90 ideas
| 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. |
| 16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
| Full Idea: For me, although the enterprise of philosophical analysis is driven by natural language, its goal is not a linguistic analysis of English but rather an expressively strong framework that may at best be seen as a revision of English. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 12) | |
| A reaction: I agree, but the problem is that there are different ideals for the revision, which may be in conflict. Logicians, mathematicians, metaphysicians, scientists, moralists and aestheticians are queueing up to improve in their own way. |
| 16292 | An explicit definition enables the elimination of what is defined [Halbach] |
| Full Idea: Explicit definitions allow for a complete elimination of the defined notion (at least in extensional contexts). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: If the context isn't extensional (concerning the things themselves) then we could define one description of it, but be unable to eliminate it under another description. Elimination is no the aim of an Aristotelian definition. Halbach refers to truth. |
| 16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
| Full Idea: Arguments from analogy are to be distrusted: at best they can serve as heuristics. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 4) |
| 16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
| Full Idea: Truth-value 'gluts' correspond to a so-called dialethic conception of truth; excluding gluts and admitting only 'gaps' leads to a conception of what is usually called 'partial' truth. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.2) | |
| A reaction: Talk of 'gaps' and 'gluts' seem to be the neatest way of categorising views of truth. I want a theory with no gaps or gluts. |
| 16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
| Full Idea: Two typed disquotation sentences, truth axioms of TB, suffice for proving that there at least two objects. Hence truth is not a logical notion if one expects logical notions to be ontologically neutral. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 21.2) |
| 16324 | Any definition of truth requires a metalanguage [Halbach] |
| Full Idea: It is plain that the distinction between object and metalanguage is required for the definability of truth. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 11) | |
| A reaction: Halbach's axiomatic approach has given up on definability, and therefore it can seek to abandon the metalanguage and examine 'type-free' theories. |
| 16293 | Traditional definitions of truth often make it more obscure, rather than less [Halbach] |
| Full Idea: A common complaint against traditional definitional theories of truth is that it is far from clear that the definiens is not more in need of clarification than the definiendum (that is, the notion of truth). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: He refers to concepts like 'correspondence', 'facts', 'coherence' or 'utility', which are said to be trickier to understand than 'true'. I suspect that philosophers like Halbach confuse 'clear' with 'precise'. Coherence is quite clear, but imprecise. |
| 16301 | If people have big doubts about truth, a definition might give it more credibility [Halbach] |
| Full Idea: If one were wondering whether truth should be considered a legitimate notion at all, a definition might be useful in dispersing doubts about its legitimacy. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 3) | |
| A reaction: Halbach is proposing to skip definitions, and try to give rules for using 'true' instead, but he doesn't rule out definitions. A definition of 'knowledge' or 'virtue' or 'democracy' might equally give those credibility. |
| 16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
| Full Idea: In semantic theories (e.g.Tarski's or Kripke's), a definition evades Tarski's Theorem by restricting the possible instances in the schema T[φ]↔φ to sentences of a proper sublanguage of the language formulating the equivalences. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: The schema says if it's true it's affirmable, and if it's affirmable it's true. The Liar Paradox is a key reason for imposing this restriction. |
| 16337 | Disquotational truth theories are short of deductive power [Halbach] |
| Full Idea: The problem of restricted deductive power has haunted disquotational theories of truth (…because they can't prove generalisations). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 19.5) |
| 16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
| Full Idea: Compositional Truth CT proves the consistency of Peano arithmetic, which is not provable in Peano arithmetic by Gödel's second incompleteness theorem. Hence the theory CT is not conservative over Peano arithmetic. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8.6) |
| 16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
| Full Idea: Choosing an axiomatic approach to truth might well be compatible with the view that truth is definable; the definability of truth is just not presupposed at the outset. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: Is it possible that a successful axiomatisation is a successful definition? |
| 16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
| Full Idea: Revision semantics is arguably the main competitor of Kripke's theory of truth among semantic truth theories. …In the former one may hope through revision to arrive at better and better models, ..sorting out unsuitable extensions of the truth predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 14) | |
| A reaction: Halbach notes later that Kripke's theory (believe it or not) is considerably simpler than revision semantics. |
| 16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
| Full Idea: If the clauses of Tarski's definition of truth are turned into axioms (as Davidson proposed) then a primitive binary predicate symbol for satisfaction is needed, as Tarski defined truth in terms of satisfaction. Standard language has a unary predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 5.2) |
| 16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach] |
| Full Idea: In the typed Compositional Truth theory CT, it is compositional because the truth of a sentence depends on the semantic values of the constituents of that sentence. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) | |
| A reaction: [axioms on p. 65 of Halbach] |
| 16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach] |
| Full Idea: Often syntactic objects are identified with their numerical codes. …Expressions of a countable formal language can be coded in the natural numbers. This allows a theory of truth to use Peano Arithmetic (with its results) as a base theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 2) | |
| A reaction: The numbering system is the famous device invented by Gödel for his great proof of incompleteness. This idea is a key to understanding modern analytic philosophy. It is the bridge which means philosophical theories can be treated mathematically. |
| 16340 | Truth axioms need a base theory, because that is where truth issues arise [Halbach] |
| Full Idea: Considering the truth axioms in the absence of a base theory is not very sensible because characteristically truth theoretic reasoning arises from the interplay of the truth axioms with the base theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 21.2) | |
| A reaction: The base theory usually seems to be either Peano arithmetic or set theory. We might say that introverted thought (e.g. in infants) has little use for truth; it is when you think about the world that truth becomes a worry. |
| 16305 | We know a complete axiomatisation of truth is not feasible [Halbach] |
| Full Idea: In the light of incompleteness phenomena, one should not expect a categorical axiomatisation of truth to be feasible, but this should not keep one from studying axiomatic theories of truth (or of arithmetic). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 3) | |
| A reaction: This, of course, is because of Gödel's famous results. It is important to be aware in this field that there cannot be a dream of a final theory, so we are just seeing what can be learned about truth. |
| 16313 | A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG] |
| Full Idea: A truth theory is 'conservative' if the addition of the truth predicate does not add any new theorems to the base theory. | |
| From: report of Volker Halbach (Axiomatic Theories of Truth [2011], 6 Df 6.6) by PG - Db (ideas) | |
| A reaction: Halbach presents the definition more formally, and this is my attempt at getting it into plain English. Halbach uses Peano Arithmetic as his base theory, but set theory is also sometimes used. |
| 16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach] |
| Full Idea: The truth theory TB (Tarski Biconditional) is all the axioms of Peano Arithmetic, including all instances of the induction schema with the truth predicate, plus all the sentences of the form T[φ] ↔ φ. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) | |
| A reaction: The biconditional formula is the famous 'snow is white' iff snow is white. The truth of the named sentence is equivalent to asserting the sentence. This is a typed theory of truth, and it is conservative over PA. |
| 16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
| Full Idea: I sort theories of truth into the large families of 'typed' and 'type-free'. Roughly, typed theories prohibit a truth predicate's application to sentences with occurrences of that predicate, and one cannot prove the truth of sentences containing 'true'. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], II Intro) | |
| A reaction: The problem sentence the typed theories are terrified of is the Liar Sentence. Typing produces a hierarchy of languages, referring down to the languages below them. |
| 16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
| Full Idea: The Friedman-Sheard truth system FS is based on compositional theory CT. The axioms of FS are obtained by relaxing the type restriction on the CT-axioms, and adding rules inferring sentences from their truth, and vice versa. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15) | |
| A reaction: The rules are called NEC and CONEC by Halbach. The system FSN is FS without the two rules. |
| 16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
| Full Idea: KF is useful for explicating Peano arithmetic, but it certainly does not come to close to being a theory that contains its own truth predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 16) | |
| A reaction: Since it is a type-free theory, its main philosophical aspiration was to contain its own truth predicate, so that is bad news (for philosophers). |
| 16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
| Full Idea: The Kripke-Feferman theory is relatively deductively very strong. In particular, it is much stronger than its competitor FS, which is based on a completely classical notion of truth. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.3) |
| 16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
| Full Idea: The Kripke-Feferman theory KF is an axiomatisation of the fixed points of an operator, that is, of a Kripkean fixed-point semantics with the Strong Kleene evaluation schema with truth-value gluts. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.1) |
| 16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
| Full Idea: Compositional Truth CT and its variants has desirable generalisations among its logical consequences, so they seem to have ousted purely disquotational theories such as TB in the discussion on deflationism. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) |
| 16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
| Full Idea: Some authors have tried to understand the deflationist claim that truth is not a substantial notion as the claim that a satisfactory axiomatisation of truth should be conservative over the base theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) |
| 16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
| Full Idea: There are two doctrines at the core of deflationism. The first says truth is a device of disquotation used to express generalisations, and the second says truth is a thin notion that contributes nothing to our knowledge of the world | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 21) |
| 16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
| Full Idea: The main criticism that deflationist theories based on the disquotation sentences or similar axioms have to meet was raised by Tarski: the disquotation sentences do not allow one to prove generalisations. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) |
| 16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
| Full Idea: Deflationists do not hold that truth is completely dispensable. They claim that truth serves the purpose of expressing infinite conjunctions or generalisations. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) | |
| A reaction: It is also of obvious value as a shorthand in ordinary conversation, but rigorous accounts can paraphrase that out. 'What he said is true'. 'Pick out the true sentences from p,q,r and s' seems to mean 'affirm some of them'. What does 'affirm' mean? |
| 8472 | Sentential logic is consistent (no contradictions) and complete (entirely provable) [Orenstein] |
| Full Idea: Sentential logic has been proved consistent and complete; its consistency means that no contradictions can be derived, and its completeness assures us that every one of the logical truths can be proved. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.5) | |
| A reaction: The situation for quantificational logic is not quite so clear (Orenstein p.98). I do not presume that being consistent and complete makes it necessarily better as a tool in the real world. |
| 8476 | Axiomatization simply picks from among the true sentences a few to play a special role [Orenstein] |
| Full Idea: In axiomatizing, we are merely sorting out among the truths of a science those which will play a special role, namely, serve as axioms from which we derive the others. The sentences are already true in a non-conventional or ordinary sense. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.5) | |
| A reaction: If you were starting from scratch, as Euclidean geometers may have felt they were doing, you might want to decide which are the simplest truths. Axiomatizing an established system is a more advanced activity. |
| 8480 | S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p' [Orenstein] |
| Full Idea: The five systems of propositional modal logic contain successively stronger conceptions of necessity. In S4 'it is poss that it is poss that p' implies 'it is poss that p'. In S5, 'it is poss that it is nec that p' implies 'it is nec that p'. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.7) | |
| A reaction: C.I. Lewis originated this stuff. Any serious student of modality is probably going to have to pick a system. E.g. Nathan Salmon says that the correct modal logic is even weaker than S4. |
| 16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
| Full Idea: In Strong Kleene logic a disjunction of two sentences is true if at least one disjunct is true, even when the other disjunct lacks a truth value. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 18) | |
| A reaction: This sounds fine to me. 'Either I'm typing this or Homer had blue eyes' comes out true in any sensible system. |
| 16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |
| Full Idea: In Weak Kleene Logic, with truth-value gaps, a sentence is neither true nor false if one of its components lacks a truth value. A line of the truth table shows a gap if there is a gap anywhere in the line, and the other lines are classical. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 18) | |
| A reaction: This will presumably apply even if the connective is 'or', so a disjunction won't be true, even if one disjunct is true, when the other disjunct is unknown. 'Either 2+2=4 or Lot's wife was left-handed' sounds true to me. Odd. |
| 8474 | Unlike elementary logic, set theory is not complete [Orenstein] |
| Full Idea: The incompleteness of set theory contrasts sharply with the completeness of elementary logic. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.5) | |
| A reaction: This seems to be Quine's reason for abandoning the Frege-Russell logicist programme (quite apart from the problems raised by Gödel. |
| 16309 | Every attempt at formal rigour uses some set theory [Halbach] |
| Full Idea: Almost any subject with any formal rigour employs some set theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 4.1) | |
| A reaction: This is partly because mathematics is often seen as founded in set theory, and formal rigour tends to be mathematical in character. |
| 8465 | Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein] |
| Full Idea: The theory of mereology has had a history of being exploited by nominalists to achieve some of the effects of set theory. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.3) | |
| A reaction: Some writers refer to mereology as a 'theory', and others as an area of study. This appears to be an interesting line of investigation. Orenstein says Quine and Goodman showed its limitations. |
| 16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
| Full Idea: The costs of giving up classical logic are easily underestimated, …the price being paid in terms of mathematical reasoning. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 16.2) | |
| A reaction: No one cares much about such costs, until you say they are 'mathematical'. Presumably this is a message to Graham Priest and his pals. |
| 16310 | A theory is some formulae and all of their consequences [Halbach] |
| Full Idea: A theory is a set of formulae closed under first-order logical consequence. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 5.1) |
| 8452 | Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein] |
| Full Idea: In traditional logic from Aristotle to Kant, universal sentences have existential import, but Brentano and Boole construed them as universal conditionals (such as 'for anything, if it is a man, then it is mortal'). | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.2) | |
| A reaction: I am sympathetic to the idea that even the 'existential' quantifier should be treated as conditional, or fictional. Modern Christians may well routinely quantify over angels, without actually being committed to them. |
| 8475 | The substitution view of quantification says a sentence is true when there is a substitution instance [Orenstein] |
| Full Idea: The substitution view of quantification explains 'there-is-an-x-such-that x is a man' as true when it has a true substitution instance, as in the case of 'Socrates is a man', so the quantifier can be read as 'it is sometimes true that'. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.5) | |
| A reaction: The word 'true' crops up twice here. The alternative (existential-referential) view cites objects, so the substitution view is a more linguistic approach. |
| 16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
| Full Idea: One cannot just accept that all the theorems of Peano arithmetic are true when one accepts Peano arithmetic as the notion of truth is not available in the language of arithmetic. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) | |
| A reaction: This is given as the reason why Kreisel and Levy (1968) introduced 'reflection principles', which allow you to assert whatever has been proved (with no mention of truth). (I think. The waters are closing over my head). |
| 16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
| Full Idea: If one endorses a theory, so one might argue, one should also take it to be sound. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) |
| 16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
| Full Idea: Soundness seems to be a notion essentially involving truth. At least I do not know how to fully express the soundness of Peano arithmetic without invoking a truth predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) | |
| A reaction: I suppose you could use some alternative locution such as 'assertible' or 'cuddly'. Intuitionists seem a bit vague about the truth end of things. |
| 16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
| Full Idea: Paradoxes that arise from interaction of predicates such as truth, necessity, knowledge, future and past truths have receive little attention. There may be many unknown paradoxes lurking when we develop frameworks with these intensional notions. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 24.2) | |
| A reaction: Nice. This is a wonderful pointer to new research in the analytic tradition, in which formal problems will gradually iron out our metaphysical framework. |
| 16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
| Full Idea: An essential feature of the liar paradox is the application of the truth predicate to a sentence with a negated occurrence of the truth predicate, though the negation can be avoided by using the conditional. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 19.3) |
| 8454 | The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein] |
| Full Idea: The 'natural' numbers are the whole numbers 1, 2, 3 and so on. The 'rational' numbers consist of the natural numbers plus the fractions. The 'real' numbers include the others, plus numbers such a pi and root-2, which cannot be expressed as fractions. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.2) | |
| A reaction: The 'irrational' numbers involved entities such as root-minus-1. Philosophical discussions in ontology tend to focus on the existence of the real numbers. |
| 16321 | The compactness theorem can prove nonstandard models of PA [Halbach] |
| Full Idea: Nonstandard models of Peano arithmetic are models of PA that are not isomorphic to the standard model. Their existence can be established with the compactness theorem or the adequacy theorem of first-order logic. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8.3) |
| 16343 | The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach] |
| Full Idea: The global reflection principle ∀x(Sent(x) ∧ Bew[PA](x) → Tx) …seems to be the full statement of the soundness claim for Peano arithmetic, as it expresses that all theorems of Peano arithmetic are true. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) | |
| A reaction: That is, an extra principle must be introduced to express the soundness. PA is, of course, not complete. |
| 16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach] |
| Full Idea: For the reduction of Peano Arithmetic to ZF set theory, usually the set of finite von Neumann ordinals is used to represent the non-negative integers. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 6) | |
| A reaction: Halbach makes it clear that this is just one mode of reduction, relative interpretability. |
| 8473 | The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein] |
| Full Idea: The question to be posed is whether is-a-member-of should be considered a logical constant, that is, does logic include set theory. Frege, Russell and Whitehead held that it did. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.5) | |
| A reaction: This is obviously the key element in the logicist programme. The objection seems to be that while first-order logic is consistent and complete, set theory is not at all like that, and so is part of a different world. |
| 16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
| Full Idea: While set theory was liberated much earlier from type restrictions, interest in type-free theories of truth only developed more recently. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 4) | |
| A reaction: Tarski's theory of truth involves types (or hierarchies). |
| 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. |
| 16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
| Full Idea: The observation that Peano arithmetic is relatively interpretable in ZF set theory is taken by many philosophers to be a reduction of numbers to sets. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 23) | |
| A reaction: Nice! Being able to express something in a different language is not the same as a reduction. Back to the drawing board. What do you really mean by a reduction? If we model something, we don't 'reduce' it to the model. |
| 8458 | Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism [Orenstein] |
| Full Idea: Modest ontologies are Nominalism (Goodman), admitting only concrete individuals; and Extensionalism (Quine/Davidson) which admits individuals and sets; but Intensionalists (Frege/Carnap/Church/Marcus/Kripke) may have propositions, properties, concepts. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.3) | |
| A reaction: I don't like sets, because of Idea 7035. Even the ontology of individuals could collapse dramatically (see the ideas of Merricks, e.g. 6124). The intensional items may be real enough, but needn't have a place at the ontological high table. |
| 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. |
| 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. |
| 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) |
| 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. |
| 16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
| Full Idea: Should necessity be treated as a predicate rather than (as in modal logic) as a sentential operator? It is odd to assign different status to necessity and truth, hampering their interaction. That all necessities are true can't be expressed by an operator. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 24.2) | |
| A reaction: [compressed] Halbach and Horsten consistently treat truth as a predicate, but maybe truth is an operator. Making necessity a predicate and not an operator would be a huge upheaval in the world of modal logic. Nice move! |
| 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) |
| 8457 | The Principle of Conservatism says we should violate the minimum number of background beliefs [Orenstein] |
| Full Idea: The principle of conservatism in choosing between theories is a maxim of minimal mutilation, stating that of competing theories, all other things being equal, choose the one that violates the fewest background beliefs held. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.2) | |
| A reaction: In this sense, all rational people should be conservatives. The idea is a modern variant of Hume's objection to miracles (Idea 2227). A Kuhnian 'paradigm shift' is the dramatic moment when this principle no longer seems appropriate. |
| 8477 | People presume meanings exist because they confuse meaning and reference [Orenstein] |
| Full Idea: A good part of the confidence people have that there are meanings rests on the confusion of meaning and reference. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.6) | |
| A reaction: An important point. Everyone assumes that sentences link to the world, but Frege shows that that is not part of meaning. Words like prepositions and conjunctions ('to', 'and') don't have 'a meaning' apart from their function and use. |
| 8471 | Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way [Orenstein] |
| Full Idea: 'Socrates is human' is true if 1) subject referent is identical with a predicate referent (Nominalism), 2) subject reference member of the predicate set, or the subject has that property (Platonism), 3) predicate set a member of the subject set (Montague) | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.3) | |
| A reaction: Orenstein offers these as alternatives to Quine's 'inscrutability of reference' thesis, which makes the sense unanalysable. |
| 16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
| Full Idea: Being able to ascribe the same proposition as a belief to persons who do not have a common language seems to be one of the main reasons to employ propositions. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 2) | |
| A reaction: Propositions concern beliefs, as well as sentence meanings. I would want to say that a dog and I could believe the same thing, and that is a non-linguistic reason to believe in propositions. Maybe 'translation' cuts out the proposition middleman? |
| 8484 | If two people believe the same proposition, this implies the existence of propositions [Orenstein] |
| Full Idea: If we can say 'there exists a p such that John believes p and Barbara believes p', logical forms such as this are cited as evidence for our ontological commitment to propositions. | |
| From: Alex Orenstein (W.V. Quine [2002], Ch.7) | |
| A reaction: Opponents of propositions (such as Quine) will, of course, attempt to revise the logical form to eliminate the quantification over propositions. See Orenstein's outline on p.171. |
| 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. |
| 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. |
| 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. |
| 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'? |
| 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. |
| 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? |
| 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? |
| 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) |