89 ideas
| 15586 | When philosophy makes itself intelligible, it commits suicide [Heidegger] |
| Full Idea: When philosophy makes itself intelligible, it commits suicide. | |
| From: Martin Heidegger (Contributions of Philosophy (On Appropriation) [1938], §259), quoted by Richard Polt - Heidegger: an introduction 5 'Contributions' | |
| A reaction: Polt describes this remark as 'theatrical', but it seems to speak for itself! |
| 15585 | Later Heidegger sees philosophy as more like poetry than like science [Heidegger, by Polt] |
| Full Idea: In his later work Heidegger came to view philosophy as closer to poetry than to science. | |
| From: report of Martin Heidegger (The Origin of the Work of Art [1935], p.178) by Richard Polt - Heidegger: an introduction 5 'Signs' |
| 15582 | Perhaps the aim of philosophy is to abolish sham problems [Heidegger] |
| Full Idea: Perhaps it is precisely the task of philosophical investigation ultimately to deprive many problems of their sham existence. | |
| From: Martin Heidegger (History of the Concept of Time [1925], p.162), quoted by Richard Polt - Heidegger: an introduction 3.§43-44 | |
| A reaction: Polt notes how very Wittgensteinian this remark is. I take this to be a very minor task of philosophy. The main task is to address the real problems. It's amazing how many people love this sort of remark. I wonder why? |
| 22223 | Being-in-the-world is projection to possibilities, thrownness among them, and fallenness within them [Heidegger, by Caputo] |
| Full Idea: Being-in-the-world is a phenomenon of 'care' with a tripartite structure: a) projection towards its possibilities, b) thrownness among those possibilities, so Dasein is not free, and c) fallenness among worldly possibilities, to neglect of its own. | |
| From: report of Martin Heidegger (Being and Time [1927]) by John D. Caputo - Heidegger p.227 | |
| A reaction: Sounds a bit Californian to me. Just living among the world's possibilities is evidently a bad thing, because you could be concentrating on yourself and your own development instead? |
| 22158 | Pheomenology seeks things themselves, without empty theories, problems and concepts [Heidegger] |
| Full Idea: 'Phenomenology' can be formulated as 'To the things themselves!' It is opposed to all free-floating constructions and accidental findings, and to conceptions which only seem to have been demonstrated. It is opposed to traditiona' pseudo-problems. | |
| From: Martin Heidegger (Being and Time [1927], Intro II.07) | |
| A reaction: It sounds as if we are invited to look at the world the way a dog might look at it. I am not at all clear what it to be gained from this approach. |
| 15574 | 'Logos' really means 'making something manifest' [Heidegger, by Polt] |
| Full Idea: Heidegger concludes that 'logos' essentially means 'making something manifest'. | |
| From: report of Martin Heidegger (Being and Time [1927], 56/33) by Richard Polt - Heidegger: an introduction 3.§7 | |
| A reaction: It would at least seem to involve revealing the truth of something, though truth doesn't seem to be central to Heidegger's thought. 'Logos' is often translated as 'an account', as well as a 'reason', so Heidegger may be right. |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| Full Idea: An 'impredicative' definition is one that uses the terms being defined in order to give the definition; in some way the definition is then circular. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], Glossary) | |
| A reaction: There has been a big controversy in the philosophy of mathematics over these. Shapiro gives the definition of 'village idiot' (which probably mentions 'village') as an example. |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| Full Idea: In classical logic definitions are thought of as revealing our attempts to refer to objects, ...but for intuitionist or constructivist logics, if our definitions do not uniquely characterize an object, we are not entitled to discuss the object. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.4) | |
| A reaction: In defining a chess piece we are obviously creating. In defining a 'tree' we are trying to respond to fact, but the borderlines are vague. Philosophical life would be easier if we were allowed a mixture of creation and fact - so let's have that. |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| Full Idea: Reductio ad absurdum arguments are ones that start by denying what one wants to prove. We then prove a contradiction from this 'denied' idea and more reasonable ideas in one's theory, showing that we were wrong in denying what we wanted to prove. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is a mathematical definition, which rests on logical contradiction, but in ordinary life (and philosophy) it would be enough to show that denial led to absurdity, rather than actual contradiction. |
| 21953 | For Heidegger there is 'ontic' truth or 'uncoveredness', as in "he is a true friend" [Heidegger, by Wrathall] |
| Full Idea: We say things like 'he is a true friend'. Heidegger calls this kind of truth 'ontic truth' or the 'uncoveredness' of entities. | |
| From: report of Martin Heidegger (On the Essence of Truth [1935]) by Mark Wrathall - Heidegger: how to read 7 | |
| A reaction: [In his later essays] The example is very bad for showing a clear alternative meaning of 'true'. I presume it can only be explained in essentialist terms - an entity is 'true' if its appearance and behaviour conforms to its essence. |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| Full Idea: For the anti-realist, truth belongs to us, it is our servant, and as such, it must be 'epistemically constrained'. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.1) | |
| A reaction: Put as clearly as this, it strikes me as being utterly and spectacularly wrong, a complete failure to grasp the elementary meaning of a concept etc. etc. If we aren't the servants of truth then we jolly we ought to be. Truth is above us. |
| 15569 | Heidegger says truth is historical, and never absolute [Heidegger, by Polt] |
| Full Idea: Heidegger is a relentless enemy of ahistorical, absolutist concepts of truth. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Richard Polt - Heidegger: an introduction 1 | |
| A reaction: I presume that if truth is not absolute then it must be relative, but Polt is a little coy about saying so. For me, anyone who says truth is relative doesn't understand the concept, and is talking about something else. |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| Full Idea: In the classical or realist view of logic the meaning of abstract symbols for logical connectives is given by the truth-tables for the symbol. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007]) | |
| A reaction: Presumably this is realist because it connects them to 'truth', but only if that involves a fairly 'realist' view of truth. You could, of course, translate 'true' and 'false' in the table to empty (formalist) symbols such a 0 and 1. Logic is electronics. |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| Full Idea: In intuitionist logic, if we do not know that we do not know A, it does not follow that we know A, so the inference (and, in general, double negation elimination) is not intuitionistically valid. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: That inference had better not be valid in any logic! I am unaware of not knowing the birthday of someone I have never heard of. Propositional attitudes such as 'know' are notoriously difficult to explain in formal logic. |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| Full Idea: Free logic is especially designed to help regiment our reasoning about fictional objects, or nonexistent objects of some sort. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.7) | |
| A reaction: This makes it sound marginal, but I wonder whether existential commitment shouldn't be eliminated from all logic. Why do fictional objects need a different logic? What logic should we use for Robin Hood, if we aren't sure whether or not he is real? |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| Full Idea: A 'subset' of A is a set containing only members of A, and a 'proper subset' is one that does not contain all the members of A. Note that the empty set is a subset of every set, but it is not a member of every set. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Is it the same empty set in each case? 'No pens' is a subset of 'pens', but is it a subset of 'paper'? Idea 8219 should be borne in mind when discussing such things, though I am not saying I agree with it. |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| Full Idea: The 'powerset' of a set is a set made up of all the subsets of a set. For example, the powerset of {3,7,9} is {null, {3}, {7}, {9}, {3,7}, {3,9}, {7,9}, {3,7,9}}. Taking the powerset of an infinite set gets us from one infinite cardinality to the next. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Note that the null (empty) set occurs once, but not in the combinations. I begin to have queasy sympathies with the constructivist view of mathematics at this point, since no one has the time, space or energy to 'take' an infinite powerset. |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| Full Idea: As a realist choice of what is basic in mathematics, set theory is rather clever, because it only makes a very simple ontological claim: that, independent of us, there exists the empty set. The whole hierarchy of finite and infinite sets then follows. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: Even so, for non-logicians the existence of the empty set is rather counterintuitive. "There was nobody on the road, so I overtook him". See Ideas 7035 and 8322. You might work back to the empty set, but how do you start from it? |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| Full Idea: Two sets are the same size if they can be placed in one-to-one correspondence. But even numbers have one-to-one correspondence with the natural numbers. So a set is infinite if it has one-one correspondence with a proper subset. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Dedekind's definition. We can match 1 with 2, 2 with 4, 3 with 6, 4 with 8, etc. Logicians seem happy to give as a definition anything which fixes the target uniquely, even if it doesn't give the essence. See Frege on 0 and 1, Ideas 8653/4. |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| Full Idea: Zermelo-Fraenkel and Gödel-Bernays set theory differ over the notions of ordinal construction and over the notion of class, among other things. Then there are optional axioms which can be attached, such as the axiom of choice and the axiom of infinity. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.6) | |
| A reaction: This summarises the reasons why we cannot just talk about 'set theory' as if it was a single concept. The philosophical interest I would take to be found in disentangling the ontological commitments of each version. |
| 15571 | The idea of an atemporal realm of validity is as implausible as medieval theology [Heidegger] |
| Full Idea: The whole idea of an atemporal realm of validity is an invention that is no less doubtful than medieval speculation about angels. | |
| From: Martin Heidegger (Basic Problems of Phenomenology [1927], p.215), quoted by Richard Polt - Heidegger: an introduction 2 'Theory' | |
| A reaction: This seems to be flatly opposed to the view of Frege, and shows why continental philosophy has largely eschewed a study of logic. It is hard for a philosopher to pursue logic extensively without commitment to the Fregean Third Realm. |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| Full Idea: The law of excluded middle is purely syntactic: it says for any well-formed formula A, either A or not-A. It is not a semantic law; it does not say that either A is true or A is false. The semantic version (true or false) is the law of bivalence. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: No wonder these two are confusing, sufficiently so for a lot of professional philosophers to blur the distinction. Presumably the 'or' is exclusive. So A-and-not-A is a contradiction; but how do you explain a contradiction without mentioning truth? |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| Full Idea: In the intuitionist version of quantification, the universal quantifier (normally read as "all") is understood as "we have a procedure for checking every" or "we have checked every". | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.5) | |
| A reaction: It seems better to describe this as 'verificationist' (or, as Dummett prefers, 'justificationist'). Intuition suggests an ability to 'see' beyond the evidence. It strikes me as bizarre to say that you can't discuss things you can't check. |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| Full Idea: The realist meets the Burali-Forti paradox by saying that all the ordinals are a 'class', not a set. A proper class is what we discuss when we say "all" the so-and-sos when they cannot be reached by normal set-construction. Grammar is their only limit. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This strategy would be useful for Class Nominalism, which tries to define properties in terms of classes, but gets tangled in paradoxes. But why bother with strict sets if easy-going classes will do just as well? Descartes's Dream: everything is rational. |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| Full Idea: The Burali-Forti paradox says that if ordinals are defined by 'gathering' all their predecessors with the empty set, then is the set of all ordinals an ordinal? It is created the same way, so it should be a further member of this 'complete' set! | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is an example (along with Russell's more famous paradox) of the problems that began to appear in set theory in the early twentieth century. See Idea 8675 for a modern solution. |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| Full Idea: The set of 'integers' is all of the negative natural numbers, and zero, together with the positive natural numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Zero always looks like a misfit at this party. Credit and debit explain positive and negative nicely, but what is the difference between having no money, and money being irrelevant? I can be 'broke', but can the North Pole be broke? |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| Full Idea: The 'rational' numbers are all those that can be represented in the form m/n (i.e. as fractions), where m and n are natural numbers different from zero. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Pythagoreans needed numbers to stop there, in order to represent the whole of reality numerically. See irrational numbers for the ensuing disaster. How can a universe with a finite number of particles contain numbers that are not 'rational'? |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| Full Idea: A number is 'irrational' just in case it cannot be represented as a fraction. An irrational number has an infinite non-repeating decimal expansion. Famous examples are pi and e. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: There must be an infinite number of irrational numbers. You could, for example, take the expansion of pi, and change just one digit to produce a new irrational number, and pi has an infinity of digits to tinker with. |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| Full Idea: The natural numbers are quite primitive, and are what we first learn about. The order of objects (the 'ordinals') is one level of abstraction up from the natural numbers: we impose an order on objects. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: Note the talk of 'levels of abstraction'. So is there a first level of abstraction? Dedekind disagrees with Friend (Idea 7524). I would say that natural numbers are abstracted from something, but I'm not sure what. See Structuralism in maths. |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| Full Idea: The 'cardinal' numbers answer the question 'How many?'; the order of presentation of the objects being counted as immaterial. Def: the cardinality of a set is the number of members of the set. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: If one asks whether cardinals or ordinals are logically prior (see Ideas 7524 and 8661), I am inclined to answer 'neither'. Presenting them as answers to the questions 'how many?' and 'which comes first?' is illuminating. |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| Full Idea: The set of 'real' numbers, which consists of the rational numbers and the irrational numbers together, represents "the continuum", since it is like a smooth line which has no gaps (unlike the rational numbers, which have the irrationals missing). | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: The Continuum is the perfect abstract object, because a series of abstractions has arrived at a vast limit in its nature. It still has dizzying infinities contained within it, and at either end of the line. It makes you feel humble. |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| Full Idea: After the multiples of omega, we can successively raise omega to powers of omega, and after that is done an infinite number of times we arrive at a new limit ordinal, which is called 'epsilon'. We have an infinite number of infinite ordinals. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: When most people are dumbstruck by the idea of a single infinity, Cantor unleashes an infinity of infinities, which must be the highest into the stratosphere of abstract thought that any human being has ever gone. |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| Full Idea: The first 'limit ordinal' is called 'omega', which is ordinal because it is greater than other numbers, but it has no immediate predecessor. But it has successors, and after all of those we come to twice-omega, which is the next limit ordinal. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: This is the gateway to Cantor's paradise of infinities, which Hilbert loved and defended. Who could resist the pleasure of being totally boggled (like Aristotle) by a concept such as infinity, only to have someone draw a map of it? See 8663 for sequel. |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| Full Idea: Since between any two rational numbers there is an infinite number of rational numbers, we could consider that we have infinity in three dimensions: positive numbers, negative numbers, and the 'depth' of infinite numbers between any rational numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: This is before we even reach Cantor's staggering infinities (Ideas 8662 and 8663), which presumably reside at the outer reaches of all three of these dimensions of infinity. The 'deep' infinities come from fractions with huge denominators. |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| Full Idea: Successful competing founding disciplines in mathematics include: the various set theories, type theory, category theory, model theory and topology. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: Or none of the above? Set theories are very popular. Type theory is, apparently, discredited. Shapiro has a version of structuralism based on model theory (which sound promising). Topology is the one that intrigues me... |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| Full Idea: Most of mathematics can be faithfully redescribed by classical (realist) set theory. More precisely, we can translate other mathematical theories - such as group theory, analysis, calculus, arithmetic, geometry and so on - into the language of set theory. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is why most mathematicians seem to regard set theory as foundational. We could also translate football matches into the language of atomic physics. |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| Full Idea: There is no interest for the mathematician in studying the number 8 in isolation from the other numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: This is a crucial and simple point (arising during a discussion of Shapiro's structuralism). Most things are interesting in themselves, as well as for their relationships, but mathematical 'objects' just are relationships. |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| Full Idea: Structuralists give a historical account of why the 'same' number occupies different structures. Numbers are equivalent rather than identical. 8 is the immediate predecessor of 9 in the whole numbers, but in the rationals 9 has no predecessor. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: I don't become a different person if I move from a detached house to a terraced house. This suggests that 8 can't be entirely defined by its relations, and yet it is hard to see what its intrinsic nature could be, apart from the units which compose it. |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| Full Idea: Structuralists disagree over whether objects in structures are 'ante rem' (before reality, existing independently of whether the objects exist) or 'in re' (in reality, grounded in the real world, usually in our theories of physics). | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: Shapiro holds the first view, Hellman and Resnik the second. The first view sounds too platonist and ontologically extravagant; the second sounds too contingent and limited. The correct account is somewhere in abstractions from the real. |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| Full Idea: According to the structuralist, mathematicians study the concepts (objects of study) such as variable, greater, real, add, similar, infinite set, which are one level of abstraction up from prima facie base objects such as numbers, shapes and lines. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.1) | |
| A reaction: This still seems to imply an ontology in which numbers, shapes and lines exist. I would have thought you could eliminate the 'base objects', and just say that the concepts are one level of abstraction up from the physical world. |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| Full Idea: Structuralism says we study whole structures: objects together with their predicates, relations that bear between them, and functions that take us from one domain of objects to a range of other objects. The objects can even be eliminated. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.1) | |
| A reaction: The unity of object and predicate is a Quinean idea. The idea that objects are inessential is the dramatic move. To me the proposal has very strong intuitive appeal. 'Eight' is meaningless out of context. Ordinality precedes cardinality? Ideas 7524/8661. |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| Full Idea: In the 'in re' version of mathematical structuralism, pattern-spotting is the process of abstraction. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: This might work for non-mathematical abstraction as well, if we are allowed to spot patterns within sensual experience, and patterns within abstractions. Properties are causal patterns in the world? No - properties cause patterns. |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| Full Idea: The main philosophical problem with the position of platonism or realism is the epistemic problem: of explaining what perception or intuition consists in; how it is possible that we should accurately detect whatever it is we are realists about. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.5) | |
| A reaction: The best bet, I suppose, is that the mind directly perceives concepts just as eyes perceive the physical (see Idea 8679), but it strikes me as implausible. If we have to come up with a special mental faculty for an area of knowledge, we are in trouble. |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| Full Idea: Central to naturalism about mathematics are 'indispensability arguments', to the effect that some part of mathematics is indispensable to our best physical theory, and therefore we ought to take that part of mathematics to be true. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 6.1) | |
| A reaction: Quine and Putnam hold this view; Field challenges it. It has the odd consequence that the dispensable parts (if they can be identified!) do not need to be treated as true (even though they might follow logically from the dispensable parts!). Wrong! |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| Full Idea: There are not enough constraints in the Formalist view of mathematics, so there is no way to select a direction for trying to develop mathematics. There is no part of mathematics that is more important than another. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 6.6) | |
| A reaction: One might reply that an area of maths could be 'important' if lots of other areas depended on it, and big developments would ripple big changes through the interior of the subject. Formalism does, though, seem to reduce maths to a game. |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| Full Idea: Too much of mathematics is rejected by the constructivist. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.1) | |
| A reaction: This was Hilbert's view. This seems to be generally true of verificationism. My favourite example is that legitimate speculations can be labelled as meaningless. |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| Full Idea: An intuitionist typically retains bivalence, but rejects the law of excluded middle. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: The idea would be to say that only T and F are available as truth-values, but failing to be T does not ensure being F, but merely not-T. 'Unproven' is not-T, but may not be F. |
| 21897 | Reducing being to the study of beings too readily accepts the modern scientific view [Heidegger, by May] |
| Full Idea: Continental philosophers, following Heidegger, see in the attempt to reduce the question of being to that of beings a symptom of an age that is too ready to accept the terms in which science conceives the world. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Todd May - Gilles Deleuze 1.04 | |
| A reaction: Interesting. I take the idea that this is a failing of the modern age to be ridiculous, since I take it to be the key metaphysical move made by Aristotle. Neverthless, Aristotle is closely in tune with modern science. For 'beings', read 'objects'. |
| 15573 | For us, Being is constituted by awareness of other sorts of Being [Heidegger] |
| Full Idea: We are Dasein - the entity who possesses - as constitutive for its understanding of existence - an understanding of the Being of all entities of a character other than its own. | |
| From: Martin Heidegger (Being and Time [1927], 34/13), quoted by Richard Polt - Heidegger: an introduction 3.§4 | |
| A reaction: This seems to connect to the emerging 'externalist' view of mind that comes with the external view of content coming from Purnam's Twin Earth idea. |
| 9273 | Heidegger turns to 'Being' to affirm the uniqueness of humans in the world [Heidegger, by Gray] |
| Full Idea: Heidegger turns to 'Being' for the same reason that Christians turn to God - to affirm the unique place of humans in the world. | |
| From: report of Martin Heidegger (Being and Time [1927]) by John Gray - Straw Dogs 2.4 | |
| A reaction: This is the first remark I have encountered that makes sense of Heidegger's Being to me! It places Heidegger as a modernist philosopher, trying to grapple with the decline of religion. I'll stick with Bertrand Russell on that. |
| 22157 | Dasein is a mode of Being distinguished by concern for its own Being [Heidegger] |
| Full Idea: Dasein is an entity which does not just occur among other entities. Rather it is ontically distinguished by the fact that, in its very Being, that Being is an issue for it. | |
| From: Martin Heidegger (Being and Time [1927], Intro I.04) | |
| A reaction: How do you distinguish the Being of normal humans from the Being of someone in a deep coma, who has no existential issues? Has that Dasein ceased to be? Why does angst create a new mode of Being, but flying doesn't? |
| 8137 | Dasein is ahead of itself in the world, and alongside encountered entities [Heidegger] |
| Full Idea: The formal existential totality of Dasein's ontological structural whole is: the Being of Dasein means ahead-of-itself-Being-already-in-(the-world) as Being-alongside (entities encountered within-the-world). | |
| From: Martin Heidegger (Being and Time [1927], I.6 41) | |
| A reaction: If you find that thought really illuminating, you are probably on the wrong website. However, the thought that we exist 'ahead of ourselves' might be a fruitful line for existentialists to explore. |
| 21951 | In company with others one's Dasein dissolves, and even the others themselves dissolve [Heidegger] |
| Full Idea: This being-with-one-another dissolves one's own Dasein completely into the kind of being of 'the others', in such a way, indeed, that the others, as distinguishable and explicit, vanish more and more. | |
| From: Martin Heidegger (Being and Time [1927], p.164), quoted by Mark Wrathall - Heidegger: how to read 5 | |
| A reaction: He seems to be describing the psychology of someone who joins a small crowd which gradually increases in size. I take this relation to others to be the basic existential dilemma, of retaining individual authenticity within a community. |
| 20745 | 'Dasein' expresses not 'what' the entity is, but its being [Heidegger] |
| Full Idea: When we designate this entity with the term 'Dasein' we are expressing not its 'what' (as if it were a table, house, or tree) but its being. | |
| From: Martin Heidegger (Being and Time [1927], p.297), quoted by Kevin Aho - Existentialism: an introduction 2 'Phenomenology' | |
| A reaction: Presumably analytic discussions of persons try to be too objective. Heidegger is trying to capture the thought at the heart of Kierkegaard's existentialism. Objectivity and subjectivity are never in conflict. Is there really a different mode of existence? |
| 8134 | The word 'dasein' is used to mean 'the manner of Being which man possesses', and also the human creature [Heidegger, by Cooper,DE] |
| Full Idea: Heidegger borrows a common German word 'dasein', meaning 'being' or 'existence', to refer both to 'the manner of Being which... man... possesses', and to the creature which possesses it. | |
| From: report of Martin Heidegger (Being and Time [1927], p.32) by David E. Cooper - Heidegger Ch.3 | |
| A reaction: This just strikes me as an elementary ontological mistake. Because something has startling properties it doesn't follow that we have a different type of Being. Magnets don't have a different type of being from ordinary iron. |
| 8135 | 'Dasein' is Being which is laid claim to, and which matters to its owner [Heidegger, by Cooper,DE] |
| Full Idea: We each of us not only have Dasein (our kind of Being), but we can lay claim to it. Also the Dasein of a thing 'is an issue for it' - we care about the kinds of creatures we can make ourselves into. | |
| From: report of Martin Heidegger (Being and Time [1927], p.67) by David E. Cooper - Heidegger Ch.3 | |
| A reaction: Heidegger says other more puzzling things about Dasein. The second half of the idea is what makes Heidegger an existentialist, and an inspiration for Sartre. |
| 21948 | Dasein is being which can understand itself, and possess itself in a way allowing authenticity [Heidegger] |
| Full Idea: Dasein is an entity which, in its very being, comports itself understandingly towards that being. ...Mineness belongs to an existent Dasein, and belongs to it as the condition which makes authenticity and inauthenticity possible. | |
| From: Martin Heidegger (Being and Time [1927], p.78), quoted by Mark Wrathall - Heidegger: how to read 1 | |
| A reaction: He might eventually persuade me that Dasein is so different from mere material being that it deserves a category of its own. But a reductive account of mind is also a reductive account of being. |
| 15584 | I say the manifestation of Being needs humans, and humans only exist as reflected in Being [Heidegger] |
| Full Idea: The fundamental thought of my thinking is precisely that Being, or the manifestation of Being, needs human beings and that, vice versa, human beings are only human beings if they are standing in the manifestation of Being. | |
| From: Martin Heidegger (Martin Heidegger in conversation [1969], p.82), quoted by Richard Polt - Heidegger: an introduction 5 'Signs' | |
| A reaction: I don't think I understand the second half of this, but I sense some sort of intuition that the consciousness of humans 'enlarges' Being, or bestows an identity on it, or some such thing. |
| 7680 | Ontology is possible only as phenomenology [Heidegger] |
| Full Idea: Ontology is possible only as phenomenology. | |
| From: Martin Heidegger (Being and Time [1927], p.31), quoted by Dale Jacquette - Ontology Ch.1 | |
| A reaction: Jacquette argues against this claim. The idea seems to be the ultimate extension of Kant, and it is not a big move to say that the only real phenomenology we can discuss is our semantics. Wrong, wrong, wrong. |
| 22161 | Readiness-to-hand defines things in themselves ontologically [Heidegger] |
| Full Idea: Readiness-to-hand is the way in which entities as they are 'in themselves' are defined ontologico-categorially. | |
| From: Martin Heidegger (Being and Time [1927], I.3.15) | |
| A reaction: I assume this is a direct reference to the problem idealists had with the thing-in-itself. It seems that the reality of a thing consists of the strengthened relationship it has with Dasein, which sounds fairly idealist to me. |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| Full Idea: What the mathematician labels an 'object' in her discipline, is called 'a place in a structure' by the structuralist. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.5) | |
| A reaction: This is a strategy for dispersing the idea of an object in the world of thought, parallel to attempts to eliminate them from physical ontology (e.g. Idea 614). |
| 15576 | Heidegger seeks a non-traditional concept of essence as 'essential unfolding' [Heidegger, by Polt] |
| Full Idea: Heidegger tries to develop a non-traditional concept of essence as 'essential unfolding' ('wesen' as a verb). | |
| From: report of Martin Heidegger (Being and Time [1927], I.4.27) by Richard Polt - Heidegger: an introduction 3.§25-7 |
| 15578 | Propositions don't provide understanding, because the understanding must come first [Heidegger, by Polt] |
| Full Idea: Propositions are not a good clue to the essence of understanding, because we must already understand things before we formulate propositions about them. | |
| From: report of Martin Heidegger (Being and Time [1927], I.5.31) by Richard Polt - Heidegger: an introduction 3.§31-3 | |
| A reaction: I like this, because I think the most important aspects of our thought and understanding are entirely non-verbal - even in cases where they seem to be highly specific and verbal. We don't understand ourselves at all! |
| 22159 | If we posit 'I' as the starting point, we miss the mind's phenomenal content [Heidegger] |
| Full Idea: One of our first tasks will be to prove that if we posit an 'I' or subject as that which is proximally given, we shall completely miss the phenomenal content of Dasein. | |
| From: Martin Heidegger (Being and Time [1927], I.1.10) | |
| A reaction: Descartes had thrown doubt on the informativeness of the phenomena, so presumably your phenomenologist is not interested in whether they reveal any truth. So why are unreliable phenomena of any interest? |
| 22160 | Our relationship to a hammer strengthens when we use [Heidegger] |
| Full Idea: The less we stare at the hammer-Thing, and the more we seize hold of it and use it, the more primordial does our relationship to it become. ...The kind of Being which equipment possesses... we call 'readiness-to-hand' [Zuhandenheit]. | |
| From: Martin Heidegger (Being and Time [1927], I.3.15) | |
| A reaction: This example would be well at home in the writings of the pragmatists. It is also an important example for existentialists. In analytic philosophy we might say the experience combines perception with direct exerience of causation. |
| 15580 | There are no raw sense-data - our experiences are of the sound or colour of something [Heidegger] |
| Full Idea: We always take a noise as the sound of something; we always take a hue as the color of something. We simply do not experience raw, uninterpreted sense-data - these are the inventions of philosophers. | |
| From: Martin Heidegger (Being and Time [1927], 207/163-4), quoted by Richard Polt - Heidegger: an introduction 3.§31-3 | |
| A reaction: This is something like the modern view of sense-data as promoted by John McDowell, rather than the experiential atoms of Russell and Moore. Experience is holistic, but that doesn't mean we can't analyse it into components. |
| 20749 | Perceived objects always appear in a context [Heidegger] |
| Full Idea: The perceptual 'something' is always in the middle of something else, it always forms part of a 'field'. | |
| From: Martin Heidegger (Being and Time [1927], p.4), quoted by Kevin Aho - Existentialism: an introduction 3 'Perceptual' | |
| A reaction: Sounds like our knowledge of electrons. Nice point. Standard analytic discussions of perceiving a glass always treat it in isolation, when it is on an expensive table near a brandy bottle. Or near a hammer. |
| 22163 | The scandal of philosophy is expecting to prove reality when the prover's Being is vague [Heidegger] |
| Full Idea: The 'scandal of philosophy' is not that this proof [of external things] has yet to be given, but that such proofs are expected and attempted again and again. ...The kind of Being of the entity which does the proving has not been made definite enough. | |
| From: Martin Heidegger (Being and Time [1927], I.6.43a) | |
| A reaction: The 'scandal' was a remark of Kant's. Presumably Heidegger's exploration of Dasein aims to establish the Being of the prover sufficiently to solve this problem (via phenomenology). |
| 21949 | Having thoughts and feelings need engagement in the world [Heidegger, by Wrathall] |
| Full Idea: Heidegger argues that having thoughts and feelings is only possible for entity that is actually engaged in the world. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Mark Wrathall - Heidegger: how to read 1 | |
| A reaction: This seems to be an a priori exclusion of the possibility of a brain in a vat. I guess the ancestor of this idea is Schopenhauer. |
| 22222 | Dasein finds itself already amongst others [Heidegger, by Caputo] |
| Full Idea: The world is a world shared with others, so that far from being a solipsistic ego ...Dasein finds itself already amongst others. | |
| From: report of Martin Heidegger (Being and Time [1927]) by John D. Caputo - Heidegger p.226 | |
| A reaction: Phenomenologists don't seem bothered about the problem of knowing other minds. If you take something for granted, it ceases to be a problem to be solved! |
| 8136 | If we work and play with other people, they are bound to be 'Dasein', intelligent agents [Heidegger, by Cooper,DE] |
| Full Idea: How do I know that other people have minds? The question is a bad one. Precisely because I encounter them at work, play and the like, it is guaranteed that they, too, are Dasein, intelligent agents. | |
| From: report of Martin Heidegger (Being and Time [1927], p.153-) by David E. Cooper - Heidegger Ch.3 | |
| A reaction: I've seen film of someone playing peek-a-boo with a bonobo ape, so presumably they have Dasein. It might be easier for the AI community to aim at building a robot with Dasein, than one which was simply conscious. |
| 22164 | When Dasein grasps something it exists externally alongside the thing [Heidegger] |
| Full Idea: When Dasein directs itself towards something and grasps it, it does not somehow first get out of an inner sphere in which it has been proximally encapsulated, but its primary kind of Being is such that it is always 'outside' alongside entities. | |
| From: Martin Heidegger (Being and Time [1927], I.2.13) | |
| A reaction: This is the first plausible fruit of phenomenology I have been able to discover. Analysing the passive mind is not very promising, but seeing what happens when we become more proactive is revealing. |
| 15579 | My active existence is defined by being able to say 'I can' [Heidegger] |
| Full Idea: The Dasein which I myself am in each instance is defined in its Being by my being able to say of it, 'I am, that is, I can'. | |
| From: Martin Heidegger (History of the Concept of Time [1925], p.298), quoted by Richard Polt - Heidegger: an introduction 3.§31-3 | |
| A reaction: I like this emphasis on the more active aspect of the Cogito idea. The whole Enlightenment account of things has them as inert, and falling under laws and theories. The Aristotelian account makes potentiality central. |
| 15583 | Certainty that I will die is more basic to my existence than the Cogito [Heidegger] |
| Full Idea: The certainty that 'I myself am in that I will die' is the basic certainty of Dasein itself. It is a genuine statement of Dasein, while 'cogito sum' is only a semblance of such a statement. | |
| From: Martin Heidegger (History of the Concept of Time [1925], p.316-7), quoted by Richard Polt - Heidegger: an introduction 4.§46-53 | |
| A reaction: This just seems to be false. Children face their existence in thought long before they face their mortality. Absorption in activity can marginalise death, but not marginalise thought. |
| 22162 | There is an everyday self, and an authentic self, when it is grasped in its own way [Heidegger] |
| Full Idea: The self of everyday Dasein is the they-self [das Man-selbst], which we distinguish from the authentic self - that is, from the Self which has been taken hold of in its own way. | |
| From: Martin Heidegger (Being and Time [1927], I.4.27) | |
| A reaction: To a novice this sounds like a requirement for increased self-consciousness during daily activity. 'Be a good animal, true to your animal self' said one of Lawrence's characters. |
| 20114 | Everyone is other, and no one is himself [Heidegger] |
| Full Idea: Everyone is other, and no one is himself. | |
| From: Martin Heidegger (Being and Time [1927], p.165), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 09 | |
| A reaction: Safranski describes this as the idea of 'structural self-evasion'. He detects the same idea in Nietzsche's 'Daybreak'. |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| Full Idea: In the hierarchy of reduction, when we investigate questions in biology, we have to assume the laws of chemistry but not of economics. We could never find a law of biology that contradicted something in physics or in chemistry. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.1) | |
| A reaction: This spells out the idea that there is a direction of dependence between aspects of the world, though we should be cautious of talking about 'levels' (see Idea 7003). We cannot choose the direction in which reduction must go. |
| 15577 | Moods are more fundamentally revealing than theories - as when fear reveals a threat [Heidegger, by Polt] |
| Full Idea: For Heidegger moods are disclosive; they show us things in a more fundamental way than theoretical propositions ever can. For example, fear reveals something as a threat. | |
| From: report of Martin Heidegger (Being and Time [1927], I.5.30) by Richard Polt - Heidegger: an introduction 3.§30 | |
| A reaction: Most modern students of emotion seem to agree. Even though they may not have specific content, it is always possible to consider the underlying cause of the mood. |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| Full Idea: The extensional presentation of a concept is just a list of the objects falling under the concept. In contrast, an intensional presentation of a concept gives a characterization of the concept, which allows us to pick out which objects fall under it. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.4) | |
| A reaction: Logicians seem to favour the extensional view, because (in the standard view) sets are defined simply by their members, so concepts can be explained using sets. I take this to be a mistake. The intensional view seems obviously prior. |
| 20748 | We do not add value to naked things; its involvement is disclosed in understanding it [Heidegger] |
| Full Idea: We do not throw a 'signification' over some naked thing which is present-at-hand, we do not stick a value on it; but when something is encountered as such, the thing in question has an involvement which is disclosed in our understanding of the world. | |
| From: Martin Heidegger (Being and Time [1927], p.190-1), quoted by George Dickie - The Myth of the Aesthetic Attitude 3 'Undoing' | |
| A reaction: Analytic philosophy and science have tried to dismantle experience, and Heidegger wants to put it back together. I would say there is a big difference between encountering a thing (which is a bit facty), and understanding it (which is more valuey). |
| 22166 | Dasein has the potential to be itself, but must be shown this in the midst of ordinariness [Heidegger] |
| Full Idea: Because Dasein is lost in the 'they', it must first find itself. It must be 'shown' to itself in its possible authenticity. In terms of its possibility, Dasein is already a potentiality-for-Being-its-self, but it needs to have this potentiality attested. | |
| From: Martin Heidegger (Being and Time [1927], II.2.54) | |
| A reaction: I wish there was some criterion for knowing when you are being yourself and when you are not. |
| 22165 | Anxiety reveals the possibility and individuality of Dasein [Heidegger] |
| Full Idea: Anxiety discloses Dasein as Being-possible, and indeed as the only kind of thing which it can be of its own accord as something individualised in individualisation. | |
| From: Martin Heidegger (Being and Time [1927], I.6.40) | |
| A reaction: Is sounds like insecurity, as a sort of trauma that shocks one into self-realisation. The idea means very little to me personally. |
| 21952 | Anxiety about death frees me to live my own life [Heidegger, by Wrathall] |
| Full Idea: For Heidegger, as a consequence of my anxiety in the face of death, I am set free to live my life as my own rather than doing things merely because others expect me to do them. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Mark Wrathall - Heidegger: how to read 7 | |
| A reaction: Contrary to Epicurus, Heidegger thinks anxiety about death is a good thing. The point is, I suppose, that we all die alone, and people who are very socially contrained need to face up to death in order to grasp their autonomy. |
| 22224 | Anxiety is the uncanniness felt when constantly fleeing from asserting one's own freedom [Heidegger, by Caputo] |
| Full Idea: Anxiety [angst] is the disturbing sense of uncanniness by which Dasein is overtaken (thrownness) when it discovers there is nothing other than its own freedom to sustain its projects (projection), and from which Dasein constantly takes flight (falling). | |
| From: report of Martin Heidegger (Being and Time [1927]) by John D. Caputo - Heidegger p.227 | |
| A reaction: This seems to be Kierkegaard's idea, unamended. In my experience anxiety only comes when I am forced into making decisions by worldly situations. An 'existential crisis' is a sort of blankness appearing where a future life was supposed to be. |
| 20767 | Culture is now dominated by boredom, so universal it is unnoticed [Heidegger, by Aho] |
| Full Idea: Heidegger came to say that the cultural mood had changed from 'anxiety' to 'boredom'. The danger is that our boredom has become so ubiquitous and all-encompassing that it is now hidden. | |
| From: report of Martin Heidegger (Contributions to Philosophy [1938]) by Kevin Aho - Existentialism: an introduction 9 'Conc' | |
| A reaction: I'm not sure what the danger of boredom is if it is 'hidden'. It rather depends what else is hidden with it. |
| 15572 | Being what it is (essentia) must be conceived in terms of Being (existence) [Heidegger] |
| Full Idea: Dasein's Being-what-it-is (essentia) must….be conceived in terms of its Being (existentia). | |
| From: Martin Heidegger (Being and Time [1927], 67/42), quoted by Richard Polt - Heidegger: an introduction 3.§2 | |
| A reaction: This seems to be the origin of Sartre's famous slogan 'existence before essence'. It seems to be a rebellion against Husserl's quest for essences. |
| 20453 | Heidegger says we must either choose an inauthentic hero, or choose yourself as hero [Heidegger, by Critchley] |
| Full Idea: Heidegger says you must choose your hero; either you choose 'das Man', the inauthentic life, or you choose yourself - the point being that you have to choose yourself as your hero in order to be authentic. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Simon Critchley - Impossible Objects: interviews 5 | |
| A reaction: If Nietzsche's 'Ecce Homo' is the model for choosing yourself as hero, I am not too sure about this idea. Needing a hero seems awfully German and romantic. Ein Heldenleben. Be your own anit-hero (like a standup comedian)? |
| 15581 | Dasein is always only that which it has chosen to be [Heidegger] |
| Full Idea: Dasein is always only that which it has chosen to be. | |
| From: Martin Heidegger (Basic Problems of Phenomenology [1927], p.278), quoted by Richard Polt - Heidegger: an introduction 3.§39-42 | |
| A reaction: I take it as significant that this is what it 'has' chosen, and not what it now 'chooses'. I might accept that my mode of existence results from past choices, but certainly not that I can choose it now. Ossified brain. |
| 3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |
| Full Idea: Stilpo asked a man whether Athena is the daughter of Zeus, and when he said yes, said,"But this statue of Athena by Phidias is the child of Phidias, so it is not a god." | |
| From: report of Stilpo (fragments/reports [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.10.5 |