13 ideas
| 12170 | Amusement rests on superiority, or relief, or incongruity [Scruton] |
| Full Idea: There are three common accounts of amusement: superiority theories (Hobbes's 'sudden glory'), 'relief from restraint' (Freud on jokes), and 'incongruity' theories (Schopenhauer). | |
| From: Roger Scruton (Laughter [1982], §5) | |
| A reaction: All three contain some truth. But one need not feel superior to laugh, and one may already be in a state of unrestraint. Schopenhauer seems closest to a good general account. |
| 12173 | The central object of amusement is the human [Scruton] |
| Full Idea: There are amusing buildings, but not amusing rocks and cliffs. If I were to propose a candidate for the formal object of amusement, then the human would be my choice, ...or at least emphasise its centrality. | |
| From: Roger Scruton (Laughter [1982], §9) | |
| A reaction: Sounds good. Animal behaviour only seems to amuse if it evokes something human. Plants would have to look a bit human to be funny. |
| 12169 | Since only men laugh, it seems to be an attribute of reason [Scruton] |
| Full Idea: Man is the only animal that laughs, so a starting point for all enquiries into laughter must be the hypothesis that it is an attribute of reason (though that gets us no further than our definition of reason). | |
| From: Roger Scruton (Laughter [1982], §1) | |
| A reaction: I would be inclined to say that both our capacity for reason and our capacity for laughter (and, indeed, our capacity for language) are a consequence of our evolved capacity for meta-thought. |
| 12172 | Objects of amusement do not have to be real [Scruton] |
| Full Idea: It is a matter of indifference whether the object of amusement be thought to be real. | |
| From: Roger Scruton (Laughter [1982], §7) | |
| A reaction: Sort of. If I say 'wouldn't it be funny if someone did x?', it is probably much less funny than if I say 'apparently he really did x'. The fantasy case has to be much funnier to evoke the laughter. |
| 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. |
| 12174 | Only rational beings are attentive without motive or concern [Scruton] |
| Full Idea: It is only rational beings who can be attentive without a motive; only rational beings who can be interested in that in which they have no interest. | |
| From: Roger Scruton (Laughter [1982], §12) | |
| A reaction: Rational beings make long term plans, so they cannot prejudge which things may turn out to be of interest to them. Scruton (a Kantian) makes it sound a little loftier than it actually is. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |