33 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. |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| Full Idea: One can distinguish at least two quite different senses of logic: as an instrument of demonstration, and perhaps as an instrument for the characterization of structures. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: This is trying to capture the proof-theory and semantic aspects, but merely 'characterizing' something sounds like a rather feeble aspiration for the semantic side of things. Isn't it to do with truth, rather than just rule-following? |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| Full Idea: Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| Full Idea: The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| Full Idea: In sentential logic there is a simple proof that all truth functions, of any number of arguments, are definable from (say) 'not' and 'and'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §0) | |
| A reaction: The point of 'say' is that it can be got down to two connectives, and these are just the usual preferred pair. |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| Full Idea: The symbols ∀ and ∃ may, to start with, be regarded as extrapolations of the truth functional connectives ∧ ('and') and ∨ ('or') to infinite domains. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §5) |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| Full Idea: One might add to one's logic an 'uncountable quantifier', or a 'Chang quantifier', or a 'two-argument quantifier', or 'Shelah's quantifier', or 'branching quantifiers'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) | |
| A reaction: [compressed - just listed for reference, if you collect quantifiers, like collecting butterflies] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| Full Idea: Skolem deduced from the Löwenheim-Skolem theorem that 'the absolutist conceptions of Cantor's theory' are 'illusory'. I think it is clear that this conclusion would not follow even if elementary logic were in some sense the true logic, as Skolem assumed. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §7) | |
| A reaction: [Tharp cites Skolem 1962 p.47] Kit Fine refers to accepters of this scepticism about the arithmetic of infinities as 'Skolemites'. |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| Full Idea: The Löwenheim-Skolem property seems to be undesirable, in that it states a limitation concerning the distinctions the logic is capable of making, such as saying there are uncountably many reals ('Skolem's Paradox'). | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| Full Idea: Soundness would seem to be an essential requirement of a proof procedure, since there is little point in proving formulas which may turn out to be false under some interpretation. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| Full Idea: Putting completeness and compactness together, one has axiomatizability. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §1) |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| Full Idea: In general, if completeness fails there is no algorithm to list the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: I.e. the theory is not effectively enumerable. |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| Full Idea: It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: An example of infinite axioms is the induction schema in first-order Peano Arithmetic. |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| Full Idea: The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| Full Idea: A complete logic has an effective enumeration of the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| Full Idea: Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job. |
| 6375 | The taste of chocolate is a 'finer-grained' sensation than the taste of sweetness [Polger] |
| Full Idea: The taste of chocolate is presumably a 'finer-grained' sensation than the taste of sweetness. | |
| From: Thomas W. Polger (Natural Minds [2004], Ch.1.4) | |
| A reaction: An interesting distinction when it comes to what they are like, and whether two very different brains can realise them. Sweetness might be the same for most creatures, but the tast of chocolate subtly different. |
| 6381 | The mind and the self are one, and the mind-self is a biological phenomenon [Polger] |
| Full Idea: We should return to the old idea that the mind and the self are one and combine it with the new idea that the mind-self is a biological phenomenon. | |
| From: Thomas W. Polger (Natural Minds [2004], §8.3) | |
| A reaction: This doesn't make allowance for the fact that some parts of my mind seem like irritating visitors, and other parts seem like the home-owner. Personally I take the self to be the brain's central controller, or the centre (forum) of brain integration. |
| 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. |
| 6378 | Teleological functions explain why a trait exists; causal-role functions say what it does [Polger] |
| Full Idea: Teleological functions help explain why a trait has come to exist; causal-role functions tell what a trait does or is apt to do. | |
| From: Thomas W. Polger (Natural Minds [2004], §5.4) | |
| A reaction: The teleological view has the merit of nesting nicely with the theory of evolution, and with Aristotelian virtue ethics (which I like). Causal-role functionalism focuses better on what is actually happening inside the head. |
| 6380 | Identity theory says consciousness is an abstraction: a state, event, process or property [Polger] |
| Full Idea: Identity theories locate consciousness at a certain order of abstraction, typically among neurophysiological states, events, processes, or properties. | |
| From: Thomas W. Polger (Natural Minds [2004], Ch.7.6) | |
| A reaction: I increasingly think that processes are the answer. My new analogy for the mind is a waterfall: its physical ontology is simple, it only exists because there is a sustained process, and it is far too complex to predict individual droplet outcomes. |
| 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. |
| 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. |
| 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. |
| 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? |
| 6379 | A mummified heart has the teleological function of circulating blood [Polger] |
| Full Idea: A preserved heart in a jar of formaldehyde has the teleological function of circulating blood. | |
| From: Thomas W. Polger (Natural Minds [2004], §5.4) | |
| A reaction: A nice illustration. |
| 6377 | Teleological notions of function say what a thing is supposed to do [Polger] |
| Full Idea: Teleological notions of function specify not just what a thing happens to do, but what it is supposed to do. | |
| From: Thomas W. Polger (Natural Minds [2004], Ch.5.3) | |
| A reaction: This is the basis of a distinct theory of the mind. It seems to be akin to the 'dispositions' of behaviourism, so that the mind becomes once more a theoretical and abstract entity, rather than a thing of occurrent events and processes. |