14 ideas
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
| Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.4) |
| 10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
| Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.2) |
| 10885 | Computer proofs don't provide explanations [Horsten] |
| Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.3) |
| 10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
| Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.3) |
| 7949 | Varied descriptions of an event will explain varied behaviour relating to it [Davidson, by Macdonald,C] |
| Full Idea: Davidson points out that we can only make sense of patterns of behaviour such as excuses if events can have more than one description. So I flip the light switch, turn on the light, illuminate the room, and alert a prowler, but I do only one thing. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Cynthia Macdonald - Varieties of Things Ch.5 | |
| A reaction: We can distinguish an event as an actual object, and as an intentional object. We can probably individuate intentional events quite well (according to our interests), but actual 'events' seem to flow into one another and overlap. |
| 18431 | Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards] |
| Full Idea: Simons's 'nuclear' option blends features of the substratum and bundle theories. First we have tropes collected by virtue of their internal relations, forming the essential kernel or nucleus. This nucleus then bears the non-essential tropes. | |
| From: report of Peter Simons (Particulars in Particular Clothing [1994], p.567) by Douglas Edwards - Properties 3.5 | |
| A reaction: [compression of Edwards's summary] This strikes me as being a remarkably good theory. I am not sure of the ontological status of properties, such that they can (unaided) combine to make part of an object. What binds the non-essentials? |
| 20020 | If one action leads directly to another, they are all one action [Davidson, by Wilson/Schpall] |
| Full Idea: Davidson (1980 ess 1) agreed with Anscombe that if a person Fs by G-ing, then her act F = her act G. For example, if someone accidentally alerts a burglar, by deliberately turning on a light, by flipping a switch, these are all the same action. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Wilson,G/Schpall,S - Action 1.2 | |
| A reaction: I would have thought there was obviously a strong conventional element in individuating actions, depending on interest. An electrician is only interest in whether the light worked. The police are only interested in the disturbance of the burglar. |
| 20072 | We explain an intention by giving an account of acting with an intention [Davidson, by Stout,R] |
| Full Idea: The early Davidson championed the approach that we explain the idea of having an intention by providing an account of what it is to act with an intention. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Rowland Stout - Action 7 'Conclusion' | |
| A reaction: This eliminates the distinction between a prior intention, and the intention that maintains a process such as speech. It sounds almost behaviourist. |
| 20045 | Acting for a reason is a combination of a pro attitude, and a belief that the action is appropriate [Davidson] |
| Full Idea: Whenever someone does something for a reason he can be characterised as (a) having some sort of pro attitude towards action of a certain kind, and (b) believing (or knowing, perceiving, noticing, remembering) that his action is of that kind. | |
| From: Donald Davidson (Action, Reasons and Causes [1963], p.3-4), quoted by Rowland Stout - Action 3 'The belief-' | |
| A reaction: This is the earlier Davidson roughly endorsing the traditional belief-desire account of action. He is giving a reductive account of reasons. Deciding reasons were not reducible may have led him to property dualism. |
| 20075 | Early Davidson says intentional action is caused by reasons [Davidson, by Stout,R] |
| Full Idea: In Davidson's earlier approach, intentional action requires causation by reasons. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Rowland Stout - Action 8 'Weakness' | |
| A reaction: A very Kantian idea, and one that seems to bestow causal powers on something which I take to be highly abstract. Thus Davidson was wrong (but in a nice way). |
| 3395 | Davidson claims that what causes an action is the reason for doing it [Davidson, by Kim] |
| Full Idea: Davidson defends the simple thesis that the reason for which an action is done is the one that causes it, …which means that agency is possible only if mental causation is possible. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Jaegwon Kim - Philosophy of Mind p.127 |
| 23734 | The best explanation of reasons as purposes for actions is that they are causal [Davidson, by Smith,M] |
| Full Idea: Davidson argues that the best interpretation of the teleological character of reason explanations is an intepretation in causal terms. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Michael Smith - The Moral Problem 4.4 | |
| A reaction: That is, this is the explanation of someone doing something 'because' they have this reason (rather than happening to have a reason). Smith observes that other mental states (such as beliefs) may also have this causal power. |
| 23737 | Reasons can give purposes to actions, without actually causing them [Smith,M on Davidson] |
| Full Idea: Only the Humean theory is able to make sense of reason explanation as a species of teleological explanation, and one may accept that reason explanations are teleological without accepting that they are causal. | |
| From: comment on Donald Davidson (Action, Reasons and Causes [1963]) by Michael Smith - The Moral Problem 4.6 | |
| A reaction: That is, reasons can give a purpose to an action, and thereby motivate it, without actually causing it. I agree with Smith. I certainly don't (usually, at least) experience reasons as directly producing my actions. Hume says desires are needed. |
| 6664 | Reasons must be causes when agents act 'for' reasons [Davidson, by Lowe] |
| Full Idea: It can be argued (by Davidson) that far from it being the case that reasons for and causes of action are quite distinct, reasons must be causes when agents act 'for' reasons. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.9 | |
| A reaction: Lowe argues against this view. The rival views to Davidson would be either that reasons are no more than desires-plus-beliefs in disguise, or that the will causes actions, and strong reasons carry a great weight with the will. I like the will. |