187 ideas
| 9218 | Maybe what distinguishes philosophy from science is its pursuit of necessary truths [Sider] |
| Full Idea: According to one tradition, necessary truth demarcates philosophical from empirical inquiry. Science identifies contingent aspects of the world, whereas philosophical inquiry reveals the essential nature of its objects. | |
| From: Theodore Sider (Reductive Theories of Modality [2003], 1) | |
| A reaction: I don't think there is a clear demarcation, and I would think that lots of generalizations about contingent truths are in philosophical territory, but I quite like this idea - even if it does make scientists laugh at philosophers. |
| 14721 | Metaphysical enquiry can survive if its conclusions are tentative [Sider] |
| Full Idea: Metaphysical enquiry can survive if we are willing to live with highly tentative conclusions. | |
| From: Theodore Sider (Four Dimensionalism [2001], Intro) | |
| A reaction: Nice. Nothing alienates the rather literal scientific sort of mind quicker that bold, dogmatic and even arrogant assertions about metaphysics. But to entirely close down metaphysical speculation for that reason is absurd. |
| 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). |
| 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) |
| 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. |
| 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. |
| 13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
| Full Idea: Formulas provable from no premises at all are often called 'theorems'. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.6) |
| 13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
| Full Idea: The method of truth tables assumes truth functionality. Truth tables are just pictures of truth functions. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.3) |
| 13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
| Full Idea: Deontic accessibility seems not to be reflexive (that it ought to be true doesn't make it true). One could argue that it is serial (that there is always a world where something is acceptable). | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.3.1) |
| 13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
| Full Idea: In D we add to K a new axiom saying that 'what's necessary is possible' (□φ→◊φ), ..and it can then be proved that tautologies are possible and contradictions are not necessary. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.4.2) |
| 13711 | System B introduces iterated modalities [Sider] |
| Full Idea: With system B we begin to be able to say something about iterated modalities. ..S4 then takes a different stand on the iterated modalities, and neither is an extension of the other. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.4.4) |
| 13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
| Full Idea: S5 is the strongest system, since it has the most valid formulas. That's because it has the fewest models; it's easy to be S5-valid since there are so few potentially falsifying models. K is the weakest system, for opposite reasons. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.3.2) | |
| A reaction: Interestingly, the orthodox view is that S5 is the correct logic for metaphysics, but it sounds a bit lax. Compare Idea 13707. |
| 13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
| Full Idea: Epistemic accessibility should be required to be reflexive (allowing Kφ→φ). S4 allows the 'KK principle', or 'positive introspection' (Kφ→KKφ), and S5 allows 'negative introspection' (¬Kφ→K¬Kφ). | |
| From: Theodore Sider (Logic for Philosophy [2010], 7.2) |
| 13714 | We can treat modal worlds as different times [Sider] |
| Full Idea: We can think of the worlds of modal logic as being times, rather than 'possible' worlds. | |
| From: Theodore Sider (Logic for Philosophy [2010], 7.3.3) |
| 13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
| Full Idea: The Converse Barcan Formula reads □∀αφ→∀α□φ (or an equivalent using ◊). | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.5.2) | |
| A reaction: I would read that as 'if all the αs happen to be φ, then αs have to be φ'. Put like that, I would have thought that it was obviously false. Sider points out that some new object could turn up which isn't φ. |
| 13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
| Full Idea: The Barcan Formula ∀x□Fx→□∀xFx is often regarded as a defect of Simple Quantified Modal Logic, though this most clearly seen in its equivalent form ◊∃xFx→∃x◊Fx. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.5.2) | |
| A reaction: [See Idea 13719 for an explanation why it might be a defect] I translate the first one as 'if xs must be F, then they are always F', and the second one as 'for x to be possibly F, there must exist an x which is possibly F'. Modality needs existence. |
| 13723 | System B is needed to prove the Barcan Formula [Sider] |
| Full Idea: The proof of the Barcan Formula require System B. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.7) |
| 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! |
| 13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
| Full Idea: Not everyone who employs intuitionistic logic is an intuitionist about mathematics. | |
| From: Theodore Sider (Logic for Philosophy [2010], 7.4.1) | |
| A reaction: This seems worthy of note, since it may be tempting to reject the logic because of the implausibility of the philosophy of mathematics. I must take intuitionist logic more seriously. |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| Full Idea: Cohen's method of 'forcing' produces a new model of ZFC from an old model by appending a carefully chosen 'generic' set. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.4) |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| Full Idea: A possible axiom is the Large Cardinal Axiom, which asserts that there are more and more stages in the cumulative hierarchy. Infinity can be seen as the first of these stages, and Replacement pushes further in this direction. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.5) |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| Full Idea: In current set theory, the search is on for new axioms to determine the size of the continuum. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §0) | |
| A reaction: This sounds the wrong way round. Presumably we seek axioms that fix everything else about set theory, and then check to see what continuum results. Otherwise we could just pick our continuum, by picking our axioms. |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| Full Idea: Most writers agree that if any sense can be made of the distinction between analytic and synthetic, then the Axiom of Extensionality should be counted as analytic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [Boolos is the source of the idea] In other words Extensionality is not worth discussing, because it simply tells you what the world 'set' means, and there is no room for discussion about that. The set/class called 'humans' varies in size. |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| Full Idea: The extensional view of sets is preferable because it is simpler, clearer, and more convenient, because it individuates uniquely, and because it can simulate intensional notions when the need arises. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [She cites Fraenkel, Bar-Hillet and Levy for this] The difficulty seems to be whether the extensional notion captures our ordinary intuitive notion of what constitutes a group of things, since that needs flexible size and some sort of unity. |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| Full Idea: The Axiom of Infinity is a simple statement of Cantor's great breakthrough. His bold hypothesis that a collection of elements that had lurked in the background of mathematics could be infinite launched modern mathematics. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: It also embodies one of those many points where mathematics seems to depart from common sense - but then most subjects depart from common sense when they get more sophisticated. Look what happened to art. |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| Full Idea: If one is interested in analysis then infinite sets are indispensable since even the notion of a real number cannot be developed by means of finite sets alone. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: [Maddy is citing Fraenkel, Bar-Hillel and Levy] So Cantor's great breakthrough (Idea 13021) actually follows from the earlier acceptance of the real numbers, so that's where the departure from common sense started. |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| Full Idea: The axiom of infinity: that there are infinite sets is to claim that completed infinite collections can be treated mathematically. In its standard contemporary form, the axioms assert the existence of the set of all finite ordinals. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.3) |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| Full Idea: The Power Set Axiom is indispensable for a set-theoretic account of the continuum, ...and in so far as those attempts are successful, then the power-set principle gains some confirmatory support. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.6) | |
| A reaction: The continuum is, of course, notoriously problematic. Have we created an extra problem in our attempts at solving the first one? |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| Full Idea: In the presence of other axioms, the Axiom of Foundation is equivalent to the claim that every set is a member of some Vα. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.3) |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| Full Idea: Jordain made consistent and ill-starred efforts to prove the Axiom of Choice. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This would appear to be the fate of most axioms. You would presumably have to use a different system from the one you are engaged with to achieve your proof. |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| Full Idea: Resistance to the Axiom of Choice centred on opposition between existence and construction. Modern set theory thrives on a realistic approach which says the choice set exists, regardless of whether it can be defined, constructed, or given by a rule. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This seems to be a key case for the ontology that lies at the heart of theory. Choice seems to be an invaluable tool for proofs, so it won't go away, so admit it to the ontology. Hm. So the tools of thought have existence? |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| Full Idea: Many theorems depend on the Axiom of Choice, including that a countable union of sets is countable, and results in analysis, topology, abstract algebra and mathematical logic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: The modern attitude seems to be to admit anything if it leads to interesting results. It makes you wonder about the modern approach of using mathematics and logic as the cutting edges of ontological thinking. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| Full Idea: The Axiom of Reducibility states that every propositional function is extensionally equivalent to some predicative proposition function. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| Full Idea: The Iterative Conception (Zermelo 1930) says everything appears at some stage. Given two objects a and b, let A and B be the stages at which they first appear. Suppose B is after A. Then the pair set of a and b appears at the immediate stage after B. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: Presumably this all happens in 'logical time' (a nice phrase I have just invented!). I suppose we might say that the existence of the paired set is 'forced' by the preceding sets. No transcendental inferences in this story? |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| Full Idea: The 'limitation of size' is a vague intuition, based on the idea that being too large may generate the paradoxes. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: This is an intriguing idea to be found right at the centre of what is supposed to be an incredibly rigorous system. |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| Full Idea: The master science can be thought of as the theory of sets with the entire range of physical objects as ur-elements. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: This sounds like Quine's view, since we have to add sets to our naturalistic ontology of objects. It seems to involve unrestricted mereology to create normal objects. |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| Full Idea: Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups. |
| 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) |
| 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. |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| Full Idea: Henkin-style semantics seem to me more plausible for plural logic than for second-order logic. | |
| From: Penelope Maddy (Second Philosophy [2007], III.8 n1) | |
| A reaction: Henkin-style semantics are presented by Shapiro as the standard semantics for second-order logic. |
| 13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
| Full Idea: On the question of the nature of genuine logical consequence, ...the most popular answer is the semantic, or model-theoretic one. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: Reading the literature, one might be tempted to think that this is the only account that anyone takes seriously. Substitutional semantics seems an interesting alternative. |
| 13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
| Full Idea: The 'modal' account of logical consequence is that it is not possible for the premises to be true and the consequent false (under some suitable notion of possibility). | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: Sider gives a nice summary of five views of logical consequence, to which Shapiro adds substitutional semantics. |
| 13680 | Maybe logical consequence is a primitive notion [Sider] |
| Full Idea: There is a 'primitivist' account, according to which logical consequence is a primitive notion. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: While sympathetic to substitutional views (Idea 13674), the suggestion here pushes me towards thinking that truth must be at the root of it. The trouble, though, is that a falsehood can be a good logical consequence of other falsehoods. |
| 13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
| Full Idea: Another answer to the question about the nature of logical consequence is a proof-theoretic one, according to which it is more a matter of provability than of truth-preservation. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: I don't like this, and prefer the model-theoretic or substitutional accounts. Whether you can prove that something is a logical consequence seems to me entirely separate from whether you can see that it is so. Gödel seems to agree. |
| 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. |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| Full Idea: A 'theorem' is defined as the last line of a proof in which each line is either an axiom or follows from earlier lines by a rule. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.7) | |
| A reaction: In other words, theorems are the axioms and their implications. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| Full Idea: A 'propositional function' is generated when one of the terms of the proposition is replaced by a variable, as in 'x is wise' or 'Socrates'. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: This implies that you can only have a propositional function if it is derived from a complete proposition. Note that the variable can be in either subject or in predicate position. It extends Frege's account of a concept as 'x is F'. |
| 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] |
| 13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
| Full Idea: When a variable is not combined with a quantifier (and so is 'free'), the result is, intuitively, semantically incomplete, and incapable of truth or falsity. | |
| From: Theodore Sider (Logic for Philosophy [2010], 4.2) |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| Full Idea: Calling a function a 'total' function 'over D' means that the function must have a well-defined output (which is a member of D) whenever it is given as inputs any n members of D. | |
| From: Theodore Sider (Logic for Philosophy [2010], 5.2) |
| 13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
| Full Idea: We might prefer λx(Fx∧Gx)(a) as the symbolization of 'John is cold and hungry', since it treats 'is cold and hungry' as a single predicate. | |
| From: Theodore Sider (Logic for Philosophy [2010], 5.5) |
| 13688 | Good axioms should be indisputable logical truths [Sider] |
| Full Idea: Since they are the foundations on which a proof rests, the axioms in a good axiomatic system ought to represent indisputable logical truths. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.6) |
| 13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
| Full Idea: Axiomatic systems do not allow reasoning with assumptions, and therefore do not allow conditional proof or reductio ad absurdum. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.6) | |
| A reaction: Since these are two of the most basic techniques of proof which I have learned (in Lemmon), I shall avoid axiomatic proof systems at all costs, despites their foundational and Ockhamist appeal. |
| 13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
| Full Idea: A proof by induction starts with a 'base case', usually that an atomic formula has some property. It then assumes an 'inductive hypothesis', that the property is true up to a certain case. The 'inductive step' then says it will be true for the next case. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.7) | |
| A reaction: [compressed] |
| 13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
| Full Idea: The style of proof called 'induction on formula construction' (or 'on the number of connectives', or 'on the length of the formula') rest on the fact that all formulas are built up from atomic formulas according to strict rules. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.7) | |
| A reaction: Hence the proof deconstructs the formula, and takes it back to a set of atomic formulas have already been established. |
| 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. |
| 13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
| Full Idea: The method of natural deduction is popular in introductory textbooks since it allows reasoning with assumptions. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.5) | |
| A reaction: Reasoning with assumptions is generally easier, rather than being narrowly confined to a few tricky axioms, You gradually show that an inference holds whatever the assumption was, and so end up with the same result. |
| 13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
| Full Idea: We can construct proofs not out of well-formed formulae ('wffs'), but out of sequents, which are some premises followed by their logical consequence. We explicitly keep track of the assumptions upon which the conclusion depends. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.5.1) | |
| A reaction: He says the method of sequents was invented by Gerhard Gentzen (the great nazi logician) in 1935. The typical starting sequents are the introduction and elimination rules. E.J. Lemmon's book, used in this database, is an example. |
| 13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
| Full Idea: A valuation function in predicate logic will assign truth values to formulas relative to variable assignments. | |
| From: Theodore Sider (Logic for Philosophy [2010], 4.2) | |
| A reaction: Sider observes that this is a 'double' relativisation (due to Tarski), since propositional logic truth was already relative to an interpretation. Now we are relative to variable assignments as well. |
| 13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
| Full Idea: The semantical notion of a logical truth is that of a valid formula, which is true in all interpretations. In propositional logic they are 'tautologies'. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.3) | |
| A reaction: This implies that there is a proof-theoretic account of logical truth as well. Intuitively a logical truth is a sequent which holds no matter which subject matter it refers to, so the semantic view sounds OK. |
| 13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
| Full Idea: It isn't clear which formulas of modal propositional logic are logical truths, ...especially for sentences that contain iterations of modal operators. Is □P→□□P a logical truth? It's hard to say. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.3) | |
| A reaction: The result, of course, is that there are numerous 'systems' for modal logic, so that you can choose the one that gives you the logical truths you want. His example is valid in S4 and S5, but not in the others. |
| 13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
| Full Idea: In model theory one normally defines some notion of truth in a model, and then uses it to define validity as truth in all models, and semantic consequence as the preservation of truth in models. | |
| From: Theodore Sider (Logic for Philosophy [2010], 10.1) |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
| Full Idea: You can establish facts of the form Γ|-φ while avoiding the agonies of axiomatic proofs by reasoning directly about models to conclusions about semantic consequence, and then citing completeness. | |
| From: Theodore Sider (Logic for Philosophy [2010], 4.5) | |
| A reaction: You cite completeness by saying that anything which you have shown to be a semantic consequence must therefore be provable (in some way). |
| 13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
| Full Idea: Compactness is intuitively surprising, ..because one might have thought there could be some contradiction latent within some infinite set, preventing it from being satisfiable, only discovered when you consider the whole set. But this can't happen. | |
| From: Theodore Sider (Logic for Philosophy [2010], 4.5) |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| Full Idea: Both Cantor's real number (Cauchy sequences of rationals) and Dedekind's cuts involved regarding infinite items (sequences or sets) as completed and subject to further manipulation, bringing the completed infinite into mathematics unambiguously. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1 n39) | |
| A reaction: So it is the arrival of the real numbers which is the culprit for lumbering us with weird completed infinites, which can then be the subject of addition, multiplication and exponentiation. Maybe this was a silly mistake? |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| Full Idea: The line of development that finally led to a coherent foundation for the calculus also led to the explicit introduction of completed infinities: each real number is identified with an infinite collection of rationals. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.3) | |
| A reaction: Effectively, completed infinities just are the real numbers. |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| Full Idea: The stunning discovery that infinity comes in different degrees led to the theory of infinite cardinal numbers, the heart of contemporary set theory. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: It occurs to me that these huge cardinals only exist in set theory. If you took away that prop, they would vanish in a puff. |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| Full Idea: By the mid 1890s Cantor was aware that there could be no set of all sets, as its cardinal number would have to be the largest cardinal number, while his own theorem shows that for any cardinal there is a larger. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: There is always a larger cardinal because of the power set axiom. Some people regard that with suspicion. |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| Full Idea: An 'inaccessible' cardinal is one that cannot be reached by taking unions of small collections of smaller sets or by taking power sets. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.5) | |
| A reaction: They were introduced by Hausdorff in 1908. |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| Full Idea: Even the fundamental theorems about limits could not [at first] be proved because the reals themselves were not well understood. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: This refers to the period of about 1850 (Weierstrass) to 1880 (Dedekind and Cantor). |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| Full Idea: A single second-order sentence has second-order semantic consequences which are all and only the truths of arithmetic, but this is cold comfort because of incompleteness; no axiomatic system draws out the consequences of this axiom. | |
| From: Theodore Sider (Logic for Philosophy [2010], 5.4.3) |
| 18182 | The extension of concepts is not important to me [Maddy] |
| Full Idea: I attach no decisive importance even to bringing in the extension of the concepts at all. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], §107) | |
| A reaction: He almost seems to equate the concept with its extension, but that seems to raise all sorts of questions, about indeterminate and fluctuating extensions. |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| Full Idea: In the ZFC cumulative hierarchy, Frege's candidates for numbers do not exist. For example, new three-element sets are formed at every stage, so there is no stage at which the set of all three-element sets could he formed. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: Ah. This is a very important fact indeed if you are trying to understand contemporary discussions in philosophy of mathematics. |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| Full Idea: To solve the Julius Caesar problem, Frege requires explicit definitions of the numbers, and he proposes his well-known solution: the number of Fs = the extension of the concept 'equinumerous with F' (based on one-one correspondence). | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: Why do there have to be Fs before there can be the corresponding number? If there were no F for 523, would that mean that '523' didn't exist (even if 522 and 524 did exist)? |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| Full Idea: If you wonder why multiplication is commutative, you could prove it from the Peano postulates, but the proof offers little towards an answer. In set theory Cartesian products match 1-1, and n.m dots when turned on its side has m.n dots, which explains it. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: 'Turning on its side' sounds more fundamental than formal set theory. I'm a fan of explanation as taking you to the heart of the problem. I suspect the world, rather than set theory, explains the commutativity. |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| Full Idea: The standard account of the relationship between numbers and sets is that numbers simply are certain sets. This has the advantage of ontological economy, and allows numbers to be brought within the epistemology of sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Maddy votes for numbers being properties of sets, rather than the sets themselves. See Yourgrau's critique. |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| Full Idea: I propose that ...numbers are properties of sets, analogous, for example, to lengths, which are properties of physical objects. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Are lengths properties of physical objects? A hole in the ground can have a length. A gap can have a length. Pure space seems to contain lengths. A set seems much more abstract than its members. |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| Full Idea: Maddy takes a natural number to be a certain property of sui generis sets, the property of having a certain number of members. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990], 3 §2) by Alex Oliver - The Metaphysics of Properties | |
| A reaction: [I believe Maddy has shifted since then] Presumably this will make room for zero and infinities as natural numbers. Personally I want my natural numbers to count things. |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| Full Idea: The set theory axioms developed in producing foundations for mathematics also have strong consequences for existing fields, and produce a theory that is immensely fruitful in its own right. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: [compressed] Second of Maddy's three benefits of set theory. This benefit is more questionable than the first, because the axioms may be invented because of their nice fruit, instead of their accurate account of foundations. |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| Full Idea: The single unified area of set theory provides a court of final appeal for questions of mathematical existence and proof. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: Maddy's third benefit of set theory. 'Existence' means being modellable in sets, and 'proof' means being derivable from the axioms. The slightly ad hoc character of the axioms makes this a weaker defence. |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| Full Idea: Set theoretic foundations bring all mathematical objects and structures into one arena, allowing relations and interactions between them to be clearly displayed and investigated. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: The first of three benefits of set theory which Maddy lists. The advantages of the one arena seem to be indisputable. |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| Full Idea: The identification of geometric points with real numbers was among the first and most dramatic examples of the power of set theoretic foundations. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: Hence the clear definition of the reals by Dedekind and Cantor was the real trigger for launching set theory. |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| Full Idea: The structure of a geometric line by rational points left gaps, which were inconsistent with a continuous line. Set theory provided an ordering that contained no gaps. These reals are constructed from rationals, which come from integers and naturals. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.2) | |
| A reaction: This completes the reduction of geometry to arithmetic and algebra, which was launch 250 years earlier by Descartes. |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| Full Idea: Our much loved mathematical knowledge rests on two supports: inexorable deductive logic (the stuff of proof), and the set theoretic axioms. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I Intro) |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| Full Idea: I am not suggesting a reduction of number theory to set theory ...There are only sets with number properties; number theory is part of the theory of finite sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], V) |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| Full Idea: A set of things is located where the aggregate of those things is located, ...but a number is simultaneously located at many different places (10 in my hand, and a baseball team) ...so numbers seem more like universals than particulars. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: My gut feeling is that Maddy's master idea (of naturalising sets by building them from ur-elements of natural objects) won't work. Sets can work fine in total abstraction from nature. |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| Full Idea: The popular challenges to platonism in philosophy of mathematics are epistemological (how are we able to interact with these objects in appropriate ways) and ontological (if numbers are sets, which sets are they). | |
| From: Penelope Maddy (Sets and Numbers [1981], I) | |
| A reaction: These objections refer to Benacerraf's two famous papers - 1965 for the ontology, and 1973 for the epistemology. Though he relied too much on causal accounts of knowledge in 1973, I'm with him all the way. |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| Full Idea: Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things. |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| Full Idea: Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5 | |
| A reaction: Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory. |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| Full Idea: Crudely, the scientist posits only those entities without which she cannot account for observations, while the set theorist posits as many entities as she can, short of inconsistency. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.5) |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| Full Idea: It could turn out that all applications of continuum mathematics in natural sciences are actually instances of idealisation. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.6) |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| Full Idea: Number words are not like normal adjectives. For example, number words don't occur in 'is (are)...' contexts except artificially, and they must appear before all other adjectives, and so on. | |
| From: Penelope Maddy (Sets and Numbers [1981], IV) | |
| A reaction: [She is citing Benacerraf's arguments] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| Full Idea: Recent commentators have noted that Frege's versions of the basic propositions of arithmetic can be derived from Hume's Principle alone, that the fatal Law V is only needed to derive Hume's Principle itself from the definition of number. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
| A reaction: Crispin Wright is the famous exponent of this modern view. Apparently Charles Parsons (1965) first floated the idea. |
| 14760 | Four-dimensionalism sees things and processes as belonging in the same category [Sider] |
| Full Idea: Four-dimensionalism does not respect a deep difference between thing-talk and process-talk, because it tends to place events and things in the same ontological category. | |
| From: Theodore Sider (Four Dimensionalism [2001], 6.1) | |
| A reaction: He then quotes Broad, Idea 14759. This idea is the best reason yet for being sympathetic to the four-dimensionalist view, because I think processes really must have a central place in any decent ontology. |
| 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? |
| 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] |
| 13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
| Full Idea: For a 'precisification' we take a trivalent interpretation and preserve the T and F values, and then assign all the third values in some way to either T or F. | |
| From: Theodore Sider (Logic for Philosophy [2010], 3.4.5) | |
| A reaction: [my informal summary of Sider's formal definition] |
| 13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
| Full Idea: In a 'supervaluation' we take a trivalent interpretation, and assign to each wff T (or F) if it is T (or F) in every precisification, leaving the third truth-value in any other cases. The wffs are then 'supertrue' or 'superfalse' in the interpretation. | |
| From: Theodore Sider (Logic for Philosophy [2010], 3.4.5) | |
| A reaction: [my non-symbolic summary] Sider says the Ts and Fs in the precisifications are assigned 'in any way you like', so supervaluation is a purely formal idea, not a technique for eliminating vagueness. |
| 13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
| Full Idea: Supervaluation preserves classical logic (even though supervaluations are three-valued), except when we add the Δ operator (meaning 'definitely' or 'determinately'). | |
| From: Theodore Sider (Logic for Philosophy [2010], 3.4.5) |
| 13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
| Full Idea: We can introduce 'sharpenings', to make vague terms precise without disturbing their semantics. Then truth (or falsity) becomes true(false)-in-all-sharpenings. You are only 'rich' if you are rich-on-all-sharpenings of the word. | |
| From: Theodore Sider (Logic for Philosophy [2010], 3.4.5) | |
| A reaction: Not very helpful. Lots of people might be considered rich in many contexts, but very few people would be considered rich in all contexts. You are still left with some vague middle ground. |
| 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. |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| Full Idea: The case of atoms makes it clear that the indispensable appearance of an entity in our best scientific theory is not generally enough to convince scientists that it is real. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.6) | |
| A reaction: She refers to the period between Dalton and Einstein, when theories were full of atoms, but there was strong reluctance to actually say that they existed, until the direct evidence was incontrovertable. Nice point. |
| 13683 | A relation is a feature of multiple objects taken together [Sider] |
| Full Idea: A relation is just a feature of multiple objects taken together. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.8) | |
| A reaction: Appealingly simple, especially for a logician, who can then just list the relevant objects as members of a set, and the job is done. But if everyone to the left of me is also taller than me, this won't quite do. |
| 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). |
| 14194 | Proper ontology should only use categorical (actual) properties, not hypothetical ones [Sider] |
| Full Idea: A proper ontology should invoke only categorical, or occurrent, properties and relations. Categorical properties involve what objects are actually like, whereas hypothetical properties 'point beyond' their instances. | |
| From: Theodore Sider (Four Dimensionalism [2001], 2.3) | |
| A reaction: This spectacularly leaves out powers and dispositions, which are actual properties which 'point beyond' their instances! This is the nub of the powers debate, and the most interesting topic in modern metaphysics. |
| 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'! |
| 14745 | If sortal terms fix the kind and the persistence conditions, we need to know what kinds there are [Sider] |
| Full Idea: Followers of the view that every entity is associated with some sortal term that answers the question 'what kind of thing is this?', and determines its persistence conditions, must answer the question what kinds of entity there are. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.3) | |
| A reaction: [He explicitly refers to David Wiggins here] In other words Wiggins has got it the wrong way round, which is my own view of his theory. Sortal terms don't grow on the trees in the Garden of Eden, available for applications. |
| 14740 | If Tib is all of Tibbles bar her tail, when Tibbles loses her tail, two different things become one [Sider] |
| Full Idea: This powerful puzzle (known to the Stoics, introduced by Geach, popularised by Wiggins) has a cat Tibbles and a proper part Tib, which is all of Tibbles except the tail. If Tibbles loses her tail, the two were distinct, but they now coincide. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.1) | |
| A reaction: [compressed] Compare a few people leave a football ground, and what was a large part of the crowd becomes the whole of the crowd. Which suggests that there is no problem if cats are like crowds. But we don't like that view of cats. |
| 14752 | Artists 'create' statues because they are essentially statues, and so lack identity with the lump of clay [Sider] |
| Full Idea: Presumably it is claimed that the artist 'created' the statue because the object created is essentially a statue, and thus cannot be identified with the unformed lump of clay with which the artist began. | |
| From: Theodore Sider (Four Dimensionalism [2001]) | |
| A reaction: This is based on Burke's views. This is sortal essentialism, rather than my own view of essence as an inner explanatory mechanism or form. If an old abstract sculpture was no longer recognised as a statue, would it necessarily still be a statue? |
| 14743 | The stage view of objects is best for dealing with coincident entities [Sider] |
| Full Idea: There are numerous cases in which there is pressure to admit coincident entities. The best way of coming to grips with this, I think, invokes the stage view. ...In the worm theory, coincident objects are no more mysterious than overlapping roads. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.1) | |
| A reaction: At this point I get nervous if in order to 'get to grips' with a phenomenon which is hard to articulate but obvious to common sense, we have to invoke a rather startling metaphysics that completely upends the common sense we started with. |
| 14747 | 'Composition as identity' says that an object just is the objects which compose it [Sider] |
| Full Idea: 'Composition as identity' says that when a thing, x, is composed of some other objects, the ys, then this is a kind of identity between the x and the ys. The industrial-strength version says object x just is the ys. Lewis says it is just an analogy. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.3) | |
| A reaction: I am averse to such a doctrine, as is Leibniz, with his insistence that an aggregate is not a unity. There has to be some sort of principle that bestows oneness on a many. I take this to be structural, and is an elucidation of hylomorphism. |
| 14757 | Mereological essentialism says an object's parts are necessary for its existence [Sider] |
| Full Idea: Mereological essentialism says that an object's parts are necessary for its existence. ....It is literally never correct to say that an thing survives a change in its parts. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.7) | |
| A reaction: Chisholm is well known for proposing this view. Sider adds a possible toughening clause, that the parts are also sufficient for the object's existence. This is a philosophers' notion of identity, not the normal English language concept. |
| 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. |
| 14727 | Three-dimensionalists assert 'enduring', being wholly present at each moment, and deny 'temporal parts' [Sider] |
| Full Idea: Three-dimensionalists say that things have no 'temporal parts', that they 'endure', and that they are wholly present at every moment of their careers. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3) | |
| A reaction: An obvious problem case for being wholly present would be the building and fitting of a large ship, where it might seem to be present before it was wholly present. |
| 14738 | Some might say that its inconsistency with time travel is a reason to favour three-dimensionalism [Sider] |
| Full Idea: Some might even regard inconsistency with time travel as an advantage of three-dimensionalism, as a vindication of a prior belief that time travel is impossible! I see no merit in these claims. | |
| From: Theodore Sider (Four Dimensionalism [2001], 7.2) | |
| A reaction: I do! Sider cheerfully says that there are good reasons to believe that time travel is possible, and then use this possibility to support his four-dimensional view, but I personally doubt his assumption. The evidence for time travel is flimsy and obscure. |
| 14726 | Four-dimensionalists assert 'temporal parts', 'perduring', and being spread out over time [Sider] |
| Full Idea: Four-dimensionalists say that things have 'temporal parts', that they 'perdure', and that they are spread out over time. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3) |
| 14728 | 4D says intrinsic change is difference between successive parts [Sider] |
| Full Idea: For four-dimensionalists intrinsic change is difference between successive temporal parts. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3.2) | |
| A reaction: This attempts a reply to the commonest criticism of four-dimensionalism - that you can't explain change if you don't have one enduring thing which undergoes the change. I get stuck of the question 'how big (temporally) is a part?'. |
| 14729 | 4D says each spatiotemporal object must have a temporal part at every moment at which it exists [Sider] |
| Full Idea: Four-dimensionalism may be formulated as the claim that, necessarily, each spatiotemporal object has a temporal part at every moment at which it exists. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3.2) | |
| A reaction: If there were tiny quantum gaps between temporal parts, that would presumably ruin the story. On this view an object has to be a 'worm', to be the thing which has the parts. |
| 14730 | Temporal parts exist, but are not prior building blocks for objects [Sider] |
| Full Idea: My four-dimensionalism implies the existence of temporal parts, but not that those parts are more fundamental, nor that the object is 'constructed' from its parts, nor that identity over time is reducible to parts. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3.2) | |
| A reaction: That's a rather negative account of temporal parts, which makes you ask what their positive role could be. Do they contribute anything to our understanding of a temporally extended object? |
| 14731 | Temporal parts are instantaneous [Sider] |
| Full Idea: Unless otherwise noted, I will think of temporal parts as being instantaneous. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3.2) | |
| A reaction: This comes up against all the Augustinian worries about the intrinsic nature of time. How many temporal parts does a typical object possess? Is a third temporal part always to be found between any two of them? How do they 'connect'? |
| 14758 | How can an instantaneous stage believe anything, if beliefs take time? [Sider] |
| Full Idea: How can an instantaneous stage believe anything? Beliefs take time. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.8) | |
| A reaction: Sider's four-dimensionalist answer is that the belief is embodied in the earlier counterparts, making belief a 'highly relational property'. I am not impressed by this answer to the very nice problem which he has raised. It's a problem for 3D, too. |
| 14762 | Four-dimensionalism says temporal parts are caused (through laws of motion) by previous temporal parts [Sider] |
| Full Idea: The sensible four-dimensionalist will claim that current temporal parts are caused to exist by previous temporal parts. The laws that govern this process are none other than the familiar laws of motion. | |
| From: Theodore Sider (Four Dimensionalism [2001], 6.3) | |
| A reaction: I keep struggling with the instantaneous natural of temporal parts, and now I find that they have to do the job of being causal relata. When do they do their job? They've gone home before they've finished clocking in. Continuance requires motion? |
| 14741 | The ship undergoes 'asymmetric' fission, where one candidate is seen as stronger [Sider] |
| Full Idea: The Ship of Theseus seems to be a case of 'asymmetric' fission (where one resultant entity has a stronger claim). Many see the continuously rebuilt ship as the stronger candidate, but each candidate, without the other, would be the original ship. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.1) |
| 13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
| Full Idea: The identity of indiscernibles (∀x∀y(∀X(Xx↔Xy)→x=y) is necessarily true, provided that we construe 'property' very broadly, so that 'being a member of such-and-such set' counts as a property. | |
| From: Theodore Sider (Logic for Philosophy [2010], 5.4.3) | |
| A reaction: Sider's example is that if the two objects are the same they must both have the property of being a member of the same singleton set, which they couldn't have if they were different. |
| 14754 | If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity [Sider] |
| Full Idea: If someone is in pain at t1 and not at t2, we might restrict Leibniz's Law so as not to apply to 'timebound' properties, ..but this is deeply unsatisfying, ...and forfeits one's claim to be discussing identity. The demands of identity are high. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.5) | |
| A reaction: [on Myro 1986] Sider's response is unsatisfying. It means a thing loses its identity (with itself?) if it has even a tiny fluctuating in its properties. Quantum changes then destroy all notions of identity. English-speakers don't use 'identity' like that. |
| 13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
| Full Idea: 'Strong necessity' requires the truth of 'necessarily φ' is all possible worlds. 'Weak necessity' merely requires that 'necessarily φ' be true in all worlds in which objects referred to within φ exist. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.6.3) | |
| A reaction: This seems to be a highly desirably distinction, given the problem of Idea 13719. It is weakly necessary that humans can't fly unaided, assuming we are referring the current feeble wingless species. That hardly seems to be strongly necessary. |
| 13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
| Full Idea: Some argue that metaphysical accessibility is intransitive. The individuals involved mustn't be too different from the actual world. A world in which I am a frog isn't metaphysically possible. Perhaps the logic is modal system B or T. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.3.1) | |
| A reaction: This sounds rather plausible and attractive to me. We don't want to say that I am necessarily the way I actually am, though, so we need criteria. Essence! |
| 13709 | Logical truths must be necessary if anything is [Sider] |
| Full Idea: On any sense of necessity, surely logical truths must be necessary. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.4) |
| 13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
| Full Idea: To show the semantic difference between counterfactuals and indicative conditionals, 'If Booth hadn't shot Lincoln someone else would have' is false, but 'If Booth didn't shoot Lincoln then someone else did' is true. | |
| From: Theodore Sider (Logic for Philosophy [2010], 8) | |
| A reaction: He notes that indicative conditionals also differ in semantics from material and strict conditionals. The first example allows a world where Lincoln was not shot, but the second assumes our own world, where he was. Contextual domains? |
| 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. |
| 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] |
| 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) |
| 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. |
| 13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
| Full Idea: There is no problem of transworld identification with de dicto modal sentence, for their evaluation does not require taking an individual from one possible world and reidentifying it in another. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.2) | |
| A reaction: If 'de dicto' is about the sentence and 'de re' is about the object (Idea 5732), how do you evaluate the sentence without at least some notion of the object to which it refers. Nec the Prime Minister chairs the cabinet. Could a poached egg do the job? |
| 14763 | Counterparts rest on similarity, so there are many such relations in different contexts [Sider] |
| Full Idea: A counterpart relation is a similarity relation. Since there are different dimensions of similarity, there are different counterpart relations. | |
| From: Theodore Sider (Four Dimensionalism [2001], 6.4) |
| 13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
| Full Idea: A problem with the Barcan Formula is it might be possible for there to exist a ghost, even though there in fact exists nothing that could be a ghost. There could have existed some 'extra' thing which could be a ghost. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.5.2) | |
| A reaction: Thus when we make modal claims, do they only refer to what actually exists, or is specified in our initial domain? Can a claim enlarge the domain? Are domains 'variable'? Simple claims about what might have existed seem to be a problem. |
| 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. |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| Full Idea: In science we treat the earth's surface as flat, we assume the ocean to be infinitely deep, we use continuous functions for what we know to be quantised, and we take liquids to be continuous despite atomic theory. | |
| From: Penelope Maddy (Naturalism in Mathematics [1997], II.6) | |
| A reaction: If fussy people like scientists do this all the time, how much more so must the confused multitude be doing the same thing all day? |
| 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. |
| 2854 | Prescriptivism says 'ought' without commitment to act is insincere, or weakly used [Hooker,B] |
| Full Idea: Prescriptivism holds that if you think one 'ought' to do a certain kind of act, and yet you are not committed to doing that act in the relevant circumstances, then you either spoke insincerely, or are using the word 'ought' in a weak sense. | |
| From: Brad W. Hooker (Prescriptivism [1995], p.640) | |
| A reaction: So that's an 'ought', but not a 'genuine ought', then? (No True Scotsman move). Someone ought to rescue that drowning child, but I can't be bothered. |
| 2856 | Universal moral judgements imply the Golden Rule ('do as you would be done by') [Hooker,B] |
| Full Idea: Prescriptivity is especially important if moral judgements are universalizable, for then we can employ golden rule-style reasoning ('do as you would be done by'). | |
| From: Brad W. Hooker (Prescriptivism [1995], p.640) |
| 20883 | Modern utilitarians value knowledge, friendship, autonomy, and achievement, as well as pleasure [Hooker,B] |
| Full Idea: Most utilitarians now think that pleasure, even if construed widely, is not the only thing desirable in itself. ...Goods also include important knowledge, friendship, autonomy, achievement and so on. | |
| From: Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 2) | |
| A reaction: That pleasure is desired is empirically verifiable, which certainly motivated Bentham. A string of other desirables each needs to be justified - but how? What would be the value of a 'friendship' if neither party got pleasure from it? |
| 20884 | Rule-utilitarians prevent things like torture, even on rare occasions when it seems best [Hooker,B] |
| Full Idea: For rule-utilitarians acts of murder, torture and so on, can be impermissible even in rare cases where they really would produce better consequences than any alternative act. | |
| From: Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 4) | |
| A reaction: It is basic to rule-utilitarianism that it trumps act-ulitilarianism, even when a particular act wins the utilitarian calculation. But that is hard to understand. Only long-term benefit could justify the rule - but that should win the calculation. |
| 20885 | Euthanasia is active or passive, and voluntary, non-voluntary or involuntary [Hooker,B] |
| Full Idea: Six types of euthanasia: 1) Active voluntary (knowing my wishes), 2) Active non-voluntary (not knowing my wishes), 3) Active involuntary (against my wishes), 4) Passive voluntary, 5) Passive non-voluntary, 6) Passive involuntary. | |
| From: Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 5) | |
| A reaction: 'Active' is intervening, and 'passive' is not intervening. A helpful framework. |
| 20882 | Euthanasia may not involve killing, so it is 'killing or not saving, out of concern for that person' [Hooker,B] |
| Full Idea: Passive euthanasia is arguably not killing, and the death involved is often painful, so let us take the term 'euthanasia' to mean 'either killing or passing up opportunities to save someone, out of concern for that person'. | |
| From: Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 1) | |
| A reaction: This sounds good, and easily settled, until you think concern for that person could have two different outcomes, depending on whether the criteria are those of the decider or of the patient. Think of religious decider and atheist patient, or vice versa. |
| 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) |
| 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. |
| 14725 | Maybe motion is a dynamical quantity intrinsic to a thing at a particular time [Sider] |
| Full Idea: There is an alternative to the Russellian 'at-at' theory of motion, according to which dynamical quantities are intrinsic to times. Whether and how an object is moving at a time is a fact about what that object is like then. | |
| From: Theodore Sider (Four Dimensionalism [2001], 2.2) | |
| A reaction: I think I find this quite appealing, because there is too much of a tendency to think of objects as passive and inert, with laws, forces, motions etc. imposed from the outside. But nature is active and dynamic. However, motion can't be wholly intrinsic. |
| 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. |
| 14735 | Space is 3D and lacks a direction; time seems connected to causation [Sider] |
| Full Idea: Unlike time, space has three dimensions and lacks a distinguishing direction; unlike space, time seems to be specially connected with causation. | |
| From: Theodore Sider (Four Dimensionalism [2001], 4.5) | |
| A reaction: These strike me as nice reasons to doubt (what I already prima facie doubt) that there is a single manifold that is 'space-time', for all that twentieth century physics tells us it is so. A century is a mere click of a clock where truth is concerned. |
| 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. |
| 14722 | Between presentism and eternalism is the 'growing block' view - the past is real, the future is not [Sider] |
| Full Idea: Intermediate between the polar opposites of presentism and eternalism is the view (defended by Broad 1923 and Tooley 1997) that the past is real but the future is not. Reality consists of a growing four-dimensional manifold, the 'growing block universe'. | |
| From: Theodore Sider (Four Dimensionalism [2001], 2.1) | |
| A reaction: The obvious and plausible basis for this is that statements about the past seem to have truthmakers, but statements about the future lack them. Does a truth always require ontological commitment? Death is cessation of existence. |
| 14724 | Presentists must deny truths about multiple times [Sider] |
| Full Idea: The presentist must deny the truth of everyday claims that concern multiple times taken together. | |
| From: Theodore Sider (Four Dimensionalism [2001], 2.2) | |
| A reaction: This rests on the extent to which every truth has an ontological commitment. You can deny the literal existence of multiple times without denying such truths. |
| 14756 | For Presentists there must always be a temporal vantage point for any description [Sider] |
| Full Idea: The Presentist acknowledges that no atemporal description of the case can be given; a vantage point must be chosen for any description. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.5) | |
| A reaction: This is because Presentists are committed to tense, which have to be either explicit or implicit in any sentence. But what of famously 'timeless' truths such as '2 and 2 are 4'? |
| 14723 | Talk using tenses can be eliminated, by reducing it to indexical connections for an utterance [Sider] |
| Full Idea: The temporal reductionist claims that tensed locutions are indexical - 'present' being the time of utterance etc. This generalises to say that nothing corresponding to tense need be admitted as a fundamental feature of the world. | |
| From: Theodore Sider (Four Dimensionalism [2001], 2.1) | |
| A reaction: [He particular cites Mellor for this view] Highly implausible. I very much doubt whether it is possible to explain the indexicality of a word like 'now' without referring to tenses. Does time only exist when sentences and thoughts occur? |
| 14734 | The B-series involves eternalism, and the reduction of tense [Sider] |
| Full Idea: The B-series has two components: eternalism - the thesis that all future entities are real - and the thesis of reducibility of tense. | |
| From: Theodore Sider (Four Dimensionalism [2001], 4.2) |
| 14736 | The B-theory is adequate, except that it omits to say which time is present [Sider] |
| Full Idea: The B-theoretic description of the world is completely adequate except that it leaves out information about which time is present. | |
| From: Theodore Sider (Four Dimensionalism [2001], 4.6) | |
| A reaction: This strikes me as a pretty basic deficiency. How could there a time which lacked a present moment? The present is when things happen. How would it qualify as time at all if it lacked past, present and future? |