142 ideas
| 11832 | We learn a concept's relations by using it, without reducing it to anything [Wiggins] |
| Full Idea: We can achieve a lot by elucidations that put a concept to use without attempting to reduce it but, in using the concept, exhibit its connexions with other concepts that are established. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], Pr.3) | |
| A reaction: This seems to be the best line of defence for analytic philosophy, given the much-cited observation that no one has successful reduced any concept by pure analysis. |
| 16512 | Semantic facts are preferable to transcendental philosophical fiction [Wiggins] |
| Full Idea: Semantical fact is almost always more interesting than transcendental philosophical fiction. | |
| From: David Wiggins (Sameness and Substance [1980], 3.1 n4) | |
| A reaction: An interesting expression of a more sophisticated recent allegiance to linguistic philosophy. There is still a strong allegiance to semantics as a major branch of philosophy, despite caution (e.g. from Nathan Salmon) about its scope. |
| 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. |
| 15647 | Truth definitions don't produce a good theory, because they go beyond your current language [Halbach] |
| Full Idea: It is far from clear that a definition of truth can lead to a philosophically satisfactory theory of truth. Tarski's theorem on the undefinability of the truth predicate needs resources beyond those of the language for which it is being defined. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: The idea is that you need a 'metalanguage' for the definition. If I say 'p' is a true sentence in language 'L', I am not making that observation from within language L. The dream is a theory confined to the object language. |
| 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. |
| 17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
| Full Idea: Item x is said to be a sufficient truth-maker for truth-bearer p just in case necessarily if x exists then p is true. ...Every truth has a sufficient truth-maker. Hence, I take it, the sum of all sufficient truth-makers is a universal truth-maker. | |
| From: Peter Forrest (General Facts,Phys Necessity, and Metaph of Time [2006], 1) | |
| A reaction: Note that it is not 'necessary', because something else might make p true instead. |
| 15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach] |
| Full Idea: In semantic theories of truth (Tarski or Kripke), a truth predicate is defined for an object-language. This definition is carried out in a metalanguage, which is typically taken to include set theory or another strong theory or expressive language. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: Presumably the metalanguage includes set theory because that connects it with mathematics, and enables it to be formally rigorous. Tarski showed, in his undefinability theorem, that the meta-language must have increased resources. |
| 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) |
| 15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach] |
| Full Idea: Axiomatic theories of truth can be presented within very weak logical frameworks which require very few resources, and avoid the need for a strong metalanguage and metatheory. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) |
| 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) |
| 15655 | Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach] |
| Full Idea: If truth is not explanatory, truth axioms should not allow proof of new theorems not involving the truth predicate. It is hence said that axiomatic truth should be 'conservative' - not implying further sentences beyond what the axioms can prove. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: [compressed] |
| 15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach] |
| Full Idea: The axiomatic approach does not presuppose that truth can be defined. Instead, a formal language is expanded by a new primitive predicate of truth, and axioms for that predicate are then laid down. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: Idea 15647 explains why Halbach thinks the definition route is no good. |
| 15654 | If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach] |
| Full Idea: If truth can be explicitly defined, it can be eliminated, whereas an axiomatized notion of truth may bring all kinds of commitments. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: The general principle that anything which can be defined can be eliminated (in an abstract theory, presumably, not in nature!) raises interesting questions about how many true theories there are which are all equivalent to one another. |
| 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. |
| 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) |
| 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) |
| 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). |
| 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) |
| 15656 | Deflationists say truth merely serves to express infinite conjunctions [Halbach] |
| Full Idea: According to many deflationists, truth serves merely the purpose of expressing infinite conjunctions. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: That is, it asserts sentences that are too numerous to express individually. It also seems, on a deflationist view, to serve for anaphoric reference to sentences, such as 'what she just said is true'. |
| 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? |
| 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) |
| 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. |
| 15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
| Full Idea: The consistency of set theory cannot be established without assumptions transcending set theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 2.1) |
| 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. |
| 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. |
| 15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach] |
| Full Idea: The reduction of 2nd-order theories (of properties or sets) to axiomatic theories of truth may be conceived as a form of reductive nominalism, replacing existence assumptions (for comprehension axioms) by ontologically innocent truth assumptions. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1) | |
| A reaction: I like this very much, as weeding properties out of logic (without weeding them out of the world). So-called properties in logic are too abundant, so there is a misfit with their role in science. |
| 15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |
| Full Idea: Quantification over (certain) properties can be mimicked in a language with a truth predicate by quantifying over formulas. Instead of saying that Tom has the property of being a poor philosopher, we can say 'x is a poor philosopher' is true of Tom. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1) | |
| A reaction: I love this, and think it is very important. He talks of 'mimicking' properties, but I see it as philosophers mistakenly attributing properties, when actually what they were doing is asserting truths involving certain predicates. |
| 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) |
| 11863 | (λx)[Man x] means 'the property x has iff x is a man'. [Wiggins] |
| Full Idea: The Lambda Abstraction Operator: We can write (λx)[Man x], which may be read as 'the property that any x has just if x is a man'. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.2) | |
| A reaction: This technical device seems to be a commonplace in modern metaphysical discussions. I'm assuming it can be used to discuss properties without venturing into second-order logic. Presumably we could call the property here 'humanity'. |
| 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) |
| 17529 | Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins] |
| Full Idea: My thesis C says that to specify something or other under which a and b coincide is to specify a concept f which qualifies for this purpose only if it yields a principle of counting for fs. ...I submit that C is false, though a near miss. | |
| From: David Wiggins (Sameness and Substance [1980], 1.1) |
| 17530 | The sortal needed for identities may not always be sufficient to support counting [Wiggins] |
| Full Idea: My principle C seems unnecessary ...since it is one thing to see how many fs there are...but another to have a perfectly general method. ...One could answer whether this f-compliant is the same as that one, but there are too many ways to articulate it. | |
| From: David Wiggins (Sameness and Substance [1980], 2.8) | |
| A reaction: His famous example is trying to count the Pope's crown, which is made of crowns. A clearer example might be a rectangular figure divided up into various overlapping rectangles. Individuation is easy, but counting is contextual. |
| 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. |
| 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). |
| 14746 | What exists can't depend on our conceptual scheme, and using all conceptual schemes is too liberal [Sider on Wiggins] |
| Full Idea: It would be incredible if what there is, rather than what we select for attention, depends on human activity and our conceptual scheme. One might expand to possible sortal concepts, rather than our language, but that amounts to four-dimensionalism. | |
| From: comment on David Wiggins (Sameness and Substance Renewed [2001]) by Theodore Sider - Four Dimensionalism 5.3 | |
| A reaction: [compression of a nice anti-Wiggins paragraph] He suggests that Wiggins is seeking an intermediate course (between narrow chauvinism about concepts, and excessive liberalism) in a discussion of natural kinds versus artifacts. |
| 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. |
| 16523 | Realist Conceptualists accept that our interests affect our concepts [Wiggins] |
| Full Idea: The realist conceptualist may cheerfully admit that the sortal concepts of which we are possessed are the creatures of our interests; …and also that there need be no one way in which we must articulate reality. | |
| From: David Wiggins (Sameness and Substance [1980], 5.2) | |
| A reaction: Wiggins calls himself a 'realist conceptualist'. In his terminology, I seem to be an 'anti-conceptualist realist'. The issue concerns aspects of reality that extend beyond our concepts. The 99th d.p. of the mass of the electron. |
| 16524 | Conceptualism says we must use our individuating concepts to grasp reality [Wiggins] |
| Full Idea: What Conceptualism entails is that, although horses and stars are not inventions or artefacts, in order to single out these things we must deploy a conceptual scheme which has been formed in such a way as to make singling them out possible. | |
| From: David Wiggins (Sameness and Substance [1980], 5.5) | |
| A reaction: I don't quite see why the 'singling out' role of the concepts is the only one that generates them, or makes them fit for purpose. In general, of course, our conceptual scheme is necessarily a response to our experience of the world. |
| 16526 | Animal classifications: the Emperor's, fabulous, innumerable, like flies, stray dogs, embalmed…. [Wiggins] |
| Full Idea: A Chinese encyclopedia classifies animals as belonging to the Emperor, embalmed, tame, sucking pigs, sirens, fabulous, stray dogs, included in this classification, frenzied, innumerable, drawn with a fine brush, etcetera, or look for afar like flies. | |
| From: David Wiggins (Sameness and Substance [1980], 5.7 n18) | |
| A reaction: [This glorious quotation comes from a story by Borges, first spotted by Foucault] |
| 12056 | An ancestral relation is either direct or transitively indirect [Wiggins] |
| Full Idea: x bears to y the 'ancestral' of the relation R just if either x bears R to y, or x bears R to some w that bears R to y, or x bears R to some w that bears R to some z that bears R to y, or..... | |
| From: David Wiggins (Substance [1995], 4.10.1) | |
| A reaction: A concept invented by Frege (1879). |
| 12050 | Substances contain a source of change or principle of activity [Wiggins] |
| Full Idea: Substances are things that have a source of change or principle of activity within them. | |
| From: David Wiggins (Substance [1995], 4.4.1) | |
| A reaction: A vey significant concession. I think we can talk of 'essences' and 'powers', and drop talk of 'substances'. 'Powers' is a much better word, because it immediately pushes the active ingredient to the forefront. |
| 16492 | Individuation needs accounts of identity, of change, and of singling out [Wiggins] |
| Full Idea: A theory of individuation must comprise at least three things: an elucidation of the primitive concept of identity or sameness; what it is to be a substance that persists through change; and what it is for a thinker to single out the same substance. | |
| From: David Wiggins (Sameness and Substance [1980], Pre 1) | |
| A reaction: [compressed] Metaphysics seems to need a theory of identity, but I am not yet convinced that it also needs a theory of 'individuation'. Never mind, press on and create one, and see how it looks. Aristotle wanted to explain predication too. |
| 16493 | Individuation can only be understood by the relation between things and thinkers [Wiggins] |
| Full Idea: Understanding the concepts involved in individuation can only be characterised by reference to observable commerce between things singled out and thinkers who think or find their way around the world precisely by singling them out. | |
| From: David Wiggins (Sameness and Substance [1980], Pre 1) | |
| A reaction: I take individuation to be relatively uninteresting, because I understand identity independently of how we single things out, but Wiggins's reliance on sortals implies that the very identity of things in the world is knee deep in mental activity. |
| 11900 | We can accept criteria of distinctness and persistence, without making the counterfactual claims [Mackie,P on Wiggins] |
| Full Idea: We might agree with Wiggins's theory of individuation, but reject his thesis that a thing's principle of individuation (of distinctness and persistence) must be preserved in all counterfactual situations. | |
| From: comment on David Wiggins (Sameness and Substance Renewed [2001]) by Penelope Mackie - How Things Might Have Been 8.7 | |
| A reaction: I'm not even convinced that initial individuation consists of falling under a sortal, and I prefer to discuss the powers of the thing, rather than counterfactual facts about behaviour. |
| 11870 | Activity individuates natural things, functions do artefacts, and intentions do artworks [Wiggins] |
| Full Idea: What a principle of activity does completely for a natural thing, and the function does imperfectly for an ordinary artefact, the artist's conception of his own making of the work must do for the painting. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.12) | |
| A reaction: This nicely sums up Wiggins on individuation, and he seems to effectively elide individuation with essence. I certainly feel uneasy that a work of art needs a quite separate account from other artefacts. Surely it is just that we are fussier about them? |
| 16496 | Singling out extends back and forward in time [Wiggins] |
| Full Idea: The singling out of a substance at a time reaches backwards and forwards to time before and after that time. | |
| From: David Wiggins (Sameness and Substance [1980], Pre 2) | |
| A reaction: Presumably this is an inferred history and persistence conditions. Sounds fine in a stable world. We assume (a priori?) that any object will have a space-time line for its duration. |
| 11866 | The idea of 'thisness' is better expressed with designation/predication and particular/universal [Wiggins] |
| Full Idea: It is hard to think of anything true and significant that could not be said using the idea of thisness not better said while respectiving the distinctions designation/predication and particular/universal. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.7) | |
| A reaction: Politis calls 'thisness' the 'ultimate subject of predication', so it is covered in logic by the name for an object. But we need to understand objects, and not just refer to them, and I'm not sure that 'universals' advance our understanding. |
| 12052 | We never single out just 'this', but always 'this something-or-other' [Wiggins] |
| Full Idea: What is singled out is never a bare this or that, but this or that something or other. | |
| From: David Wiggins (Substance [1995], 4.5.1) | |
| A reaction: I like, in ontological speculation, to contemplate the problem of the baffling archaeological find. 'This thing I have dug up - what the hell IS it?'. Wiggins is contemptuous of the term 'thisness', and the idea of bare particulars. |
| 13128 | 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins] |
| Full Idea: 'Ultimate sortals' are said to be non-subordinated, disjoint from one another, and uniquely paired with each object. Because of this, the ultimate sortal cannot be a satisfactory explication of the notion of an ontological category. | |
| From: comment on David Wiggins (Identity and Spatio-Temporal Continuity [1971], p.75) by Jan Westerhoff - Ontological Categories §26 | |
| A reaction: My strong intuitions are that Wiggins is plain wrong, and Westerhoff gives the most promising reasons for my intuition. The simplest point is that objects can obviously belong to more than one category. |
| 16495 | The only singling out is singling out 'as' something [Wiggins] |
| Full Idea: There could be no singling out tout court unless there could be singling out 'as'. | |
| From: David Wiggins (Sameness and Substance [1980], Pre 2) | |
| A reaction: I find this claim baffling. Do animals categorise everything they engage with? Are we unable to engage with something if we have not yet categorised it? Surely picking it out is prior to saying that sort of thing it is? |
| 16501 | In Aristotle's sense, saying x falls under f is to say what x is [Wiggins] |
| Full Idea: To say that x falls under f - or that x is an f - is to say what x is (in the sense Aristotle isolated). | |
| From: David Wiggins (Sameness and Substance [1980], 2.1) | |
| A reaction: This is a key claim in Wiggins's main principle. I'm not convinced. He wants one main sortal to do all the work. I don't think Aristotle at all intended the 'nature' of an individual thing to be given by a single sortal under which it falls. |
| 16506 | Every determinate thing falls under a sortal, which fixes its persistence [Wiggins] |
| Full Idea: We can expect that, for every completely determinate continuant, there will be at least one sortal concept that it falls under and that determines a principle of persistence for it. | |
| From: David Wiggins (Sameness and Substance [1980], 2.4) | |
| A reaction: I think he has the 'determines' relation the wrong way round! Being a tiger doesn't determine anything about persistence. It is having that nature and those persistence conditions which make it a tiger. And why does he optimistically 'expect' this? |
| 12055 | Sortal predications are answers to the question 'what is x?' [Wiggins] |
| Full Idea: Predications which answer the question 'what is x?' are often called 'sortal predications' in present-day philosophy. | |
| From: David Wiggins (Substance [1995], 4.10.1) | |
| A reaction: The word 'sortal' comes from Locke. Wiggins is the guru of 'sortal essentialism'. I just can't believe that in answer to the question 'what really is David Wiggins?' that he would be happy with a sequence of categorisations. |
| 12059 | A river may change constantly, but not in respect of being a river [Wiggins] |
| Full Idea: To say that the river is changing constantly in every respect is not to say that it is changing in respect of being a river. | |
| From: David Wiggins (Substance [1995], 4.11.2) | |
| A reaction: Can't a river become a lake, or a mere stream? Wiggins's proposal does not help with the problem of a river which sometimes dries up (as my local river sometimes does). At what point do we decide it is no longer a river? |
| 12063 | Sortal classification becomes science, with cross reference clarifying individuals [Wiggins] |
| Full Idea: The sense of the sortal term under which we pick out an individual expands into the scientific account of things of that kind, where the account clarifies what is at issue in questions of sameness and difference of specimens of that kind. | |
| From: David Wiggins (Substance [1995], 4.13.1) | |
| A reaction: This is how the sortal approach is supposed to deal with individuals. So the placid tiger reveals much by falling under 'tiger', and a crucial extra bit by falling under 'placid'. See Idea 12053 for problems with this proposal. |
| 12051 | If the kinds are divided realistically, they fall into substances [Wiggins] |
| Full Idea: Substance are what the world is articulated into when the segments of kinds corresponds to the real divisions in reality. | |
| From: David Wiggins (Substance [1995], 4.5.1) | |
| A reaction: This is very helpful in clarifying Wiggins's very obscurely expressed views. He appears to be saying that if we divide the sheep from the goats correctly, we reveal sheep-substance and goat-substance (one substance per species). Crazy! |
| 12053 | 'Human being' is a better answer to 'what is it?' than 'poet', as the latter comes in degrees [Wiggins] |
| Full Idea: One person can be more or less of a poet than another, so 'poet' is not a conclusory answer to the question 'What is it that is singled out here?' 'Poet' rides on the back of the answer 'human being'. | |
| From: David Wiggins (Substance [1995], 4.5.1) | |
| A reaction: So apparently one must assign a natural kind, and not just a class. Wiggins lacks science fiction imagination. In the genetic salad of the far future, being a poet may be more definitive than being a human being. See Idea 12063. |
| 12054 | Secondary substances correctly divide primary substances by activity-principles and relations [Wiggins] |
| Full Idea: A system of secondary substances with a claim to separate reality into its genuine primary substances must arise from an understanding of a set of principles of activity on the basis of which identities can be glossed in terms of determinate relations. | |
| From: David Wiggins (Substance [1995], 4.5.1) | |
| A reaction: I translate this as saying that individual essences are categorised according to principles which explain behaviour and relations. I'm increasingly bewildered by the 'secondary substances' Wiggins got from 'Categories', and loves so much. |
| 11896 | A sortal essence is a thing's principle of individuation [Wiggins, by Mackie,P] |
| Full Idea: Wiggins bases sortal essentialism on the notion that a thing's principle of individuation is essential to it. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Penelope Mackie - How Things Might Have Been 7.1 | |
| A reaction: This idea has failed to make much impression on me. I seem to be the only person who doesn't understand the concept of 'individuation'. Please let me know exactly what it means. Type individuation is not individual individuation, I presume. |
| 15835 | Wiggins's sortal essentialism rests on a thing's principle of individuation [Wiggins, by Mackie,P] |
| Full Idea: Wiggins bases sortal essentialism on the notion that a thing's principle of individuation is essential to it. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Penelope Mackie - How Things Might Have Been 7.1 | |
| A reaction: My problem with this is that individuation is a human activity, not an intrinsic feature of the entities in the external world. Entities presumably have a 'unity', but I'm not sure about a 'principle' that does that job, though Aristotle is sympathetic. |
| 11841 | The evening star is the same planet but not the same star as the morning star, since it is not a star [Wiggins] |
| Full Idea: The evening star is the same planet but not the same star as the morning star. For Venus is not a star. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.3) | |
| A reaction: This is a nice objection to the idea that identity is entirely a matter of falling under the same sortal category. |
| 10679 | 'Sortalism' says parts only compose a whole if it falls under a sort or kind [Wiggins, by Hossack] |
| Full Idea: 'Sortalism' endorses the view that some things have parts, but denies that every collection of things composes something. Whenever there is a particular, there must be a sort or kind to which it belongs. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Keith Hossack - Plurals and Complexes 7 | |
| A reaction: What is the status of 'the first of its kind'? This seems to say that a token only has identity if it has type-identity. This sounds wildly wrong to me. I've made a 'thing' for you, but I haven't decided what it is yet. |
| 14363 | Identity a=b is only possible with some concept to give persistence and existence conditions [Wiggins, by Strawson,P] |
| Full Idea: Wiggins says an identity a=b stands no chance of being true unless there is some concept f under which a falls and under which b falls, which 'determines identity, persistence and existence conditions for members of its extension'. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Peter F. Strawson - Review of 'Sameness and Substance' p.604 | |
| A reaction: This is the first clear statement I have met of Wiggins's central idea, upon which his sortal essentialism is built. Strawson's exposition adds that each thing necessarily falls under the 'highest' appropriate sortal ('dog', rather than 'terrier'). |
| 14364 | A thing is necessarily its highest sortal kind, which entails an essential constitution [Wiggins, by Strawson,P] |
| Full Idea: In Wiggins's theory, necessity carries over from the kind to constitution. If Toby is necessarily a dog and 'dog' is a natural kind term, then Toby necessarily has the constitution of a dog, the features of which make up the real essence of being a dog. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Peter F. Strawson - Review of 'Sameness and Substance' p.605 | |
| A reaction: The essence will then presumably consist of all and only the characteristics which are shared by all dogs whatsoever. So how do you decide the borderline between wolf and dog? Why isn't a wolf a dog? |
| 11851 | Many predicates are purely generic, or pure determiners, rather than sortals [Wiggins] |
| Full Idea: There are countless predicates in English that have the appearance of sortal predicates but are purely generic (animal, machine, artefact), or are pure determinables for sortal determination (space-occupier, entity, substance). | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.6) | |
| A reaction: This is preparing the ground for a specification of a sortal which defines something essential as being the hallmark of identity. It is never quite clear to me whether Wiggins's case rests on a nominal or a real essence. |
| 11865 | The possibility of a property needs an essential sortal concept to conceive it [Wiggins] |
| Full Idea: A thing could have a property only if its having the property could be conceived, and that requires some sortal concept which adequately answers the Aristotelian question what the thing is. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.5) | |
| A reaction: [Algebra omitted!] The core idea of Wiggins's theory. It seems at first glance to be a revival of Aristotelian essentialism, but his view of that seems to merely involve falling into a category. He treats sortal concepts as Aristotle's 'primary being'. |
| 12047 | We refer to persisting substances, in perception and in thought, and they aid understanding [Wiggins] |
| Full Idea: A substance is a persisting and somehow basic object of reference that is there to be discovered in perception and thought, an object whose claim to be recognized as a real entity is a claim on our aspirations to understand the world. | |
| From: David Wiggins (Substance [1995], 4.1) | |
| A reaction: A lot of components are assigned by Wiggins to the concept, and the tricky job, inititiated by Aristotle, is to fit all the pieces together nicely. Personally I am wondering if the acceptance of 'essences' implies dropping 'substances'. |
| 14744 | Objects can only coincide if they are of different kinds; trees can't coincide with other trees [Wiggins, by Sider] |
| Full Idea: Wiggins says that coincidence is possible only between objects of different kinds. Trees and cats coincide with aggregates of matter, but never trees with trees or cats with cats. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Theodore Sider - Four Dimensionalism 5.3 | |
| A reaction: At first glance this sounds quite plausible, but I think this commitment to the priority of kinds produces huge confusion, given that we only derive our notions of kinds from inductions derived from individuals. Language perpetuates old inductions. |
| 11852 | Is the Pope's crown one crown, if it is made of many crowns? [Wiggins] |
| Full Idea: The Pope's crown is made of crowns. There is no definite answer, when the Pope is wearing his crown, to the question 'how many crowns does he have on his head?' | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.7) | |
| A reaction: A very nice example, in which the identity of the item seems clear enough, until you try to apply a sortal to it. I can't get excited about it, though, because calling it one 'crown' creates uncertainty, but calling it the 'Pope's crown' doesn't. |
| 11875 | Boundaries are not crucial to mountains, so they are determinate without a determinate extent [Wiggins] |
| Full Idea: It can be perfectly determinate which mountain x is without x's extent's being determinate. A mountain is not, after all, something essentially demarcated by its extent or boundary. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 6.5) | |
| A reaction: This endorses something I have always wanted to assert ('a vague boundary is still a boundary'), but with the interesting addition that one might think about vagueness in terms of what is essential to a thing. Hm.... |
| 12057 | Matter underlies things, composes things, and brings them to be [Wiggins] |
| Full Idea: Matter ex hypothesi is what ultimately underlies (to huperkeimenon) a thing; it is that from which something comes to be and which remains as a non-coincidental component in the thing's make-up. | |
| From: David Wiggins (Substance [1995], 192a30) | |
| A reaction: This is an interesting prelude to the much more comprehensive discussion of matter in Metaphysics, where he crucially adds the notion of 'form', and gives it priority over the underlying matter. |
| 14749 | Identity is an atemporal relation, but composition is relative to times [Wiggins, by Sider] |
| Full Idea: Wiggins points out that identity is an atemporal relation whereas composition, like parthood, holds only relative to times. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Theodore Sider - Four Dimensionalism 5.3 | |
| A reaction: If David Cameron is identical to the Prime Minister, that doesn't seem to be atemporal. If x=7 in this problem, I can change x to something else in the next problem. x had better not be equal to 7 and to 9. |
| 11844 | If I destroy an item, I do not destroy each part of it [Wiggins] |
| Full Idea: If I repair or destroy an item, I do not repair or destroy each part of it (and since each part of a part is a part this would be difficult). | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.6) | |
| A reaction: This seems like a nice refutation of any attempt to claim that a thing is no more than the sum of its parts, but one could analyse the notion of 'destroy', and find it just meant introducing gaps between parts. |
| 11861 | We can forget about individual or particularized essences [Wiggins] |
| Full Idea: Let us be realistic, and forget about individual or particularized essences. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.2) | |
| A reaction: This is the rather weird position you reach if you follow Wiggins's 'modest' essentialism, deriving from a thing merely falling under a sortal, or into a category. What is a natural kind, if its members don't each have a shared essence? |
| 16509 | Natural kinds are well suited to be the sortals which fix substances [Wiggins] |
| Full Idea: Among the best candidates to play the roles of sortal and substantial predicates are the natural kind words. | |
| From: David Wiggins (Sameness and Substance [1980], 3.1) | |
| A reaction: There is always a danger of circularity with this kind of approach. How do we distinguish the genuine natural kinds from the dubious ones? |
| 11871 | Essences are not explanations, but individuations [Wiggins] |
| Full Idea: Essences of natural things are not fancified vacuities parading themselves ...as the ultimate explanation of everything that happens in the world. They are natures whose possession is a precondition of their owners being divided from the rest of reality. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 5.2) | |
| A reaction: Thus Wiggins rejects the explanation account of essence, with an assertion of his own (highly implausible) view that essence is about individuation rather than about behaviour. Individuation strikes me as an entirely human activity, and not 'real'. |
| 11879 | Essentialism is best represented as a predicate-modifier: □(a exists → a is F) [Wiggins, by Mackie,P] |
| Full Idea: Wiggins's proposal of a predicate-modifier account is the best formal representation of essential statements. ...This simple version is perfectly adequate to represent the claim that a is essentially-F: □(a exists → a is F). | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001], Ch.4) by Penelope Mackie - How Things Might Have Been 1.2 | |
| A reaction: I suppose that is right. Having an essence is a feature of an entity, but it has to boil done to characteristics that define the entity, and which it must presumably always have. Could an entity ever lack its essence? |
| 16514 | Artefacts are individuated by some matter having a certain function [Wiggins] |
| Full Idea: Ordinary artefacts are individuated, rather indeterminately and arbitrarily, by reference to a parcel of matter so organised as to subserve a certain function. | |
| From: David Wiggins (Sameness and Substance [1980], 3.3) |
| 16510 | Nominal essences don't fix membership, ignore evolution, and aren't contextual [Wiggins] |
| Full Idea: Nominal essences are unsatisfactory because they fail either of necessity or of sufficiency for membership of the intended kind, they leave unexplained how sortals can evolve, and there is no room for culture or context in our reference to kinds. | |
| From: David Wiggins (Sameness and Substance [1980], 3.1) | |
| A reaction: [a compression of a paragraph] I would have thought that Locke would just say it is tough luck if nominal essences can't do all these things, because that's just the way it is, folks. |
| 11835 | The nominal essence is the idea behind a name used for sorting [Wiggins] |
| Full Idea: Things being ranked under Names into sorts only as they agree with certain abstract ideas, to which we have annexed the Names, the essence of each sort comes to nothing but that abstract idea which the sortal name stands for. This is the nominal Essence. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], III.iii.15) | |
| A reaction: He contrasts 'nominal essence' with 'real essence'. A key passage for David Wiggins. One shouldn't put too much emphasis on nominal essence, since it means that someone referred to as 'that idiot over there' (you, perhaps) is necessarily an idiot. |
| 16503 | 'What is it?' gives the kind, nature, persistence conditions and identity over time of a thing [Wiggins] |
| Full Idea: The question 'what is it?' refers to the persistence and lifespan of an entity, and so manifests the identity over time of an entity and its persistence, between persistence and existence, and between its existence and being the kind of thing it is. | |
| From: David Wiggins (Sameness and Substance [1980], 2.1) | |
| A reaction: The idea that establishing the kind of a thing can do all this work strikes me as false. The lifespan of a 'human' can be between five minutes and a hundred years. Humans have a clear death, but thunderstorms don't. |
| 11876 | It is easier to go from horses to horse-stages than from horse-stages to horses [Wiggins] |
| Full Idea: If horse-stages made sense at all, it would be easier to go from horses to horse-stages than to go from horse-stages to horses. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 6.9) | |
| A reaction: A nice remark, analogous to 'it is easier to break a vase than to mend it'. Going from horse-stages to horses is the classic difficulty for 'bundle theories' (of objects, or persons): what is it that unites the bundle? |
| 16499 | A restored church is the same 'church', but not the same 'building' or 'brickwork' [Wiggins] |
| Full Idea: We can say of Hume's church that the present church is the same 'church' as the old parish church but not the same 'building' or the same 'stonework' as the old parish church. | |
| From: David Wiggins (Sameness and Substance [1980], 1.5) | |
| A reaction: Unconvinced. This seems to make a 'church' into an abstraction, which might even exist in the absence of any building. And it seems to identify a building with its stonework. Wiggins yearns for a neat solution, but it ain't here. |
| 16515 | A thing begins only once; for a clock, it is when its making is first completed [Wiggins] |
| Full Idea: A thing starts existing only once; and in the case of a clock its proper beginning was at about the time when its maker finished it. | |
| From: David Wiggins (Sameness and Substance [1980], 3.3) | |
| A reaction: I love the example that challenges this. Take the clock's parts and use them to make other clocks, then collect them up and reassemble the first clock. If the first clock has persisted through this, you have too many clocks. Wiggins spots some of this. |
| 11858 | The question is not what gets the title 'Theseus' Ship', but what is identical with the original [Wiggins] |
| Full Idea: Let us remember that the title in question is not the title to the sobriquet 'Theseus' Ship'; it is the title to identity with Theseus' ship, a particular ship originating from the eighth century B.C. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 3.4) | |
| A reaction: There is an assumption here that identity is defined by origin. What is the origin of the identity of those huge football clubs that began under the name of some village team in 1875? What is the origin of 'England' as a single entity? |
| 16517 | Priests prefer the working ship; antiquarians prefer the reconstruction [Wiggins] |
| Full Idea: Dispute might break out between priests who favoured the working ship and antiquarians who preferred the reconstruction. | |
| From: David Wiggins (Sameness and Substance [1980], 3.3) | |
| A reaction: This captures the contextual nature of the dispute very succinctly. Wiggins, of course, thinks that sortals will settle the matter. Fat chance. |
| 11843 | Identity over a time and at a time aren't different concepts [Wiggins] |
| Full Idea: People often speak of identity over time and distinguish it from identity at a time. But identity is just identity. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.3) | |
| A reaction: I myself am guilty of such usage, but it doesn't imply a commitment to a multivocal concept. The epistemological issues (of explaining what it is now, and simply reidentifying it later) seem profoundly different. Hume only admits identity over time. |
| 11864 | Hesperus=Hesperus, and Phosphorus=Hesperus, so necessarily Phosphorus=Hesperus [Wiggins] |
| Full Idea: The simple proof (from Ruth Barcan Marcus) is: Hesperus is necessarily Hesperus, so if Phosphorus is Hesperus, then Phosphorus is necessarily Hesperus. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.3) | |
| A reaction: This is the famous idea which she noticed well before Kripke. The point is that the simple logic of the case bestows a necessity on the identity. We shouldn't be confused by the a posteriori and contingent nature of the discovery. |
| 16498 | Identity cannot be defined, because definitions are identities [Wiggins] |
| Full Idea: Since any definition is an identity, identity itself cannot be defined. | |
| From: David Wiggins (Sameness and Substance [1980], 1.2 n7) | |
| A reaction: This sounds too good to be true! I can't think of an objection, so, okay, identity cannot possibly be defined. We can give synonyms for it, I suppose. [Wrong, says Rumfitt! Definitions can also be equivalences!] |
| 11831 | The formal properties of identity are reflexivity and Leibniz's Law [Wiggins] |
| Full Idea: The formal properties of identity are the reflexivity of identity, and Leibniz's Law (if x is the same as y, then whatever is true of one is true of the other). | |
| From: David Wiggins (Sameness and Substance Renewed [2001], Pr.2) | |
| A reaction: Presumably transitivity will also apply, and, indeed, symmetry. He seems to mean something like the 'axiomatic formal properties'. |
| 16497 | Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity [Wiggins] |
| Full Idea: The principle of Leibniz's Law marks off what is peculiar to identity and differentiates it in a way in which transitivity, symmetry and reflexivity (all shared by 'exact similarity, 'equality in pay', etc.) do not. | |
| From: David Wiggins (Sameness and Substance [1980], 1.2) |
| 16502 | Identity is primitive [Wiggins] |
| Full Idea: Identity is a primitive notion. | |
| From: David Wiggins (Sameness and Substance [1980], 2.1) | |
| A reaction: To be a true primitive it would have to be univocal, but it seems to me that 'identity' comes in degrees. The primitive concept is the minimal end of the degrees, but there are also more substantial notions of identity. |
| 14362 | Relative Identity is incompatible with the Indiscernibility of Identicals [Wiggins, by Strawson,P] |
| Full Idea: Wiggins argues that Geach's Relative Identity is incompatible with the formal properties of identity, which include, besides transitivity, symmetry and reflexivity, the complete community of properties defined by the Indiscernibility of Identicals. | |
| From: report of David Wiggins (Sameness and Substance Renewed [2001]) by Peter F. Strawson - Review of 'Sameness and Substance' p.603 | |
| A reaction: The tricky part is that Wiggins then goes on to say that identity depends on sortals, which sounds very close to the Geach view. I find disentangling them tricky. See Idea 14363 for a helpful comment from Strawson. |
| 11838 | Relativity of Identity makes identity entirely depend on a category [Wiggins] |
| Full Idea: The thesis of Relativity of Identity (which I steadfastly oppose) ..suggests that it makes all the difference to keeping track of continuants through space and time which concept one subsumes something under. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 1.1) | |
| A reaction: [Geach I take to be the villain of this idea] The point is that identity is entirely relative to the sortal concept, where Wiggins wants to make identity a combination of the object itself and our concept of it (I think). |
| 11847 | To identify two items, we must have a common sort for them [Wiggins] |
| Full Idea: As a necessary condition of the truth of an identity claim, some common sort f will have to be found to which they each belong. That is the point at which the primary question of identity can come into focus. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.2) | |
| A reaction: This is the plainest English expression I can find of Wiggins's main thesis. He maintains this thesis, while adamantly denying the idea that identity consists entirely of falling under a concept. |
| 16521 | A is necessarily A, so if B is A, then B is also necessarily A [Wiggins] |
| Full Idea: The famous proof of Barcan Marcus about necessity of identity comes down to simply this: Hesperus is necessarily Hesperus, so if Phosphorus is Hesperus, Phosphorus is necessarily Hesperus. | |
| From: David Wiggins (Sameness and Substance [1980], 4.3) | |
| A reaction: Since the identity of Hesperus and Phosphorus was an a posteriori discovery, this was taken to be the inception of the idea that there are a posteriori necessities. The conclusion seems obvious. One thing is necessarily one thing. |
| 16505 | By the principle of Indiscernibility, a symmetrical object could only be half of itself! [Wiggins] |
| Full Idea: The full Identity of Indiscernibles excludes the existence in this world of a symmetrical object, which is reduced to half of itself by the principle. If symmetrical about all planes that bisect it, it is precluded altogether from existence. | |
| From: David Wiggins (Sameness and Substance [1980], 2.2) | |
| A reaction: A really nice objection. Do the parts even need to be symmetrical? My eyeballs can't be identical to one another, presumably. Electrons already gave the principle big trouble. |
| 11839 | Do both 'same f as' and '=' support Leibniz's Law? [Wiggins] |
| Full Idea: Is Leibniz's Law as true for 'is the same as' as it is for '='? | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 1.2) | |
| A reaction: [By Leibniz's Law he means if they are the same, they support the same truths] |
| 11845 | Substitutivity, and hence most reasoning, needs Leibniz's Law [Wiggins] |
| Full Idea: Leibniz's Law underwrites the substitutivity of identity and this is a principle not long dispensable in any form of reasoning. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.7) | |
| A reaction: Thus the modern fashion of deriving our metaphysics from our logic. Presumably we can derive it from our epistemology too, or even from our intuitions, if we thought they were good enough as evidence. |
| 16494 | We want to explain sameness as coincidence of substance, not as anything qualitative [Wiggins] |
| Full Idea: The notion of sameness or identity that we are to elucidate is not that of any degree of qualitative similarity but of coincidence as a substance - a notion as primitive as predication. | |
| From: David Wiggins (Sameness and Substance [1980], Pre 2) | |
| A reaction: This question invites an approach to identity through our descriptions of it, rather than to the thing itself. There is no problem in ontology of two substances being 'the same', because they are just one substance. |
| 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! |
| 16522 | It is hard or impossible to think of Caesar as not human [Wiggins] |
| Full Idea: It is hard or impossible to conceive of Caesar's not being a man (human). | |
| From: David Wiggins (Sameness and Substance [1980], 4.5) | |
| A reaction: So is it 'hard' or is it 'impossible'? Older generations of philosophers simply didn't read enough science fiction. Any short story could feature Caesar's failure to be a man. His assassination was a disaster for the Martian invasion of 44 BCE. |
| 11869 | Possible worlds rest on the objects about which we have suppositions [Wiggins] |
| Full Idea: Worlds are the shadows of our suppositions and they take on their identity from these. Suppositions take on their identity from (inter alia) the objects they relate to. If they sever themselves from these objects, then they collapse. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.11) | |
| A reaction: Sounds good. My picture is of possibilities which are suggested by objecfs in the actual world, with extreme possibilities being at fifth-remove from actuality. Any worlds that go beyond natural possibility are just there for fun. |
| 15432 | Structural universals might serve as possible worlds [Forrest, by Lewis] |
| Full Idea: Forrest proposed that structural universals should serve as ersatz possible worlds. | |
| From: report of Peter Forrest (Ways Worlds Could Be [1986]) by David Lewis - Against Structural Universals 'Intro' | |
| A reaction: I prefer powers to property universals. Perhaps a possible world is a maximal set of co-existing dispositions? |
| 11850 | Not every story corresponds to a possible world [Wiggins] |
| Full Idea: It is perfectly notorious that not every story corresponds to a possible world. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.4) | |
| A reaction: Thus a fantasy castle might be decorated with 'beautiful circular squares', or be threatened by a lump of enriched uranium twenty feet in diameter. Wiggins is replying to the claim that a possible world represents a 'story'. |
| 16525 | Our sortal concepts fix what we find in experience [Wiggins] |
| Full Idea: What sortal concepts we can bring to bear upon experience determines what we can find there. | |
| From: David Wiggins (Sameness and Substance [1980], 5.6) | |
| A reaction: Wiggins would wince at being classed among linguistic relativists of the Sapir-Whorf type, but that's where I'm putting this idea. Wiggins is a realist, who knows there are things out there our concepts miss. He compares it to a fishing net. He's wrong. |
| 12064 | The category of substance is more important for epistemology than for ontology [Wiggins] |
| Full Idea: For us the importance of the category of substance, if it has any importance, is not so much ontological as relative to our epistemological circumstances and the conditions under which we have to undertake inquiry. | |
| From: David Wiggins (Substance [1995], 4.13.2) | |
| A reaction: This seems to be a rather significant concession. Wiggins has revived the notion of substance in recent times, but he is not quite adding it to the furniture of the world. Personally I increasingly think we can dump it, in ontology and epistemology. |
| 12049 | Naming the secondary substance provides a mass of general information [Wiggins] |
| Full Idea: Answering 'what is it?' with the secondary substance identifies an object with a class of continuants which survive certain changes, come into being in certain ways, are qualified in certain ways, behave in certain ways, and cease to be in certain ways. | |
| From: David Wiggins (Substance [1995], 4.3.3) | |
| A reaction: Thus the priority of this sort of answer is that a huge range of explanations immediately flow from it. I take the explanation to be prior, and the primary substance to be prior, since secondary substance is inductively derived from it. |
| 11848 | Asking 'what is it?' nicely points us to the persistence of a continuing entity [Wiggins] |
| Full Idea: The special effectiveness of the 'what is it?' question is that, in the case of continuants, it refers us back to our constantly exercised idea of the persistence and life-span of an entity. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 2.2) | |
| A reaction: Compare 'this is a human' with 'this is a member of a family noted for its longevity'. We can't simply answer 'what is it?' by tossing it into the nearest category. I say we need an individual essence for explanation, not just a sortal. |
| 12065 | Seeing a group of soldiers as an army is irresistible, in ontology and explanation [Wiggins] |
| Full Idea: It seems mandatory to an observer of soldiers to give 'the final touch of unity' to their aggregate entity (the army). ...Similar claims arise with the ontological and explanatory claims of other corporate entities. | |
| From: David Wiggins (Substance [1995], 4.13.3) | |
| A reaction: Wiggins must say (following Leibniz Essays II.xxiv,1) that we add the unity, but I take the view that an army has powers, and hence offers explanations, which are lacking in a merely group of disparate soldiers. So an army has an essence and identity. |
| 11859 | The mind conceptualizes objects; yet objects impinge upon the mind [Wiggins] |
| Full Idea: The mind conceptualizes objects; yet objects impinge upon the mind. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 3.6) | |
| A reaction: I like this piece of simple common sense. I personally don't think you can reach first base in a sensible discussion if you don't face up to both sides of this idea (especially the second half, which many philosophers, especially of language, neglect). |
| 16518 | We conceptualise objects, but they impinge on us [Wiggins] |
| Full Idea: The mind conceptualises objects, yet objects impinge upon the mind. | |
| From: David Wiggins (Sameness and Substance [1980], 3.5) | |
| A reaction: A very nice statement of the relationship, and the fact that we don't just make our concepts up. |
| 11836 | We can use 'concept' for the reference, and 'conception' for sense [Wiggins] |
| Full Idea: We can use the Fregean 'concept' on the level of reference and naming, and prefer the word 'conception' for the Kantian idea of the sense, or the information needed to understand the concept. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], Pr.5) | |
| A reaction: This is a nice suggestion, and at first blush I think it should be adopted. Sometimes philosophers regret adopting a terminology several hundred years after it has been agreed. |
| 16511 | A 'conception' of a horse is a full theory of what it is (and not just the 'concept') [Wiggins] |
| Full Idea: A 'conception' of horse is a theory of what a horse is, or what it is to be a horse. The conception is in no way the same as the concept. The conception is of the concept. | |
| From: David Wiggins (Sameness and Substance [1980], 3.1) | |
| A reaction: Wiggins sounds confident about a sharp distinction here, which I doubt, but some such distinction seems to required. I quite like Williams's 'fat' and 'thin' concepts. |
| 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? |
| 11860 | Lawlike propensities are enough to individuate natural kinds [Wiggins] |
| Full Idea: For all the purposes of identity and individuation of things that belong to natural kinds..., it is enough to have regard for the lawlike propensities of members of the kind. | |
| From: David Wiggins (Sameness and Substance Renewed [2001], 4.1) | |
| A reaction: This may have got things in reverse, since it is hard to see how you could pick out any laws if you didn't assume the existence of natural kinds which were causing the regularities in the behaviour. |