84 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). |
| 13634 | Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro] |
| Full Idea: In a sense, satisfaction is the notion of 'truth in a model', and (as Hodes 1984 elegantly puts it) 'truth in a model' is a model of 'truth'. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: So we can say that Tarski doesn't offer a definition of truth itself, but replaces it with a 'model' of truth. |
| 13643 | Aristotelian logic is complete [Shapiro] |
| Full Idea: Aristotelian logic is complete. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.5) | |
| A reaction: [He cites Corcoran 1972] |
| 13651 | A set is 'transitive' if contains every member of each of its members [Shapiro] |
| Full Idea: If, for every b∈d, a∈b entails that a∈d, the d is said to be 'transitive'. In other words, d is transitive if it contains every member of each of its members. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.2) | |
| A reaction: The alternative would be that the members of the set are subsets, but the members of those subsets are not themselves members of the higher-level set. |
| 13647 | Choice is essential for proving downward Löwenheim-Skolem [Shapiro] |
| Full Idea: The axiom of choice is essential for proving the downward Löwenheim-Skolem Theorem. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) |
| 13631 | Are sets part of logic, or part of mathematics? [Shapiro] |
| Full Idea: Is there a notion of set in the jurisdiction of logic, or does it belong to mathematics proper? | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: It immediately strikes me that they might be neither. I don't see that relations between well-defined groups of things must involve number, and I don't see that mapping the relations must intrinsically involve logical consequence or inference. |
| 13654 | It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro] |
| Full Idea: In set theory it is central to the iterative conception that the membership relation is well-founded, ...which means there are no infinite descending chains from any relation. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.4) |
| 13640 | Russell's paradox shows that there are classes which are not iterative sets [Shapiro] |
| Full Idea: The argument behind Russell's paradox shows that in set theory there are logical sets (i.e. classes) that are not iterative sets. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.3) | |
| A reaction: In his preface, Shapiro expresses doubts about the idea of a 'logical set'. Hence the theorists like the iterative hierarchy because it is well-founded and under control, not because it is comprehensive in scope. See all of pp.19-20. |
| 13666 | Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro] |
| Full Idea: Iterative sets do not exhibit a Boolean structure, because the complement of an iterative set is not itself an iterative set. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) |
| 13653 | 'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro] |
| Full Idea: A 'well-ordering' of a set X is an irreflexive, transitive, and binary relation on X in which every non-empty subset of X has a least element. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.3) | |
| A reaction: So there is a beginning, an ongoing sequence, and no retracing of steps. |
| 13627 | There is no 'correct' logic for natural languages [Shapiro] |
| Full Idea: There is no question of finding the 'correct' or 'true' logic underlying a part of natural language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: One needs the context of Shapiro's defence of second-order logic to see his reasons for this. Call me romantic, but I retain faith that there is one true logic. The Kennedy Assassination problem - can't see the truth because drowning in evidence. |
| 13642 | Logic is the ideal for learning new propositions on the basis of others [Shapiro] |
| Full Idea: A logic can be seen as the ideal of what may be called 'relative justification', the process of coming to know some propositions on the basis of others. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.3.1) | |
| A reaction: This seems to be the modern idea of logic, as opposed to identification of a set of 'logical truths' from which eternal necessities (such as mathematics) can be derived. 'Know' implies that they are true - which conclusions may not be. |
| 13668 | Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro] |
| Full Idea: Bernays (1918) formulated and proved the completeness of propositional logic, the first precise solution as part of the Hilbert programme. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.1) |
| 13669 | Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro] |
| Full Idea: In 1910 Weyl observed that set theory seemed to presuppose natural numbers, and he regarded numbers as more fundamental than sets, as did Fraenkel. Dedekind had developed set theory independently, and used it to formulate numbers. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.2) |
| 13667 | Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro] |
| Full Idea: Skolem and Gödel were the main proponents of first-order languages. The higher-order language 'opposition' was championed by Zermelo, Hilbert, and Bernays. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2) |
| 13662 | First-order logic was an afterthought in the development of modern logic [Shapiro] |
| Full Idea: Almost all the systems developed in the first part of the twentieth century are higher-order; first-order logic was an afterthought. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) |
| 13624 | The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro] |
| Full Idea: The 'triumph' of first-order logic may be related to the remnants of failed foundationalist programmes early this century - logicism and the Hilbert programme. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: Being complete must also be one of its attractions, and Quine seems to like it because of its minimal ontological commitment. |
| 13660 | Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro] |
| Full Idea: Tharp (1975) suggested that compactness, semantic effectiveness, and the Löwenheim-Skolem properties are consequences of features one would want a logic to have. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: I like this proposal, though Shapiro is strongly against. We keep extending our logic so that we can prove new things, but why should we assume that we can prove everything? That's just what Gödel suggests that we should give up on. |
| 13673 | The notion of finitude is actually built into first-order languages [Shapiro] |
| Full Idea: The notion of finitude is explicitly 'built in' to the systems of first-order languages in one way or another. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1) | |
| A reaction: Personally I am inclined to think that they are none the worse for that. No one had even thought of all these lovely infinities before 1870, and now we are supposed to change our logic (our actual logic!) to accommodate them. Cf quantum logic. |
| 15944 | Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine] |
| Full Idea: Shapiro preferred second-order logic to set theory because second-order logic refers only to the relations and operations in a domain, and not to the other things that set-theory brings with it - other domains, higher-order relations, and so forth. | |
| From: report of Stewart Shapiro (Foundations without Foundationalism [1991]) by Shaughan Lavine - Understanding the Infinite VII.4 |
| 13629 | Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro] |
| Full Idea: Three systems of semantics for second-order languages: 'standard semantics' (variables cover all relations and functions), 'Henkin semantics' (relations and functions are a subclass) and 'first-order semantics' (many-sorted domains for variable-types). | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: [my summary] |
| 13650 | Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro] |
|
Full Idea:
In 'Henkin' semantics, in a given model |
|
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 3.3) |
| 13645 | In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro] |
| Full Idea: In the standard semantics of second-order logic, by fixing a domain one thereby fixes the range of both the first-order variables and the second-order variables. There is no further 'interpreting' to be done. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 3.3) | |
| A reaction: This contrasts with 'Henkin' semantics (Idea 13650), or first-order semantics, which involve more than one domain of quantification. |
| 13649 | Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro] |
| Full Idea: The counterparts of Completeness, Compactness and the Löwenheim-Skolem theorems all fail for second-order languages with standard semantics, but hold for Henkin or first-order semantics. Hence such logics are much like first-order logic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: Shapiro votes for the standard semantics, because he wants the greater expressive power, especially for the characterization of infinite structures. |
| 13626 | Semantic consequence is ineffective in second-order logic [Shapiro] |
| Full Idea: It follows from Gödel's incompleteness theorem that the semantic consequence relation of second-order logic is not effective. For example, the set of logical truths of any second-order logic is not recursively enumerable. It is not even arithmetic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: I don't fully understand this, but it sounds rather major, and a good reason to avoid second-order logic (despite Shapiro's proselytising). See Peter Smith on 'effectively enumerable'. |
| 13637 | If a logic is incomplete, its semantic consequence relation is not effective [Shapiro] |
| Full Idea: Second-order logic is inherently incomplete, so its semantic consequence relation is not effective. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1) |
| 13632 | Finding the logical form of a sentence is difficult, and there are no criteria of correctness [Shapiro] |
| Full Idea: It is sometimes difficult to find a formula that is a suitable counterpart of a particular sentence of natural language, and there is no acclaimed criterion for what counts as a good, or even acceptable, 'translation'. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) |
| 13674 | We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro] |
| Full Idea: The main role of substitutional semantics is to reduce ontology. As an alternative to model-theoretic semantics for formal languages, the idea is to replace the 'satisfaction' relation of formulas (by objects) with the 'truth' of sentences (using terms). | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) | |
| A reaction: I find this very appealing, and Ruth Barcan Marcus is the person to look at. My intuition is that logic should have no ontology at all, as it is just about how inference works, not about how things are. Shapiro offers a compromise. |
| 13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
| Full Idea: The 'satisfaction' relation may be thought of as a function from models, assignments, and formulas to the truth values {true,false}. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: This at least makes clear that satisfaction is not the same as truth. Now you have to understand how Tarski can define truth in terms of satisfaction. |
| 13644 | Semantics for models uses set-theory [Shapiro] |
| Full Idea: Typically, model-theoretic semantics is formulated in set theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.5.1) |
| 13636 | An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro] |
| Full Idea: An axiomatization is 'categorical' if all its models are isomorphic to one another; ..hence it has 'essentially only one' interpretation [Veblen 1904]. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1) |
| 13670 | Categoricity can't be reached in a first-order language [Shapiro] |
| Full Idea: Categoricity cannot be attained in a first-order language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.3) |
| 13658 | Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro] |
| Full Idea: A language has the Downward Löwenheim-Skolem property if each satisfiable countable set of sentences has a model whose domain is at most countable. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: This means you can't employ an infinite model to represent a fact about a countable set. |
| 13659 | Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro] |
| Full Idea: A language has the Upward Löwenheim-Skolem property if for each set of sentences whose model has an infinite domain, then it has a model at least as big as each infinite cardinal. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: This means you can't have a countable model to represent a fact about infinite sets. |
| 13648 | The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro] |
| Full Idea: The Löwenheim-Skolem theorems mean that no first-order theory with an infinite model is categorical. If Γ has an infinite model, then it has a model of every infinite cardinality. So first-order languages cannot characterize infinite structures. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: So much of the debate about different logics hinges on characterizing 'infinite structures' - whatever they are! Shapiro is a leading structuralist in mathematics, so he wants second-order logic to help with his project. |
| 13675 | Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro] |
| Full Idea: The Upward Löwenheim-Skolem theorem fails (trivially) with substitutional semantics. If there are only countably many terms of the language, then there are no uncountable substitution models. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) | |
| A reaction: Better and better. See Idea 13674. Why postulate more objects than you can possibly name? I'm even suspicious of all real numbers, because you can't properly define them in finite terms. Shapiro objects that the uncountable can't be characterized. |
| 13635 | 'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro] |
| Full Idea: A logic is 'weakly sound' if every theorem is a logical truth, and 'strongly sound', or simply 'sound', if every deduction from Γ is a semantic consequence of Γ. Soundness indicates that the deductive system is faithful to the semantics. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: Similarly, 'weakly complete' is when every logical truth is a theorem. |
| 13628 | We can live well without completeness in logic [Shapiro] |
| Full Idea: We can live without completeness in logic, and live well. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: This is the kind of heady suggestion that American philosophers love to make. Sounds OK to me, though. Our ability to draw good inferences should be expected to outrun our ability to actually prove them. Completeness is for wimps. |
| 13630 | Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro] |
| Full Idea: It is sometimes said that non-compactness is a defect of second-order logic, but it is a consequence of a crucial strength - its ability to give categorical characterisations of infinite structures. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: The dispute between fans of first- and second-order may hinge on their attitude to the infinite. I note that Skolem, who was not keen on the infinite, stuck to first-order. Should we launch a new Skolemite Crusade? |
| 13646 | Compactness is derived from soundness and completeness [Shapiro] |
| Full Idea: Compactness is a corollary of soundness and completeness. If Γ is not satisfiable, then, by completeness, Γ is not consistent. But the deductions contain only finite premises. So a finite subset shows the inconsistency. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: [this is abbreviated, but a proof of compactness] Since all worthwhile logics are sound, this effectively means that completeness entails compactness. |
| 13661 | A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro] |
| Full Idea: A logical language is 'semantically effective' if the collection of logically true sentences is a recursively enumerable set of strings. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) |
| 13641 | Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro] |
| Full Idea: 'Definitions' of integers as pairs of naturals, rationals as pairs of integers, reals as Cauchy sequences of rationals, and complex numbers as pairs of reals are reductive foundations of various fields. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.1) | |
| A reaction: On p.30 (bottom) Shapiro objects that in the process of reduction the numbers acquire properties they didn't have before. |
| 13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
| Full Idea: The main problem of characterizing the natural numbers is to state, somehow, that 0,1,2,.... are all the numbers that there are. We have seen that this can be accomplished with a higher-order language, but not in a first-order language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) |
| 13677 | Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro] |
| Full Idea: By convention, the natural numbers are the finite ordinals, the integers are certain equivalence classes of pairs of finite ordinals, etc. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.3) |
| 13652 | The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro] |
| Full Idea: The 'continuum' is the cardinality of the powerset of a denumerably infinite set. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.2) |
| 13657 | First-order arithmetic can't even represent basic number theory [Shapiro] |
| Full Idea: Few theorists consider first-order arithmetic to be an adequate representation of even basic number theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5 n28) | |
| A reaction: This will be because of Idea 13656. Even 'basic' number theory will include all sorts of vast infinities, and that seems to be where the trouble is. |
| 13656 | Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro] |
| Full Idea: There are sets of natural numbers definable in set-theory but not in arithmetic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.3.3) |
| 13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
| Full Idea: It is claimed that aiming at a universal language for all contexts, and the thesis that logic does not involve a process of abstraction, separates the logicists from algebraists and mathematicians, and also from modern model theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) | |
| A reaction: I am intuitively drawn to the idea that logic is essentially the result of a series of abstractions, so this gives me a further reason not to be a logicist. Shapiro cites Goldfarb 1979 and van Heijenoort 1967. Logicists reduce abstraction to logic. |
| 13625 | Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro] |
| Full Idea: I extend Quinean holism to logic itself; there is no sharp border between mathematics and logic, especially the logic of mathematics. One cannot expect to do logic without incorporating some mathematics and accepting at least some of its ontology. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: I have strong sales resistance to this proposal. Mathematics may have hijacked logic and warped it for its own evil purposes, but if logic is just the study of inferences then it must be more general than to apply specifically to mathematics. |
| 13663 | Some reject formal properties if they are not defined, or defined impredicatively [Shapiro] |
| Full Idea: Some authors (Poincaré and Russell, for example) were disposed to reject properties that are not definable, or are definable only impredicatively. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) | |
| A reaction: I take Quine to be the culmination of this line of thought, with his general rejection of 'attributes' in logic and in metaphysics. |
| 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. |
| 13638 | Properties are often seen as intensional; equiangular and equilateral are different, despite identity of objects [Shapiro] |
| Full Idea: Properties are often taken to be intensional; equiangular and equilateral are thought to be different properties of triangles, even though any triangle is equilateral if and only if it is equiangular. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.3) | |
| A reaction: Many logicians seem to want to treat properties as sets of objects (red being just the set of red things), but this looks like a desperate desire to say everything in first-order logic, where only objects are available to quantify over. |
| 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. |
| 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. |
| 5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |
| Full Idea: For Bradley, the happiness of the individual is not to be understood in terms of his desires and needs, but rather in terms of his values - which is to say, in terms of those of his desires which he incorporates into his self. | |
| From: report of F.H. Bradley (Ethical Studies [1876]) by Roger Scruton - Short History of Modern Philosophy Ch.16 | |
| A reaction: Good. Bentham will reduce the values to a further set of desires, so that a value is a complex (second-level?) desire. I prefer to think of values as judgements, but I like Scruton's phrase of 'incorporating into his self'. Kant take note (Idea 1452). |
| 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. |