26 ideas
| 19404 | Necessities rest on contradiction, and contingencies on sufficient reason [Leibniz] |
| Full Idea: The principle of contradiction is the principle of necessity, and the principle that a sufficient reason must be given is the principle of contingency. | |
| From: Gottfried Leibniz (On Sufficient Reason [1686], p.95) | |
| A reaction: [this paragraph is actually undated] Contradictions occur in concrete actuality, as well as in theories and formal systems. If so, then there are necessities in nature. Are they discoverable a posteriori? Leibniz says not. |
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| Full Idea: Frege rejected the traditional categories as importing psychological and linguistic impurities into logic. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Ian Rumfitt - The Boundary Stones of Thought 1.2 | |
| A reaction: Resisting such impurities is the main motivation for making logic entirely symbolic, but it doesn't follow that the traditional categories have to be dropped. |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| Full Idea: Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions. | |
| From: Gottlob Frege (Function and Concept [1891], p.38) | |
| A reaction: In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions. |
| 8492 | Relations are functions with two arguments [Frege] |
| Full Idea: Functions of one argument are concepts; functions of two arguments are relations. | |
| From: Gottlob Frege (Function and Concept [1891], p.39) | |
| A reaction: Nowadays we would say 'two or more'. Another interesting move in the aim of analytic philosophy to reduce the puzzling features of the world to mathematical logic. There is, of course, rather more to some relations than being two-argument functions. |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| Full Idea: I am of the opinion that arithmetic is a further development of logic, which leads to the requirement that the symbolic language of arithmetic must be expanded into a logical symbolism. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: This may the the one key idea at the heart of modern analytic philosophy (even though logicism may be a total mistake!). Logic and arithmetical foundations become the master of ontology, instead of the servant. The jury is out on the whole enterprise. |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| Full Idea: Frege regarded the existence of horses as a property of the concept 'horse'. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Fred Sommers - Intellectual Autobiography 'Realism' |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| Full Idea: Frege's theory of properties (which he calls 'concepts') yields too few properties, by identifying coextensive properties, and also too many, by letting every predicate express a property. | |
| From: comment on Gottlob Frege (Function and Concept [1891]) by DH Mellor / A Oliver - Introduction to 'Properties' §2 | |
| A reaction: Seems right; one extension may have two properties (have heart/kidneys), two predicates might express the same property. 'Cutting nature at the joints' covers properties as well as objects. |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| Full Idea: I regard a regular definition of 'object' as impossible, since it is too simple to admit of logical analysis. Briefly: an object is anything that is not a function, so that an expression for it does not contain any empty place. | |
| From: Gottlob Frege (Function and Concept [1891], p.32) | |
| A reaction: Here is the core of the programme for deriving our ontology from our logic and language, followed through by Russell and Quine. Once we extend objects beyond the physical, it becomes incredibly hard to individuate them. |
| 12790 | Generalisations must be invariant to explain anything [Leuridan] |
| Full Idea: A generalisation is explanatory if and only if it is invariant. | |
| From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §4) | |
| A reaction: [He cites Jim Woodward 2003] I dislike the idea that generalisations and regularities explain anything at all, but this rule sounds like a bare minimum for being taken seriously in the space of explanations. |
| 12789 | Biological functions are explained by disposition, or by causal role [Leuridan] |
| Full Idea: The main alternative to the dispositional theory of biological functions (which confer a survival-enhancing propensity) is the etiological theory (effects are functions if they play a role in the causal history of that very component). | |
| From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §3) | |
| A reaction: [Bigelow/Pargetter 1987 for the first, Mitchell 2003 for the second] The second one sounds a bit circular, but on the whole a I prefer causal explanations to dispositional explanations. |
| 14388 | Mechanisms must produce macro-level regularities, but that needs micro-level regularities [Leuridan] |
| Full Idea: Nothing can count as a mechanism unless it produces some macro-level regular behaviour. To produce macro-level regular behaviour, it has to rely on micro-level regularities. | |
| From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §5) | |
| A reaction: This is the core of Leuridan's argument that regularities are more basic than mechanisms. It doesn't follow, though, that the more basic a thing is the more explanatory work it can do. I say mechanisms explain more than low-level regularities do. |
| 12787 | Mechanisms can't explain on their own, as their models rest on pragmatic regularities [Leuridan] |
| Full Idea: To model a mechanism one must incorporate pragmatic laws. ...As valuable as the concept of mechanism and mechanistic explanation are, they cannot replace regularities nor undermine their relevance for scientific explanation. | |
| From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §1) | |
| A reaction: [See Idea 12786 for 'pragmatic laws'] I just don't see how the observation of a regularity is any sort of explanation. I just take a regularity to be something interesting which needs to be explained. |
| 14384 | We can show that regularities and pragmatic laws are more basic than mechanisms [Leuridan] |
| Full Idea: Summary: mechanisms depend on regularities, there may be regularities without mechanisms, models of mechanisms must incorporate pragmatic laws, and pragmatic laws do not depend epistemologically on mechanistic models. | |
| From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §1) | |
| A reaction: See Idea 14382 for 'pragmatic' laws. I'm quite keen on mechanisms, so this is an arrow close to the heart, but at this point I say that my ultimate allegiance is to powers, not to mechanisms. |
| 14386 | Mechanisms are ontologically dependent on regularities [Leuridan] |
| Full Idea: Mechanisms are ontologically dependent on the existence of regularities. | |
| From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §3) | |
| A reaction: This seems to be the Humean rearguard action in favour of the regularity account of laws. Wrong, but a nice paper. This point shows why only powers (despite their vagueness!) are the only candidate for the bottom level of explanation. |
| 14389 | There is nothing wrong with an infinite regress of mechanisms and regularities [Leuridan] |
| Full Idea: I see nothing metaphysically wrong in an infinite ontological regress of mechanisms and regularities. | |
| From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §5) | |
| A reaction: This is a pretty unusual view, and I can't accept it. My revulsion at this regress is precisely the reason why I believe in powers, as the bottom level of explanation. |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| Full Idea: Concepts, for Frege, are the ontological counterparts of predicative expressions. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: That sounds awfully like what many philosophers call 'universals'. Frege, as a platonist (at least about numbers), I would take to be in sympathy with that. At least we can say that concepts seem to be properties. |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| Full Idea: Frege had a notorious difficulty over the concept 'horse', when he suggests that if we wish to assert something about a concept, we are obliged to proceed indirectly by speaking of an object that represents it. | |
| From: report of Gottlob Frege (Function and Concept [1891], Ch.2.II) by Bob Hale - Abstract Objects | |
| A reaction: This sounds like the thin end of a wedge. The great champion of objects is forced to accept them here as a façon de parler, when elsewhere they have ontological status. |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| Full Idea: A concept in logic is closely connected with what we call a function. Indeed, we may say at once: a concept is a function whose value is always a truth-value. ..I give the name 'function' to what is meant by the 'unsaturated' part. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: So a function becomes a concept when the variable takes a value. Problems arise when the value is vague, or the truth-value is indeterminable. |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| Full Idea: For Frege, concepts differ from objects in being inherently incomplete in nature. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This is because they are 'unsaturated', needing a quantified variable to complete the sentence. This could be a pointer towards Quine's view of properties, as simply an intrinsic feature of predication about objects, with no separate identity. |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| Full Idea: From sameness of meaning there does not follow sameness of thought expressed. A fact about the Morning Star may express something different from a fact about the Evening Star, as someone may regard one as true and the other false. | |
| From: Gottlob Frege (Function and Concept [1891], p.14) | |
| A reaction: This all gets clearer if we distinguish internalist and externalist theories of content. Why take sides on this? Why not just ask 'what is in the speaker's head?', 'what does the sentence mean in the community?', and 'what is the corresponding situation?' |
| 14387 | Rather than dispositions, functions may be the element that brought a thing into existence [Leuridan] |
| Full Idea: The dispositional theory of biological functions is not unquestioned. The main alternative is the etiological theory: a component's effect is a function of that component if it has played an essential role in the causal history of its existence. | |
| From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §3) | |
| A reaction: [He cites S.D. Mitchell 2003] Presumably this account is meant to fit into a theory of evolution in biology. The obvious problem is where something comes into existence for one reason, and then acquires a new function (such as piano-playing). |
| 14382 | Pragmatic laws allow prediction and explanation, to the extent that reality is stable [Leuridan] |
| Full Idea: A generalization is a 'pragmatic law' if it allows of prediction, explanation and manipulation, even if it fails to satisfy the traditional criteria. To this end, it should describe a stable regularity, but not necessarily a universal and necessary one. | |
| From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §1) | |
| A reaction: I am tempted to say of this that all laws are pragmatic, given that it is rather hard to know whether reality is stable. The universal laws consist of saying that IF reality stays stable in certain ways, certain outcomes will ensue necessarily. |
| 14385 | Strict regularities are rarely discovered in life sciences [Leuridan] |
| Full Idea: Strict regularities are rarely if ever discovered in the life sciences. | |
| From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §2) | |
| A reaction: This is elementary once it is pointed out, but too much philosophy have science has aimed at the model provided by the equations of fundamental physics. Science is a broad church, to employ an entertaining metaphor. |
| 19403 | Each of the infinite possible worlds has its own laws, and the individuals contain those laws [Leibniz] |
| Full Idea: As there are an infinity of possible worlds, there are also an infinity of laws, some proper to one, another to another, and each possible individual of any world contains in its own notion the laws of its world. | |
| From: Gottfried Leibniz (On Sufficient Reason [1686], p.95) | |
| A reaction: Hence Leibniz is not really a scientific essentialist, in that he doesn't think the laws arise out of the nature of the matter consituting the world. I wonder if the primitive matter of bodies which attaches to the monads is the same in each world? |
| 14383 | A 'law of nature' is just a regularity, not some entity that causes the regularity [Leuridan] |
| Full Idea: By 'law of nature' or 'natural law' I mean a generalization describing a regularity, not some metaphysical entity that produces or is responsible for that regularity. | |
| From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §1 n1) | |
| A reaction: I take the second version to be a relic of a religious world view, and having no place in a naturalistic metaphysic. The regularity view is then the only player in the field, and the question is, can we do more? Can't we explain regularities? |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |
| Full Idea: The ontological proof of God's existence suffers from the fallacy of treating existence as a first-level concept. | |
| From: Gottlob Frege (Function and Concept [1891], p.38 n) | |
| A reaction: [See Idea 8490 for first- and second-order functions] This is usually summarised as the idea that existence is a quantifier rather than a predicate. |