34 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) |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
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. |
7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
Full Idea: Libet himself points out that the conscious decisions still have the power to 'endorse' or 'cancel', so to speak, the processes initiated by the earlier cortical activity: no action will result if the action's execution is consciously countermanded. | |
From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by David Papineau - Thinking about Consciousness 1.4 | |
A reaction: This is why Libet's findings do not imply 'epiphenomenalism'. It seems that part of a decisive action is non-conscious, undermining the all-or-nothing view of consciousness. Searle tries to smuggle in free will at this point (Idea 3817). |
6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
Full Idea: Libet found that a subject's conscious choice to move was about a fifth of a second before movement, and thus later than the onset of the brain's so-called 'readiness potential', which seems to imply that unconscious processes initiates action. | |
From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.9 | |
A reaction: Of great interest to philosophers! It seems to make conscious choices epiphenomenal. The key move, I think, is to give up the idea of consciousness as being all-or-nothing. My actions are still initiated by 'me', but 'me' shades off into unconsciousness. |
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) |
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) |
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. |
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. |
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. |
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) |
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) |
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) |
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) |