19 ideas
| 20320 | Truth is what unites, and the profound truths create a community [Jaspers] |
| Full Idea: Truth is what unites. ...[p.145] The most profound truth is that which all men might understand so as to form one community. | |
| From: Karl Jaspers (Philosophy [1932], vol.2) | |
| A reaction: Nice slogan, for robust realists like me. The hallmark of truth is our convergence on it. This is a 20th century existentialist perfectly expounding the enlightenment dream. The best rhetoric is truthful rhetoric. |
| 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. |
| 20323 | Freedom needs knowledge, the possibility of arbitrariness, and law [Jaspers] |
| Full Idea: Without knowledge there is no freedom ....and without an arbitrary act there is no freedom, ....and there is no freedom without law. | |
| From: Karl Jaspers (Philosophy [1932], vol.2) | |
| A reaction: He emphasises that an arbitrary act is not a free act, but it is a precondition for being free. The submission to law is active freedom. If you believe in education (and you should) you must believe that knowledge is liberating. |
| 20322 | I am aware that freedom is possible, and the freedom is not in theory, but in seeking freedom [Jaspers] |
| Full Idea: Either there is no freedom or it is in asking about it. But what makes me ask is an original will to be free, so my freedom is anticipated in the fact of asking. I cannot prove it first, then will it. I will it because I am conscious of its possibility. | |
| From: Karl Jaspers (Philosophy [1932], vol.2) | |
| A reaction: This presents the subjective claims for free will rather more persuasively than usual. I am conscious of a possibility that I might flap my arms and fly, so that doesn't establish anything. But yearning to be free is a sort of freedom. |
| 20324 | My freedom increases as I broaden my vision of possiblities and motives [Jaspers] |
| Full Idea: I become free by incessantly broadening my worldly orientation, by limitlessly visualising premises and possibilities of action, and by allowing all motives to speak to me. ...The more the totality determines my vision the freer I know I am. | |
| From: Karl Jaspers (Philosophy [1932], vol.2) | |
| A reaction: This matches my naturalistic view of responsibility for actions, which are those performed by the 'full' and knowing self. I note that freedom comes in degrees for him, so he presumably don't believe in absolute freedom. It is wholly subjective. |
| 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'). |
| 20318 | My helplessness in philosophising reveals my being, and begins its upsurge [Jaspers] |
| Full Idea: Philosophising, not knowing, brings me to myself. The helplessness to which philosophising reduces me when I doubt its origin is an expressions of the helplessness of my self-being, and the reality of philosophising is the incipient upsurge of that being. | |
| From: Karl Jaspers (Philosophy [1932], vol.2) | |
| A reaction: I like the sound of 'philosophy as a way of life', and loosely aspire to it, but I'm still not sure what it means, other than a good way to pass the time. The idea that it leads to higher modes of being sounds a bit arrogant. But it is a good thing! |
| 20321 | The struggle for Existenz is between people who are equals, and are utterly honest [Jaspers] |
| Full Idea: The struggle for Existenz has to do with ...with utter candour, with the elimination of all kinds of power and superiority, with the other's self-being as well as with my own. | |
| From: Karl Jaspers (Philosophy [1932], vol.2) | |
| A reaction: This is reminiscent of Aristotle's conclusion that democracy is the society which is most conducive to true friendship. I like Jaspers's idea that existential enquiry is a team game. |
| 20325 | Once we grasp freedom 'from' things, then freedom 'for' things becomes urgent [Jaspers] |
| Full Idea: Once the question of 'freedom from what?' has been answered by shattering all objectivities, the question of 'freedom for what?' becomes all the more urgent. | |
| From: Karl Jaspers (Philosophy [1932], vol.2) | |
| A reaction: A quintessential existentialist idea, and its most appealing aspect. Message to all teenagers: don't get bogged down in what you are prevented from doing, but focus on what you can do. The first problem will melt away. (Unless you are in handcuffs....). |
| 20317 | Mundane existence is general, falling under universals, but Existens is unique to individuals [Jaspers] |
| Full Idea: Mundane being, the being we know, is general because it is generally valid for everyone. ...Existenz is never general, and thus not a case that might be subsumed as particular under a universal. | |
| From: Karl Jaspers (Philosophy [1932], vol.2) | |
| A reaction: I'm trying to visualise a mode of existence which would fulfil only me, answering to my unique nature, but it looks like a vain delusion. I may be a one-off combination, but I see all of my ingredients in various other people. |
| 20315 | 'Existenz' is the potential being, which I could have, and ought to have [Jaspers] |
| Full Idea: There is the being which in the phenomenality of existence is not but can be, ought to be, and therefore decides in time whether it is in eternity. This being is myself as 'Existenz'. | |
| From: Karl Jaspers (Philosophy [1932], vol.2) | |
| A reaction: This is quintessentially existentialist, in its claim that my mode of being could be quite other than it is. Personally I aim to fulfil the being I've got. Play the cards you have been dealt. |
| 20319 | We want the correct grasp on being that is neither solipsism nor absorption in the crowd [Jaspers] |
| Full Idea: We want our philosophising to illuminate the free, original, communicative grasp on being that will let us meet the constant threat of solipsism or universalism in existence. | |
| From: Karl Jaspers (Philosophy [1932], vol.2) | |
| A reaction: This sounds like the political wing of existentialism: the aim to get the right relationship between citizens - not too withdrawn, and not swallowed in the crowd. Liberal democracy, I should think. |
| 20316 | Every decision I make moves towards or away from fulfilled Existenz [Jaspers] |
| Full Idea: My Existenz, as a possibility, takes a step toward being or away from being, toward nothingness, in every choice or decision I make. | |
| From: Karl Jaspers (Philosophy [1932], vol.2) | |
| A reaction: The existential idea of action involves what you are, as well as what you do. There seems to be a paradox. My being is plastic, and can change enormously, so I should take responsibility for the change. But who is in charge of the changes? |