81 ideas
| 15010 | Your metaphysics is 'cheating' if your ontology won't support the beliefs you accept [Sider] |
| Full Idea: Ontological 'cheaters' are those ne'er-do-well metaphysicians (such as presentists, phenomenalists, or solipsists) who refuse to countenance a sufficiently robust conception of the fundamental to underwrite the truths they accept. | |
| From: Theodore Sider (Writing the Book of the World [2011], 08.4) | |
| A reaction: Presentists are placed in rather insalubrious company here, The notion of 'cheaters' is nice, and I associate it with Australian philosophy, and the reason that was admired by David Lewis. |
| 14977 | Metaphysics is not about what exists or is true or essential; it is about the structure of reality [Sider] |
| Full Idea: Metaphysics, at bottom, is about the fundamental structure of reality. Not about what's necessarily true. Not about what properties are essential. Not about conceptual analysis. Not about what there is. Structure. | |
| From: Theodore Sider (Writing the Book of the World [2011], 01) | |
| A reaction: The opening words of his book. I take them to be absolutely correct, and to articulate the new orthodoxy about metaphysics which has emerged since about 1995. He expands this as being about patterns, categories and joints. |
| 14994 | Extreme doubts about metaphysics also threaten to undermine the science of unobservables [Sider] |
| Full Idea: The most extreme critics of metaphysics base their critique on sweeping views about language (logical positivism), or knowledge (empiricism), ...but this notoriously threatens the science of unobservables as much as it threatens metaphysics. | |
| From: Theodore Sider (Writing the Book of the World [2011], 05.1) | |
| A reaction: These criticisms also threaten speculative physics (even about what is possibly observable). |
| 15003 | It seems unlikely that the way we speak will give insights into the universe [Sider] |
| Full Idea: It has always seemed odd that insight into the fundamental workings of the universe should be gained by reflection on how we think and speak. | |
| From: Theodore Sider (Writing the Book of the World [2011], 07.8) | |
| A reaction: A nice expression of what should by now be obvious to all philosophers - that analysis of language is not going to reveal very much. It is merely clearing the undergrowth so that we can go somewhere. |
| 14986 | Conceptual analysts trust particular intuitions much more than general ones [Sider] |
| Full Idea: Conceptual analysts generally regard intuitive judgements about particular cases as being far more diagnostic than intuitive judgements about general principles. | |
| From: Theodore Sider (Writing the Book of the World [2011], 02.4 n7) | |
| A reaction: Since I take the aim to be the building up an accurate picture about general truths, it would be daft to just leap to our intuitions about those general truths. Equally you can't cut intuition out of the picture (pace Ladyman). |
| 18274 | Analysis complicates a statement, but only as far as the complexity of its meaning [Wittgenstein] |
| Full Idea: Analysis makes the statement more complicated than it was; but it cannot and ought not to make it more complicated than its meaning (Bedeutung) was to begin with. When the statement is as complex as its meaning, then it is completely analysed. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 46e) | |
| A reaction: But how do you assess how complex the 'Bedeutung' was before you started? |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| Full Idea: Dedkind gave a rigorous proof of the principle of definition by recursion, permitting recursive definitions of addition and multiplication, and hence proofs of the familiar arithmetical laws. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 13 'Deriv' |
| 14981 | Philosophical concepts are rarely defined, and are not understood by means of definitions [Sider] |
| Full Idea: Philosophical concepts of interest are rarely reductively defined; still more rarely does our understanding of such concepts rest on definitions. ...(We generally understand concepts to the extent that we know what role they play in thinking). | |
| From: Theodore Sider (Writing the Book of the World [2011], 02.1) | |
| A reaction: I'm not sure that I agree with this. I suspect that Sider has the notion of definition in mind that is influenced by lexicography. Aristotle's concept of definition I take to be lengthy and expansive, and that is very relevant to philosophy. |
| 15015 | It seems possible for a correct definition to be factually incorrect, as in defining 'contact' [Sider] |
| Full Idea: Arguably, 'there is absolutely no space between two objects in contact' is false, but definitional of 'contact'. ...We need a word for true definitional sentences. I propose: 'analytic'. | |
| From: Theodore Sider (Writing the Book of the World [2011], 09.8) |
| 14992 | We don't care about plain truth, but truth in joint-carving terms [Sider] |
| Full Idea: What we care about is truth in joint-carving terms, not just truth. | |
| From: Theodore Sider (Writing the Book of the World [2011], 04.5) | |
| A reaction: The thought is that it matters what conceptual scheme is used to express the truth (the 'ideology'). Truths can be true but uninformative or unexplanatory. |
| 15012 | Orthodox truthmaker theories make entities fundamental, but that is poor for explanation [Sider] |
| Full Idea: According to the entrenched truthmaker theorist, the fundamental facts consist just of facts citing the existence of entities. It's hard to see how all the complexity we experience could possibly be explained from that sparse basis. | |
| From: Theodore Sider (Writing the Book of the World [2011], 08.5) | |
| A reaction: This may be the 'entrenched' truthmaker view, but it is not clear why there could not be more complicated fundamental truthmakers, with structure as well as entities. And powers. |
| 15023 | The Barcan schema implies if X might have fathered something, there is something X might have fathered [Sider] |
| Full Idea: If we accept the Barcan and converse Barcan schemas, this leads to surprising ontological consequences. Wittgenstein might have fathered something, so, by the Barcan schema, there is something that Wittgenstein might have fathered. | |
| From: Theodore Sider (Writing the Book of the World [2011], 11.9) | |
| A reaction: [He cites Tim Williamson for this line of thought] I was liking the Barcan picture, by now I am backing away fast. They cannot be serious! |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| Full Idea: A set is 'Dedekind-infinite' iff there exists a one-to-one function that maps a set into a proper subset of itself. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §64) by E Reck / M Price - Structures and Structuralism in Phil of Maths n 7 | |
| A reaction: Sounds as if it is only infinite if it is contradictory, or doesn't know how big it is! |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| Full Idea: Dedekind had an interesting proof of the Axiom of Infinity. He held that I have an a priori grasp of the idea of my self, and that every idea I can form the idea of that idea. Hence there are infinitely many objects available to me a priori. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], no. 66) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 12 'Numb' | |
| A reaction: Who said that Descartes' Cogito was of no use? Frege endorsed this, as long as the ideas are objective and not subjective. |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| Full Idea: Dedekind plainly had fusions, not collections, in mind when he avoided the empty set and used the same symbol for membership and inclusion - two tell-tale signs of a mereological conception. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], 2-3) by Michael Potter - Set Theory and Its Philosophy 02.1 | |
| A reaction: Potter suggests that mathematicians were torn between mereology and sets, and eventually opted whole-heartedly for sets. Maybe this is only because set theory was axiomatised by Zermelo some years before Lezniewski got to mereology. |
| 15004 | 'Gunk' is an object in which proper parts all endlessly have further proper parts [Sider] |
| Full Idea: An object is 'gunky' if each of its parts has further proper parts; thus gunk involves infinite descent in the part-whole relation. | |
| From: Theodore Sider (Writing the Book of the World [2011], 07.11.2) |
| 14984 | Which should be primitive in mereology - part, or overlap? [Sider] |
| Full Idea: Should our fundamental theory of part and whole take 'part' or 'overlap' as primitive? | |
| From: Theodore Sider (Writing the Book of the World [2011], 02.3) |
| 16908 | We can dispense with self-evidence, if language itself prevents logical mistakes [Jeshion on Wittgenstein] |
| Full Idea: The 'self-evidence' of which Russell talks so much can only be dispensed with in logic if language itself prevents any logical mistake. | |
| From: comment on Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 4) by Robin Jeshion - Frege's Notion of Self-Evidence 4 | |
| A reaction: Jeshion presents this as a key idea, turning against Frege, and is the real source of the 'linguistic turn' in philosophy. If self-evidence is abandoned, then language itself is the guide to truth, so study language. I think I prefer Frege. See Quine? |
| 14980 | There is a real issue over what is the 'correct' logic [Sider] |
| Full Idea: Certain debates over the 'correct' logic are genuine, and not linguistic or conceptual. | |
| From: Theodore Sider (Writing the Book of the World [2011], 01.3) | |
| A reaction: It is rather hard to give arguments in favour of this view, but I am pleased to have the authority of Sider with me. |
| 15000 | 'It is raining' and 'it is not raining' can't be legislated, so we can't legislate 'p or ¬p' [Sider] |
| Full Idea: I cannot legislate-true 'It is raining' and I cannot legislate true 'It is not raining', so if I cannot legislate either true then I cannot legislate-true the disjunction 'it is raining or it is not raining'. | |
| From: Theodore Sider (Writing the Book of the World [2011], 06.5) | |
| A reaction: This strikes me as a very simple and very persuasive argument against the idea that logic is a mere convention. I take disjunction to be an abstract summary of how the world works. Sider seems sympathetic. |
| 15020 | Classical logic is good for mathematics and science, but less good for natural language [Sider] |
| Full Idea: Despite its brilliant success in mathematics and fundamental science, classical logic applies uneasily to natural language. | |
| From: Theodore Sider (Writing the Book of the World [2011], 10.6) | |
| A reaction: He gives examples of the conditional, and debates over the meaning of 'and', 'or' and 'not', and also names and quantifiers. Many modern philosophical problems result from this conflict. |
| 15029 | Modal accounts of logical consequence are simple necessity, or essential use of logical words [Sider] |
| Full Idea: The simplest modal account is that logical consequence is just necessary consequence; another modal account says that logical consequences are modal consequences that involve only logical words essentially. | |
| From: Theodore Sider (Writing the Book of the World [2011], 12.3) | |
| A reaction: [He cites Quine's 'Carnap and Logical Truth' for the second idea] Sider is asserting that Humeans like him dislike modality, and hence need a nonmodal account of logical consequence. |
| 18276 | A statement's logical form derives entirely from its constituents [Wittgenstein] |
| Full Idea: The logical form of the statement must already be given in the forms of its constituents. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 23e) | |
| A reaction: This would evidently require each constituent to have a 'logical form'. It is hard to see what that could beyond its part of speech. Do two common nouns have the same logical form? |
| 6563 | 'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin] |
| Full Idea: Wittgenstein's 'fundamental idea' is that the 'and' and 'not' which guarantee the truth of "not p and not-p" are meaningful, but do not get their meaning by representing or standing for or referring to some kind of entity; they are non-referring terms. | |
| From: report of Ludwig Wittgenstein (Notebooks 1914-1916 [1915], §37) by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
| A reaction: Wittgenstein then defines the terms using truth tables, to show what they do, rather than what they stand for. This seems to me to be a candidate for the single most important idea in the history of the philosophy of logic. |
| 15019 | Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral [Sider] |
| Full Idea: Some say that logical constants are those expressions that are defined by their proof-theoretic roles, others that they are the expressions whose semantic values are permutation-invariant, and still others that they are the topic-neutral expressions. | |
| From: Theodore Sider (Writing the Book of the World [2011], 10.3) | |
| A reaction: [He cites MacFarlane 2005 as giving a survey of this] |
| 15001 | 'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted [Sider] |
| Full Idea: 'Tonk' is stipulated by Prior to stand for a meaning that obeys the elimination and introduction rules; but there simply is no such meaning; 'tonk' cannot be interpreted so as to obey the rules. | |
| From: Theodore Sider (Writing the Book of the World [2011], 06.5) | |
| A reaction: 'Tonk' thus seems to present a problem for so-called 'natural' deduction, if the natural deduction consists of nothing more than obey elimination and introduction rules. |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| Full Idea: Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: Does this fit real numbers and complex numbers, as well as natural numbers? Frege was concerned by the lack of objectivity in this sort of view. What sort of arithmetic might the Martians have created? Numbers register sameness too. |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| Full Idea: It was primarily Dedekind's accomplishment to define the integers, rationals and reals, taking only the system of natural numbers for granted. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by A.George / D.J.Velleman - Philosophies of Mathematics Intro |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| Full Idea: Dedekind and Cantor said the cardinals may be defined in terms of the ordinals: The cardinal number of a set S is the least ordinal onto whose predecessors the members of S can be mapped one-one. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 5 |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| Full Idea: Dedekind said that the notion of order, rather than that of quantity, is the central notion in the definition of number. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
| A reaction: Compare Aristotle's nice question in Idea 646. My intuition is that quantity comes first, because I'm not sure HOW you could count, if you didn't think you were changing the quantity each time. Why does counting go in THAT particular order? Cf. Idea 8661. |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| Full Idea: Dedekind's ordinals are not essentially either ordinals or cardinals, but the members of any progression whatever. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §243 | |
| A reaction: This is part of Russell's objection to Dedekind's structuralism. The question is always why these beautiful structures should actually be considered as numbers. I say, unlike Russell, that the connection to counting is crucial. |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| Full Idea: Dedekind set up the axiom that the gap in his 'cut' must always be filled …The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - Introduction to Mathematical Philosophy VII | |
| A reaction: This remark of Russell's is famous, and much quoted in other contexts, but I have seen the modern comment that it is grossly unfair to Dedekind. |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| Full Idea: One view, favoured by Dedekind, is that the cut postulates a real number for each cut in the rationals; it does not identify real numbers with cuts. ....A view favoured by later logicists is simply to identify a real number with a cut. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 | |
| A reaction: Dedekind is the patriarch of structuralism about mathematics, so he has little interest in the existenc of 'objects'. |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| Full Idea: If we scrutinize closely what is done in counting an aggregate of things, we see the ability of the mind to relate things to things, to let a thing correspond to a thing, or to represent a thing by a thing, without which no thinking is possible. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
| A reaction: I don't suppose it occurred to Dedekind that he was reasserting Hume's observation about the fundamental psychology of thought. Is the origin of our numerical ability of philosophical interest? |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| Full Idea: A system S is said to be infinite when it is similar to a proper part of itself. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], V.64) |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| Full Idea: Dedekind's natural numbers: an object is in a set (0 is a number), a function sends the set one-one into itself (numbers have unique successors), the object isn't a value of the function (it isn't a successor), plus induction. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William D. Hart - The Evolution of Logic 5 | |
| A reaction: Hart notes that since this refers to sets of individuals, it is a second-order account of numbers, what we now call 'Second-Order Peano Arithmetic'. |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| Full Idea: Dedekind's idea is that the set of natural numbers has zero as a member, and also has as a member the successor of each of its members, and it is the smallest set satisfying this condition. It is the intersection of all sets satisfying the condition. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| Full Idea: It is Dedekind's categoricity result that convinces most of us that he has articulated our implicit conception of the natural numbers, since it entitles us to speak of 'the' domain (in the singular, up to isomorphism) of natural numbers. | |
| From: comment on Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ian Rumfitt - The Boundary Stones of Thought 9.1 | |
| A reaction: The main rival is set theory, but that has an endlessly expanding domain. He points out that Dedekind needs second-order logic to achieve categoricity. Rumfitt says one could also add to the 1st-order version that successor is an ancestral relation. |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| Full Idea: Dedekind proves mathematical induction, while Peano regards it as an axiom, ...and Peano's method has the advantage of simplicity, and a clearer separation between the particular and the general propositions of arithmetic. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §241 |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| Full Idea: Dedekind is the philosopher-mathematician with whom the structuralist conception originates. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §3 n13) by Fraser MacBride - Structuralism Reconsidered | |
| A reaction: Hellman says the idea grew naturally out of modern mathematics, and cites Hilbert's belief that furniture would do as mathematical objects. |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| Full Idea: Dedekindian abstraction says mathematical objects are 'positions' in a model, while Cantorian abstraction says they are the result of abstracting on structurally similar objects. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §6 | |
| A reaction: The key debate among structuralists seems to be whether or not they are committed to 'objects'. Fine rejects the 'austere' version, which says that objects have no properties. Either version of structuralism can have abstraction as its basis. |
| 15017 | Supervenience is a modal connection [Sider] |
| Full Idea: Supervenience is just a kind of modal connection. | |
| From: Theodore Sider (Writing the Book of the World [2011], 09.10) | |
| A reaction: It says what would happen, as well as what does. This is big for Sider because he rejects modality as a feature of actuality. I think the world is crammed full of modal facts, so supervenience should be a handy tool for me. |
| 15008 | Is fundamentality in whole propositions (and holistic), or in concepts (and atomic)? [Sider] |
| Full Idea: The locus of fundamentality for a Finean is the whole proposition, whereas for me it is the proposition-part. Fundamentality is holistic for the Finean, atomistic for me. | |
| From: Theodore Sider (Writing the Book of the World [2011], 08.3) | |
| A reaction: This is because Kit Fine has pushed fundamentality into a relation (grounding), rather than into the particular entities involved (if I understand Sider's reading of him aright). My first intuition is to side with Sider. I'm on Sider's side... |
| 15013 | Tables and chairs have fundamental existence, but not fundamental natures [Sider] |
| Full Idea: The existence of tables and chairs is just as fundamental as the existence of electrons (in contrast, perhaps, with smirks and shadows, which do not exist fundamentally). However, tables and chairs have nonfundamental natures. | |
| From: Theodore Sider (Writing the Book of the World [2011], 08.7) | |
| A reaction: This seems to be a good clarification, and to me the 'nature' of something points towards its essence. However, I suppose he refers here to the place of something in a dependence hierarchy. But then, why does it have that place? What power? |
| 23472 | The sense of propositions relies on the world's basic logical structure [Wittgenstein] |
| Full Idea: In order for a proposition to be CAPABLE of making sense, the world must already have the logical structure it has. The logic of the world is prior to all truth and falsehood. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], p.14c) | |
| A reaction: It seems that in Tractatus it is propositions about facts which are true or false, but prior to the facts are substance and the objects, and it is there that we find the logical structure of the world. I see this view as modern stoicism. |
| 15014 | Unlike things, stuff obeys unrestricted composition and mereological essentialism [Sider] |
| Full Idea: Stuff obeys unrestricted composition and mereological essentialism, whereas things do not. | |
| From: Theodore Sider (Writing the Book of the World [2011], 09.6.2) | |
| A reaction: [He cites Markosian 2004] |
| 15009 | We must distinguish 'concrete' from 'abstract' and necessary states of affairs. [Sider] |
| Full Idea: The truthmaker theorist's 'concrete' states of affairs must be distinguished from necessarily existing 'abstract' states of affairs. | |
| From: Theodore Sider (Writing the Book of the World [2011], 08.4) | |
| A reaction: [He cites Plantinga's 'Nature of Necessity' for the second one; I presume the first one is Armstrong] |
| 14983 | Accept the ontology of your best theory - and also that it carves nature at the joints [Sider] |
| Full Idea: We can add to the Quinean advice to believe the ontology of your best theory that you should also regard the ideology of your best theory as carving at the joints. | |
| From: Theodore Sider (Writing the Book of the World [2011], 02.3) | |
| A reaction: I've never liked the original Quinean formulation, but this is much better. I just take my ontological commitments to reside in me, not in whatever theory I am currently employing. I may be dubious about my own theory. |
| 14978 | A property is intrinsic if an object alone in the world can instantiate it [Sider] |
| Full Idea: Chisholm and Kim proposed a modal notion of an 'intrinsic' property - that a property is intrinsic if and only if it is possibly instantiated by an object that is alone in the world. | |
| From: Theodore Sider (Writing the Book of the World [2011], 01.2) | |
| A reaction: [He cites Chisholm 1976:127 and Kim 1982:59-60] Sider then gives a counterexample from David Lewis (Idea 14979). |
| 14995 | Predicates can be 'sparse' if there is a universal, or if there is a natural property or relation [Sider] |
| Full Idea: For Armstrong a predicate is sparse when there exists a corresponding universal; for Lewis, a predicate is sparse when there exists a corresponding natural property or relation. | |
| From: Theodore Sider (Writing the Book of the World [2011], 06) | |
| A reaction: I like 'sparse' properties, but have no sympathy with Armstrong, and am cautious about Lewis. I like Shoemaker's account, which makes properties even sparser. 'Abundant' so-called properties are my pet hate. They are 'predicates'! |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| Full Idea: A thing (an object of our thought) is completely determined by all that can be affirmed or thought concerning it. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], I.1) | |
| A reaction: How could you justify this as an observation? Why can't there be unthinkable things (even by God)? Presumably Dedekind is offering a stipulative definition, but we may then be confusing epistemology with ontology. |
| 15026 | Essence (even if nonmodal) is not fundamental in metaphysics [Sider] |
| Full Idea: We should not regard nonmodal essence as being metaphysically basic: fundamental theories need essence no more than they need modality. | |
| From: Theodore Sider (Writing the Book of the World [2011], 12.1) | |
| A reaction: He is discussing Kit Fine, and notes that Fine offers a nonmodal view of essence, but still doesn't make it fundamental. I am a fan of essences, but making them fundamental in metaphysics seems unlikely. |
| 15030 | Humeans say that we decide what is necessary [Sider] |
| Full Idea: The spirit of Humeanism is that necessity is not a realm to be discovered. We draw the lines around what is necessary. | |
| From: Theodore Sider (Writing the Book of the World [2011], 12.3) | |
| A reaction: I disagree, but it is hard to argue the point. My intuitions are that the obvious necessities of logic and mathematics reflect the way nature has to be. The deepest necessities are patterns (about which God has no choice). |
| 15031 | Modal terms in English are entirely contextual, with no modality outside the language [Sider] |
| Full Idea: English modals are context-dependent through and through; there is no stable 'outer modality'. | |
| From: Theodore Sider (Writing the Book of the World [2011], 12.7) | |
| A reaction: Sider has been doing so well up to here. To me this is swallowing the bait of linguistic approaches to philosophy which he has fought so hard to avoid. |
| 15027 | If truths are necessary 'by convention', that seems to make them contingent [Sider] |
| Full Idea: If □φ says that φ is true by convention, then □φ would apparently turn out to be contingent, since statements about what conventions we adopt are not themselves true by convention. The main axioms of S4 and S5 would be false. | |
| From: Theodore Sider (Writing the Book of the World [2011], 12.1) |
| 15028 | Conventionalism doesn't seem to apply to examples of the necessary a posteriori [Sider] |
| Full Idea: Conventionalism is apparently inapplicable to Kripke's and Putnam's examples of the necessary a posteriori (and, relatedly, to de re modality). | |
| From: Theodore Sider (Writing the Book of the World [2011], 12.1) | |
| A reaction: [Sidelle 1989 discusses this] |
| 15033 | Humeans says mathematics and logic are necessary because that is how our concept of necessity works [Sider] |
| Full Idea: Why are logical (or mathematical, or analytic...) truths necessary? The Humean's answer is that this is just how our concept of necessity works. | |
| From: Theodore Sider (Writing the Book of the World [2011], 12.11) | |
| A reaction: This is why I (unlike Sider) am not a Humean. If we agreed that 'necessary' meant 'whatever is decreed by the Pope', that would so obviously not be necessary that we would have to start searching nature for true necessities. |
| 15025 | The world does not contain necessity and possibility - merely how things are [Sider] |
| Full Idea: At bottom, the world is an amodal place. Necessity and possibility do not carve at the joints; ultimate reality is not 'full of threats and promises' (Goodman). The book of the world says how things are, not how they must or might be. | |
| From: Theodore Sider (Writing the Book of the World [2011], 12) | |
| A reaction: Nice to see this expressed so clearly. I find it much easier to disagree with as a result. At first blush I would say that if you haven't noticed that the world is full of threats and promises, you should wake up and smell the coffee. Actuality is active. |
| 23500 | My main problem is the order of the world, and whether it is knowable a priori [Wittgenstein] |
| Full Idea: The great problem around which everything turns that I write is: is there an order in the world a priori, and if so what does it consist in? | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 15.06.01) | |
| A reaction: Morris identifies this as a 'Kantian question'. I trace it back to stoicism. This question has never bothered me. It just seems weird to think that you can infer reality from the examination of your own thinking. Perhaps I should take it more seriously? |
| 14988 | A theory which doesn't fit nature is unexplanatory, even if it is true [Sider] |
| Full Idea: 'Theories' based on bizarre, non-joint-carving classifications are unexplanatory even when true. | |
| From: Theodore Sider (Writing the Book of the World [2011], 03.1) | |
| A reaction: This nicely pinpoints why I take explanation to be central to whole metaphysical enterprise. |
| 14982 | If I used Ramsey sentences to eliminate fundamentality from my theory, that would be a real loss [Sider] |
| Full Idea: If the entire theory of this book were replaced by its Ramsey sentence, omitting all mention of fundamentality, something would seem to be lost. | |
| From: Theodore Sider (Writing the Book of the World [2011], 02.2 n2) | |
| A reaction: It is a moot point whether Ramsey sentences actually eliminate anything from the ontology, but trying to wriggle out of ontological commitment looks a rather sad route to follow. |
| 14989 | Problem predicates in induction don't reflect the structure of nature [Sider] |
| Full Idea: 'Is nonblack', 'is a nonraven', and 'grue' fail to carve at the joints. | |
| From: Theodore Sider (Writing the Book of the World [2011], 03.3) | |
| A reaction: A lot more than this needs to said, but this remark encapsulates why I find most of these paradoxes of induction uninteresting. They are all the creations of logicians, rather than of scientists. |
| 14997 | Two applications of 'grue' do not guarantee a similarity between two things [Sider] |
| Full Idea: The applicability of 'grue' to each of a pair of particulars does not guarantee the similarity of those particulars. | |
| From: Theodore Sider (Writing the Book of the World [2011], 06.2) | |
| A reaction: Grue is not a colour but a behaviour. If two things are 'mercurial' or 'erratic', will that ensure a similarity at any given moment? |
| 14990 | Bayes produces weird results if the prior probabilities are bizarre [Sider] |
| Full Idea: In the Bayesian approach, bizarre prior probability distributions will result in bizarre responses to evidence. | |
| From: Theodore Sider (Writing the Book of the World [2011], 03.3) | |
| A reaction: This is exactly what you find when people with weird beliefs encounter ridiculous evidence for things. It doesn't invalidate the formula, but just says rubbish in rubbish out. |
| 15005 | Explanations must cite generalisations [Sider] |
| Full Idea: Explanations must cite generalisations. | |
| From: Theodore Sider (Writing the Book of the World [2011], 07.13) | |
| A reaction: I'm uneasy about this. Presumably some events have a unique explanation - a unique mechanism, perhaps. Language is inescapably general in its nature - which I take to be Aristotle's reason for agreeing the Sider. [Sider adds mechanisms on p.159] |
| 15011 | If the ultimate explanation is a list of entities, no laws, patterns or mechanisms can be cited [Sider] |
| Full Idea: Ultimate explanations always terminate in the citation of entities; but since a mere list of entities is so unstructured, these 'explanations' cannot be systematized with detailed general laws, patterns, or mechanisms. | |
| From: Theodore Sider (Writing the Book of the World [2011], 08.5) | |
| A reaction: We just need to distinguish between ultimate ontology and ultimate explanations. I think explanations peter out at the point where we descend below the mechanisms. Patterns or laws don't explain on their own. Causal mechanisms are the thing. |
| 15018 | Intentionality is too superficial to appear in the catalogue of ultimate physics [Sider] |
| Full Idea: One day the physicists will complete the catalogue of ultimate and irreducible properties of things. When they do, the like of spin, charm and charge will perhaps appear on the list. But aboutness sure won't; intentionality simply doesn't go that deep. | |
| From: Theodore Sider (Writing the Book of the World [2011], 4 Intro) | |
| A reaction: Fodor's project is to give a reductive, and perhaps eliminative, account of intentionality of mind, while leaving open what one might do with the phenomenological aspects. Personally I don't think they will appear on the list either. |
| 22323 | The philosophical I is the metaphysical subject, the limit - not a part of the world [Wittgenstein] |
| Full Idea: The philosophical I is not the man, not the human body, or the human soul of wh9ch psychology treats, but the metaphysical subject, the limit - not a part of the world. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 1916. 2 Sep), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 58 Intro | |
| A reaction: This is to treat the self as a phenomenon of thought, rather than of a human being. So if a machine could think, would it hence necessarily have a metaphysical self? |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| Full Idea: By applying the operation of abstraction to a system of objects isomorphic to the natural numbers, Dedekind believed that we obtained the abstract system of natural numbers, each member having only properties consequent upon its position. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Dummett - The Philosophy of Mathematics | |
| A reaction: Dummett is scornful of the abstractionism. He cites Benacerraf as a modern non-abstractionist follower of Dedekind's view. There seems to be a suspicion of circularity in it. How many objects will you abstract from to get seven? |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| Full Idea: If in an infinite system, set in order, we neglect the special character of the elements, simply retaining their distinguishability and their order-relations to one another, then the elements are the natural numbers, created by the human mind. | |
| From: Richard Dedekind (Nature and Meaning of Numbers [1888], VI.73) | |
| A reaction: [compressed] This is the classic abstractionist view of the origin of number, but with the added feature that the order is first imposed, so that ordinals remain after the abstraction. This, of course, sounds a bit circular, as well as subjective. |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| Full Idea: Dedekind's conception is psychologistic only if that is the only way to understand the abstraction that is involved, which it is not. | |
| From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William W. Tait - Frege versus Cantor and Dedekind IV | |
| A reaction: This is a very important suggestion, implying that we can retain some notion of abstractionism, while jettisoning the hated subjective character of private psychologism, which seems to undermine truth and logic. |
| 23481 | Propositions assemble a world experimentally, like the model of a road accident [Wittgenstein] |
| Full Idea: In the proposition a world is as it were put together experimentally. (As when in the law court in Paris a motor-car accident is represented by means of dolls, etc). | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 14.09.29) | |
| A reaction: [see Tractatus 4.031] This is the first appearance of LW's picture (or model) theory of meaning. It may well be the best theory of meaning anyone has come up with, since meaning being out in the world strikes me as absurd. |
| 14999 | Prior to conventions, not all green things were green? [Sider] |
| Full Idea: It is absurd to say that 'before we introduced our conventions, not all green things were green'. | |
| From: Theodore Sider (Writing the Book of the World [2011], 06.5) | |
| A reaction: Well… Different cultures label the colours of the rainbow differently, and many of them omit orange. I suspect the blue/green borderline has shifted. |
| 14998 | Conventions are contingent and analytic truths are necessary, so that isn't their explanation [Sider] |
| Full Idea: To suggest that analytic truths make statements about linguistic conventions is a nonstarter; statements about linguistic conventions are contingent, whereas the statements made by typical analytic sentences are necessary. | |
| From: Theodore Sider (Writing the Book of the World [2011], 06.5) | |
| A reaction: That 'anything yellow is extended' is not just a convention should be fairly obvious, and it is obviously necessary. But we can say that bachelors are necessarily unmarried men - given the current convention. |
| 15016 | Analyticity has lost its traditional role, which relied on truth by convention [Sider] |
| Full Idea: Nothing can fully play the role traditionally associated with analyticity, for much of that traditional role presupposed the doctrine of truth by convention. | |
| From: Theodore Sider (Writing the Book of the World [2011], 09.8) | |
| A reaction: Sider rejects Quine's attack on analyticity, but accepts his critique of truth by convention. |
| 4678 | Absolute prohibitions are the essence of ethics, and suicide is the most obvious example [Wittgenstein] |
| Full Idea: If suicide is allowed, then everything is allowed. If anything is not allowed, then suicide is not allowed. This throws a light on the nature of ethics, for suicide is, so to speak, the elementary sin. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], end), quoted by Jonathan Glover - Causing Death and Saving Lives §13 | |
| A reaction: This reveals the religious streak in Wittgenstein. I am reluctant to judge suicide, but this seems wrong. Should a 'jumper' worry if they land on someone else and kill them? Of course they should. |
| 14985 | The notion of law doesn't seem to enhance physical theories [Sider] |
| Full Idea: Adding the notion of law to physical theory doesn't seem to enhance its explanatory power. | |
| From: Theodore Sider (Writing the Book of the World [2011], 02.4) | |
| A reaction: I agree with his scepticism about laws, although Sider offers it as part of his scepticism about modal facts being included in explanations of actuality. Personally I like dispositions, but not laws. See the ideas of Stephen Mumford. |
| 14987 | Many of the key theories of modern physics do not appear to be 'laws' [Sider] |
| Full Idea: That spacetime is 4D Lorentzian manifold, that the universe began with a singularity, and in a state of low entropy, are all central to physics, but it is a stretch to call them 'laws'. ...It has been argued that there are no laws of biology. | |
| From: Theodore Sider (Writing the Book of the World [2011], 03.1) |
| 14991 | Space has real betweenness and congruence structure (though it is not the Euclidean concepts) [Sider] |
| Full Idea: In metaphysics, space is intrinsically structured; the genuine betweenness and congruence relations are privileged in a way that Euclidean-betweenness and Euclidean-congruence are not. | |
| From: Theodore Sider (Writing the Book of the World [2011], 03.4) | |
| A reaction: I note that Einstein requires space to be 'curved', which implies that it is a substance with properties. |
| 15021 | The central question in the philosophy of time is: How alike are time and space? [Sider] |
| Full Idea: The central question in the philosophy of time is: How alike are time and space? | |
| From: Theodore Sider (Writing the Book of the World [2011], 11.1) |
| 15024 | The spotlight theorists accepts eternal time, but with a spotlight of the present moving across it [Sider] |
| Full Idea: The spotlight theorist accepts the block universe, but also something in addition: a joint-carving monadic property of presentness, which is possessed by just one moment of time, and which 'moves', to be possessed by later and later times. | |
| From: Theodore Sider (Writing the Book of the World [2011], 11.9) | |
| A reaction: This seems better than the merely detached eternalist view, which seems to ignore the key phenomenon. I just can't comprehend any theory which makes the future as real as the past. |