15 ideas
| 10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
| Full Idea: The If-thenist view seems to apply straightforwardly only to the axiomatised portions of mathematics. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: He cites Lakatos to show that cutting-edge mathematics is never axiomatised. One might reply that if the new mathematics is any good then it ought to be axiomatis-able (barring Gödelian problems). |
| 10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
| Full Idea: If we identify logic with first-order logic, and mathematics with the collection of first-order theories, then maybe we can continue to maintain the If-thenist position. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: The problem is that If-thenism must rely on rules of inference. That seems to mean that what is needed is Soundness, rather than Completeness. That is, inference by the rules must work properly. |
| 10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
| Full Idea: Containing only logical notions is not a necessary condition for being a logical truth, since a logical truth such as 'all men are men' may contain non-logical notions such as 'men'. | |
| From: Alan Musgrave (Logicism Revisited [1977], §3) | |
| A reaction: [He attributes this point to Russell] Maybe it is only a logical truth in its general form, as ∀x(x=x). Of course not all 'banks' are banks. |
| 10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
| Full Idea: The standard modern view of logical truth is that a statement is logically true if it comes out true in all interpretations in all (non-empty) domains. | |
| From: Alan Musgrave (Logicism Revisited [1977], §3) |
| 10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
| Full Idea: The axiom of Peano which states that no two numbers have the same successor requires the Axiom of Infinity for its proof. | |
| From: Alan Musgrave (Logicism Revisited [1977], §4 n) | |
| A reaction: [He refers to Russell 1919:131-2] The Axiom of Infinity is controversial and non-logical. |
| 10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
| Full Idea: Formalism seems to exclude from consideration all creative, growing mathematics. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: [He cites Lakatos in support] I am not immediately clear why spotting the remote implications of a formal system should be uncreative. The greatest chess players are considered to be highly creative and imaginative. |
| 10063 | Formalism is a bulwark of logical positivism [Musgrave] |
| Full Idea: Formalism is a bulwark of logical positivist philosophy. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: Presumably if you drain all the empirical content out of arithmetic and geometry, you are only left with the bare formal syntax, of symbols and rules. That seems to be as analytic as you can get. |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
| From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
| A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
| 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. |
| 10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
| Full Idea: Logical positivists did not adopt old-style logicism, but rather logicism spiced with varying doses of If-thenism. | |
| From: Alan Musgrave (Logicism Revisited [1977], §4) | |
| A reaction: This refers to their account of mathematics as a set of purely logical truths, rather than being either empirical, or a priori synthetic. |
| 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. |
| 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. |