128 ideas
| 14912 | There is no test for metaphysics, except devising alternative theories [Ladyman/Ross] |
| Full Idea: The metaphysician has no test for the truth of her beliefs except that other metaphysicians can't think of obviously superior alternative beliefs. (They can always think of possibly superior ones, in profusion). | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.7) | |
| A reaction: [they cite Van Fraassen for this view] At least this seems to concede that some metaphysical views can be rejected by the observation of beliefs that are superior. Almost everyone has rejected Lewis on possible worlds for this reason. |
| 14904 | Metaphysics builds consilience networks across science [Ladyman/Ross] |
| Full Idea: Metaphysics is the enterprise of critically elucidating consilience networks across the sciences. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.3) | |
| A reaction: I don't disagree with this. The issue, I think, is how abstract you are prepared to go. At high levels of abstraction, it is very hard to keep in touch with the empirical research. There are truths, though, at that high level. It is clearest in logic. |
| 14907 | Progress in metaphysics must be tied to progress in science [Ladyman/Ross] |
| Full Idea: To the extent that metaphysics is closely motivated by science, we should expect to make progress in metaphysics iff we can expect to make progress in science. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.3) | |
| A reaction: To defer to and respect science does not necessitate that metaphysics cannot do independent work. I take there to be truths at a high-level of abstraction that are independent of the physical sciences, just as there are truths of chess or economics. |
| 14908 | Metaphysics must involve at least two scientific hypotheses, one fundamental, and add to explanation [Ladyman/Ross] |
| Full Idea: Principle of Naturalist Closure: A serious metaphysical claim must involve at least two scientific hypotheses, at least one from fundamental physics, and explain more than what the two hypotheses explain separately. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.3) | |
| A reaction: [compressed, from their longer qualified version] The idea that metaphysics should add to explanation is close to my heart. I am musing over whether essences add to explanation, which would be total anathema to Ladyman and Ross. |
| 14910 | Some science is so general that it is metaphysical [Ladyman/Ross] |
| Full Idea: Some scientific propositions are sufficiently general as themselves to be metaphysical. Our notion of metaphysics is thus recursive, and requires no attempt to identify a boundary between metaphysical and scientific propositions. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.5 n45) | |
| A reaction: Note that this still leaves room for some metaphysics which is not science, though see Idea 14904 for their views on that. |
| 14940 | Cutting-edge physics has little to offer metaphysics [Ladyman/Ross] |
| Full Idea: There is little positive by way of implications for metaphysics that we can adduce from cutting-edge physics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.2) | |
| A reaction: My personal suspicion is that this will always be the case, even though there may be huge advances in physics, and I offer that as a reason why metaphysicians do not (pace Ladyman and Ross) need to study physics. They grasp 'negative' lessons. |
| 14945 | The aim of metaphysics is to unite the special sciences with physics [Ladyman/Ross] |
| Full Idea: The demand to unify the special sciences with physics is, according to us, the motivation for having any metaphysics at all. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.1) | |
| A reaction: The crunch question is whether metaphysicians are allowed to develop their own concepts for this task, or whether they can only make links between the concepts employed by the scientists. I vote for the former. |
| 14898 | Modern metaphysics pursues aesthetic criteria like story-writing, and abandons scientific truth [Ladyman/Ross] |
| Full Idea: The criteria of adequacy for metaphysics have come apart from anything to do with truth. Rather they are internal and peculiar to philosophy, they are semi-aesthetic, and they have more in common with the virtues of story-writing than with science. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.1) | |
| A reaction: Part of a sustained polemic against contemporary analytic metaphysics. I love metaphysics, but they may be right. Writers like Sider, Fine, Lowe, Lewis, Stalnaker, Kripke, Armstrong, Dummett seem to tell independent stories, that really are works of art. |
| 14899 | Why think that conceptual analysis reveals reality, rather than just how people think? [Ladyman/Ross] |
| Full Idea: Why should we think that the products of conceptual analysis reveal anything about the deep structure of reality, rather than telling us about how some class of people think about and categorize reality? | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.2) | |
| A reaction: One line, associated with Jackson, is that analysis tells you not about reality, but about what to make of your experiences of reality when you have them. It would be a foolish scientist who paid no attention to his or her conceptual scheme. |
| 14936 | A metaphysics based on quantum gravity could result in almost anything [Ladyman/Ross] |
| Full Idea: We cannot say what the metaphysical implications of quantum gravity are, but they range from eleven dimensions to two, from continuous fundamental structure to a discrete one, and from universal symmetries to no symmetries. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.2) | |
| A reaction: I offer this observation as a good reason for doubting whether the project of building our metaphysics directly onto our fundamental physics has much prospect of success. Quantum gravity is the unified theory they are all hoping for. |
| 14905 | The supremacy of science rests on its iterated error filters [Ladyman/Ross] |
| Full Idea: The epistemic supremacy of science rests on repeated iteration of institutional error filters. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.3) | |
| A reaction: You could add repeated iteration of institutional error filters to journals about astrology, but it wouldn't thereby acquire epistemic supremacy. It is the tangible nature of the evidence which bestows the authority. |
| 14897 | We should abandon intuitions, especially that the world is made of little things, and made of something [Ladyman/Ross] |
| Full Idea: Abandoning intuitions is usually regarded as a cost rather than a benefit. By contrast, as naturalists we are not concerned with preserving intuitions at all (especially that the world is composed of little things, and that it must be made of something). | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.1) |
| 10237 | Coherence is a primitive, intuitive notion, not reduced to something formal [Shapiro] |
| Full Idea: I take 'coherence' to be a primitive, intuitive notion, not reduced to something formal, and so I do not venture a rigorous definition of it. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.8) | |
| A reaction: I agree strongly with this. Best to talk of 'the space of reasons', or some such. Rationality extends far beyond what can be formally defined. Coherence is the last court of appeal in rational thought. |
| 10204 | An 'implicit definition' gives a direct description of the relations of an entity [Shapiro] |
| Full Idea: An 'implicit definition' characterizes a structure or class of structures by giving a direct description of the relations that hold among the places of the structure. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) | |
| A reaction: This might also be thought of as a 'functional definition', since it seems to say what the structure or entity does, rather than give the intrinsic characteristics that make its relations and actions possible. |
| 10206 | Modal operators are usually treated as quantifiers [Shapiro] |
| Full Idea: It is common now, and throughout the history of philosophy, to interpret modal operators as quantifiers. This is an analysis of modality in terms of ontology. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) |
| 10208 | Axiom of Choice: some function has a value for every set in a given set [Shapiro] |
| Full Idea: One version of the Axiom of Choice says that for every set A of nonempty sets, there is a function whose domain is A and whose value, for every a ∈ A, is a member of a. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 1) |
| 10252 | The Axiom of Choice seems to license an infinite amount of choosing [Shapiro] |
| Full Idea: If the Axiom of Choice says we can choose one member from each of a set of non-empty sets and put the chosen elements together in a set, this licenses the constructor to do an infinite amount of choosing. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 6.3) | |
| A reaction: This is one reason why the Axiom was originally controversial, and still is for many philosophers. |
| 10207 | Anti-realists reject set theory [Shapiro] |
| Full Idea: Anti-realists reject set theory. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) | |
| A reaction: That is, anti-realists about mathematical objects. I would have thought that one could accept an account of sets as (say) fictions, which provided interesting models of mathematics etc. |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 10259 | The two standard explanations of consequence are semantic (in models) and deductive [Shapiro] |
| Full Idea: The two best historical explanations of consequence are the semantic (model-theoretic), and the deductive versions. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 7.2) | |
| A reaction: Shapiro points out the fictionalists are in trouble here, because the first involves commitment to sets, and the second to the existence of deductions. |
| 10257 | Intuitionism only sanctions modus ponens if all three components are proved [Shapiro] |
| Full Idea: In some intuitionist semantics modus ponens is not sanctioned. At any given time there is likely to be a conditional such that it and its antecedent have been proved, but nobody has bothered to prove the consequent. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 6.7) | |
| A reaction: [He cites Heyting] This is a bit baffling. In what sense can 'it' (i.e. the conditional implication) have been 'proved' if the consequent doesn't immediately follow? Proving both propositions seems to make the conditional redundant. |
| 14943 | Maybe mathematical logic rests on information-processing [Ladyman/Ross] |
| Full Idea: It is claimed that mathematical logic can be understood in terms of information-processing. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.5) | |
| A reaction: [They cite Chaitin 1987] I don't understand how this would work, but it is still worth quoting. This would presumably make logic rest on processes rather than on entities. I quite like that. |
| 10253 | Either logic determines objects, or objects determine logic, or they are separate [Shapiro] |
| Full Idea: Ontology does not depend on language and logic if either one has the objects determining the logic, or the objects are independent of the logic. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 6.4) | |
| A reaction: I favour the first option. I think we should seek an account of how logic grows from our understanding of the physical world. If this cannot be established, I shall invent a new Mad Logic, and use it for all my future reasoning, with (I trust) impunity. |
| 10251 | The law of excluded middle might be seen as a principle of omniscience [Shapiro] |
| Full Idea: The law of excluded middle might be seen as a principle of omniscience. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 6.3) | |
| A reaction: [E.Bishop 1967 is cited] Put that way, you can see why a lot of people (such as intuitionists in mathematics) might begin to doubt it. |
| 10212 | Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and' [Shapiro] |
| Full Idea: To some extent, every truth-functional connective differs from its counterpart in ordinary language. Classical conjunction, for example, is timeless, whereas the word 'and' often is not. 'Socrates runs and Socrates stops' cannot be reversed. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 3) | |
| A reaction: Shapiro suggests two interpretations: either the classical connectives are revealing the deeper structure of ordinary language, or else they are a simplification of it. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 10209 | A function is just an arbitrary correspondence between collections [Shapiro] |
| Full Idea: The modern extensional notion of function is just an arbitrary correspondence between collections. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 1) | |
| A reaction: Shapiro links this with the idea that a set is just an arbitrary collection. These minimalist concepts seem like a reaction to a general failure to come up with a more useful and common sense definition. |
| 10268 | Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro] |
| Full Idea: Maybe plural quantifiers should themselves be understood in terms of classes (or sets). | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 7.4) | |
| A reaction: [Shapiro credits Resnik for this criticism] |
| 10235 | A sentence is 'satisfiable' if it has a model [Shapiro] |
| Full Idea: Normally, to say that a sentence Φ is 'satisfiable' is to say that there exists a model of Φ. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.8) | |
| A reaction: Nothing is said about whether the model is impressive, or founded on good axioms. Tarski builds his account of truth from this initial notion of satisfaction. |
| 10240 | Model theory deals with relations, reference and extensions [Shapiro] |
| Full Idea: Model theory determines only the relations between truth conditions, the reference of singular terms, the extensions of predicates, and the extensions of the logical terminology. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.9) |
| 10239 | The central notion of model theory is the relation of 'satisfaction' [Shapiro] |
| Full Idea: The central notion of model theory is the relation of 'satisfaction', sometimes called 'truth in a model'. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.9) |
| 10214 | Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro] |
| Full Idea: No object-language theory determines its ontology by itself. The best possible is that all models are isomorphic, in which case the ontology is determined 'up to isomorphism', but only if the domain is finite, or it is stronger than first-order. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 2.5) | |
| A reaction: This seems highly significant when ontological claims are being made, and is good support for Shapiro's claim that the structures matter, not the objects. There is a parallel in Tarksi's notion of truth-in-all-models. [The Skolem Paradox is the problem] |
| 10238 | The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro] |
| Full Idea: Set theorists often point out that the set-theoretical hierarchy contains as many isomorphism types as possible; that is the point of the theory. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.8) | |
| A reaction: Hence there are a huge number of models for any theory, which are then reduced to the one we want at the level of isomorphism. |
| 10234 | Any theory with an infinite model has a model of every infinite cardinality [Shapiro] |
| Full Idea: The Löwenheim-Skolem theorems (which apply to first-order formal theories) show that any theory with an infinite model has a model of every infinite cardinality. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.8) | |
| A reaction: This aspect of the theorems is the Skolem Paradox. Shapiro argues that in first-order this infinity of models for arithmetic must be accepted, but he defends second-order model theory, where 'standard' models can be selected. |
| 10201 | Virtually all of mathematics can be modeled in set theory [Shapiro] |
| Full Idea: It is well known that virtually every field of mathematics can be reduced to, or modelled in, set theory. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) | |
| A reaction: The word 'virtually' is tantalising. The fact that something can be 'modeled' in set theory doesn't mean it IS set theory. Most weather can be modeled in a computer. |
| 10213 | Real numbers are thought of as either Cauchy sequences or Dedekind cuts [Shapiro] |
| Full Idea: Real numbers are either Cauchy sequences of rational numbers (interpreted as pairs of integers), or else real numbers can be thought of as Dedekind cuts, certain sets of rational numbers. So π is a Dedekind cut, or an equivalence class of sequences. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 2.5) | |
| A reaction: This question is parallel to the question of whether natural numbers are Zermelo sets or Von Neumann sets. The famous problem is that there seems no way of deciding. Hence, for Shapiro, we are looking at models, not actual objects. |
| 18243 | Understanding the real-number structure is knowing usage of the axiomatic language of analysis [Shapiro] |
| Full Idea: There is no more to understanding the real-number structure than knowing how to use the language of analysis. .. One learns the axioms of the implicit definition. ...These determine the realtionships between real numbers. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.9) | |
| A reaction: This, of course, is the structuralist view of such things, which isn't really interested in the intrinsic nature of anything, but only in its relations. The slogan that 'meaning is use' seems to be in the background. |
| 18245 | Cuts are made by the smallest upper or largest lower number, some of them not rational [Shapiro] |
| Full Idea: A Dedekind Cut is a division of rationals into two set (A1,A2) where every member of A1 is less than every member of A2. If n is the largest A1 or the smallest A2, the cut is produced by n. Some cuts aren't produced by rationals. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 5.4) |
| 10236 | There is no grounding for mathematics that is more secure than mathematics [Shapiro] |
| Full Idea: We cannot ground mathematics in any domain or theory that is more secure than mathematics itself. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.8) | |
| A reaction: This pronouncement comes after a hundred years of hard work, notably by Gödel, so we'd better believe it. It might explain why Putnam rejects the idea that mathematics needs 'foundations'. Personally I'm prepare to found it in countable objects. |
| 10256 | For intuitionists, proof is inherently informal [Shapiro] |
| Full Idea: For intuitionists, proof is inherently informal. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 6.7) | |
| A reaction: This thought is quite appealing, so I may have to take intuitionism more seriously. It connects with my view of coherence, which I take to be a notion far too complex for precise definition. However, we don't want 'proof' to just mean 'persuasive'. |
| 10202 | Natural numbers just need an initial object, successors, and an induction principle [Shapiro] |
| Full Idea: The natural-number structure is a pattern common to any system of objects that has a distinguished initial object and a successor relation that satisfies the induction principle | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) | |
| A reaction: If you started your number system with 5, and successors were only odd numbers, something would have gone wrong, so a bit more seems to be needed. How do we decided whether the initial object is 0, 1 or 2? |
| 10205 | Mathematics originally concerned the continuous (geometry) and the discrete (arithmetic) [Shapiro] |
| Full Idea: Originally, the focus of geometry was space - matter and extension - and the subject matter of arithmetic was quantity. Geometry concerned the continuous, whereas arithmetic concerned the discrete. Mathematics left these roots in the nineteenth century. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) | |
| A reaction: Mathematicians can do what they like, but I don't think philosophers of mathematics should lose sight of these two roots. It would be odd if the true nature of mathematics had nothing whatever to do with its origin. |
| 10222 | Mathematical foundations may not be sets; categories are a popular rival [Shapiro] |
| Full Idea: Foundationalists (e.g. Quine and Lewis) have shown that mathematics can be rendered in theories other than the iterative hierarchy of sets. A dedicated contingent hold that the category of categories is the proper foundation (e.g. Lawvere). | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 3.3) | |
| A reaction: I like the sound of that. The categories are presumably concepts that generate sets. Tricky territory, with Frege's disaster as a horrible warning to be careful. |
| 10218 | Baseball positions and chess pieces depend entirely on context [Shapiro] |
| Full Idea: We cannot imagine a shortstop independent of a baseball infield, or a piece that plays the role of black's queen bishop independent of a chess game. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 3.1) | |
| A reaction: This is the basic thought that leads to the structuralist view of things. I must be careful because I like structuralism, but I have attacked the functionalist view in many areas, because it neglects the essences of the functioning entities. |
| 10224 | The even numbers have the natural-number structure, with 6 playing the role of 3 [Shapiro] |
| Full Idea: The even numbers and the natural numbers greater than 4 both exemplify the natural-number structure. In the former, 6 plays the 3 role, and in the latter 8 plays the 3 role. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 3.5) | |
| A reaction: This begins to sound a bit odd. If you count the even numbers, 6 is the third one. I could count pebbles using only evens, but then presumably '6' would just mean '3'; it wouldn't be the actual number 6 acting in a different role, like Laurence Olivier. |
| 10228 | Could infinite structures be apprehended by pattern recognition? [Shapiro] |
| Full Idea: It is contentious, to say the least, to claim that infinite structures are apprehended by pattern recognition. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.1) | |
| A reaction: It only seems contentious for completed infinities. The idea that the pattern continues in same way seems (pace Wittgenstein) fairly self-evident, just like an arithmetical series. |
| 10230 | The 4-pattern is the structure common to all collections of four objects [Shapiro] |
| Full Idea: The 4-pattern is the structure common to all collections of four objects. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.2) | |
| A reaction: This seems open to Frege's objection, that you can have four disparate abstract concepts, or four spatially scattered items of unknown pattern. It certainly isn't a visual pattern, but then if the only detectable pattern is the fourness, it is circular. |
| 10249 | The main mathematical structures are algebraic, ordered, and topological [Shapiro] |
| Full Idea: According to Bourbaki, there are three main types of structure: algebraic structures, such as group, ring, field; order structures, such as partial order, linear order, well-order; topological structures, involving limit, neighbour, continuity, and space. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 5.5) | |
| A reaction: Bourbaki is mentioned as the main champion of structuralism within mathematics. |
| 10273 | Some structures are exemplified by both abstract and concrete [Shapiro] |
| Full Idea: Some structures are exemplified by both systems of abstracta and systems of concreta. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 8.2) | |
| A reaction: It at least seems plausible that one might try to build a physical structure that modelled arithmetic (an abacus might be an instance), so the parallel is feasible. Then to say that the abstract arose from modelling the physical seems equally plausible. |
| 10276 | Mathematical structures are defined by axioms, or in set theory [Shapiro] |
| Full Idea: Mathematical structures are characterised axiomatically (as implicit definitions), or they are defined in set theory. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 8.3) | |
| A reaction: Presumably earlier mathematicians had neither axiomatised their theories, nor expressed them in set theory, but they still had a good working knowledge of the relationships. |
| 10270 | The main versions of structuralism are all definitionally equivalent [Shapiro] |
| Full Idea: Ante rem structuralism, eliminative structuralism formulated over a sufficiently large domain of abstract objects, and modal eliminative structuralism are all definitionally equivalent. Neither is to be ontologically preferred, but the first is clearer. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 7.5) | |
| A reaction: Since Shapiro's ontology is platonist, I would have thought there were pretty obvious grounds for making a choice between that and eliminativm, even if the grounds are intuitive rather than formal. |
| 10221 | Is there is no more to structures than the systems that exemplify them? [Shapiro] |
| Full Idea: The 'in re' view of structures is that there is no more to structures than the systems that exemplify them. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 3.3) | |
| A reaction: I say there is more than just the systems, because we can abstract from them to a common structure, but that doesn't commit us to the existence of such a common structure. |
| 10248 | Number statements are generalizations about number sequences, and are bound variables [Shapiro] |
| Full Idea: According to 'in re' structuralism, a statement that appears to be about numbers is a disguised generalization about all natural-number sequences; the numbers are bound variables, not singular terms. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 5.3.4) | |
| A reaction: Any theory of anything which comes out with the thought that 'really it is a variable, not a ...' has my immediate attention and sympathy. |
| 10220 | Because one structure exemplifies several systems, a structure is a one-over-many [Shapiro] |
| Full Idea: Because the same structure can be exemplified by more than one system, a structure is a one-over-many. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 3.3) | |
| A reaction: The phrase 'one-over-many' is a classic Greek hallmark of a universal. Cf. Idea 10217, where Shapiro talks of arriving at structures by abstraction, through focusing and ignoring. This sounds more like a creation than a platonic universal. |
| 10223 | There is no 'structure of all structures', just as there is no set of all sets [Shapiro] |
| Full Idea: There is no 'structure of all structures', just as there is no set of all sets. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 3.4) | |
| A reaction: If one cannot abstract from all the structures to a higher level, why should Shapiro have abstracted from the systems/models to get the over-arching structures? |
| 8703 | Shapiro's structuralism says model theory (comparing structures) is the essence of mathematics [Shapiro, by Friend] |
| Full Idea: Shapiro's structuralism champions model theory as the branch of mathematics that best describes mathematics. The essence of mathematical activity is seen as an exercise in comparing mathematical structures to each other. | |
| From: report of Stewart Shapiro (Philosophy of Mathematics [1997], 4.4) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: Note it 'best describes' it, rather than being foundational. Assessing whether propositional logic is complete is given as an example of model theory. That makes model theory a very high-level activity. Does it capture simple arithmetic? |
| 10274 | Does someone using small numbers really need to know the infinite structure of arithmetic? [Shapiro] |
| Full Idea: According to structuralism, someone who uses small natural numbers in everyday life presupposes an infinite structure. It seems absurd that a child who learns to count his toes applies an infinite structure to reality, and thus presupposes the structure. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 8.2) | |
| A reaction: Shapiro says we can meet this objection by thinking of smaller structures embedded in larger ones, with the child knowing the smaller ones. |
| 10200 | We distinguish realism 'in ontology' (for objects), and 'in truth-value' (for being either true or false) [Shapiro] |
| Full Idea: We must distinguish between 'realism in ontology' - that mathematical objects exist - and 'realism in truth-value', which is suggested by the model-theoretic framework - that each well-formed meaningful sentence is non-vacuously either true or false. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) | |
| A reaction: My inclination is fairly strongly towards realism of the second kind, but not of the first. A view about the notion of a 'truth-maker' might therefore be required. What do the truths refer to? Answer: not objects, but abstractions from objects. |
| 10210 | If mathematical objects are accepted, then a number of standard principles will follow [Shapiro] |
| Full Idea: One who believes in the independent existence of mathematical objects is likely to accept the law of excluded middle, impredicative definitions, the axiom of choice, extensionality, and arbitrary sets and functions. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 1) | |
| A reaction: The underlying thought is that since the objects pre-exist, all of the above simply describe the relations between them, rather than having to actually bring the objects into existence. Personally I would seek a middle ground. |
| 10215 | Platonists claim we can state the essence of a number without reference to the others [Shapiro] |
| Full Idea: The Platonist view may be that one can state the essence of each number, without referring to the other numbers. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 3.1) | |
| A reaction: Frege certainly talks this way (in his 'borehole' analogy). Fine, we are asked to spell out the essence of some number, without making reference either to any 'units' composing it, or to any other number adjacent to it or composing it. Reals? |
| 10233 | Platonism must accept that the Peano Axioms could all be false [Shapiro] |
| Full Idea: A traditional Platonist has to face the possibility that all of the Peano Axioms are false. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.7) | |
| A reaction: This would be because the objects exist independently, and so the Axioms are a mere human attempt at pinning them down. For the Formalist the axioms create the numbers, and so couldn't be false. This makes me, alas, warm to platonism! |
| 10244 | Intuition is an outright hindrance to five-dimensional geometry [Shapiro] |
| Full Idea: Even if spatial intuition provides a little help in the heuristics of four-dimensional geometry, intuition is an outright hindrance for five-dimensional geometry and beyond. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 5.2) | |
| A reaction: One might respond by saying 'so much the worse for five-dimensional geometry'. One could hardly abolish the subject, though, so the point must be taken. |
| 10280 | A stone is a position in some pattern, and can be viewed as an object, or as a location [Shapiro] |
| Full Idea: For each stone, there is at least one pattern such that the stone is a position in that pattern. The stone can be treated in terms of places-are-objects, or places-are-offices, to be filled with objects drawn from another ontology. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 8.4) | |
| A reaction: I believe this is the story J.S. Mill had in mind. His view was that the structures move off into abstraction, but it is only at the empirical and physical level that we can possibly learn the structures. |
| 10254 | Can the ideal constructor also destroy objects? [Shapiro] |
| Full Idea: Can we assume that the ideal constructor cannot destroy objects? Presumably the ideal constructor does not have an eraser, and the collection of objects is non-reducing over time. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 6.5) | |
| A reaction: A very nice question, which platonists should enjoy. |
| 10255 | Presumably nothing can block a possible dynamic operation? [Shapiro] |
| Full Idea: Presumably within a dynamic system, once the constructor has an operation available, then no activity can preclude the performance of the operation? | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 6.5) | |
| A reaction: There seems to be an interesting assumption in static accounts of mathematics, that all the possible outputs of (say) a function actually exist with a theory. In an actual dynamic account, the constructor may be smitten with lethargy. |
| 10279 | Can we discover whether a deck is fifty-two cards, or a person is time-slices or molecules? [Shapiro] |
| Full Idea: Can we 'discover' whether a deck is really identical with its fifty-two cards, or whether a person is identical with her corresponding time-slices, molecules, or space-time points? This is like Benacerraf's problem about numbers. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997]) | |
| A reaction: Shapiro is defending the structuralist view, that each of these is a model of an agreed reality, so we cannot choose a right model if they all satisfy the necessary criteria. |
| 14942 | Only admit into ontology what is explanatory and predictive [Ladyman/Ross] |
| Full Idea: We reject any grounds other than explanatory and predictive utility for admitting something into our ontology. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.3) | |
| A reaction: Now you are talking. This is something like my thesis (which I take to be Aristotelian) - that without the drive for explanation we wouldn't even think of metaphysics, and so metaphysics should be understood in that light. |
| 14948 | To be is to be a real pattern [Ladyman/Ross] |
| Full Idea: To be is to be a real pattern. ....Real patterns carry information about other real patterns. ...It's patterns all the way down. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.4) | |
| A reaction: I've plucked these bleeding from context, but they are obviously intended as slogans. Is there pattern 'inside' an electron? Are electrons all exterior? |
| 14947 | Any process can be described as transfer of measurable information [Ladyman/Ross] |
| Full Idea: Reference to transfer of some (in principle) quantitatively measurable information is a highly general way of describing any process. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.3) | |
| A reaction: That does not, of course, mean that that is what a process is. A waterfall is an archetypal process, but it is a bit more than a bunch of information. Actually its complexity may place its information beyond measurement. |
| 14941 | We say there is no fundamental level to ontology, and reality is just patterns [Ladyman/Ross] |
| Full Idea: The tentative metaphysical hypothesis of this book, which is open to empirical falsification, is that there is no fundamental level, that the real patterns criterion of reality is the last word in ontology. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.3) | |
| A reaction: I wouldn't hold your breath waiting for the empirical falsification to arrive (or vanish). Their commitment to real patterns (or structures) leaves me a bit baffled. |
| 10227 | The abstract/concrete boundary now seems blurred, and would need a defence [Shapiro] |
| Full Idea: The epistemic proposals of ontological realists in mathematics (such as Maddy and Resnik) has resulted in the blurring of the abstract/concrete boundary. ...Perhaps the burden is now on defenders of the boundary. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.1) | |
| A reaction: As Shapiro says, 'a vague boundary is still a boundary', so we need not be mesmerised by borderline cases. I would defend the boundary, with the concrete just being physical. A chair is physical, but our concept of a chair may already be abstract. |
| 10226 | Mathematicians regard arithmetic as concrete, and group theory as abstract [Shapiro] |
| Full Idea: Mathematicians use the 'abstract/concrete' label differently, with arithmetic being 'concrete' because it is a single structure (up to isomorphism), while group theory is considered more 'abstract'. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.1 n1) | |
| A reaction: I would say that it is the normal distinction, but they have moved the significant boundary up several levels in the hierarchy of abstraction. |
| 10493 | If concrete is spatio-temporal and causal, and abstract isn't, the distinction doesn't suit physics [Ladyman/Ross] |
| Full Idea: It is said that concrete objects have causal powers while abstract ones do not, or that concrete objects exist in space and time while abstract ones do not, but these categories seem crude and inappropriate for modern physics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.6) | |
| A reaction: I don't find this convincing. He gives example of peculiar causation, but I don't believe modern physics proposes any entities which are totally acausal and non-spatiotemporal. Maybe the distinction needs a defence. |
| 14934 | Concrete and abstract are too crude for modern physics [Ladyman/Ross] |
| Full Idea: The categories of concrete and abstract seem crude and inappropriate for modern physics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.6) | |
| A reaction: They don't persuade me of this idea. At some point physicists need to decide the ontological status of the basic stuffs they are investigating. I'll give them a thousand years, and then I want an answer. Do they only deal in 'ideal' entities? |
| 14909 | Physicalism is 'part-whole' (all parts are physical), or 'supervenience/levels' (dependence on physical) [Ladyman/Ross] |
| Full Idea: There is part-whole physicalism, that everything is exhausted by basic constituents that are themselves physical, or supervenience or levels physicalism, that the putatively non-physical is dependent on the physical. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.3) | |
| A reaction: The cite Hüttemann and Papineau 2005. I am not convinced by this distinction. Ladyman and Ross oppose the first one. I'm thinking the second one either collapses into the first one, or it isn't physicalism. Higher levels are abstractions. |
| 10262 | Fictionalism eschews the abstract, but it still needs the possible (without model theory) [Shapiro] |
| Full Idea: Fictionalism takes an epistemology of the concrete to be more promising than concrete-and-abstract, but fictionalism requires an epistemology of the actual and possible, secured without the benefits of model theory. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 7.2) | |
| A reaction: The idea that possibilities (logical, natural and metaphysical) should be understood as features of the concrete world has always struck me as appealing, so I have (unlike Shapiro) no intuitive problems with this proposal. |
| 10277 | Structuralism blurs the distinction between mathematical and ordinary objects [Shapiro] |
| Full Idea: One result of the structuralist perspective is a healthy blurring of the distinction between mathematical and ordinary objects. ..'According to the structuralist, physical configurations often instantiate mathematical patterns'. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 8.4) | |
| A reaction: [The quotation is from Penelope Maddy 1988 p.28] This is probably the main reason why I found structuralism interesting, and began to investigate it. |
| 14926 | Relations without relata must be treated as universals, with their own formal properties [Ladyman/Ross] |
| Full Idea: The best sense that can be made of a relation without relata is the idea of a universal. Thus the relation 'larger than' has formal properties that are independent of the contingencies of their instantiation. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.4) | |
| A reaction: Russell was keen on the idea that relations are universals, and presumably for this reason. I struggle to grasp uninstantiated but nevertheless real 'greater than' relations. They are abstractions from things, not separate universals. |
| 14929 | A belief in relations must be a belief in things that are related [Ladyman/Ross] |
| Full Idea: Many philosophers say that one cannot intelligibly subscribe to the reality of relations unless one is also committed to the fact of some things that are related. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.5) | |
| A reaction: Ladyman and Ross try to argue against this view, but the idea makes a strong impression on me. Your ontology seems to be rather strange if you have a set of structural relations that await things to slot into the structure. |
| 14925 | The normal assumption is that relations depend on properties of the relata [Ladyman/Ross] |
| Full Idea: The idea that there could be relations which do not supervene on the properties of their relata runs counter to a deeply entrenched way of thinking. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.4) | |
| A reaction: Ladyman and Ross are trying to defend the idea of 'structure' which is independent of the objects that occupy the nodes of the structure. Tricky. |
| 14931 | That there are existent structures not made of entities is no stranger than the theory of universals [Ladyman/Ross] |
| Full Idea: Is the main metaphysical idea we propose (of existent structures that are not composed out of more basic entities) any more obscure or bizarre than the instantiation relation in the theory of universals? | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.5) | |
| A reaction: No, it is not more bizarre than that, but that isn't much of a reason to believe their theory. See Idea 8699, and many ideas about structure in mathematics. Ladyman and Ross still smack of platonism, even if they are rooted in particle physics. |
| 14932 | Causal essentialism says properties are nothing but causal relations [Ladyman/Ross] |
| Full Idea: Causal essentialism is the doctrine that the causal relations that properties bear to other properties exhaust their natures. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.5 n50) | |
| A reaction: [They cite Shoemaker, Mumford and Bird for this] Personally I don't see this view as offering relations as fundamental. The whole point is to explain everything. The only plausible primitive notion is of a power - which then generates the relations. |
| 14920 | If science captures the modal structure of things, that explains why its predictions work [Ladyman/Ross] |
| Full Idea: If theorists are able sometimes to capture the objective modal structure of the world then it is no surprise that successful novel prediction sometimes works. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.4) | |
| A reaction: This is a rather important idea, particularly for my approach. I say we should demand more explanations, and explanations of successful prediction are far from obvious in a regularity account of nature. |
| 14952 | Things are constructs for tracking patterns (and not linguistic, because animals do it) [Ladyman/Ross] |
| Full Idea: Individual things are constructs built for second-best tracking of real patterns. They are not necessarily linguistic constructions, since some non-human animals almost certainly cognitively construct them. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.5) | |
| A reaction: Delighted to see animals making an appearance. Fans of language-based metaphysics please note. If they are fictional constructs, why do they do such a good job of tracking? What generates the 'superficial' appearance that there are objects? |
| 10272 | The notion of 'object' is at least partially structural and mathematical [Shapiro] |
| Full Idea: The very notion of 'object' is at least partially structural and mathematical. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 8.1) | |
| A reaction: [In the context, Shapiro clearly has physical objects in mind] This view seems to fit with Russell's 'relational' view of the physical world, though Russell rejected structuralism in mathematics. I take abstraction to be part of perception. |
| 14950 | Maybe individuation can be explained by thermodynamic depth [Ladyman/Ross] |
| Full Idea: Scientists have developed principles for understanding individuation in terms of the production of thermodynamic depth. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.5) | |
| A reaction: [They cite J.Collier for this view] Interesting, even though I don't really understand 'thermodynamic depth'. Ladyman and Ross reject it, but there is a whiff of a theory of individuation from within physics. |
| 14927 | Physics seems to imply that we must give up self-subsistent individuals [Ladyman/Ross] |
| Full Idea: There is growing convergence among philosophers of physics that physics motivates abandonment of a metaphysics that posits fundamental self-subsistent individuals. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.4) | |
| A reaction: They cite fermions as an example, which only seem to be given an identity by the relations into which they enter. It is a bit cheeky to simultaneously offer this idea, and despise van Inwagen and Merricks for the same object nihilism. |
| 14944 | There is no single view of individuals, because different sciences operate on different scales [Ladyman/Ross] |
| Full Idea: There is no single account of what individuals there are because, we argue, the special sciences may disagree about the bounds and status of individuals since they describe the world at different scales. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.8) | |
| A reaction: This seems to deny that nature has actual joints, and so seems to me to be a form of anti-realism (which they would deny). Why shouldn't there be a single view which unites all of these special sciences? |
| 14946 | There are no cats in quantum theory, and no mountains in astrophysics [Ladyman/Ross] |
| Full Idea: At the quantum scale there are no cats; at scales appropriate for astrophysics there are no mountains. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.2) | |
| A reaction: I don't find this convincing. Since cats are made of quantised entities, they do exist in that world, but are of little interest when trying to understand it. Similarly, astrophysicists hardly deny the existence of mountains! |
| 14928 | Things are abstractions from structures [Ladyman/Ross] |
| Full Idea: Individual things are locally focused abstractions from modal structure. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.4) | |
| A reaction: I am a fan of the role of abstraction in our understanding of the world, despite my limited progress in trying to explicate the idea. I can't decide whether or not there are any things. A bit basic, that! |
| 10275 | A blurry border is still a border [Shapiro] |
| Full Idea: A blurry border is still a border. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 8.3) | |
| A reaction: This remark deserves to be quoted in almost every area of philosophy, against those who attack a concept by focusing on its vague edges. Philosophers should focus on central cases, not borderline cases (though the latter may be of interest). |
| 14892 | The idea of composition, that parts of the world are 'made of' something, is no longer helpful [Ladyman/Ross] |
| Full Idea: It is no longer helpful to conceive of either the world, or particular systems of the world that we study in partial isolation, as 'made of' anything at all. …Our target here is the metaphysical idea of composition. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.1) | |
| A reaction: This is argued by them from the point of view of fundamental physics as the provider of our basic metaphysics about the world. Personally I really really want to know what electrons are made of, but I know no one is going to tell me. They may even laugh. |
| 14949 | A sum of things is not a whole if the whole does not support some new generalisation [Ladyman/Ross] |
| Full Idea: A nostril, a city and a trumpet solo is not a real pattern, because identification of it supports no generalisations not supported by identification of the three conjuncts considered separately. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.4) | |
| A reaction: This is a nice try at offering a criterion for unity, but I doubt whether it will work, because an ingenious person could come up with wild generalisations. These three combined make possible a charming new line of poetry. |
| 14951 | We treat the core of a pattern as an essence, in order to keep track of it [Ladyman/Ross] |
| Full Idea: We focus on diagnostic features of real patterns that we can treat as 'core', which reliably predict that our attention is still tracking the same real pattern. These are Locke's 'essence of particulars', or Putnam's 'hidden structures'. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.5) | |
| A reaction: They seemed to be ashamed of themselves for proposing this, and call it a 'second-best' epistemological device. They seem to imply that they are useful fictions, but why shouldn't the hidden structures be real? They might both identify and explain. |
| 14958 | A continuous object might be a type, with instances at each time [Ladyman/Ross] |
| Full Idea: Why should not 'Napoleon' be a type, of which 'Napoleon in 1805' and 'Napoleon in 1813' are instances? | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 5.6) | |
| A reaction: That is very nice. That might be a view that suits presentism, where the timed instances never co-exist, and so have the sort of abstract existence that we associate with types. |
| 10258 | Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro] |
| Full Idea: For many philosophers the logical notions of possibility and necessity are exceptions to a general scepticism, perhaps because they have been reduced to model theory, via set theory. Thus Φ is logically possible if there is a model that satisfies it. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 7.1) | |
| A reaction: Initially this looks a bit feeble, like an empiricist only believing what they actually see right now, but the modern analytical philosophy project seems to be the extension of logical accounts further and further into what we intuit about modality. |
| 14903 | Quantum mechanics seems to imply single-case probabilities [Ladyman/Ross] |
| Full Idea: Quantum mechanics seems to imply single-case probabilities. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.3) | |
| A reaction: I know they keep telling us about such things, but I remain cautious. I think all the physicists have done is delved a bit deeper into something they don't understand. |
| 14923 | In quantum statistics, two separate classical states of affairs are treated as one [Ladyman/Ross] |
| Full Idea: In quantum statistics, what would be regarded as two possible states of affairs classically is treated as one possible state of affairs. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.1) |
| 10266 | Why does the 'myth' of possible worlds produce correct modal logic? [Shapiro] |
| Full Idea: The fact that the 'myth' of possible worlds happens to produce the correct modal logic is itself a phenomenon in need of explanation. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 7.4) | |
| A reaction: The claim that it produces 'the' correct modal logic seems to beg a lot of questions, given the profusion of modal systems. This is a problem with any sort of metaphysics which invokes fictionalism - what were those particular fictions responding to? |
| 14955 | Rats find some obvious associations easier to learn than less obvious ones [Ladyman/Ross] |
| Full Idea: Contrary to early behaviourist dogma, associations are not all equally learnable. Rats learn to associate eating with nausea, and a flash with a shock, much more easily than either complementary pairing. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 5.2) | |
| A reaction: That looks like an argue for some sort of innate knowledge, but experiments to disentangle eating from nausea must be rather hard to set up. |
| 14918 | The doctrine of empiricism does not itself seem to be empirically justified [Ladyman/Ross] |
| Full Idea: If to be an empiricist is to believe that 'experience is the sole source of information about the world', the problem is that this does not itself seem to be justifiable by experience. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.3.1) | |
| A reaction: [The quotation is from Van Fraassen 1985 p.253] This is the classic 'turning the tables' move in argument, invented by the Greeks. It is hard to offer anything other than intuition in the first move of any metaphysical theory. |
| 14891 | There is no reason to think our intuitions are good for science or metaphysics [Ladyman/Ross] |
| Full Idea: There is no reason to imagine that our habitual intuitions and inferential responses are well designed for science or for metaphysics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.1) |
| 14915 | The theory of evolution was accepted because it explained, not because of its predictions [Ladyman/Ross] |
| Full Idea: Darwin's theory of evolution was accepted by the scientific community because of its systematizing and explanatory power, and in spite of its lack of novel predictive success. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.1.3) | |
| A reaction: I am keen on the centrality of explanation to all of our thinking, metaphysical as well as physical, so I like this one. In general I like accounts of science that pay more attention to biology, and less to physics. |
| 14916 | What matters is whether a theory can predict - not whether it actually does so [Ladyman/Ross] |
| Full Idea: We suggest a modal account of novel prediction. That a theory could predict some unknown phenomenon is what matters, not whether it actually did so predict. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.1.3) | |
| A reaction: They also emphasise predicting new types of thing, rather than particular items. Some theories are powerful on explanation, but not so concerned with prediction. See Idea 14915. |
| 14922 | The Ramsey sentence describes theoretical entities; it skips reference, but doesn't eliminate it [Ladyman/Ross] |
| Full Idea: It is a mistake to think that the Ramsey sentence allows us to eliminate theoretical entities, for it still states that they exist. It is just that they are referred to not directly, by means of theoretical terms, but by description. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.4.1) |
| 14921 | The Ramsey-sentence approach preserves observations, but eliminates unobservables [Ladyman/Ross] |
| Full Idea: If one replaces the assertions of a first-order theory with its Ramsey sentence (giving a quantified predicate variable for a theoretical term), the observational consequences are carried over, but direct reference to unobservables is eliminated. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.4.1) | |
| A reaction: Thus this rewriting of theories is popular with empiricists, and this draws attention to the way you can change the ontological commitments simply by paraphrase. ...However, see Idea 14922. |
| 14953 | Induction is reasoning from the observed to the unobserved [Ladyman/Ross] |
| Full Idea: Induction is any form of reasoning that proceeds from claims about observed phenomena to claims about unobserved phenomena. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.5) | |
| A reaction: Most accounts of induction seem to imply that they lead to generalisations, rather than just some single unobserved thing. This definition is in line with David Lewis's. |
| 14914 | Inductive defences of induction may be rule-circular, but not viciously premise-circular [Ladyman/Ross] |
| Full Idea: The inductive defence of induction may be circular but not viciously so, because it is rule circular (defending the rule being used) but not premise circular (where the conclusion is in one of the premises). | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.1.2) | |
| A reaction: [They cite Braithwaite 1953 and Carnap 1952 for this] This strikes me as clutching at straws, when the whole procedure of induction is inescapably precarious. It is simply all we have available. |
| 14913 | We explain by deriving the properties of a phenomenon by embedding it in a large abstract theory [Ladyman/Ross] |
| Full Idea: Theoretical explanation is the derivation of the properties of a relatively concrete and observable phenomenon by means of an embedding into some larger, relatively abstract and unobservable theoretical structure. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.1.1) | |
| A reaction: [they are citing Michael Friedman 1981 p.1] This sounds like covering law explanation, but the theoretical structure will be a set of intersecting laws, rather than a single law. How do you explain the theoretical structure? |
| 10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
| Full Idea: The epistemological account of mathematical structures depends on the size and complexity of the structure, but small, finite structures are apprehended through abstraction via simple pattern recognition. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) | |
| A reaction: Yes! This I take to be the reason why John Stuart Mill was not a fool in his discussion of the pebbles. Successive abstractions (and fictions) will then get you to more complex structures. |
| 14930 | Maybe the only way we can think about a domain is by dividing it up into objects [Ladyman/Ross] |
| Full Idea: Speculating cautiously about psychology, it is possible that dividing a domain up into objects is the only way we can think about it. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.5) | |
| A reaction: Typical physicists - they speculate about psychology instead of studying it. Have they no respect for science? Neverthless my speculative psychology agrees with theirs. This fact may well be the key to all of metaphysics. |
| 14939 | Two versions of quantum theory say that the world is deterministic [Ladyman/Ross] |
| Full Idea: In the Bohm version of quantum theory, and the Everett approach, the world comes out deterministic after all. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.2) | |
| A reaction: This is just in case anyone wants to trumpet the idea that quantum theory has established indeterminism. It is particularly daft to think that quantum indeterminacy makes free will possible (or even actual). |
| 14911 | Science is opposed to downward causation [Ladyman/Ross] |
| Full Idea: When someone pronounces for downward causation they are in opposition to science. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.6 n54) | |
| A reaction: Downward causation is the key issue in any debate about whether minds exhibit excitingly 'emergent' properties that somehow put them outside the realm of normal physics. I take that to be nonsense, and I side with science here. |
| 10229 | Simple types can be apprehended through their tokens, via abstraction [Shapiro] |
| Full Idea: Some realists argue that simple types can be apprehended through their tokens, via abstraction. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.2) | |
| A reaction: One might rephrase that to say that types are created by abstraction from tokens (and then preserved in language). |
| 10217 | We can apprehend structures by focusing on or ignoring features of patterns [Shapiro] |
| Full Idea: One way to apprehend a particular structure is through a process of pattern recognition, or abstraction. One observes systems in a structure, and focuses attention on the relations among the objects - ignoring features irrelevant to their relations. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 3.1) | |
| A reaction: A lovely statement of the classic Aristotelian abstractionist approach of focusing-and-ignoring. But this is made in 1997, long after Frege and Geach ridiculed it. It just won't go away - not if you want a full and unified account of what is going on. |
| 9554 | We can focus on relations between objects (like baseballers), ignoring their other features [Shapiro] |
| Full Idea: One can observe a system and focus attention on the relations among the objects - ignoring those features of the objects not relevant to the system. For example, we can understand a baseball defense system by going to several games. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], p.74), quoted by Charles Chihara - A Structural Account of Mathematics | |
| A reaction: This is Shapiro perpetrating precisely the wicked abstractionism which Frege and Geach claim is ridiculous. Frege objects that abstract concepts then become private, but baseball defences are discussed in national newspapers. |
| 10231 | Abstract objects might come by abstraction over an equivalence class of base entities [Shapiro] |
| Full Idea: Perhaps we can introduce abstract objects by abstraction over an equivalence relation on a base class of entities, just as Frege suggested that 'direction' be obtained from parallel lines. ..Properties must be equinumerous, but need not be individuated. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.5) | |
| A reaction: [He cites Hale and Wright as the originators of this} It is not entirely clear why this is 'abstraction', rather than just drawing attention to possible groupings of entities. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 14956 | Explanation by kinds and by clusters of properties just express the stability of reality [Ladyman/Ross] |
| Full Idea: Philosophers sometimes invoke natural kinds as if they explain the possibility of explanation. This is characteristically neo-scholastic. That anything can be explained, and that properties cluster together, express one fact: reality is relatively stable. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 5.6) | |
| A reaction: Odd idea. I would have thought that if there are indeed kinds and clusters, this would explain a great deal more than mere stability. Or, more accurately, they would invite a more substantial explanation than mere stability would seem to need. |
| 14957 | There is nothing more to a natural kind than a real pattern in nature [Ladyman/Ross] |
| Full Idea: Everything that a naturalist could legitimately want from the concept of a natural kind can be had simply by reference to real patterns. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 5.6) | |
| A reaction: I think I agree with this, and with the general idea that natural kinds are overrated. There are varying degrees of stability in nature, and where there is a lot of stability our inductive reasoning can get to work. And that's it. |
| 14954 | Causation is found in the special sciences, but may have no role in fundamental physics [Ladyman/Ross] |
| Full Idea: The idea of causation, as it is used in science, finds its exemplars in the special sciences, and it is presently open empirical question whether that notion will have any ultimate role to play in fundamental physics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.5) | |
| A reaction: Note that they seem to always have a notion of 'ultimate' physics hovering over their account. I wonder. There is nothing in this idea to make me think that I should eliminate the idea of causation from my metaphysics. |
| 14902 | Science may have uninstantiated laws, inferred from approaching some unrealised limit [Ladyman/Ross] |
| Full Idea: It is possible that uninstantiated laws can be established in science, and consequently bear explanatory weight, ..if we need reasons for thinking that the closer conditions get to some limit, the more they approximate to some ideal. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.3) | |
| A reaction: [The cite Hüttemann 2004] I am dubious about laws, but I take this to be a point in favour of inference to the best explanation, and against accounts of laws as supervenient of how things actually are. |
| 14937 | That the universe must be 'made of' something is just obsolete physics [Ladyman/Ross] |
| Full Idea: It is a metaphysical residue of obsolete physics to suppose that the universe is 'made of' anything. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.2) | |
| A reaction: They quote Smolin as saying that it is 'processes' which are fundamental. And yet surely there must be something there to undergo a process? Surely we don't have eternal platonic processes? |
| 14900 | In physics, matter is an emergent phenomenon, not part of fundamental ontology [Ladyman/Ross] |
| Full Idea: Physics has taught us that matter in the sense of extended stuff is an emergent phenomenon that has no counterpart in fundamental ontology. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.3) | |
| A reaction: They contrast this point with futile debates among philosopher between atomists (partless particles) and gunkists (parts all the way down). |
| 14924 | If spacetime is substantial, what is the substance? [Ladyman/Ross] |
| Full Idea: It is fair to ask: if spacetime is a substance, what is the substance in question? | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.2) | |
| A reaction: Personally I love the question 'If it exists, what is it made of?', though physicists seem to think that this reveals a gormless misunderstanding. To my question Keith Hossack retorted 'What are the atoms made of?' |
| 14901 | Spacetime may well be emergent, rather than basic [Ladyman/Ross] |
| Full Idea: Contemporary physics takes very seriously the idea that spacetime itself is emergent from some more fundamental structure. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.3) |
| 14938 | A fixed foliation theory of quantum gravity could make presentism possible [Ladyman/Ross] |
| Full Idea: It has been pointed out that presentism is an open question in so far as a fixed foliation theory of quantum gravity has not been ruled out. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.2 n75) | |
| A reaction: [They cite B.Monton for this point] I don't understand this idea, but I'll have it anyway. Google 'fixed foliation' for me, as I'm too busy. |