45 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) |
23623 | Predicativism says only predicated sets exist [Hossack] |
Full Idea: Predicativists doubt the existence of sets with no predicative definition. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 02.3) | |
A reaction: This would imply that sets which encounter paradoxes when they try to be predicative do not therefore exist. Surely you can have a set of random objects which don't fall under a single predicate? |
23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
Full Idea: The iterative conception justifies Power Set, but cannot justify a satisfactory theory of von Neumann ordinals, so ZFC appropriates Replacement from NBG set theory. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
A reaction: The modern approach to axioms, where we want to prove something so we just add an axiom that does the job. |
23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
Full Idea: The limitation of size conception of sets justifies the axiom of Replacement, but cannot justify Power Set, so NBG set theory appropriates the Power Set axiom from ZFC. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
A reaction: Which suggests that the Power Set axiom is not as indispensable as it at first appears to be. |
23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
Full Idea: The sentence connective 'and' also has an order-sensitive meaning, when it means something like 'and then'. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.4) | |
A reaction: This is support the idea that orders are a feature of reality, just as much as possible concatenation. Relational predicates, he says, refer to series rather than to individuals. Nice point. |
23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
Full Idea: The reason the two predicates 'before' and 'after' are needed is not to express different relations, but to indicate its order. Since there can be difference of order without difference of relation, the nature of relations is not the source of order. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.3) | |
A reaction: This point is to refute Russell's 1903 claim that order arises from the nature of relations. Hossack claims that it is ordered series which are basic. I'm inclined to agree with him. |
23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
Full Idea: The transfinite ordinal numbers are important in the theory of proofs, and essential in the theory of recursive functions and computability. Mathematics would be incomplete without them. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.1) | |
A reaction: Hossack offers this as proof that the numbers are not human conceptual creations, but must exist beyond the range of our intellects. Hm. |
23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
Full Idea: I propose that numbers are properties, not sets. Magnitudes are a kind of property, and numbers are magnitudes. …Natural numbers are properties of pluralities, positive reals of continua, and ordinals of series. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro) | |
A reaction: Interesting! Since time can have a magnitude (three weeks) just as liquids can (three litres), it is not clear that there is a single natural property we can label 'magnitude'. Anything we can manage to measure has a magnitude. |
23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
Full Idea: Numbers cannot be mental objects constructed by our own minds: there exists at most a potential infinity of mental constructions, whereas the axioms of mathematics require an actual infinity of numbers. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro 2) | |
A reaction: Doubt this, but don't know enough to refute it. Actual infinities were a fairly late addition to maths, I think. I would think treating fictional complete infinities as real would be sufficient for the job. Like journeys which include imagined roads. |
16185 | Causality indicates which properties are real [Cartwright,N] |
Full Idea: Causality is a clue to what properties are real. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], 9.3) | |
A reaction: An interesting variant on the Shoemaker proposal that properties actually are causal. I'm not sure that there is anything more to causality that the expression in action of properties, which I take to be powers. Structures are not properties. |
16182 | Two main types of explanation are by causes, or by citing a theoretical framework [Cartwright,N] |
Full Idea: In explaining a phenomenon one can cite the causes of that phenomenon; or one can set the phenomenon in a general theoretical framework. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], 4.1) | |
A reaction: The thing is, you need to root an explanation in something taken as basic, and theoretical frameworks need further explanation, whereas causes seem to be basic. |
16184 | An explanation is a model that fits a theory and predicts the phenomenological laws [Cartwright,N] |
Full Idea: To explain a phenomenon is to find a model that fits it into the basic framework of the theory and that thus allows us to derive analogues for the messy and complicated phenomenological laws that are true of it. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], 8.3) | |
A reaction: This summarises the core of her view in this book. She is after models rather than laws, and the models are based on causes. |
16171 | The covering law view assumes that each phenomenon has a 'right' explanation [Cartwright,N] |
Full Idea: The covering-law account supposes that there is, in principle, one 'right' explanation for each phenomenon. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
A reaction: Presumably the law is held to be 'right', but there must be a bit of flexibility in describing the initial conditions, and the explanandum itself. |
16167 | Laws get the facts wrong, and explanation rests on improvements and qualifications of laws [Cartwright,N] |
Full Idea: We explain by ceteris paribus laws, by composition of causes, and by approximations that improve on what the fundamental laws dictate. In all of these cases the fundamental laws patently do not get the facts right. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
A reaction: It is rather headline-grabbing to say in this case that laws do not get the facts right. If they were actually 'wrong' and 'lied', there wouldn't be much point in building explanations on them. |
16169 | Laws apply to separate domains, but real explanations apply to intersecting domains [Cartwright,N] |
Full Idea: When different kinds of causes compose, we want to explain what happens in the intersection of different domains. But the laws we use are designed only to tell truly what happens in each domain separately. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
A reaction: Since presumably the laws are discovered through experiments which try to separate out a single domain, in those circumstances they actually are true, so they don't 'lie'. |
16176 | Covering-law explanation lets us explain storms by falling barometers [Cartwright,N] |
Full Idea: Much criticism of the original covering-law model objects that it lets in too much. It seems we can explain Henry's failure to get pregnant by his taking birth control pills, and we can explain the storm by the falling barometer. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.0) | |
A reaction: I take these examples to show that true explanations must be largely causal in character. The physicality of causation is what matters, not 'laws'. I'd say the same of attempts to account for causation through counterfactuals. |
16177 | I disagree with the covering-law view that there is a law to cover every single case [Cartwright,N] |
Full Idea: Covering-law theorists tend to think that nature is well-regulated; in the extreme, that there is a law to cover every case. I do not. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.2) | |
A reaction: The problem of coincidence is somewhere at the back of this thought. Innumerable events have their own explanations, but it is hard to explain their coincidence (see Aristotle's case of bumping into a friend in the market). |
16180 | You can't explain one quail's behaviour by just saying that all quails do it [Cartwright,N] |
Full Idea: 'Why does that quail in the garden bob its head up and down in that funny way whenever it walks?' …'Because they all do'. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], 3.5) | |
A reaction: She cites this as an old complaint against the covering-law model of explanation. It captures beautifully the basic error of the approach. We want to know 'why', rather than just have a description of the pattern. 'They all do' is useful information. |
16183 | In science, best explanations have regularly turned out to be false [Cartwright,N] |
Full Idea: There are a huge number of cases in the history of science where we now know our best explanations were false. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], 5.3) | |
A reaction: [She cites Laudan 1981 for this] The Ptolemaic system and aether are the standard example cited for this. I believe strongly in the importance of best explanation. Only a fool would just accept the best explanation available. Coherence is needed. |
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) |
16175 | A cause won't increase the effect frequency if other causes keep interfering [Cartwright,N] |
Full Idea: A cause ought to increase the frequency of the effect, but this fact may not show up in the probabilities if other causes are at work. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], 1.1) | |
A reaction: [She cites Patrick Suppes for this one] Presumably in experimental situations you can weed out the interference, but that threatens to eliminate mere 'probability' entirely. |
6781 | There are fundamental explanatory laws (false!), and phenomenological laws (regularities) [Cartwright,N, by Bird] |
Full Idea: Nancy Cartwright distinguishes between 'fundamental explanatory laws', which we should not believe, and 'phenomenological laws', which are regularities established on the basis of observation. | |
From: report of Nancy Cartwright (How the Laws of Physics Lie [1983]) by Alexander Bird - Philosophy of Science Ch.4 | |
A reaction: The distinction is helpful, so that we can be clearer about what everyone is claiming. We can probably all agree on the phenomenological laws, which are epistemological. Personally I claim truth for the best fundamental explanatory laws. |
16166 | Laws of appearances are 'phenomenological'; laws of reality are 'theoretical' [Cartwright,N] |
Full Idea: Philosophers distinguish phenomenological from theoretical laws. Phenomenological laws are about appearances; theoretical ones are about the reality behind the appearances. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
A reaction: I'm suspecting that Humeans only really believe in the phenomenological kind. I'm only interested in the theoretical kind, and I take inference to the best explanation to be the bridge between the two. Cartwright rejects the theoretical laws. |
16179 | Good organisation may not be true, and the truth may not organise very much [Cartwright,N] |
Full Idea: There is no reason to think that the principles that best organise will be true, nor that the principles that are true will organise much. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.5) | |
A reaction: This is aimed at the Mill-Ramsey-Lewis account of laws, as axiomatisations of the observed patterns in nature. |
16178 | There are few laws for when one theory meets another [Cartwright,N] |
Full Idea: Where theories intersect, laws are usually hard to come by. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.3) | |
A reaction: There are attempts at so-called 'bridge laws', to get from complex theories to simple ones, but her point is well made about theories on the same 'level'. |
16170 | To get from facts to equations, we need a prepared descriptions suited to mathematics [Cartwright,N] |
Full Idea: To get from a detailed factual knowledge of a situation to an equation, we must prepare the description of the situation to meet the mathematical needs of the theory. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
A reaction: She is clearly on to something here, as Galileo is blatantly wrong in his claim that the book of nature is written in mathematics. Mathematics is the best we can manage in getting a grip on the chaos. |
16181 | Simple laws have quite different outcomes when they act in combinations [Cartwright,N] |
Full Idea: For explanation simple laws must have the same form when they act together as when they act singly. ..But then what the law states cannot literally be true, for the consequences that occur if it acts alone are not what occurs when they act in combination. | |
From: Nancy Cartwright (How the Laws of Physics Lie [1983], 3.6) | |
A reaction: This is Cartwright's basic thesis. Her point is that the laws 'lie', because they claim to predict a particular outcome which never ever actually occurs. She says we could know all the laws, and still not be able to explain anything. |
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) |
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) |
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) |
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) |