31 ideas
| 22026 | Philosophy is homesickness - the urge to be at home everywhere [Novalis] |
| Full Idea: Philosophy is actually homesickness - the urge to be everywhere at home. | |
| From: Novalis (General Draft [1799], 45) | |
| A reaction: The idea of home [heimat] is powerful in German culture. The point of romanticism was seen as largely concerning restless souls like Byron and his heroes, who do not feel at home. Hence ironic detachment. |
| 6848 | Humour is practically enacted philosophy [Critchley] |
| Full Idea: Humour, for me, is practically enacted philosophy. | |
| From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.198) | |
| A reaction: This may be overstating it, as the funniest jokes may be the least philosophical, and remarks may be faintly amusing but very profound. Lear and his Fool make up a single worldview together. |
| 6847 | Humour can give a phenomenological account of existence, and point to change [Critchley] |
| Full Idea: Humour provides an oblique phenomenology of ordinary life; it is a way of describing the situation of our existence, and, at its best, it indicates how we might change that situation. | |
| From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.198) | |
| A reaction: The trouble is that this leads us to relentlessly political standup comedians who aren't very funny. Critichley may have a problem with remarks which are very funny precisely because they are so politically incorrect. I sympathise, though. |
| 6844 | Scientism is the view that everything can be explained causally through scientific method [Critchley] |
| Full Idea: Scientism is the belief that all phenomena can be explained through the methodology of the natural sciences, and the belief that, therefore, all phenomena are capable of a causal explanation. | |
| From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.196) | |
| A reaction: He links two ideas together, but I tend to subscribe fully to the second idea, but less fully to the first. Scientific method, if there is such a thing (Idea 6804), may not be the best way to lay bare the causal network of reality. |
| 6835 | German idealism aimed to find a unifying principle for Kant's various dualisms [Critchley] |
| Full Idea: In his Third Critique Kant established a series of dualisms (pure/practical reason, nature/freedom, epistemology/ethics) but failed to provide a unifying principle; German idealism can be seen as an attempt to provide this principle. | |
| From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.187) | |
| A reaction: He cites 'subject', 'spirit', 'art', 'will to power', 'praxis' and 'being' as candidates. This is a helpful overview for someone struggling to get to grips with that tradition. |
| 6837 | Since Hegel, continental philosophy has been linked with social and historical enquiry. [Critchley] |
| Full Idea: In continental philosophy from Hegel onwards, systematic philosophical questions have to be linked to socio-historical enquiry, and the distinctions between philosophy, history and society begin to fall apart. | |
| From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.188) | |
| A reaction: I have a strong sales resistance to this view of philosophy, just as I would if it was said about mathematics. It seems to imply a bogus view that history exhibits direction and purpose (the 'Whig' view). There are pure reasons among the prejudices. |
| 6836 | Continental philosophy fights the threatened nihilism in the critique of reason [Critchley] |
| Full Idea: If reason must criticise itself (in Kant) how does one avoid total scepticism? In my view, the problem that has animated the continental tradition since Jacobi (early 19th cent) is the threat of nihilism. | |
| From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.188) | |
| A reaction: As an outsider to 'continental' philosophy, this is the most illuminating remark I have read about it. It is not only a plausible account of the movement, but also a very worth aim, which should be taken seriously by analytical philosophers. |
| 6838 | Continental philosophy is based on critique, praxis and emancipation [Critchley] |
| Full Idea: The basic map of the continental tradition can be summarised in three terms: critique, praxis and emancipation. | |
| From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.189) | |
| A reaction: I wince at 'emancipation', which seems to take freedom as of unquestionably high value, instead of being one of the principles up for question in social philosophy. There are more presuppositions in Marxist than in analytical philosophy. |
| 6845 | Continental philosophy has a bad tendency to offer 'one big thing' to explain everything [Critchley] |
| Full Idea: In continental philosophy there is a pernicious tendency to explain everything in terms of 'one big thing', such as the 'death drive' (Freud), 'being' (Heidegger), 'the real' (Lacan), 'power' (Foucault), 'the other' (Levinas), or 'différance' (Derrida). | |
| From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.197) | |
| A reaction: From a fan of this type of philosophy, this is a refreshing remark, because if pinpoints a very off-putting feature. Each of these 'big things' should be up for question, not offered as axiomatic assumptions that explain everything else. |
| 6846 | Phenomenology is a technique of redescription which clarifies our social world [Critchley] |
| Full Idea: Phenomenology (as in the later Husserl) is for me a way of assembling reminders which clarify the social world in which we exist; it is a technique of redescription. | |
| From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.198) | |
| A reaction: I'm not sure if I can identify with this as a target for philosophy, but it is interesting and sound worthy of effort. Critchley offers this as the best strand in 'continental' philosophy, rather than the big explanatory ideas. |
| 13520 | A 'tautology' must include connectives [Wolf,RS] |
| Full Idea: 'For every number x, x = x' is not a tautology, because it includes no connectives. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 1.2) |
| 13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
| Full Idea: Deduction Theorem: If T ∪ {P} |- Q, then T |- (P → Q). This is the formal justification of the method of conditional proof (CPP). Its converse holds, and is essentially modus ponens. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 1.3) |
| 13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
| Full Idea: Universal Generalization: If we can prove P(x), only assuming what sort of object x is, we may conclude ∀xP(x) for the same x. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 1.3) | |
| A reaction: This principle needs watching closely. If you pick one person in London, with no presuppositions, and it happens to be a woman, can you conclude that all the people in London are women? Fine in logic and mathematics, suspect in life. |
| 13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
| Full Idea: Universal Specification: from ∀xP(x) we may conclude P(t), where t is an appropriate term. If something is true for all members of a domain, then it is true for some particular one that we specify. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 1.3) |
| 13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
| Full Idea: Existential Generalization (or 'proof by example'): From P(t), where t is an appropriate term, we may conclude ∃xP(x). | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 1.3) | |
| A reaction: It is amazing how often this vacuous-sounding principles finds itself being employed in discussions of ontology, but I don't quite understand why. |
| 13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
| Full Idea: Empty Set Axiom: ∃x ∀y ¬ (y ∈ x). There is a set x which has no members (no y's). The empty set exists. There is a set with no members, and by extensionality this set is unique. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 2.3) | |
| A reaction: A bit bewildering for novices. It says there is a box with nothing in it, or a pair of curly brackets with nothing between them. It seems to be the key idea in set theory, because it asserts the idea of a set over and above any possible members. |
| 13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
| Full Idea: The comprehension axiom says that any collection of objects that can be clearly specified can be considered to be a set. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 2.2) | |
| A reaction: This is virtually tautological, since I presume that 'clearly specified' means pinning down exact which items are the members, which is what a set is (by extensionality). The naïve version is, of course, not so hot. |
| 13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
| Full Idea: One of the most appealing features of first-order logic is that the two 'turnstiles' (the syntactic single |-, and the semantic double |=), which are the two reasonable notions of logical consequence, actually coincide. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.3) | |
| A reaction: In the excitement about the possibility of second-order logic, plural quantification etc., it seems easy to forget the virtues of the basic system that is the target of the rebellion. The issue is how much can be 'expressed' in first-order logic. |
| 13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
| Full Idea: The 'completeness' of first order-logic does not mean that every sentence or its negation is provable in first-order logic. We have instead the weaker result that every valid sentence is provable. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.3) | |
| A reaction: Peter Smith calls the stronger version 'negation completeness'. |
| 13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
| Full Idea: Model theory helps one to understand what it takes to specify a mathematical structure uniquely. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.1) | |
| A reaction: Thus it is the development of model theory which has led to the 'structuralist' view of mathematics. |
| 13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
| Full Idea: A 'structure' in model theory has a non-empty set, the 'universe', as domain of variables, a subset for each 'relation', some 'functions', and 'constants'. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.2) |
| 13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
| Full Idea: Model theory uses set theory to show that the theorem-proving power of the usual methods of deduction in mathematics corresponds perfectly to what must be true in actual mathematical structures. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], Pref) | |
| A reaction: That more or less says that model theory demonstrates the 'soundness' of mathematics (though normal arithmetic is famously not 'complete'). Of course, he says they 'correspond' to the truths, rather than entailing them. |
| 13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
| Full Idea: The three foundations of first-order model theory are the Completeness theorem, the Compactness theorem, and the Löwenheim-Skolem-Tarski theorem. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.3) | |
| A reaction: On p.180 he notes that Compactness and LST make no mention of |- and are purely semantic, where Completeness shows the equivalence of |- and |=. All three fail for second-order logic (p.223). |
| 13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
| Full Idea: An 'isomorphism' is a bijection between two sets that preserves all structural components. The interpretations of each constant symbol are mapped across, and functions map the relation and function symbols. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.4) |
| 13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
| Full Idea: The Löwenheim-Skolem-Tarski theorem demonstrates a serious limitation of first-order logic, and is one of primary reasons for considering stronger logics. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.7) |
| 13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
| Full Idea: It is valuable to know that a theory is complete, because then we know it cannot be strengthened without passing to a more powerful language. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.5) |
| 13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
| Full Idea: Deductive logic, including first-order logic and other types of logic used in mathematics, is 'monotonic'. This means that we never retract a theorem on the basis of new givens. If T|-φ and T⊆SW, then S|-φ. Ordinary reasoning is nonmonotonic. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 1.7) | |
| A reaction: The classic example of nonmonotonic reasoning is the induction that 'all birds can fly', which is retracted when the bird turns out to be a penguin. He says nonmonotonic logic is a rich field in computer science. |
| 13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
| Full Idea: Less theoretically, an ordinal is an equivalence class of well-orderings. Formally, we say a set is 'transitive' if every member of it is a subset of it, and an ordinal is a transitive set, all of whose members are transitive. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 2.4) | |
| A reaction: He glosses 'transitive' as 'every member of a member of it is a member of it'. So it's membership all the way down. This is the von Neumann rather than the Zermelo approach (which is based on singletons). |
| 13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
| Full Idea: One of the great achievements of modern mathematics has been the unification of its many types of objects. It began with showing geometric objects numerically or algebraically, and culminated with set theory representing all the normal objects. | |
| From: Robert S. Wolf (A Tour through Mathematical Logic [2005], Pref) | |
| A reaction: His use of the word 'object' begs all sorts of questions, if you are arriving from the street, where an object is something which can cause a bruise - but get used to it, because the word 'object' has been borrowed for new uses. |
| 19591 | Desire for perfection is an illness, if it turns against what is imperfect [Novalis] |
| Full Idea: An absolute drive toward perfection and completeness is an illness, as soon as it shows itself to be destructive and averse toward the imperfect, the incomplete. | |
| From: Novalis (General Draft [1799], 33) | |
| A reaction: Deep and true! Novalis seems to be a particularist - hanging on to the fine detail of life, rather than being immersed in the theory. These are the philosophers who also turn to literature. |
| 6843 | Perceiving meaninglessness is an achievement, which can transform daily life [Critchley] |
| Full Idea: If nihilism is the threat of the collapse of meaning, then my position is that one has to accept meaninglessness as an achievement, as an accomplishment that permits a transformed relation to everyday life. | |
| From: Simon Critchley (Interview with Baggini and Stangroom [2001], p.193) | |
| A reaction: This sounds cheerfully upbeat and life-enhancing, but I don't quite see how it works. One could easily end up laughing at the most appalling tragedies, and that seems to me to be an inappropriate (Aristotelian word) way to respond to tragedy. |