24 ideas
| 17992 | The main aim of philosophy is to describe the whole Universe. [Moore,GE] |
| Full Idea: It seems to me that the most important and interesting thing which philosophers have tried to do ...is to give a general description of the whole of the Universe. | |
| From: G.E. Moore (Some Main Problems of Philosophy [1911], Ch. 1) | |
| A reaction: He adds that they aim to show what is in it, and what might be in it, and how the two relate. This sort of big view is the one I favour. I think the hallmark of philosophical thought is a high level of generality. He next proceeds to defend common sense. |
| 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. |
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| Full Idea: The axiom of choice has a troubled history, but is now standard in mathematics. It could be replaced with a principle of comprehension for functions), or one could omit the variables ranging over functions. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], n 3) |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| Full Idea: Early study of first-order logic revealed a number of important features. Gödel showed that there is a complete, sound and effective deductive system. It follows that it is Compact, and there are also the downward and upward Löwenheim-Skolem Theorems. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| Full Idea: Some authors argue that second-order logic (with standard semantics) is not logic at all, but is a rather obscure form of mathematics. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| Full Idea: If the goal of logical study is to present a canon of inference, a calculus which codifies correct inference patterns, then second-order logic is a non-starter. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: This seems to be because it is not 'complete'. However, moves like plural quantification seem aimed at capturing ordinary language inferences, so the difficulty is only that there isn't a precise 'calculus'. |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| Full Idea: Informally, logical consequence is sometimes defined in terms of the meanings of a certain collection of terms, the so-called 'logical terminology'. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: This seems to be a compositional account, where we build a full account from an account of the atomic bits, perhaps presented as truth-tables. |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| Full Idea: Second-order variables can range over properties, sets, or relations on the items in the domain-of-discourse, or over functions from the domain itself. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| Full Idea: Upward Löwenheim-Skolem: if a set of first-order formulas is satisfied by a domain of at least the natural numbers, then it is satisfied by a model of at least some infinite cardinal. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| Full Idea: Both of the Löwenheim-Skolem Theorems fail for second-order languages with a standard semantics | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.3.2) |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| Full Idea: The Löwenheim-Skolem theorem is usually taken as a sort of defect (often thought to be inevitable) of the first-order logic. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: [He is quoting Wang 1974 p.154] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| Full Idea: Downward Löwenheim-Skolem: a finite or denumerable set of first-order formulas that is satisfied by a model whose domain is infinite is satisfied in a model whose domain is the natural numbers | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| Full Idea: Full second-order logic has all the expressive power needed to do mathematics, but has an unworkable model theory. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) | |
| A reaction: [he credits Cowles for this remark] Having an unworkable model theory sounds pretty serious to me, as I'm not inclined to be interested in languages which don't produce models of some sort. Surely models are the whole point? |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| Full Idea: In studying second-order logic one can think of relations and functions as extensional or intensional, or one can leave it open. Little turns on this here, and so words like 'property', 'class', and 'set' are used interchangeably. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.2.1) | |
| A reaction: Important. Students of the metaphysics of properties, who arrive with limited experience of logic, are bewildered by this attitude. Note that the metaphysics is left wide open, so never let logicians hijack the metaphysical problem of properties. |
| 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. |
| 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? |