31 ideas
| 3798 | An overexamined life is as bad as an unexamined one [Dennett] |
| Full Idea: The unexamined life may not be worth living, but the overexamined life is nothing to write home about either. | |
| From: Daniel C. Dennett (Elbow Room: varieties of free will [1984], §4.2) | |
| A reaction: Presumably he means a life which is all theory and no practice. Compare Idea 343. |
| 3801 | Rationality requires the assumption that things are either for better or worse [Dennett] |
| Full Idea: We must assume that something matters - that some things are for better and some things are for worse, for without that our assumed rationality would have nothing on which to get a purchase. | |
| From: Daniel C. Dennett (Elbow Room: varieties of free will [1984], §7.1) | |
| A reaction: It does seem that rationality wouldn't exist as an activity without some value to motivate it. |
| 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 Michèle 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. |
| 9476 | If dispositions are more fundamental than causes, then they won't conceptually reduce to them [Bird on Lewis] |
| Full Idea: Maybe a disposition is a more fundamental notion than a cause, in which case Lewis has from the very start erred in seeking a causal analysis, in a traditional, conceptual sense, of disposition terms. | |
| From: comment on David Lewis (Causation [1973]) by Alexander Bird - Nature's Metaphysics 2.2.8 | |
| A reaction: Is this right about Lewis? I see him as reducing both dispositions and causes to a set of bald facts, which exist in possible and actual worlds. Conditionals and counterfactuals also suffer the same fate. |
| 8425 | For true counterfactuals, both antecedent and consequent true is closest to actuality [Lewis] |
| Full Idea: A counterfactual is non-vacuously true iff it takes less of a departure from actuality to make the consequent true along with the antecedent than it does to make the antecedent true without the consequent. | |
| From: David Lewis (Causation [1973], p.197) | |
| A reaction: Almost every theory proposed by Lewis hangs on the meaning of the word 'close', as used here. If you visited twenty Earth-like worlds (watch Startrek?), it would be a struggle to decide their closeness to ours in rank order. |
| 3802 | Why pronounce impossible what you cannot imagine? [Dennett] |
| Full Idea: You say you cannot imagine that p, and therefore declare that p is impossible. Mightn't that be hubris? | |
| From: Daniel C. Dennett (Elbow Room: varieties of free will [1984], §7.3) |
| 3795 | Causal theories require the "right" sort of link (usually unspecified) [Dennett] |
| Full Idea: In causal theories of knowledge and reference, the causal chain between object and thought must be of the "right" sort - the nature of rightness to be specified later, typically. | |
| From: Daniel C. Dennett (Elbow Room: varieties of free will [1984], §3.3 n14) | |
| A reaction: This is now the standard objection to a purely causal account of reference. Which of the many causal chains causes the meaning? Knowledge of maths is a further problem for it. |
| 3797 | I am the sum total of what I directly control [Dennett] |
| Full Idea: Control is the ultimate criterion of the self: I am the sum total of the parts I control directly. | |
| From: Daniel C. Dennett (Elbow Room: varieties of free will [1984], §4.2) | |
| A reaction: This looks awfully like a flagrant self-contradiction, and I think it is. It seems pretty obvious that there is at least a distinction between the bit or bits that do the controlling, and the bits that get controlled. |
| 3800 | You can be free even though force would have prevented you doing otherwise [Dennett, by PG] |
| Full Idea: If a brain implant would compel you to perform an action which you in fact freely choose, then you are free, but couldn't have done otherwise. | |
| From: report of Daniel C. Dennett (Elbow Room: varieties of free will [1984], §6.1) by PG - Db (ideas) |
| 3803 | Can we conceive of a being with a will freer than our own? [Dennett] |
| Full Idea: Can I even conceive of beings whose wills are freer than our own? | |
| From: Daniel C. Dennett (Elbow Room: varieties of free will [1984], §7.3) |
| 3794 | Foreknowledge permits control [Dennett] |
| Full Idea: Foreknowledge is what permits control. | |
| From: Daniel C. Dennett (Elbow Room: varieties of free will [1984], §3.2) |
| 3791 | Awareness of thought is a step beyond awareness of the world [Dennett] |
| Full Idea: The creature who is not only sensitive to patterns in its environment, but also sensitive to patterns in its own reactions to patterns in its environment, has taken a major step. | |
| From: Daniel C. Dennett (Elbow Room: varieties of free will [1984], §2.2) |
| 8424 | Determinism says there can't be two identical worlds up to a time, with identical laws, which then differ [Lewis] |
| Full Idea: By determinism I mean that the prevailing laws of nature are such that there do not exist any two possible worlds which are exactly alike up to that time, which differ thereafter, and in which those laws are never violated. | |
| From: David Lewis (Causation [1973], p.196) | |
| A reaction: This would mean that the only way an action of free will could creep in would be if it accepted being a 'violation' of the laws of nature. Fans of free will would probably prefer to call it a 'natural' phenomenon. I'm with Lewis. |
| 3796 | The active self is a fiction created because we are ignorant of our motivations [Dennett] |
| Full Idea: Faced with our inability to 'see' where the centre or source of our free actions is,…we exploit the gaps in our self-knowledge by filling it with a mysterious entity, the unmoved mover, the active self. | |
| From: Daniel C. Dennett (Elbow Room: varieties of free will [1984], §4.1) | |
| A reaction: I am convinced that there is no such things as free will; its origins are to be found in religion, where it is a necessary feature of a very supreme God. I don't believe for a moment that we need to believe in free will. |
| 8420 | A proposition is a set of possible worlds where it is true [Lewis] |
| Full Idea: I identify a proposition with the set of possible worlds where it is true. | |
| From: David Lewis (Causation [1973], p.193) | |
| A reaction: As it stands, I'm baffled by this. How can 'it is raining' be a set of possible worlds? I assume it expands to refer to the truth-conditions, among possibilities as well as actualities. 'It is raining' fits all worlds where it is raining. |
| 8405 | A theory of causation should explain why cause precedes effect, not take it for granted [Lewis, by Field,H] |
| Full Idea: Lewis thinks it is a major defect in a theory of causation that it builds in the condition that the time of the cause precede that of the effect: that cause precedes effect is something we ought to explain (which his counterfactual theory claims to do). | |
| From: report of David Lewis (Causation [1973]) by Hartry Field - Causation in a Physical World | |
| A reaction: My immediate reaction is that the chances of explaining such a thing are probably nil, and that we might as well just accept the direction of causation as a given. Even philosophers balk at the question 'why doesn't time go backwards?' |
| 8427 | I reject making the direction of causation axiomatic, since that takes too much for granted [Lewis] |
| Full Idea: One might stipulate that a cause must always precede its effect, but I reject this solution. It won't solve the problem of epiphenomena, it rejects a priori any backwards causation, and it trivializes defining time-direction through causation. | |
| From: David Lewis (Causation [1973], p.203) | |
| A reaction: [compressed] Not strong arguments, I would say. Maybe apparent causes are never epiphenomenal. Maybe backwards causation is impossible. Maybe we must use time to define causal direction, and not vice versa. |
| 8419 | The modern regularity view says a cause is a member of a minimal set of sufficient conditions [Lewis] |
| Full Idea: In present-day regularity analyses, a cause is defined (roughly) as any member of any minimal set of actual conditions that are jointly sufficient, given the laws, for the existence of the effect. | |
| From: David Lewis (Causation [1973], p.193) | |
| A reaction: This is the view Lewis is about to reject. It seem to summarise the essence of the Mackie INUS theory. This account would make the presence of oxygen a cause of almost every human event. |
| 10392 | It is just individious discrimination to pick out one cause and label it as 'the' cause [Lewis] |
| Full Idea: We sometimes single out one among all the causes of some event and call it 'the' cause. ..We may select the abnormal causes, or those under human control, or those we deem good or bad, or those we want to talk about. This is invidious discrimination. | |
| From: David Lewis (Causation [1973]) | |
| A reaction: This is the standard view expressed by Mill - presumably the obvious empiricist line. But if we specify 'the pre-conditions' for an event, we can't just mention ANY fact prior to the effect - there is obvious relevance. So why not for 'the' cause as well? |
| 8421 | Regularity analyses could make c an effect of e, or an epiphenomenon, or inefficacious, or pre-empted [Lewis] |
| Full Idea: In the regularity analysis of causes, instead of c causing e, c might turn out to be an effect of e, or an epiphenomenon, or an inefficacious effect of a genuine cause, or a pre-empted cause (by some other cause) of e. | |
| From: David Lewis (Causation [1973], p.194) | |
| A reaction: These are Lewis's reasons for rejecting the general regularity account, in favour of his own particular counterfactual account. It is unlikely that c would be regularly pre-empted or epiphenomenal. If we build time's direction in, it won't be an effect. |
| 17524 | Lewis has basic causation, counterfactuals, and a general ancestral (thus handling pre-emption) [Lewis, by Bird] |
| Full Idea: Lewis's basic account has a basic causal relation, counterfactual dependence, and the general causal relation is the ancestral of this basic one. ...This is motivated by counterfactual dependence failing to be general because of the pre-emption problem. | |
| From: report of David Lewis (Causation [1973]) by Alexander Bird - Causation and the Manifestation of Powers p.161 | |
| A reaction: It is so nice when you struggle for ages with a topic, and then some clever person summarises it clearly for you. |
| 17525 | The counterfactual view says causes are necessary (rather than sufficient) for their effects [Lewis, by Bird] |
| Full Idea: The Humean idea, developed by Lewis, is that rather than being sufficient for their effects, causes are (counterfactual) necessary for their effects. | |
| From: report of David Lewis (Causation [1973]) by Alexander Bird - Causation and the Manifestation of Powers p.162 |
| 8397 | Counterfactual causation implies all laws are causal, which they aren't [Tooley on Lewis] |
| Full Idea: Some counterfactuals are based on non-causal laws, such as Newton's Third Law of Motion. 'If no force one way, then no force the other'. Lewis's counterfactual analysis implies that one force causes the other, which is not the case. | |
| From: comment on David Lewis (Causation [1973]) by Michael Tooley - Causation and Supervenience 5.2 | |
| A reaction: So what exactly does 'cause' my punt to move forwards? Basing causal laws on counterfactual claims looks to me like putting the cart before the horse. |
| 8423 | My counterfactual analysis applies to particular cases, not generalisations [Lewis] |
| Full Idea: My (counterfactual) analysis is meant to apply to causation in particular cases; it is not an analysis of causal generalizations. Those presumably quantify over particulars, but it is hard to match natural language to the quantifiers. | |
| From: David Lewis (Causation [1973], p.195) | |
| A reaction: What authority could you have for asserting a counterfactual claim, if you only had one observation? Isn't the counterfactual claim the hallmark of a generalisation? For one case, 'if not-c, then not-e' is just a speculation. |
| 8426 | One event causes another iff there is a causal chain from first to second [Lewis] |
| Full Idea: One event is the cause of another iff there exists a causal chain leading from the first to the second. | |
| From: David Lewis (Causation [1973], p.200) | |
| A reaction: It will be necessary to both explain and identify a 'chain'. Some chains are extremely tenuous (Alexander could stop a barrel of beer). Go back a hundred years, and the cause of any present event is everything back then. |
| 4795 | Lewis's account of counterfactuals is fine if we know what a law of nature is, but it won't explain the latter [Cohen,LJ on Lewis] |
| Full Idea: Lewis can elucidate the logic of counterfactuals on the assumption that you are not at all puzzled about what a law of nature is. But if you are puzzled about this, it cannot contribute anything towards resolving your puzzlement. | |
| From: comment on David Lewis (Causation [1973]) by L. Jonathan Cohen - The Problem of Natural Laws p.219 | |
| A reaction: This seems like a penetrating remark. The counterfactual theory is wrong, partly because it is epistemological instead of ontological, and partly because it refuses to face the really difficult problem, of what is going on out there. |