99 ideas
19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
Full Idea: Aristotle takes wisdom to come in two forms, the practical and the theoretical, the former of which is good judgement about how to act, and the latter of which is deep knowledge or understanding. | |
From: report of Aristotle (works [c.330 BCE]) by Dennis Whitcomb - Wisdom Intro | |
A reaction: The interesting question is then whether the two are connected. One might be thoroughly 'sensible' about action, without counting as 'wise', which seems to require a broader view of what is being done. Whitcomb endorses Aristotle on this idea. |
20121 | Grammar only reveals popular metaphysics [Nietzsche] |
Full Idea: The snares of grammar are the metaphysics of the people. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
A reaction: If you have this elitist view of metaphysics, then linguistic analysis is just a branch of anthropology. |
1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
Full Idea: For Aristotle logos is the ability to speak rationally about, with the hope of attaining knowledge, questions of value. | |
From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.26 |
1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
Full Idea: Aristotle is the great theoretician who articulates a vision of a world in which natural and stable structures can be rationally discovered. His is the most optimistic and richest view of the possibilities of logos | |
From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.95 |
8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
Full Idea: A real definition, according to the Aristotelian tradition, gives the essence of the kind of thing defined. Man is defined as a rational animal, and thus rationality and animality are of the essence of each of us. | |
From: report of Aristotle (works [c.330 BCE]) by Willard Quine - Vagaries of Definition p.51 | |
A reaction: Compare Idea 4385. Personally I prefer the Aristotelian approach, but we may have to say 'We cannot identify the essence of x, and so x cannot be defined'. Compare 'his mood was hard to define' with 'his mood was hostile'. |
4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
Full Idea: For Aristotle, to give a definition one must first state the genus and then the differentia of the kind of thing to be defined. | |
From: report of Aristotle (works [c.330 BCE]) by J.O. Urmson - Aristotle's Doctrine of the Mean p.157 | |
A reaction: Presumably a modern definition would just be a list of properties, but Aristotle seeks the substance. How does he define a genus? - by placing it in a further genus? |
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. |
24082 | Is the will to truth the desire to avoid deception? [Nietzsche] |
Full Idea: This unconditional will to truth: what is it? Is it the will not to let oneself be deceived? Is it the will not to deceive? | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §344) | |
A reaction: He is hunting for the evolutionary origin of the love of truth, in the needs of a community. In that sense, I would have thought it was just the pressure to get the facts right, because error is dangerous. Nice thought, though. |
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. |
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. |
13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
Full Idea: Aristotle proposes to relativise unity and plurality, so that a single object can be both one (indivisible) and many (divisible) simultaneously, without contradiction, relative to different measures. Wholeness has degrees, with the strength of the unity. | |
From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.12 | |
A reaction: [see Koslicki's account of Aristotle for details] As always, the Aristotelian approach looks by far the most promising. Simplistic mechanical accounts of how parts make wholes aren't going to work. We must include the conventional and conceptual bit. |
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? |
4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality. | |
From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4 | |
A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional. |
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. |
20360 | We Germans value becoming and development more highly than mere being of what 'is' [Nietzsche] |
Full Idea: We Germans are Hegelians insofar as we instinctively attribute a deeper sense and richer value to becoming and development than to what 'is'. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §357) | |
A reaction: I always doubt Nietzsche's claims about 'we Germans' or 'we philosophers'. They say that, intellectually, everyone is either French or German, and my immediate response was to embrace being German. So becoming is where it's at. |
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). |
13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
Full Idea: Aristotle's discussion of the unmoved mover and of the soul confirms the suspicion that form, when it is not thought of as the object represented in a definition, plays the role of the ultimate mereological atom within his system. | |
From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 6.6 | |
A reaction: Aristotle is concerned with which things are 'divisible', and he cites these two examples as indivisible, but they may be too unusual to offer an actual theory of how Aristotle builds up wholes from atoms. He denies atoms in matter. |
13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
Full Idea: Thus in Aristotle we may think of an object's formal components as a sort of recipe for how to build wholes of that particular kind. | |
From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.5 | |
A reaction: In the elusive business of pinning down what Aristotle means by the crucial idea of 'form', this analogy strikes me as being quite illuminating. It would fit DNA in living things, and the design of an artifact. |
24077 | Necessity is thought to require an event, but is only an after-effect of the event [Nietzsche] |
Full Idea: Necessity is supposed to be the cause of something coming to be: in truth it is often only an effect of what has come to be. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §205) | |
A reaction: This sounds like an account of the traditional idea of destiny - which sees inevitability in some major event, which was previously unpredictable. |
5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
Full Idea: Aristotle thinks that in general we have knowledge or understanding when we grasp causes, and he distinguishes three fundamental types of knowledge - theoretical, practical and productive. | |
From: report of Aristotle (works [c.330 BCE]) by Alan D. Code - Aristotle | |
A reaction: Productive knowledge we tend to label as 'knowing how'. The centrality of causes for knowledge would get Aristotle nowadays labelled as a 'naturalist'. It is hard to disagree with his three types, though they may overlap. |
20126 | The strength of knowledge is not its truth, but its entrenchment in our culture [Nietzsche] |
Full Idea: The strength of knowledge does not depend on its degree of truth but on its age, on the degree to which it has been incorporated, in its character as a condition of life. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §110) | |
A reaction: This seems to be the rather modern idea (in Foucault, perhaps) of knowledge as a central component of culture, rather than as an eternal revelation of facts. Note that he is talking about its 'strength', not its veracity or degree of support. |
11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
Full Idea: The notion of a priori truth is conspicuously absent in Aristotle. | |
From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5 | |
A reaction: Cf. Idea 11240. |
20119 | We became increasingly conscious of our sense impressions in order to communicate them [Nietzsche] |
Full Idea: The emergence of our sense impressions into our consciousness, the ability to fix them and, as it were, exhibit them externally, increased proportionally with the need to communicate them to others by means of signs. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
A reaction: He says in the same section that such ideas (plus his thoughts on consciousness) are the essence of his 'Perspectivism'. In effect, knowledge is not an individual activity, but a team game |
23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
Full Idea: Aristotle is a rationalist …but reason for him is a disposition which we only acquire over time. Its acquisition is made possible primarily by perception and experience. | |
From: report of Aristotle (works [c.330 BCE]) by Michael Frede - Aristotle's Rationalism p.173 | |
A reaction: I would describe this process as the gradual acquisition of the skill of objectivity, which needs the right knowledge and concepts to evaluate new experiences. |
16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
Full Idea: Since Aristotle generally prefers a metaphysical theory that accords with common intuitions, he frequently relies on facts about language to guide his metaphysical claims. | |
From: report of Aristotle (works [c.330 BCE]) by Mary Louise Gill - Aristotle on Substance Ch.5 | |
A reaction: I approve of his procedure. I take intuition to be largely rational justifications too complex for us to enunciate fully, and language embodies folk intuitions in its concepts (especially if the concepts occur in many languages). |
20122 | We have no organ for knowledge or truth; we only 'know' what is useful to the human herd [Nietzsche] |
Full Idea: We simply lack any organ for knowledge, for 'truth'; we 'know' [das Erkennen] (or believe or imagine) just as much as may be useful in the interests of the human herd, the species; and this 'utility' is ultimately also a mere belief. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
A reaction: [Section §354 is fascinating!] An odd idea, that we can only have truth is we have an 'organ' for it. It seems plausible that the whole brain is a truth machine. This seems like pure pragmatism, with all its faults. Falsehoods can be useful. |
4423 | We assume causes, geometry, motion, bodies etc to live, but they haven't been proved [Nietzsche] |
Full Idea: We have fixed up a world for ourselves in which we can live, with bodies, lines, planes, causes, motion and form; without these articles of faith nobody would endure life. But that does not mean they have been proved. Life is no argument. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §121) | |
A reaction: It is hard to disagree. A lot of recent thought suggests that they are Hume's 'natural beliefs', like truth and induction, which simply can't be proved. 'Unprovable' does not mean 'incorrect', however. |
6579 | Nietzsche's perspectivism says our worldview depends on our personality [Nietzsche, by Fogelin] |
Full Idea: Nietzsche recommends an extreme version of perspectivism in holding that a person's view of the world is a function of that person's life-affirming (Heraclitean) or life-denying (Parmenidean) personality. | |
From: report of Friedrich Nietzsche (The Gay (Joyful) Science [1882]) by Robert Fogelin - Walking the Tightrope of Reason Ch.3 | |
A reaction: Fogelin recommends Nehamas on this topic. I am not convinced Nietzsche takes such an individual view as is implied here. See Idea 4420, for example. This view is in tune with Charles Taylor's view that our values shape our understanding of our selves. |
24083 | It would be absurd to say we are only permitted our own single perspective [Nietzsche] |
Full Idea: I think today we are at least far removed from the ridiculous immodesty of decreeing from our corner that one is permitted to have perspectives only from this corner. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §374) | |
A reaction: He goes on to speculate about the possibility of infinite perspectives, most of them unknowable to us. But Nietzsche was not a simple relativism. The obvious concept needed to accompany a many-perspectives view is consensus. |
16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
Full Idea: Plato's unity of science principle states that all - legitimate - sciences are ultimately about the Forms. Aristotle's principle states that all sciences must be, ultimately, about substances, or aspects of substances. | |
From: report of Aristotle (works [c.330 BCE], 1) by Julius Moravcsik - Aristotle on Adequate Explanations 1 |
11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
Full Idea: For Aristotle things which explain (the explanantia) are facts, which should not be associated with the modern view that says explanations are dependent on how we conceive and describe the world (where causes are independent of us). | |
From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 2.1 | |
A reaction: There must be some room in modern thought for the Aristotelian view, if some sort of robust scientific realism is being maintained against the highly linguistic view of philosophy found in the twentieth century. |
3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
Full Idea: The standard Aristotelian doctrine of species and genus in the theory of anything whatever involves specifying what the thing is in terms of something more general. | |
From: report of Aristotle (works [c.330 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.10 |
12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
Full Idea: The view that essential properties are those in virtue of which other significant properties of the subjects under investigation can be explained is encountered repeatedly in Aristotle's work. | |
From: report of Aristotle (works [c.330 BCE]) by Joan Kung - Aristotle on Essence and Explanation IV | |
A reaction: What does 'significant' mean here? I take it that the significant properties are the ones which explain the role, function and powers of the object. |
20115 | All of our normal mental life could be conducted without consciousness [Nietzsche] |
Full Idea: We could think, feel, will and remember, and we could also 'act', and yet none of this would have to enter our consciousness. The whole of life would be possible without, as it were, seeing itself in a mirror. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
A reaction: He credits Leibniz with this line of thought. Nowadays the unconscious aspects of thought are a commonplace, not just from Freud, but from neuroscience. We have no idea how conscious other animals are. Nietzsche attributes consciousness to communication. |
20117 | Only the need for communication has led to consciousness developing [Nietzsche] |
Full Idea: I surmise that consciousness has developed only under the pressure of the need for communication; ...consciousness is really only a net of communication between human beings. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
A reaction: An interesting speculation, well ahead of its time. Given that thought does not require consciousness, as he claims, it is not quite clear why communication needs it. Presumably two robots can communicate. But Idea 20118 is good. |
20118 | Only our conscious thought is verbal, and this shows the origin of consciousness [Nietzsche] |
Full Idea: Only conscious thinking takes the form of words, which is to say signs of communication, and this fact uncovers the origin of consciousness. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
A reaction: Chicken-and-egg question here. Persinally I take consciousnes to be associated with meta-thought, which bestows huge power, and I take language to arise from meta-thought. |
20116 | Most of our lives, even the important parts, take place outside of consciousness [Nietzsche] |
Full Idea: By far the greatest proportion of our life takes place without this mirroring effect [of consciousness]; and this is true even of our thinking, feeling and willing life, however offensive this may sound to older philosophers. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
A reaction: Nietzsche didn't just hint at the possibility of a (Freudian) sub-conscious - he was whole-heartedly committed to it, and Freud gave him credit for it. I think philosophers are only just beginning to digest this crucial idea. |
20120 | Whatever moves into consciousness becomes thereby much more superficial [Nietzsche] |
Full Idea: Whatever becomes conscious becomes by the same token shallow, thin, relatively stupid, general, sign, herd signal; all becoming conscious involves a great and thorough corruption, falsification, reduction to superficialities, and generalisation. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
A reaction: Nietzsche would have made a great speech writer for someone. This vision is increasingly how I see people. It is a view reinforced by modern neuroscience, which suggests that we greatly overestimate the conscious part of ourselves. |
2932 | 'Know thyself' is impossible and ridiculous [Nietzsche] |
Full Idea: "Everybody is farthest away - from himself"; and the maxim "know thyself" addressed to human beings by a god, is almost malicious. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) | |
A reaction: Expressed with characteristcally Nietzschean brio, but I couldn't agree more, and it is a very important truth. You can only require full self-knowledge if the whole mind is available to be known, and that isn't even remotely the case. |
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. |
24078 | Thoughts cannot be fully reproduced in words [Nietzsche] |
Full Idea: Even one's thoughts one cannot reproduce entirely in words. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §244) | |
A reaction: I suppose this is the germ of Derrida, who seems to see little connection between thought and speech. I take this idea to be entirely correct. Our simplistic view of language reduces the fluidity and many dimensions of thought to a pile of lego bricks. |
24081 | Most of our intellectual activity is unconscious [Nietzsche] |
Full Idea: Only now is the truth dawning on us that the biggest part by far of our intellectual activity takes place unconsciously, and unfelt by us. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §333) | |
A reaction: Note that this is 'intellectual activity', and just the hidden rumblings of instincts and emotions. I think he is right. Philosophers want to verbalise everything, but I don't think the main insights of philosophical thinking are verbal. |
23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
Full Idea: Aristotle, and also the Stoics, denied rationality to animals. …The Platonists, the Pythagoreans, and some more independent Aristotelians, did grant reason and intellect to animals. | |
From: report of Aristotle (works [c.330 BCE]) by Richard Sorabji - Rationality 'Denial' | |
A reaction: This is not the same as affirming or denying their consciousness. The debate depends on how rationality is conceived. |
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. |
11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
Full Idea: The notion of analytic truth is conspicuously absent in Aristotle. | |
From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5 | |
A reaction: Cf. Idea 11239. |
2933 | Why do you listen to the voice of your conscience? [Nietzsche] |
Full Idea: Why do you listen to the voice of your conscience? | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) | |
A reaction: Nice question. It is perfectly plausible to say that I seem to feel guilty about doing something, but can't see any reason why I should. |
6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
Full Idea: To the best of my knowledge (and somewhat to my surprise), Aristotle never actually says that man is a rational animal; however, he all but says it. | |
From: report of Aristotle (works [c.330 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
A reaction: When I read this I thought that this database would prove Fogelin wrong, but it actually supports him, as I can't find it in Aristotle either. Descartes refers to it in Med.Two. In Idea 5133 Aristotle does say that man is a 'social being'. But 22586! |
20141 | Higher human beings see and hear far more than others, and do it more thoughtfully [Nietzsche] |
Full Idea: What distinguishes the higher human being from the lower is that the former see and hear immeasurably more, and see and hear thoughtfully - and precisely this distinguishes human beings from animals, and the higher animals from the lower. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §301) | |
A reaction: Since most people are well equipped with eyes and ears, I take it that this phenomenon, if true, arises from the 'higher' type of person having more interest in what they experience. |
24076 | A morality ranks human drives and actions, for the sake of the herd, and subordinating individuals [Nietzsche] |
Full Idea: Whenever we encounter a morality we find an estimation and order of rank of human drives and actions. These are always the expression of the needs of a community and herd. The individual is valued only as a function of the herd. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §116) | |
A reaction: A particularly clear summary of Nietzsche's understanding of modern morality (which he rejects). I tend to see values as what is important, but Nietzsche sees them as a ranking. Could be both. I see the individualism here as existentialist. |
22471 | Nietzsche thought it 'childish' to say morality isn't binding because it varies between cultures [Nietzsche, by Foot] |
Full Idea: Nietzsche was not simply a run-of-the-mill moral relativist. He branded as 'childish' the idea that no morality can be binding because moral valuations are necessarily different among different nations. | |
From: report of Friedrich Nietzsche (The Gay (Joyful) Science [1882], §345) by Philippa Foot - Nietzsche's Immoralism p.146 | |
A reaction: Relativists about knowledge and morality are inclined to take quotations from Nietzsche out of context. The existence of this database probably exacerbates such intellectual wickedness. Get a feeling for the whole thinker! |
2935 | No two actions are the same [Nietzsche] |
Full Idea: There neither are nor can be actions which are the same. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) |
20198 | Many virtues are harmful traps, but that is why other people praise them [Nietzsche] |
Full Idea: Virtues like industriousness, obedience, chastity, filial piety and justice are usually harmful to those who possess them. When you have a real, whole virtue you are its victim. But your neighbour praises your virtue precisely on that account. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §021) | |
A reaction: This is the conspiracy theory of virtue. We want people to do menial or undesirable jobs, so we dress them up as wonderful virtues, and make people feel good for possessing them. There must be some truth in this. |
4275 | You cannot advocate joyful wisdom while rejecting pity, because the two are complementary [Scruton on Nietzsche] |
Full Idea: Pity and good cheer are complementary, ..so there is something contradictory in a philosophy that advocates joyful wisdom, while slandering pity as the enemy of the higher life. | |
From: comment on Friedrich Nietzsche (The Gay (Joyful) Science [1882]) by Roger Scruton - Animal Rights and Wrongs p.35 | |
A reaction: A good objection to Nietzsche. He has a rather solipsistic view of joyful exuberance etc., and fails to realise how social such things must be. In that, Nietzsche was caught in the romantic tradition of Wordsworth and co. |
2934 | To see one's own judgement as a universal law is selfish [Nietzsche] |
Full Idea: It is selfish to experience one's own judgement as a universal law. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) |
24080 | We should give style to our character - by applying an artistic plan to its strengths and weaknesses [Nietzsche] |
Full Idea: One thing is essential - 'giving style' to one's character. It is practised by the one who surveys everything that his nature offers in strengths and weaknesses, and subjects it to an artistic plan until each thing appears as art and reason. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §290) | |
A reaction: Clearly existentialist, in its proposal to change one's own character. I invite the reader to consider applying this to themselves - and I submit that it is an impossible project. Nice thought, though. |
20125 | The ethical teacher exists to give purpose to what happens necessarily and without purpose [Nietzsche] |
Full Idea: That what happens necessarily, spontaneously and without any purpose, may henceforth appear to be done for some purpose, and strike man as rational and an ultimate commandment, the ethical teacher comes on stage, as teacher of the purpose of existence. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §001) | |
A reaction: This doesn't look like much of a solution to the problem of nihilism, unless the teacher plants an idea in us which endures and grows. Nietzsche's 'eternal recurrence' was supposed to be just such an idea. |
9306 | To ward off boredom at any cost is vulgar [Nietzsche] |
Full Idea: To ward off boredom at any cost is vulgar. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §042) | |
A reaction: Ignoring 'vulgar', this is a nice thought. Do affluent retired people now travel so much because they are terrified of boredom? What would they end up doing if they stayed at home and lived through the boredom to something else? |
24079 | The best life is the dangerous life [Nietzsche] |
Full Idea: The secret of harvesting the greatest fruitfulness and the greatest enjoyment from existence is: live dangerously! | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §283) | |
A reaction: I treasured this quotation when I was 17, but failed to live up to it. |
2936 | Imagine if before each of your actions you had to accept repeating the action over and over again [Nietzsche] |
Full Idea: Suppose a demon were to say to you, "This life as you have lived it, you will have to live once more and innumerable times more". …Then the question in each thing, "Do you desire this once more and innumerable times more?" would lie across your actions. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §341) | |
A reaction: If you were stuck in nihilistic indifference, this thought might not be enough to rouse you from your torpor. If all possibilities in life are boring, repetition cannot pep it up, or make it any worse. But I still love this idea! |
6842 | Nietzsche says facing up to the eternal return of meaninglessness is the response to nihilism [Nietzsche, by Critchley] |
Full Idea: Nietzsche is overwhelmingly concerned with how to respond to nihilism, and he offers the concept of eternal return; the Overman is one who can affirm over and over that one is equal to meaninglessness, without turning to despair or idols. | |
From: report of Friedrich Nietzsche (The Gay (Joyful) Science [1882], §342) by Simon Critchley - Interview with Baggini and Stangroom p.192 | |
A reaction: I agree with Critchley that this is not much of a recipe for ordinary people's lives, and I don't even find it very congenial for a tough-minded philosopher. We should make the best of the cards we are dealt, however feeble they may appear. |
11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
Full Idea: It is the mark of an educated mind to be able to entertain an idea without accepting it. | |
From: Aristotle (works [c.330 BCE]) | |
A reaction: The epigraph on a David Chalmers website. A wonderful remark, and it should be on the wall of every beginners' philosophy class. However, while it is in the spirit of Aristotle, it appears to be a misattribution with no ancient provenance. |
3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
Full Idea: Aristotle was asked how much educated men were superior to those uneducated; "As much," he said, "as the living are to the dead." | |
From: report of Aristotle (works [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 05.1.11 |
8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
Full Idea: Aristotle developed his own distinction between potential infinity (never running out) and actual infinity (there being a collection of an actual infinite number of things, such as places, times, objects). He decided that actual infinity was incoherent. | |
From: report of Aristotle (works [c.330 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 1.3 | |
A reaction: Friend argues, plausibly, that this won't do, since potential infinity doesn't make much sense if there is not an actual infinity of things to supply the demand. It seems to just illustrate how boggling and uncongenial infinity was to Aristotle. |
12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
Full Idea: Aristotle's conception of matter permits any kind of matter to become any other kind of matter. | |
From: report of Aristotle (works [c.330 BCE]) by David Wiggins - Substance 4.11.2 | |
A reaction: This is obviously crucial background information when we read Aristotle on matter. Our 92+ elements, and fixed fundamental particles, gives a quite different picture. Aristotle would discuss form and matter quite differently now. |
2931 | God is dead, and we have killed him [Nietzsche] |
Full Idea: God is dead. God remains dead. And we have killed him. | |
From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §125) |
22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |
Full Idea: Aristotle said that the conception of gods arose among mankind from two originating causes, namely from events which concern the soul and from celestial phenomena. | |
From: report of Aristotle (works [c.330 BCE], Frag 10) by Sextus Empiricus - Against the Physicists (two books) I.20 | |
A reaction: The cosmos suggests order, and possible creation. What do events of the soul suggest? It doesn't seem to be its non-physical nature, because Aristotle is more of a functionalist. Puzzling. (It says later that gods are like the soul). |