48 ideas
| 8558 | One system has properties, powers, events, similarity and substance [Shoemaker] |
| Full Idea: There is a system of internally related concepts containing the notion of a property, the notion of a causal power, the concept of an event, the concept of similarity, and the concept of a persisting substance. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §07) | |
| A reaction: A nice example of a modern metaphysical system, one which I find fairly congenial. His notion of events is Kim's, which involves his properties. The persisting substance is the one I am least clear about. |
| 8559 | Analysis aims at internal relationships, not reduction [Shoemaker] |
| Full Idea: The goal of philosophical analysis should not be reductive analysis but rather the charting of internal relationships. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §07) | |
| A reaction: See Idea 8558 for an attempt by Shoemaker himself. The idea that there has never been a successful analysis has become a truism among pessimistic analytic philosophers. But there are wonderful relationship maps (Quine, Davidson, Lewis, Lowe). |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| Full Idea: On Zermelo's view, predicative definitions are not only indispensable to mathematics, but they are unobjectionable since they do not create the objects they define, but merely distinguish them from other objects. | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Shaughan Lavine - Understanding the Infinite V.1 | |
| A reaction: This seems to have an underlying platonism, that there are hitherto undefined 'objects' lying around awaiting the honour of being defined. Hm. |
| 17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
| Full Idea: Starting from set theory as it is historically given ...we must, on the one hand, restrict these principles sufficiently to exclude as contradiction and, on the other, take them sufficiently wide to retain all that is valuable in this theory. | |
| From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro) | |
| A reaction: Maddy calls this the one-step-back-from-disaster rule of thumb. Zermelo explicitly mentions the 'Russell antinomy' that blocked Frege's approach to sets. |
| 17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
| Full Idea: Set theory is that branch whose task is to investigate mathematically the fundamental notions 'number', 'order', and 'function', taking them in their pristine, simple form, and to develop thereby the logical foundations of all of arithmetic and analysis. | |
| From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro) | |
| A reaction: At this point Zermelo seems to be a logicist. Right from the start set theory was meant to be foundational to mathematics, and not just a study of the logic of collections. |
| 10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
| Full Idea: Zermelo-Fraenkel axioms: Existence (at least one set); Extension (same elements, same set); Specification (a condition creates a new set); Pairing (two sets make a set); Unions; Powers (all subsets make a set); Infinity (set of successors); Choice | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15 |
| 13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
| Full Idea: Zermelo proposed his listed of assumptions (including the controversial Axiom of Choice) in 1908, in order to secure his controversial proof of Cantor's claim that ' we can always bring any well-defined set into the form of a well-ordered set'. | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1 | |
| A reaction: This is interesting because it sometimes looks as if axiom systems are just a way of tidying things up. Presumably it is essential to get people to accept the axioms in their own right, the 'old-fashioned' approach that they be self-evident. |
| 17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
| Full Idea: I intend to show how the entire theory created by Cantor and Dedekind can be reduced to a few definitions and seven principles, or axioms, which appear to be mutually independent. | |
| From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro) | |
| A reaction: The number of axioms crept up to nine or ten in subsequent years. The point of axioms is maximum reduction and independence from one another. He says nothing about self-evidence (though Boolos claimed a degree of that). |
| 13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
| Full Idea: Zermelo's Pairing Axiom superseded (in 1930) his original 1908 Axiom of Elementary Sets. Like Union, its only justification seems to rest on 'limitations of size' and on the 'iterative conception'. | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.3 | |
| A reaction: Maddy says of this and Union, that they seem fairly obvious, but that their justification is of prime importance, if we are to understand what the axioms should be. |
| 13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
| Full Idea: Zermelo used a weak form of the Axiom of Foundation to block Russell's paradox in 1906, but in 1908 felt that the form of his Separation Axiom was enough by itself, and left the earlier axiom off his published list. | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.2 | |
| A reaction: Foundation turns out to be fairly controversial. Barwise actually proposes Anti-Foundation as an axiom. Foundation seems to be the rock upon which the iterative view of sets is built. Foundation blocks infinite descending chains of sets, and circularity. |
| 13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
| Full Idea: The most characteristic Zermelo axiom is Separation, guided by a new rule of thumb: 'one step back from disaster' - principles of set generation should be as strong as possible short of contradiction. | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.4 | |
| A reaction: Why is there an underlying assumption that we must have as many sets as possible? We are then tempted to abolish axioms like Foundation, so that we can have even more sets! |
| 13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
| Full Idea: Zermelo assumes that not every predicate has an extension but rather that given a set we may separate out from it those of its members satisfying the predicate. This is called 'separation' (Aussonderung). | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by William D. Hart - The Evolution of Logic 3 |
| 13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
| Full Idea: In Zermelo's set theory, the Burali-Forti Paradox becomes a proof that there is no set of all ordinals (so 'is an ordinal' has no extension). | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by William D. Hart - The Evolution of Logic 3 |
| 18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
| Full Idea: For Zermelo the successor of n is {n} (rather than Von Neumann's successor, which is n U {n}). | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Naturalism in Mathematics I.2 n8 | |
| A reaction: I could ask some naive questions about the comparison of these two, but I am too shy about revealing my ignorance. |
| 13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
| Full Idea: Zermelo was a reductionist, and believed that theorems purportedly about numbers (cardinal or ordinal) are really about sets, and since Von Neumann's definitions of ordinals and cardinals as sets, this has become common doctrine. | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.8 | |
| A reaction: Frege has a more sophisticated take on this approach. It may just be an updating of the Greek idea that arithmetic is about treating many things as a unit. A set bestows an identity on a group, and that is all that is needed. |
| 9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
| Full Idea: In Zermelo's set-theoretic definition of number, 2 is a member of 3, but not a member of 4; in Von Neumann's definition every number is a member of every larger number. This means they have two different structures. | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by James Robert Brown - Philosophy of Mathematics Ch. 4 | |
| A reaction: This refers back to the dilemma highlighted by Benacerraf, which was supposed to be the motivation for structuralism. My intuition says that the best answer is that they are both wrong. In a pattern, the nodes aren't 'members' of one another. |
| 15092 | Formerly I said properties are individuated by essential causal powers and causing instantiation [Shoemaker, by Shoemaker] |
| Full Idea: My 1980 paper said properties are individuated by causal features - the contribution they make to the causal powers of things, and also how their instantiation can be caused. Collectively, these causal features are the essence of a property. | |
| From: report of Sydney Shoemaker (Causality and Properties [1980], I) by Sydney Shoemaker - Causal and Metaphysical Necessity | |
| A reaction: The later paper worries about uncertainty over individuation. The view I favour is that 'powers' is a much better term for what is basic, and this allows 'properties' to be the complex notion we use in real life, as innumberable power-combinations. |
| 8543 | Genuine properties are closely related to genuine changes [Shoemaker] |
| Full Idea: Our intuitions as to what are, and what are not, genuine properties are closely related to our intuitions as to what are, and what are not, genuine changes. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §02) | |
| A reaction: A simple but brilliant insight. Somehow we must hack through the plethora of bogus properties and get to the real ones, cutting nature at the joints. Here we have the principle needed for the task. |
| 8551 | Properties must be essentially causal if we can know and speak about them [Shoemaker] |
| Full Idea: Only if some causal theory of properties is true can it be explained how properties are capable of engaging our knowledge, and our language, in the way they do. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §05) | |
| A reaction: Exactly. This also the reason why epiphenomenalism doesn't make sense about consciousness (Idea 7379). The fact that something has causal powers doesn't mean that it just IS a causal power. A bomb isn't an explosion. |
| 8557 | To ascertain genuine properties, examine the object directly [Shoemaker] |
| Full Idea: There is a plausible way of distinguishing genuine and mere-Cambridge properties. To decide whether an emerald is green the thing to do is to examine it, but a mere-Cambridge property is settled by observations at a remote time and place. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §06) | |
| A reaction: Scientific essentialism is beautifully simple! Schoemaker is good at connecting the epistemology to the ontology. If you examined a mirror, you might think it contained reflections. |
| 15761 | We should abandon the idea that properties are the meanings of predicate expressions [Shoemaker] |
| Full Idea: I think we should abandon the idea that properties are the meanings of predicate expressions. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §04) | |
| A reaction: Right. I have Shoemaker on my side, and he is a distinguished and senior member of the philosophical community. I don't just prefer not to use 'predicate' and 'property' indistinguishably - philosophers should really really give it up! |
| 15756 | Some truths are not because of a thing's properties, but because of the properties of related things [Shoemaker] |
| Full Idea: Sometimes a predicate is true of a thing, not because (or only because) of any properties it has, but because something else, perhaps something related to it in certain ways, has certain properties. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §02) | |
| A reaction: I'm on mission to prize predicates and properties apart, and the strategy is to focus on what is true of something, given that this may not ascribe a property to the thing. |
| 15758 | Things have powers in virtue of (which are entailed by) their properties [Shoemaker] |
| Full Idea: There is a distinction between powers, and the properties in virtue of which things have they powers they have (n8: 'in virtue of' means that there is a lawlike truth, which turns out to be the properties entailing the powers). | |
| From: Sydney Shoemaker (Causality and Properties [1980], §03) | |
| A reaction: To me this is an ontology which rests something very clear (a power) on something very indeterminate (a 'property'). |
| 8547 | One power can come from different properties; a thing's powers come from its properties [Shoemaker] |
| Full Idea: It is possible to have the same power (e.g. being poisonous) in virtue of having very different properties. ..So it is in virtue of a thing's properties that the thing has the powers that it has. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §03) | |
| A reaction: This strikes me as an accurate and helpful picture. It means that true properties give rise to powers, and categorial or relational or whimsical properties must have their ontological status judged by that standard. |
| 8549 | Properties are functions producing powers, and powers are functions producing effects [Shoemaker] |
| Full Idea: Powers are functions from circumstances to causal effects, and properties (on which powers depend) can be thought of as functions from sets of properties to sets of powers. Maybe we should call properties 'second-order powers', as they produce powers. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §04) | |
| A reaction: He presents property as both a function, and a component of the function. This is the core picture on which modern scientific essentialism is built. See under Natural Theory|Laws of Nature. |
| 12678 | Shoemaker says all genuine properties are dispositional [Shoemaker, by Ellis] |
| Full Idea: I am against Shoemaker's strong dispositionalism, according to which all genuine properties are dispositional. | |
| From: report of Sydney Shoemaker (Causality and Properties [1980]) by Brian Ellis - The Metaphysics of Scientific Realism 3 | |
| A reaction: This is because Ellis argues that some properties are categorical, and are needed to underly the active dispositional ones. I think I side with Shoemaker, but this needs more thought. |
| 8545 | A causal theory of properties focuses on change, not (say) on abstract properties of numbers [Shoemaker] |
| Full Idea: My account of properties concerns those with respect to which change is possible; it is not intended to apply to such properties of numbers as being even and being prime. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §02) | |
| A reaction: You could argue that while these properties may not cause change, they are abstract powers. Being even allows division by 2, and being prime blocks it. I say patterns are the basis, and dividing groups of physical objects is involved. |
| 15757 | 'Square', 'round' and 'made of copper' show that not all properties are dispositional [Shoemaker] |
| Full Idea: Surely we make a distinction beween dispositional and nondispositional properties, and can mention paradigms of both sorts. ....It seems plain that predicates like 'square', 'round' and 'made of copper' are not dispositional. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §03) | |
| A reaction: It might be possible to account for squareness and roundness in dispositional ways, and it is certainly plausible to say that 'made of copper' is not a property (even when it is a true predicate). |
| 15759 | The identity of a property concerns its causal powers [Shoemaker] |
| Full Idea: What makes a property the property it is, what determines its identity, is its potential for contributing to the causal powers of the things that have it. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §04) | |
| A reaction: Does this mean that the 'potential' to act is the essence of the property, or is a property of the property, or is wholly identical with the property? Or is this just epistemological - whatever individuates the property for observers? |
| 15760 | Properties are clusters of conditional powers [Shoemaker] |
| Full Idea: A thing has a 'conditional power' when it has a power conditionally upon the possession of certain properties. ...We can then express my view by saying that properties are clusters of conditional powers. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §04) | |
| A reaction: His example is a knife-shaped thing, which conditionally cuts wood if it is made of steel. Shoemaker rejected this in 1998. Mumford/Anjum prefer the earlier view. Which is fundamental? Powers are simple and primitive. Properties are complex. |
| 15762 | Could properties change without the powers changing, or powers change without the properties changing? [Shoemaker] |
| Full Idea: Could a thing undergo radical change with respect to its properties without undergoing any change in its causal powers, or undergo radical change in its causal powers without undergoing any change in the properties that underlie these powers? | |
| From: Sydney Shoemaker (Causality and Properties [1980], §05) | |
| A reaction: I don't accept properties underlying powers, but these two questions at least force us to see how closely the two are linked. |
| 8552 | If properties are separated from causal powers, this invites total elimination [Shoemaker] |
| Full Idea: The disassociation of property identity from causal potentiality is an invitation to eliminate reference to properties from our explanatory hypotheses altogether. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §05) | |
| A reaction: Just as epiphenomenalism about consciousness is a step towards eliminativism. This seems to describe Quine's reaction to Goodman, in moving from predicate nominalism to elimination of properties. I agree with Shoemaker. |
| 4040 | The notions of property and of causal power are parts of a single system of related concepts [Shoemaker] |
| Full Idea: The notion of a property and the notion of a causal power belong to a system of internally related concepts, no one of which can be explicated without the use of the other. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §07) | |
| A reaction: Sounds good. It is hard to conceive of a property which has no causal powers, or a causal power that doesn't arise from a property. |
| 15765 | Actually, properties are individuated by causes as well as effects [Shoemaker] |
| Full Idea: I should probably modify my view, and say that properties are individuated by their possible causes as well as by their possible effects. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §11) | |
| A reaction: (This is in an afterword responding to criticism by Richard Boyd) He doesn't use the word 'individuate' in the essay. That term always strikes me as smacking too much of epistemology, and not enough of ontology. Who cares how you individuate something? |
| 8548 | Dispositional predicates ascribe powers, and the rest ascribe properties [Shoemaker] |
| Full Idea: By and large, dispositional predicates ascribe powers while nondispositional monadic predicates ascribe properties that are not powers in the same sense. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §03) | |
| A reaction: The powers are where the properties come into contact with the rest of the world, so you would expect dispositions to be found at that level, rather than at the deeper level of properties. Sounds good to me. |
| 9485 | Universals concern how things are, and how they could be [Shoemaker, by Bird] |
| Full Idea: Shoemaker contends that universals concern the way things could be, not merely the way any things actually are. | |
| From: report of Sydney Shoemaker (Causality and Properties [1980]) by Alexander Bird - Nature's Metaphysics 3.2.2 | |
| A reaction: If you want to retain universals within a scientific essentialist view (and I would rather not), then this seems like the only way to go. |
| 8550 | Triangular and trilateral are coextensive, but different concepts; but powers and properties are the same [Shoemaker] |
| Full Idea: It is natural to say that 'being triangular' and 'being trilateral', though necessarily coextensive, are different properties. But what are distinct are the concepts and meanings. If properties are not meanings of predicates, these are identical. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §04) | |
| A reaction: A good test example. Being renate (kidney) and being cordate (heart) are different, because being cordate produces a thumping noise. Shoemaker's example is pretty much Phosphorus/Hesperus. |
| 8555 | There is no subset of properties which guarantee a thing's identity [Shoemaker] |
| Full Idea: There is, putting aside historical properties and 'identity properties', no subset of the properties of a thing which constitutes an individual essence, so that having those properties is necessary and sufficient for being that particular thing. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §05) | |
| A reaction: He asserts this rather dogmatically. If he says a thing can lose its essence, I agree, but it seems to me that there must be a group of features which will guarantee that (if they are present) it has that identity. |
| 8554 | Possible difference across worlds depends on difference across time in the actual world [Shoemaker] |
| Full Idea: The ways in which a given thing can be different in different possible worlds depend on the ways in which such a thing can be different at different times in the actual world. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §05) | |
| A reaction: Where change in a thing is possible across time in the actual world seems to require a combination of experiment and imagination. Unimaginability does not entail necessity, but it may be the best guide we have got. |
| 15764 | 'Conceivable' is either not-provably-false, or compatible with what we know? [Shoemaker] |
| Full Idea: We could use 'conceivable' to say it is not provable that it is not the case, or we could use it to say that it is compatible with what we know. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §10) | |
| A reaction: Rather significant, since the first one would seem to allow in a great deal that the second one would rule out. Any disproof of some natural possibility founders on the remark that 'you never know'. |
| 8562 | It is possible to conceive what is not possible [Shoemaker] |
| Full Idea: It is possible to conceive what is not possible. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §10) | |
| A reaction: The point here is that, while we cannot clearly conceive the impossible in a world like mathematics, we can conceive of impossible perceptions in the physical world, such as a bonfire burning under water. |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |
| 8556 | Grueness is not, unlike green and blue, associated with causal potential [Shoemaker] |
| Full Idea: Grueness, as defined by Goodman, is not associated in the way greenness and blueness are with causal potentialities. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §06) | |
| A reaction: Expressed rather more simply in Idea 7296. 'Grue' is a characteristic production of a predicate nominalist (i.e. Goodman), and that theory is just wrong. The account of properties must mesh with the account of induction. |
| 8542 | If causality is between events, there must be reference to the properties involved [Shoemaker] |
| Full Idea: Any account of causality as a relation between events should involve, in a central way, reference to the properties of the constituent objects of the events. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §01) | |
| A reaction: This remark, with which I wholeheartedly agree, is aimed at Davidson, who seems to think you need know no more about an event than the way in which someone chooses to describe it. Metaphysics must dig deeper, even if science can't. |
| 8560 | If causal laws describe causal potentialities, the same laws govern properties in all possible worlds [Shoemaker] |
| Full Idea: To the extent that causal laws can be viewed as propositions describing the causal potentialities of properties, it is impossible that the same properties should be governed by different causal laws in different possible worlds. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §08) | |
| A reaction: [He has just asserted that causal potentialities are essential to properties] This is the dramatic basic claim of scientific essentialism, which grows out of Shoemaker's causal account of properties. Note that the laws are just descriptions. |
| 15763 | If properties are causal, then causal necessity is a species of logical necessity [Shoemaker] |
| Full Idea: My theory of properties as causal appears to have the consequence that causal laws are logically necessary, and that causal necessity is just a species of logical necessity. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §09) | |
| A reaction: Where he writes 'logical' necessity I would claim that he really means 'metaphysical' necessity. The point, I take it, is that given the existence of those properties, certain causal efforts must always follow from them. I agree. |
| 8561 | If a world has different causal laws, it must have different properties [Shoemaker] |
| Full Idea: If there are worlds in which the causal laws are different from those that prevail in this world, ..then the properties will have to be different as well. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §09) | |
| A reaction: The next question is whether the same stuff (e.g. gold or water) could have different properties, and I take the the scientific essentialism answer to be 'no'. So the actual stuff (substances?) would have to be different. |
| 8553 | It looks as if the immutability of the powers of a property imply essentiality [Shoemaker] |
| Full Idea: There is a prima facie case for saying that the immutability of the causal potentialities of a property implies their essentiality. ...If they cannot vary across time, they also cannot vary across possible worlds. | |
| From: Sydney Shoemaker (Causality and Properties [1980], §05) | |
| A reaction: This is only the beginning of scientific essentialism, but one of the targets is to save the phenomena. It is also involves unimaginability (of different powers from a given property) implying necessity. |