31 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! |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| Full Idea: We can define a set by 'enumeration' (by listing the items, within curly brackets), or by 'abstraction' (by specifying the elements as instances of a property), pretending that they form a determinate totality. The latter is written {x | x is P}. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
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Full Idea:
The 'Cartesian Product' of two sets, written A x B, is the relation which pairs every element of A with every element of B. So A x B = { |
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| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| Full Idea: A binary relation in a set is a 'partial ordering' just in case it is reflexive, antisymmetric and transitive. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| Full Idea: Principle of Determinacy: For every object a and every set S, either a is an element of S or a is not an element of S. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.2) |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| Full Idea: Principle of Specification: Whenever we can specify a determinate totality of objects, we shall say that there is a set whose elements are precisely the objects that we have specified. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) | |
| A reaction: Compare the Axiom of Specification. Zalabardo says we may wish to consider sets of which we cannot specify the members. |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| Full Idea: A formula of a first-order language is a 'sentence' just in case it has no free variables. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.2) |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| Full Idea: A formula is the 'logical consequence' of a set of formulas (Γ |= φ) if for every structure in the language and every variable interpretation of the structure, if all the formulas within the set are true and the formula itself is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| Full Idea: A propositional logic sentence is a 'logical consequence' of a set of sentences (written Γ |= φ) if for every admissible truth-assignment all the sentences in the set Γ are true, then φ is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: The definition is similar for predicate logic. |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| Full Idea: In propositional logic, any set containing ¬ and at least one of ∧, ∨ and → is expressively complete. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.8) |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| Full Idea: The semantic pattern of a first-order language is the ways in which truth values depend on which individuals instantiate the properties and relations which figure in them. ..So we pair a truth value with each combination of individuals, sets etc. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.3) | |
| A reaction: So truth reduces to a combination of 'instantiations', which is rather like 'satisfaction'. |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| Full Idea: We can look at semantics from the point of view of how truth values are determined by instantiations of properties and relations, or by asking how we can build, using the resources of the language, a proposition corresponding to a given semantic pattern. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) | |
| A reaction: The second version of semantics is model theory. |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| Full Idea: A truth assignment is a function from propositions to the set {T,F}. We will think of T and F as the truth values true and false, but for our purposes all we need to assume about the identity of these objects is that they are different from each other. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: Note that T and F are 'objects'. This remark is important in understanding modern logical semantics. T and F can be equated to 1 and 0 in the language of a computer. They just mean as much as you want them to mean. |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| Full Idea: In first-order languages, logically true sentences are true in all structures. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| Full Idea: A propositional logic sentence is 'logically true', written |= φ, if it is true for every admissible truth-assignment. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| Full Idea: A set of formulas of a first-order language is 'satisfiable' if there is a structure and a variable interpretation in that structure such that all the formulas of the set are true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| Full Idea: A propositional logic set of sentences Γ is 'satisfiable' if there is at least one admissible truth-assignment that makes all of its sentences true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| Full Idea: A structure is a model of a sentence if the sentence is true in the model; a structure is a model of a set of sentences if they are all true in the structure. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| Full Idea: Defining a set by induction enables us to use the method of proof by induction to establish that all the elements of the set have a certain property. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.3) |
| 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. |
| 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. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |