28 ideas
| 2653 | If the parts of the universe are subject to the law of nature, the whole universe must also be subject to it [Cicero] |
| Full Idea: If the parts of the universe are subject to the law of nature, then the universe itself must be subject to this law. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.86) |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
| Full Idea: The supposition that a diamond or organism should truly have emergent properties is that they appear at certain complex levels of organisation, but are not explainable (even in principle) in terms of any more fundamental properties of the system. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |
| 2628 | Why would mind mix with matter if it didn't need it? [Cicero] |
| Full Idea: If the gods have no need of the sensible world, why mix up mind with water and water with mind, if mind can exist by itself without any need of matter? | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.24) | |
| A reaction: This question migrates into our puzzles about why a separate mental substance would be produced by evolution. If it is device physical systems use to promote themselves, mental substance is reduced to an inferior and dependent role. |
| 20814 | Eloquence educates, exhorts, comforts, distracts and unites us, and raises us from savagery [Cicero] |
| Full Idea: How wonderful is the power of eloquence! It enables us to learn and to teach. We use it to exhort and persuade, to comfort the unfortunate, to distract the timid and calm the passionate. It unites us in law and society, and raises us from savagery. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], 2.147) | |
| A reaction: [compressed] Cicero would have been well aware of the doubts about rhetoric felt by Socrates (and possibly Plato). Cicero was probably the greatest Roman orator. |
| 2640 | We have the death penalty, but still have thousands of robbers [Cicero] |
| Full Idea: We have robbers by the thousand, although they have the penalty of death before their eyes. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.86) |
| 2652 | Some regard nature simply as an irrational force that imparts movement [Cicero] |
| Full Idea: Some regard nature as an irrational force which merely imparts a mechanical motion to material bodies. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.81) |
| 3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |
| Full Idea: Given what heat is and what water is, it is literally impossible for water to be heated beyond a certain point at normal atmospheric pressure without boiling. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |
| 2645 | Why shouldn't the gods fear their own destruction? [Cicero] |
| Full Idea: Why should the gods not be apprehensive of their own possible dissolution? | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.114) |
| 2627 | I wonder whether loss of reverence for the gods would mean the end of all virtue [Cicero] |
| Full Idea: I do not know whether, if our reverence for the gods were lost, we should not also see the end of good faith, of human brotherhood, and even of justice itself, which is the keystone of all the virtues. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.3) |
| 2651 | God doesn't obey the laws of nature; they are subject to the law of God [Cicero] |
| Full Idea: God is not subject to obey the laws of nature. It is nature that is subject to the laws of God. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.77) |
| 2634 | It seems clear to me that we have an innate idea of the divine [Cicero] |
| Full Idea: Let us take it as agreed that we have a preconception or "an innate idea" (as I have called it) or a prior knowledge of the divine. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.44) |
| 2636 | Many primitive people know nothing of the gods [Cicero] |
| Full Idea: There must be many wild and primitive peoples who have no idea of the gods at all. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.62) |
| 2647 | It is obvious from order that someone is in charge, as when we visit a gymnasium [Cicero] |
| Full Idea: If one comes into a gymnasium and sees everything properly arranged and carried on in order, one does not imagine these arrangements to be accidental, but infers that there is someone in command whose orders are obeyed. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.15) |
| 2655 | If the barbarians of Britain saw a complex machine, they would be baffled, but would know it was designed [Cicero] |
| Full Idea: If someone were to take the celestial globe of Posidonius and show it to the people of Britain, would a single one of those barbarians fail to see that it was the product of a conscious intelligence? | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.88) |
| 2656 | Chance is no more likely to create the world than spilling lots of letters is likely to create a famous poem [Cicero] |
| Full Idea: If someone thinks chance made the world, he should also think that if an infinite number of the letters of the alphabet were shaken together and poured out on the ground it would be possible for them to spell out the whole 'Annals' of Ennius. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.93) |
| 2650 | If a person cannot feel the power of God when looking at the stars, they are probably incapable of feeling [Cicero] |
| Full Idea: If any man cannot feel the power of God when he looks upon the stars, then I doubt whether he is capable of any feeling at all. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.55) |
| 2657 | If everything with regular movement and order is divine, then recurrent illnesses must be divine [Cicero] |
| Full Idea: Are we to find a divinity in every regular movement and in everything which happens in a constant order? If so, we shall have to say that tertian and quartan agues are divine because their course and recurrence is absolutely uniform. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], III.24) |
| 2638 | Either the gods are identical, or one is more beautiful than another [Cicero] |
| Full Idea: Are the gods all exactly the same? If not, then one must be more beautiful than another. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.80) |
| 2635 | The gods are happy, so virtuous, so rational, so must have human shape [Cicero] |
| Full Idea: We agree the gods are happy, and no happiness is possible without virtue: there is no virtue without reason: and reason is associated only with the human form: then it must follow that the gods themselves have human shape. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.48) |
| 2641 | Why believe in gods if you have never seen them? [Cicero] |
| Full Idea: Did you ever actually see a god? Then why do you believe that gods exist? | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.88) |
| 2659 | The lists of good men who have suffered and bad men who have prospered are endless [Cicero] |
| Full Idea: Time would fail me if I tried to list all the good men for whom things have turned out badly. So it would if I tried to mention all the wicked who have prospered. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], III.80) |
| 2658 | The gods blame men for having vices, but they could have given us enough reason to avoid them [Cicero] |
| Full Idea: You gods say that the fault lies in the vices of mankind. But you could have endowed men with reason in a form which would exclude all vice and crime. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], III.76) |