
| A reaction: Does it? If a particle proceeds from a to b, how is that causation? ...But the problem is that the particle kicks open the door when it arrives (i.e. makes changes). We wouldn't call it causation if the transference didn't change any properties. |
| 8433 | There are few traces of an event before it happens, but many afterwards [Lewis, by Horwich] |
| Full Idea: Lewis claims that most events are over-determined by subsequent states of the world, but not by their history. That is, the future of every event contains many independent traces of its occurrence, with little prior indication that it would happen. | |
| From: report of David Lewis (Counterfactual Dependence and Time's Arrow [1979]) by Paul Horwich - Lewis's Programme p.209 | |
| A reaction: Lewis uses this asymmetry to deduce the direction of causation, and hence the direction of time. Most people (including me, I think) would prefer to use the axiomatic direction of time to deduce directions of causation. Lewis was very wicked. |
| 8330 | Are causes sufficient for the event, or necessary, or both? [Sosa/Tooley] |
| Full Idea: An early view of causation (Mill and Hume) is whatever is (ceteris paribus) sufficient for the event. A second view (E.Nagel) is that the cause should just be necessary. Some (R.Taylor) even contemplate the cause having to be necessary and sufficient. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §2) | |
| A reaction: A cause can't be necessary if there is some other way to achieve the effect. A single cause is not sufficient if many other factors are also essential. If neither of those is right, then 'both' is wrong. Enter John Mackie... |
| 8325 | The dominant view is that causal laws are prior; a minority say causes can be explained singly [Sosa/Tooley] |
| Full Idea: The dominant view is that causal laws are more basic than causal relations, with relations being logically supervenient on causal laws, and on properties and event relations; some, though, defend the singularist view, in which events alone can be related. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §1) | |
| A reaction: I am deeply suspicious about laws (see Idea 5470). I suspect that the laws are merely descriptions of the regularities that arise from the single instances of causation. We won't explain the single instances, but then laws don't 'explain' them either. |