11 ideas
| 18261 | A simplification which is complete constitutes a definition [Kant] |
| Full Idea: By dissection I can make the concept distinct only by making the marks it contains clear. That is what analysis does. If this analysis is complete ...and in addition there are not so many marks, then it is precise and so constitutes a definition. | |
| From: Immanuel Kant (Wiener Logik [1795], p.455), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
| A reaction: I think Aristotle would approve of this. We need to grasp that a philosophical definition is quite different from a lexicographical definition. 'Completeness' may involve quite a lot. |
| 9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
| Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought. | |
| From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2 | |
| A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects. |
| 22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
| Full Idea: In logic the question is not one of contingent but of necessary rules, not how to think, but how we ought to think. | |
| From: Immanuel Kant (Wiener Logik [1795], p.16), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Trans' | |
| A reaction: Presumably it aspires to the objectivity of a single correct account of how we all ought to think. I'm sympathetic to that, rather than modern cultural relativism about reason. Logic is rooted in nature, not in arbitrary convention. |
| 15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
| Full Idea: Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections. | |
| From: report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I | |
| A reaction: I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue. |
| 18260 | If we knew what we know, we would be astonished [Kant] |
| Full Idea: If we only know what we know ...we would be astonished by the treasures contained in our knowledge. | |
| From: Immanuel Kant (Wiener Logik [1795], p.843), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
| A reaction: Nice remark. He doesn't require immediat recall of knowledge. You can't be required to know that you know something. That doesn't imply externalism, though. I believe in securely founded internal knowledge which is hard to recall. |
| 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. |
| 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. |