36 ideas
12780 | We can grasp the wisdom of God a priori [Leibniz] |
Full Idea: We can grasp the wisdom of God a priori, and not from the order of the phenomena alone. ... For the senses put nothing forward concerning metaphysical matters. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
A reaction: Nice instance of the aspirations of big metaphysics, before Kant cut it down to size. The claim is not far off Plato's, that by dialectic we can work out the necessities of the Forms, to which even the gods must bow. Are necessities really kept from us? |
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) |
12774 | Without a substantial chain to link monads, they would just be coordinated dreams [Leibniz] |
Full Idea: If that substantial chain [vinculum substantiale] for monads did not exist, all bodies, together with all of their qualities, would be nothing but well-founded phenomena, like a rainbow or an image in a mirror, continual dreams perfectly in agreement. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1712.02.05) | |
A reaction: [The first appearance, apparently, of the 'susbtantial chain' in his writings] I take this to be a hugely significant move, either a defeat for monads, or the arrival of common sense. Spiritual monads must unify things, so they can't just be 'parallel'. |
12777 | Monads do not make a unity unless a substantial chain is added to them [Leibniz] |
Full Idea: Monads do not constitute a complete composite substance, since they make up, not something one per se, but only a mere aggregate, unless some substantial chain is added. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1712.05.26) | |
A reaction: This is the clearest statement in the Des Bosses letters of the need for something extra to unite monads. Since the main role of monads was to replace substances, which are only postulated to provide unity, this is rather a climb-down. |
12782 | Monads control nothing outside of themselves [Leibniz] |
Full Idea: Monads aren't a principle of operation for things outside of themselves. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
A reaction: This is why Leibniz has got into a tangle, and is proposing his 'substantial chain' to join the monads together. I suspect that he would have dumped monads if he had lived a bit longer. |
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. |
12778 | There is active and passive power in the substantial chain and in the essence of a composite [Leibniz] |
Full Idea: I do not say there is a chain midway between matter and form, but that the substantial form and primary matter of the composite, in the Scholastic sense (the primitive power, active and passive) are in the chain, and in the essence of the composite. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
A reaction: Note that this implies an essence of primitive power, and not just a collection of all properties. This is the clearest account in these letters of the nature of the 'substantial chain' he has added to his monads. |
12783 | Primitive force is what gives a composite its reality [Leibniz] |
Full Idea: The first entelechy of a composite is a constitutive part of the composite substance, namely its primitive force. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
A reaction: For me, Leibniz's most interesting proposal is to characterise Aristotelian 'form' as an active thing, which offers an intrinsic account of movement, and a bottom level for explanations. There always remains the inexplicable. Why anything? Why this? |
12775 | Things seem to be unified if we see duration, position, interaction and connection [Leibniz] |
Full Idea: Important relations are duration (order of successive things) and position (order of coexisting things) and interaction. Position without a thing mediating is presence. Beyond these is connection when things move one another. Thus things seem to be one. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1712.02.05) | |
A reaction: [compressed] This is the best account I can find of his epistemological angle on the unity of things. They are symptoms of the inner power of unification, and he says that God sees these relations most clearly. |
12776 | Every substance is alive [Leibniz] |
Full Idea: Every substance is alive. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1712.02.05) | |
A reaction: The most charitable interpretation of this is that substances are what have unity, and the best model of unity that we can grasp is the unity of an organism. The less charitable view is that he literally thinks a pebble is 'alive'. Hm. |
12753 | A substantial bond of powers is needed to unite composites, in addition to monads [Leibniz] |
Full Idea: Some realising thing must bring it about that composite substance contains something substantial besides monads, otherwise composites will be mere phenomena. The scholastics' active and passive powers are the substantial bond I am urging. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.01.13), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 9 | |
A reaction: [compressed] This appears to be a major retreat, in the last year of Leibniz's life, from the full monadology he had espoused. How do monads connect to matter, and thus unify it? He is returning to Aristotelian hylomorphism. |
12781 | A composite substance is a mere aggregate if its essence is just its parts [Leibniz] |
Full Idea: An aggregate, but not a composite substance, is resolved into parts. A composite substance only needs the coming together of parts, but is not essentially constituted by them, otherwise it would be an aggregate. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
A reaction: The point is that there is more to some things than there mere parts. Only some unifying principle, in addition to the mere parts, bestows a unity. Mereology is a limited activity if it has nothing to say about this issue. |
12779 | There is a reason why not every possible thing exists [Leibniz] |
Full Idea: There is a reason why not every possible thing exists. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
A reaction: This is the kind of wonderful speculative metaphysical remark that we are not allowed to make any more. Needless to say, he doesn't tell us what the reason is. Overcrowding, perhaps. |
12785 | Truth is mutually agreed perception [Leibniz] |
Full Idea: In the mutual agreement of perceivers consists the truth of the phenomena. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
A reaction: This remark is startling close to the 'perspectivism' that crops up in the late notebooks of Nietzsche. Leibniz was keen on relativism in many areas, starting with the nature of space. I personally think Leibniz meant 'knowledge' rather than 'truth'. |
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. |
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. |
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. |
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. |
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. |
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. |
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'. |
12784 | Allow no more miracles than are necessary [Leibniz] |
Full Idea: Miracles should not be increased beyond necessity. | |
From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
A reaction: Leibniz defends miracles (where Spinoza dismisses them). This remark is, of course, an echo of Ockham's Razor, that 'entities' should not be multiplied beyond necessity. It is hard to disagree with his proposal. Zero might be result, though. |