53 ideas
| 6961 | An analogy begins to break down as soon as the two cases differ [Hume] |
| Full Idea: But wherever you depart, in the least, from the similarity of the cases, you diminish proportionably the evidence; and may at last bring it to a very weak analogy. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 2) |
| 9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
| Full Idea: The best known axiomatization of PL is Whitehead/Russell. There are four axioms: (p∨p)→p, q→(p∨q), (p→q)→(q∨p), and (q→r)→((p∨q)→(p∨r)), plus Substitution and Modus Ponens rules. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by GE Hughes/M Cresswell - An Introduction to Modal Logic Ch.1 |
| 21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
| Full Idea: The axiom of Reducibility ...is crucial in the reduction of classes to logic, ...and seems to be a quite legitimate logical notion for Russell. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 6.4 | |
| A reaction: This is an unusual defence of the axiom, which is usually presumed to have been kicked into the long grass by Quine. If one could reduce classes to logic, that would destroy the opposition to logicism in a single neat coup. |
| 10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell adduces two reasons against the extensional view of classes, namely the existence of the null class (which cannot very well be a collection), and the unit classes (which would have to be identical with their single elements). | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Structure and Ontology p.459 | |
| A reaction: Gödel believes in the reality of classes. I have great sympathy with Russell, when people start to claim that sets are not just conveniences to help us think about things, but actual abstract entities. Is the singleton of my pencil is on this table? |
| 18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
| Full Idea: Classes, so far as we introduce them, are merely symbolic or linguistic conveniences, not genuine objects. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.72), quoted by Penelope Maddy - Naturalism in Mathematics III.2 |
| 8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
| Full Idea: Russell call 'if...then' implication, when the material conditional is a much better account; C.I.Lewis (in founding modern modal logic) preserved Russell's confusion by creating 'strict implication', and called that implication. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Willard Quine - Reply to Professor Marcus p.177 | |
| A reaction: [A compession of Quine's paragraph]. All of this assumes that logicians can give an accurate account of what if...then means, when ordinary usage is broad and vague. Strict implication seems to drain all the normal meaning out of 'if...then'. |
| 9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
| Full Idea: In Mr Russell's idea of implication, if twenty random sentences from a newspaper were put in a hat, and two of them drawn at random, one will certainly imply the other, and it is an even bet the implication will be mutual. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by C.I. Lewis - A Pragmatic Conception of the A Priori p.366 | |
| A reaction: This sort of lament leads modern logicians to suggest 'relevance' as an important criterion. It certainly seems odd that so-called 'classical logic' should contain a principle so at variance with everyday reasoning. |
| 21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
| Full Idea: Russell did not view logic as an uninterpreted calculus awaiting interpretations [the modern view]. Rather, logic is a single 'interpreted' body of a priori truths, of propositions rather than sentence forms - but maximally general and topic neutral. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 1 | |
| A reaction: This is the view which Wittgenstein challenged, saying logic is just conventional. Linsky claims that Russell's logicism is much more plausible, once you understand his view of logic. |
| 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
| Full Idea: In 'Principia' a young science was enriched with a new abstract theory of relations, ..and not only Cantor's set theory but also ordinary arithmetic and the theory of measurement are treated from this abstract relational standpoint. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 | |
| A reaction: I presume this is accounting for relations in terms of ordered sets. |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| Full Idea: For Russell the real number 2 is the class of rationals less than 2 (i.e. 2/1). ...Notice that on this definition, real numbers are classes of rational numbers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| Full Idea: Although Russell takes numbers to be certain classes, his 'no-class' theory then eliminates all mention of classes in favour of the 'propositional functions' that define them; and in the case of the numbers these just are the numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by David Bostock - Philosophy of Mathematics 9.B.4 |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| Full Idea: Russell and Whitehead took arithmetic to be higher-order logic, ..and came close to identifying numbers with numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.148 | |
| A reaction: The point here is 'higher-order'. |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| Full Idea: Unlike Frege, Russell and Whitehead were not realists about mathematical objects, and whereas Frege thought that only arithmetic and analysis are branches of logic, they think the vast majority of mathematics (including geometry) is essentially logical. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: If, in essence, Descartes reduced geometry to algebra (by inventing co-ordinates), then geometry ought to be included. It is characteristic of Russell's hubris to want to embrace everything. |
| 10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
| Full Idea: What is missing, above all, in 'Principia', is a precise statement of the syntax of the formalism. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 |
| 10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
| Full Idea: Russell and Whitehead's ramified theory of types worked not with sets, but with propositional functions (similar to Frege's concepts), with a more restrictive assignment of variables, insisting that bound, as well as free, variables be of lower type. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.3 | |
| A reaction: I don't fully understand this (and no one seems much interested any more), but I think variables are a key notion, and there is something interesting going on here. I am intrigued by ordinary language which behaves like variables. |
| 8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
| Full Idea: The Russell/Whitehead type theory reduces mathematics to a consistent founding discipline, but is criticised for not really being logic. They could not prove the existence of infinite sets, and introduced a non-logical 'axiom of reducibility'. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.6 | |
| A reaction: To have reduced most of mathematics to a founding discipline sounds like quite an achievement, and its failure to be based in pure logic doesn't sound too bad. However, it seems to reduce some maths to just other maths. |
| 10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
| Full Idea: In the system of 'Principia Mathematica', it is not only the axioms of infinity and reducibility which go beyond pure logic, but also the initial conception of a universal domain of individuals and of a domain of predicates. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.267) by Paul Bernays - On Platonism in Mathematics p.267 | |
| A reaction: This sort of criticism seems to be the real collapse of the logicist programme, rather than Russell's paradox, or Gödel's Incompleteness Theorems. It just became impossible to stick strictly to logic in the reduction of arithmetic. |
| 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
| Full Idea: Russell and Whitehead are particularly careful to avoid paradox, and consider the paradoxes to indicate that we create mathematical reality. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: This strikes me as quite a good argument. It is certainly counterintuitive that reality, and abstractions from reality, would contain contradictions. The realist view would be that we have paradoxes because we have misdescribed the facts. |
| 8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell insisted on the vicious circle principle, and thus rejected impredicative definitions, which resulted in an unwieldy ramified type theory, with the ad hoc axiom of reducibility. Ramsey's simpler theory was impredicative and avoided the axiom. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 | |
| A reaction: Nowadays the theory of types seems to have been given up, possibly because it has no real attraction if it lacks the strict character which Russell aspired to. |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| Full Idea: Trivially, the Identity of Indiscernibles says that two individuals, Castor and Pollux, cannot have all properties in common. For Castor must have the properties of being identical with Castor and not being identical with Pollux, which Pollux can't share. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913], I p.57) by Robert Merrihew Adams - Primitive Thisness and Primitive Identity 2 | |
| A reaction: I suspect that either the property of being identical with itself is quite vacuous, or it is parasytic on primitive identity, or it is the criterion which is actually used to define identity. Either way, I don't find this claim very illuminating. |
| 21285 | Events are baffling before experience, and obvious after experience [Hume] |
| Full Idea: Every event, before experience, is equally difficult and incomprehensible; and every event, after experience, is equally easy and intelligible. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 8) | |
| A reaction: If you don't believe this, spend some time watching documentaries about life in the deep oceans. Things beyond imagination swim around in front of you. But we can extrapolate, once the possibilities are revealed by experience. |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| Full Idea: By analyzing the paradoxes to which Cantor's set theory had led, ..Russell brought to light the amazing fact that our logical intuitions (concerning such notions as truth, concept, being, class) are self-contradictory. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.452 | |
| A reaction: The main intuition that failed was, I take it, that every concept has an extension, that is, there are always objects which will or could fall under the concept. |
| 21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
| Full Idea: The multiple relations theory of judgement proposes that assertions about propositions are dependent upon genuine facts involving belief and other attitude relations, subjects of those attitudes, and the constituents of the belief. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 7.2 | |
| A reaction: This seems to require a commitment to universals (especially relations) with which we can be directly acquainted. I prefer propositions, but as mental entities, not platonic entities. |
| 23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
| Full Idea: When a judgement occurs, there is a certain complex entity, composed of the mind and the various objects of the judgement. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44) | |
| A reaction: This is Russell's multiple-relation theory of judgement, which replaced his earlier belief in unified propositions (now 'false abstractions'). He seems to have accepted Locke's view, that the act of judgement produces the unity. |
| 23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus | |
| A reaction: Morris says this is Russell's multiple-relations theory of judgement. The theory accompanies the rejection of the concept of the unified proposition. When I hear 'Socrates had a mole on his shoulder' I get the meaning without judging. |
| 23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
| Full Idea: When Russell moved to his multiple relation theory of judgement …he then faced difficulties making sense of the unity of sentences. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.44) by Michael Morris - Guidebook to Wittgenstein's Tractatus 3A | |
| A reaction: Roughly, he seems committed to saying that there is only unity if you think there is unity; there is no unity in a sentence prior to the act of judgement. |
| 18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging, and we no longer have an incomplete symbol. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap | |
| A reaction: Personally I would have thought that you needed to know the meaning properly before you could make the judgement, but then he is Bertrand Russell and I'm not. |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
| Full Idea: A 'proposition', in the sense in which a proposition is supposed to be the object of a judgement, is a false abstraction, because a judgement has several objects, not one. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus 2E | |
| A reaction: This is the rejection of the 'Russellian' theory of propositions, in favour of his multiple-relations theory of judgement. But why don't the related objects add up to a proposition about a state of affairs? |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |
| 6959 | We can't assume God's perfections are like our ideas or like human attributes [Hume] |
| Full Idea: But let us beware, lest we think, that our ideas anywise correspond to his perfections, or that his attributes have any resemblance to these qualities among men. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 2) |
| 6957 | The objects of theological reasoning are too big for our minds [Hume] |
| Full Idea: But in theological reasonings … we are employed upon objects, which, we must be sensible, are too large for our grasp. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 1) |
| 21255 | No being's non-existence can imply a contradiction, so its existence cannot be proved a priori [Hume] |
| Full Idea: Nothing that is distinctly conceivable implies a contradiction. Whatever we conceive of as existent we can also conceive as non-existent. So there is no being whose non-existence implies a contradiction. So no being's existence is demonstrable. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 9) | |
| A reaction: I totally subscribe to this idea, and take claims that nature actually contains contradictions (based on the inevitable quantum mechanics) to be ridiculous. Nature is the embodiment, chief exemplar and prime test of consistency. |
| 21254 | A chain of events requires a cause for the whole as well as the parts, yet the chain is just a sum of parts [Hume] |
| Full Idea: The whole chain or succession [of causes and effects], taken together, is not caused by anything, and yet it is evident that it requires a cause or reason, as much as any particular object which begins to exist in time. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 9) | |
| A reaction: This is such a major and significant idea. With blinkers on we think our questions are answered. Then someone (a philosopher, inevitably) makes you pull back and ask a much wider and more difficult question. |
| 1435 | If something must be necessary so that something exists rather than nothing, why can't the universe be necessary? [Hume] |
| Full Idea: What was it that determined something to exist rather than nothing? ...This implies a necessary being… But why may not the material universe be the necessarily existent being? | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 9) | |
| A reaction: There certainly seems no need for whatever the necessary thing is that it qualify as a 'god'. If could be a necessary subatomic particle that suddenly triggers reactions. |
| 6962 | The thing which contains order must be God, so see God where you see order [Hume] |
| Full Idea: By supposing something to contain the principle of its order within itself, we really assert it to be God; and the sooner we arrive at that divine being, so much the better. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 4) |
| 6960 | Analogy suggests that God has a very great human mind [Hume] |
| Full Idea: Since the effects resemble, we must infer by analogy that the causes also resemble; and that the Author of Nature is somewhat similar to the mind of man, though possessed of much larger faculties, proportioned to the grandeur of his work. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 2) |
| 6963 | Why would we infer an infinite creator from a finite creation? [Hume] |
| Full Idea: By this method of reasoning, you renounce all claim to infinity in any of the attributes of the deity. For … the cause ought only to be proportioned to the effect, and the effect, so far as it falls under our cognizance, is not infinite. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 5) |
| 21279 | If the divine cause is proportional to its effects, the effects are finite, so the Deity cannot be infinite [Hume] |
| Full Idea: By this method of reasoning you renounce all claim to infinity in any of the attributes of the Deity. The cause ought to be proportional to the effect, and the effect, so far as it falls under our cognizance, is not infinite. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 5) | |
| A reaction: You cannot deny that the Deity MAY be infinite, be only accept that your evidence is not enough to prove it. But if nothing infinite has been observed, it is a reasonable provisional inference that nothing infinite exists. |
| 21280 | From a ship you would judge its creator a genius, not a mere humble workman [Hume] |
| Full Idea: It is uncertain whether all the excellences of the work can justly be ascribed to the workman. If we survey a ship, what an exalted idea must we form of the ingenuity of the carpenter ...and what surprise must we feel when we find him a stupid mechanic. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 5) | |
| A reaction: You can at least infer that the ship was not made entirely by makers who are ignorant of carpentry. Somewhere in the divine team there must exist the skills that produce whatever we observe? |
| 21282 | Design cannot prove a unified Deity. Many men make a city, so why not many gods for a world? [Hume] |
| Full Idea: How can you prove the unity of a Deity? A great number of men join in building a house or ship, in rearing a city; why may not several deities combine in contriving and framing a world? | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 5) | |
| A reaction: You might look at the Cistine Chapel ceiling and conclude that only a team could have achieve such a thing. Since there is no way to infer how many gods might be involved, then one god is a possible theory. |
| 21281 | This excellent world may be the result of a huge sequence of trial-and-error [Hume] |
| Full Idea: Many worlds might have been botched and bungled, throughout an eternity, ere this system was struck out; many fruitless trials made, and a slow but continued improvement carried on during infinite ages in the art of world-making. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 5) | |
| A reaction: Lee Smolin, a modern cosmographer, suggests that this evolution may have led to the current universe, after a long train of selective creations. The idea of natural selection was waiting to happen in 1760. |
| 21283 | Humans renew their species sexually. If there are many gods, would they not do the same? [Hume] |
| Full Idea: Men are mortal and renew their species by generation. Why must this circumstance, so universal, so essential, be excluded from those numerous and limited deities? | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 5) | |
| A reaction: Hume observes that this would be like the Greek gods. Hume makes mincemeat of attempts to prove the existence of God merely by analogy with human affairs. |
| 21284 | This Creator god might be an infant or incompetent or senile [Hume] |
| Full Idea: [Maybe] this world ...was only the first essay of some infant deity ...or it is the work only of some dependent, inferior deity, the object of derision to his superiors ...or it is the product of the dotage of some superannuated deity... | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 5) | |
| A reaction: His opponent in the dialogue rejoices that, in the face of these sacreligious fantasies, Hume still accepts the likelihood of some sort of design. Hume is right that it is not much of a theory if nothing can be said about the Designer. |
| 21286 | Motion often begins in matter, with no sign of a controlling agent [Hume] |
| Full Idea: Motion in many instances begins in matter, without any known voluntary agent; to suppose always, in these cases, an unknown voluntary agent is mere hypothesis, attended with no advantages. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 8) | |
| A reaction: This is the modern 'powers' view of science, and a direct contradiction of Plato's claims in The Laws. It seems a bit primitive to assume that magnetism must be the work of some god. |
| 21287 | The universe could settle into superficial order, without a designer [Hume] |
| Full Idea: The universe goes on in a succession of chaos and disorder. But is it not possible that it may settle at last, so as not to lose its inherent motion and active force, yet so as to produce a uniformity of appearance, amidst the continual fluctuation. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 8) | |
| A reaction: From what I know of the constant fluctuation of virtual particles (e.g. inside protons) this is exactly what actually is happening. There is an 'appearance' of order, but at the lowest level this is not the case. |
| 21288 | Ideas arise from objects, not vice versa; ideas only influence matter if they are linked [Hume] |
| Full Idea: In all known instances, ideas are copied from real objects. You reverse this order and give thought the precedence. ...Thought has no influence upon matter except where that matter is so conjoined with it as to have an equal reciprocal influence upon it. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 8) | |
| A reaction: He allows something like mental causation, provided mind and brain are closely linked. Hume brings out the close relationship between divine design theories, and the mind-body problem. |
| 21256 | A surprise feature of all products of 9 looks like design, but is actually a necessity [Hume] |
| Full Idea: The products of 9 always compose either 9 or some lesser product of 9, if you add the characters of the product. To a superficial observer this regularity appears as chance or design, but a skilful algebraist sees it as necessity. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 9) | |
| A reaction: An example of this universal generality is that 369 is a product of 9 (9x41), and if you add 3, 6 and 9 you get 18, which is 2x9. Similar examples occur in nature, such as crystals, which are necessary once the atomic structure is known. |
| 6964 | From our limited view, we cannot tell if the universe is faulty [Hume] |
| Full Idea: It is impossible for us to tell, from our limited views, whether this system contains any great faults. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 5) |
| 6966 | Creation is more like vegetation than human art, so it won't come from reason [Hume] |
| Full Idea: If the universe is more like animal bodies and vegetables than works of human art, it is more probable that its cause resembles the cause of the former than of the latter, and its cause should be ascribed to generation rather than to reason of design. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 7) |
| 6967 | Order may come from an irrational source as well as a rational one [Hume] |
| Full Idea: Why an orderly system may not be spun from the belly as well as from the brain, it will be difficult … to give a satisfactory reason. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 7) |
| 6958 | How can we pronounce on a whole after a brief look at a very small part? [Hume] |
| Full Idea: A very small part of this great system, during a very short time, is very imperfectly discovered to us: and do we thence pronounce decisively concerning the origin of the whole? | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 2) |
| 6965 | The universe may be the result of trial-and-error [Hume] |
| Full Idea: Many worlds might have been botched and bungled, throughout an eternity, ere this system was struck out. | |
| From: David Hume (Dialogues Concerning Natural Religion [1751], Part 5) |