38 ideas
| 21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
| Full Idea: The ban on 'impredicative' definitions says you can't define a class in terms of a totality to which that class must be seen as belonging. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: So that would be defining 'citizen' in terms of the community to which the citizen belongs? If you are asked to define 'community' and 'citizen' together, where do you start? But how else can it be done? Russell's Reducibility aimed to block this. |
| 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) |
| 21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
| Full Idea: The Axiom of Reducibility avoids impredicativity, by asserting that for any predicate of given arguments defined by quantifying over higher-order functions or classes, there is another co-extensive but predicative function of the same type of arguments. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Eventually the axiom seemed too arbitrary, and was dropped. Linsky's book explores it. |
| 21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
| Full Idea: The theory of definite descriptions may eliminate apparent commitment to such entities as the present King of France, but certainly not to the present Queen of England. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.3) |
| 21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
| Full Idea: With the principle of extensionality anything true of one propositional functions will be true of every coextensive one. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.3) |
| 21723 | The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B] |
| Full Idea: The problem for logicism was to find definitions of the primitive notions of Peano's theory, number, successor and 0, in terms of logical notions, so that the postulates could then be derived by logic alone. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7) | |
| A reaction: Both Frege and Russell defined numbers as equivalence classes. Successor is easily defined (in various ways) in set theory. An impossible set can exemplify zero. The trouble for logicism is this all relies on sets. |
| 21721 | Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B] |
| Full Idea: The higher types are needed for intensional phenomena, cases where the same class is picked out by distinct propositional functions. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.4) | |
| A reaction: I take it that in this way 'x is renate' can be distinguished from 'x is cordate', a task nowadays performed by possible worlds. |
| 21703 | Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B] |
| Full Idea: The types is 'ramified' because there are further differences between the type of a function defined in terms of a quantifier ranging over other functions and the type of those other functions, despite the functions applying to the same simple type. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Not sure I understand this, but it evidently created difficulties for dealing with actual mathematics, and Ramsey showed how you could manage without the ramifications. |
| 21714 | The ramified theory subdivides each type, according to the range of the variables [Linsky,B] |
| Full Idea: The original ramified theory of types ...furthern subdivides each of the types of the 'simple' theory according to the range of the bound variables used in the definition of each propositional function. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: For a non-intiate like me it certainly sounds disappointing that such a bold and neat theory because a tangle of complications. Ramsey and Russell in the 1920s seem to have dropped the ramifications. |
| 21713 | Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B] |
| Full Idea: It is often thought that Logicism was a failure, because after Frege's contradiction, Russell required obviously nonlogical principles, in order to develop mathematics. The axioms of Reducibility, Infinity and Choice are cited. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: Infinity and Choice remain as axioms of the standard ZFC system of set theory, which is why set theory is always assumed to be 'up to its neck' in ontological commitments. Linsky argues that Russell saw ontology in logic. |
| 21715 | For those who abandon logicism, standard set theory is a rival option [Linsky,B] |
| Full Idea: ZF set theory is seen as a rival to logicism as a foundational scheme. Set theory is for those who have given up the project of reducing mathematics to logic. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.1) | |
| A reaction: Presumably there are other rivals. Set theory has lots of ontological commitments. One could start at the other end, and investigate the basic ontological commitments of arithmetic. I have no idea what those might be. |
| 21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
| Full Idea: Rather than directly constructing properties as sets of objects and proving neat facts about properties by proxy, we can assert biconditionals, such as that an object has a property if and only if it is in a certain set. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.6) | |
| A reaction: Linsky is describing Russell's method of logical construction. I'm not clear what is gained by this move, but at least it is a variant of the usual irritating expression of properties as sets of objects. |
| 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. |
| 3158 | Theories of intentionality presuppose rationality, so can't explain it [Dennett] |
| Full Idea: Intentional theory is vacuous as psychology because it presupposes and does not explain rationality or intelligence. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.15?) | |
| A reaction: Virtually every philosophical theory seems to founder because it presupposes something like the thing it is meant to explain. I agree that 'intentionality' is a slightly airy concept that would probably reduce to something better. |
| 3159 | Beliefs and desires aren't real; they are prediction techniques [Dennett] |
| Full Idea: Intentional systems don't really have beliefs and desires, but one can explain and predict their behaviour by ascribing beliefs and desires to them. This strategy is pragmatic, not right or wrong. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.7?) | |
| A reaction: If the ascription of beliefs and desires explains behaviour, then that is good grounds for thinking they might be real features of the brain, and even if that is not so, they are real enough as abstractions from brain events, like the 'economic climate'. |
| 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) |
| 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) |
| 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. |
| 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) |
| 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) |
| 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. |
| 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? |
| 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. |
| 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) |
| 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. |
| 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) |
| 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) |
| 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) |