16 ideas
| 9271 | Human knowledge may not produce well-being; the examined life may not be worth living [Gray] |
| Full Idea: Human knowledge is one thing, human well-being another. There is no predetermined harmony between the two. The examined life may not be worth living. | |
| From: John Gray (Straw Dogs [2002], 1.9) | |
| A reaction: John Gray has set himself up as the Eeyore of modern times, but this point may obviously be correct. Presumably Socrates meant that the examined life was better even if the result was less 'well-being'. Even Gray doesn't want a lobotomy. |
| 9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
| Full Idea: ZF set theory is a first-order axiomatization. Variables range over sets, there are no second-order variables, and primitive predicates are just 'equals' and 'member of'. The axiom of extensionality says sets with the same members are identical. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 7) | |
| A reaction: If the eleven members of the cricket team are the same as the eleven members of the hockey team, is the cricket team the same as the hockey team? Our cricket team is better than our hockey team, so different predicates apply to them. |
| 9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
| Full Idea: The main alternative to ZF is two-sorted theories, with some variables ranging over classes. Classes have more generous existence assumptions: there is a universal class, containing all sets, and a class containing all ordinals. Classes are not members. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 7.1.1) | |
| A reaction: My intuition is to prefer strict systems when it comes to logical theories. The whole point is precision. Otherwise we could just think about things, and skip all this difficult symbolic stuff. |
| 9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
| Full Idea: It must not be concluded from the rejection of excluded middle that intuitionistic logic operates with three values: true, false, and neither true nor false. It does not make use of true and false, but only with a construction being a proof. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 8.1) | |
| A reaction: This just sounds like verificationism to me, with all its problems. It seems to make speculative statements meaningless, which can't be right. Realism has lots of propositions which are assumed to be true or false, but also unknowable. |
| 9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
| Full Idea: First-order logic is distinguished by generalizations (quantification) only over objects: second-order logic admits generalizations or quantification over properties or kinds of objects, and over relations between them, and functions defined over them. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
| A reaction: Second-order logic was introduced by Frege, but is (interestingly) rejected by Quine, because of the ontological commitments involved. I remain unconvinced that quantification entails ontological commitment, so I'm happy. |
| 9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
| Full Idea: There are two ways of characterizing logical truths and correct inference. Proof-theoretic or syntactic characterizations, if the formalization admits of proof or derivation; and model-theoretic or semantic versions, being true in all interpretations. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
| A reaction: Dummett calls this distinction 'fundamental'. The second one involves truth, and hence meaning, where the first one just responds to rules. ..But how can you have a notion of correctly following a rule, without a notion of truth? |
| 9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
| Full Idea: It can be argued that the notion of ordinal numbers is more fundamental than that of cardinals. To count objects, we must count them in sequence. ..The theory of ordinals forms the substratum of Cantor's theory of cardinals. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 5) | |
| A reaction: Depends what you mean by 'fundamental'. I would take cardinality to be psychologically prior ('that is a lot of sheep'). You can't order people by height without first acquiring some people with differing heights. I vote for cardinals. |
| 9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
| Full Idea: The number 4 cannot be characterized solely by its position in a system, because it has different positions in the system of natural numbers and that of the positive whole numbers, whereas these systems have the very same structure. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 6.1) | |
| A reaction: Dummett seems to think this is fairly decisive against structuralism. There is also the structure of the real numbers. We will solve this by saying that the wholes are abstracted from the naturals, which are abstracted from the reals. Job done. |
| 9275 | Knowledge does not need minds or nervous systems; it is found in all living things [Gray] |
| Full Idea: Knowledge does not need minds, or even nervous systems. It is found in all living things. | |
| From: John Gray (Straw Dogs [2002], 2.10) | |
| A reaction: I consider it a misnomer to call such things 'knowledge', for which I have much higher standards. Gray is talking about 'information'. Knowledge needs reasons, and possibility of error, not just anticipatory behaviour. |
| 9276 | The will hardly ever does anything; most of our life just happens to us [Gray] |
| Full Idea: We think our actions express our decisions, but in nearly all of our life, willing decides nothing. We cannot wake up or fall asleep, remember or forget our dreams, summon or banish our thoughts, by deciding to do so. | |
| From: John Gray (Straw Dogs [2002], 2.12) | |
| A reaction: Gray's point does not rule out occasional total control over mental life, but his point is important. The traditional picture is of a life controlled, so the will is seen as at the centre of a person, but it just isn't the case. |
| 9278 | Nowadays we identify the free life with the good life [Gray] |
| Full Idea: We do not value freedom more than people did in earlier times, but we have identified the good life with the chosen life. | |
| From: John Gray (Straw Dogs [2002], 3.13) | |
| A reaction: Interesting. This is Enlightenment liberalism gradually filtering down into common consciousness, especially via the hegemony of American culture. I sympathise the Gray; don't get me wrong, but I think freedom is overrated. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 9280 | Over forty percent of the Earth's living tissue is human [Gray] |
| Full Idea: Humans co-opt over forty per cent of the Earth's living tissue. | |
| From: John Gray (Straw Dogs [2002], 4.15) | |
| A reaction: If you add our domestic animals, I understand that the figure goes up to 95 per cent! I take this to be virtually the only significant ecological fact - population, population, population. Why are there so many cars? So many carbon footprints? |
| 9279 | What was our original sin, and how could Christ's suffering redeem it? [Gray] |
| Full Idea: No one can say what was humankind's original sin, and no one understands how the suffering of Christ can redeem it. | |
| From: John Gray (Straw Dogs [2002], 4.1) | |
| A reaction: This nicely articulates a problem that has half bothered me, but I have never put into words. I always assumed Eve committed the sin, and Adam cops the blame for not controlling his woman. Dying for our sins has always puzzled me. |
| 9272 | Without Christianity we lose the idea that human history has a meaning [Gray] |
| Full Idea: For Christians, it is because they occur in history that the lives of humans have a meaning that the lives of other animals do not. ..If we truly leave Christianity behind, we must give up the idea that human history has a meaning. | |
| From: John Gray (Straw Dogs [2002], 2.3) | |
| A reaction: Interesting. Compare the dispute between 'whig' and 'tory' historians, the former of whom believe that history is going somewhere. |