16 ideas
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| Full Idea: We have something like perception of the objects of set theory, shown by the axioms forcing themselves on us as being true. I don't see why we should have less confidence in this kind of perception (i.e. mathematical intuition) than in sense perception. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.483), quoted by Michčle Friend - Introducing the Philosophy of Mathematics 2.4 | |
| A reaction: A famous strong expression of realism about the existence of sets. It is remarkable how the ingredients of mathematics spread themselves before the mind like a landscape, inviting journeys - but I think that just shows how minds cope with abstractions. |
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| Full Idea: Gödel proved the classical relative consistency of the axiom V = L (which implies the axiom of choice and the generalized continuum hypothesis). This established the full independence of the continuum hypothesis from the other axioms. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Hilary Putnam - Mathematics without Foundations | |
| A reaction: Gödel initially wanted to make V = L an axiom, but the changed his mind. Maddy has lots to say on the subject. |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| Full Idea: The set-theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the senses are for physics. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.271), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 03.4 |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| Full Idea: Gödel proved that the Continuum Hypothesis was not inconsistent with the axioms of set theory. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15 |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| Full Idea: Gödel proved that (if set theory is consistent) we cannot refute the continuum hypothesis, and Cohen proved that (if set theory is consistent) we cannot prove it either. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by William D. Hart - The Evolution of Logic 10 |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
| Full Idea: Evidently the 'given' underlying mathematics is closely related to the abstract elements contained in our empirical ideas. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], Suppl) | |
| A reaction: Yes! The great modern mathematical platonist says something with which I can agree. He goes on to hint at a platonic view of the structure of the empirical world, but we'll let that pass. |
| 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. |
| 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. |
| 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. |
| 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). |
| 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. |
| 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 |
| 6017 | Nomos is king [Pindar] |
| Full Idea: Nomos is king. | |
| From: Pindar (poems [c.478 BCE], S 169), quoted by Thomas Nagel - The Philosophical Culture | |
| A reaction: This seems to be the earliest recorded shot in the nomos-physis wars (the debate among sophists about moral relativism). It sounds as if it carries the full relativist burden - that all that matters is what has been locally decreed. |