29 ideas
| 9307 | Modern Western culture suddenly appeared in Jena in the 1790s [Svendsen] |
| Full Idea: Foucault was right to say that Jena in the 1790s was the arena where the fundamental interests in modern Western culture suddenly had their breakthrough. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.2) | |
| A reaction: [Hölderlin, Novalis, Tieck, Schlegel, based on Kant and Fichte] Romanticism seems to have been born then. Is that the essence of modernism? Foucault and his pals are hoping to destroy the Enlightenment by ignoring it, but that is modern too. |
| 9297 | You can't understand love in terms of 'if and only if...' [Svendsen] |
| Full Idea: I once began reading a philosophical article on love. The following statement soon came up: 'Bob loves Kate if and only if...' At that point I stopped reading. Such a formalized approach was unsuitable, because the actual phenomenon would be lost. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Pref) | |
| A reaction: It is hard to disagree! However, if your best friend comes to you and says, 'I can't decide whether I am really in love with Kate; what do you think?', how are you going to respond. You offer 'if and only if..', but in a warm and sympathetic way! |
| 9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
| Full Idea: Everything we know about the empty set is relational; we know that nothing is the membership relation to it. But what do we know about its 'intrinsic properties'? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: Set theory seems to depend on the concept of the empty set. Modern theorists seem over-influenced by the Quine-Putnam view, that if science needs it, we must commit ourselves to its existence. |
| 9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
| Full Idea: In simple type theory, there is a null set of type 1, a null set of type 2, a null set of type 3..... (Quine has expressed his distaste for this). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.4) | |
| A reaction: It is bad enough trying to individuate the unique null set, without whole gangs of them drifting indistinguishably through the logical fog. All rational beings should share Quine's distaste, even if Quine is wrong. |
| 9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
| Full Idea: In the Gödelian realistic view of set theory the statement that there is a null set as the assertion of the existence in the real world of a set that has no members. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It seems to me obvious that such a claim is nonsense on stilts. 'In the beginning there was the null set'? |
| 9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
| Full Idea: In the structuralist view of sets, in structures of a certain sort the null set is taken to be a position (or point) that will be such that no other position (or point) will be in the membership relation to it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It would be hard to conceive of something having a place in a structure if nothing had a relation to it, so is the null set related to singeton sets but not there members. It will be hard to avoid Platonism here. Set theory needs the null set. |
| 9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
| Full Idea: What is it about the intrinsic properties of just that one unit set in virtue of which Bill Clinton is related to just it and not to any other unit sets in the set-theoretical universe? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If we all kept pet woodlice, we had better not hold a wood louse rally, or we might go home with the wrong one. My singleton seems seems remarkably like yours. Could we, perhaps, swap, just for a change? |
| 9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
| Full Idea: The set theorist cannot tell us anything about the true relationship of membership. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If three unrelated objects suddenly became members of a set, it is hard to see how the world would have changed, except in the minds of those thinking about it. |
| 9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
| Full Idea: ZFU set theory talks about physical objects (the urelements), and hence is in some way about the physical world. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.5) | |
| A reaction: This sounds a bit surprising, given that the whole theory would appear to be quite unaffected if God announced that idealism is true and there are no physical objects. |
| 9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
| Full Idea: A pack of wolves is not thought to go out of existence just because some member of the pack is killed. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.5) | |
| A reaction: The point is that the formal extensional notion of a set doesn't correspond to our common sense notion of a group or class. Even a highly scientific theory about wolves needs a loose notion of a wolf pack. |
| 9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
| Full Idea: Everything one needs to do with relations in mathematics can be done by taking a relation to be a set of ordered pairs. (Ordered triples etc. can be defined as order pairs, so that <x,y,z> is <x,<y,z>>). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.2) | |
| A reaction: How do we distinguish 'I own my cat' from 'I love my cat'? Or 'I quite like my cat' from 'I adore my cat'? Nevertheless, this is an interesting starting point for a discussion of relations. |
| 9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
| Full Idea: In first-order logic a set of sentences is 'consistent' iff there is an interpretation (or structure) in which the set of sentences is true. ..For Frege, though, a set of sentences is consistent if it is not possible to deduce a contradiction from it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.1) | |
| A reaction: The first approach seems positive, the second negative. Frege seems to have a higher standard, which is appealing, but the first one seems intuitively right. There is a possible world where this could work. |
| 9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
| Full Idea: With the invention of analytic geometry (by Fermat and then Descartes) physical space could be represented as having a mathematical structure, which could eventually lead to its axiomatization (by Hilbert). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.3) | |
| A reaction: The idea that space might have axioms seems to be pythagoreanism run riot. I wonder if there is some flaw at the heart of Einstein's General Theory because of this? |
| 10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
| Full Idea: Chihara's 'constructability theory' is nominalist - mathematics is reducible to a simple theory of types. Instead of talk of sets {x:x is F}, we talk of open sentences Fx defining them. Existence claims become constructability of sentence tokens. | |
| From: report of Charles Chihara (A Structural Account of Mathematics [2004]) by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.81 | |
| A reaction: This seems to be approaching the problem in a Fregean way, by giving an account of the semantics. Chihara is trying to evade the Quinean idea that assertion is ontological commitment. But has Chihara retreated too far? How does he assert existence? |
| 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
| Full Idea: If mathematics shares whatever confirmation accrues to the theories using it, would it not be reasonable to suppose that mathematics shares whatever disconfirmation accrues to the theories using it? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 05.8) | |
| A reaction: Presumably Quine would bite the bullet here, although maths is much closer to the centre of his web of belief, and so far less likely to require adjustment. In practice, though, mathematics is not challenged whenever an experiment fails. |
| 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
| Full Idea: Evidently, no scientific explanations of specific phenomena would collapse as a result of any hypothetical discovery that no mathematical objects exist. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.1) | |
| A reaction: It is inconceivable that anyone would challenge this claim. A good model seems to be drama; a play needs commitment from actors and audience, even when we know it is fiction. The point is that mathematics doesn't collapse either. |
| 9308 | If subjective and objective begin to merge, then so do primary and secondary qualities [Svendsen] |
| Full Idea: It is doubtful whether the traditional dichotomy between the strictly subjective and the strictly objective can still be maintained; if not, we must also revise the distinction between primary and secondary qualities. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.3) | |
| A reaction: Very perceptive. The reason why I am so keen to hang onto the primary/secondary distinction is because I want to preserve objectivity (and realism). I much prefer Locke to Hume, as empiricist spokesmen. |
| 9309 | Emotions have intentional objects, while a mood is objectless [Svendsen] |
| Full Idea: An emotion normally has an intentional object, while a mood is objectless. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.3) | |
| A reaction: It doesn't follow that the object of the emotion is clearly understood, or even that it is conscious. One may experience rising anger while struggling to see what its object is. Artistic symbolism seems to involve objects that create moods. |
| 9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
| Full Idea: What I refer to as an 'equivalence class' (of line segments of a particular length) is an open sentence in my Constructibility Theory. I just use this terminology of the Platonist for didactic purposes. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.10) | |
| A reaction: This is because 'equivalence classes' is committed to the existence of classes, which is Quinean Platonism. I am with Chihara in wanting a story that avoids such things. Kit Fine is investigating similar notions of rules of construction. |
| 9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
| Full Idea: Causal theories of reference seem doomed to failure for the case of reference to mathematical entities, since such entities are evidently causally inert. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.3) | |
| A reaction: Presumably you could baptise a fictional entity such as 'Polonius', and initiate a social causal chain, with a tradition of reference. You could baptise a baby in absentia. |
| 9304 | Death appears to be more frightening the less one has lived [Svendsen] |
| Full Idea: Death appears to be more frightening the less one has lived. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.2) | |
| A reaction: [He credits Adorno with this] A good thought, which should be immediately emailed to Epicurus for comment. Which is worse - to die when you have barely started your great work (Ramsey), or dying in full flow (Schubert)? |
| 9301 | Boredom is so radical that suicide could not overcome it; only never having existed would do it [Svendsen] |
| Full Idea: Boredom is so radical that it cannot even be overcome by suicide, only by something completely impossible - not to have existed at all. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.1) | |
| A reaction: [he cites Fernando Pessoa for this] The actor George Sanders left a suicide note saying that he was just bored. A cloud of boredom is left hanging in the air where he was. |
| 9302 | We are bored because everything comes to us fully encoded, and we want personal meaning [Svendsen] |
| Full Idea: Boredom results from a lack of personal meaning, which is due to the fact that all objects and actions come to us fully encoded, while we (as descendants of Romanticism) insist on a personal meaning. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.2) | |
| A reaction: This idea justifies me categorising Boredom under Existentialism. This is an excellent idea, and perfectly captures the experience of most teenagers, for whom it is impossible to impose a personal meaning on such a vast cultural reality. |
| 9310 | The profoundest boredom is boredom with boredom [Svendsen] |
| Full Idea: In the profound form of boredom, I am bored by boredom itself. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.3) | |
| A reaction: Boredom is boring, which is why I try to avoid it. Third-level boredom is a rather enchanting idea. It sounds remarkably similar to the Buddha experiencing enlightenment. |
| 9298 | We can be unaware that we are bored [Svendsen] |
| Full Idea: It is perfectly possible to be bored without being aware of the fact. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.1) | |
| A reaction: True. Also, I sometimes mistake indecision for boredom. It becomes very hard to say for certain whether you are bored. I am certain that I am bored if I am forced to do something which has no interest for me. The big one is free-but-bored. |
| 9311 | We have achieved a sort of utopia, and it is boring, so that is the end of utopias [Svendsen] |
| Full Idea: There can hardly be any new utopias. To the extent that we can imagine a utopia, it must already have been realised. A utopia cannot, by definition, include boredom, but the 'utopia' we are living in is boring. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.4) | |
| A reaction: Compare Idea 8989. Lots of people (including me) think that we have achieved a kind of liberal, democratic, individualistic 'utopia', but the community needs of people are not being met, so we still have a way to go. |
| 9303 | The concept of 'alienation' seems no longer applicable [Svendsen] |
| Full Idea: I do not believe that the concept of 'alienation' is all that applicable any more. | |
| From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.1) | |
| A reaction: Interesting but puzzling. If alienation is the key existential phenomenon of a capitalist society, why should it fade away if we remain capitalist? He is proposing that it has metamorphosed into boredom, which may be a different sort of alienation. |
| 9425 | Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis] |
| Full Idea: Later Lewis said we must choose between the intersection of the axioms of the tied best systems. He chose for laws the axioms that are in all the tied systems (but then there may be few or no axioms in the intersection). | |
| From: comment on David Lewis (Subjectivist's Guide to Objective Chance [1980], p.124) by Stephen Mumford - Laws in Nature |
| 9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |
| Full Idea: An 'atomless gunk' is defined to be an individual possessing no parts that are atoms. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], App A) | |
| A reaction: [Lewis coined it] If you ask what are a-toms made of and what are ideas made of, the only answer we can offer is that the a-toms are made of gunk, and the ideas aren't made of anything, which is still bad news for the existence of ideas. |