84 ideas
| 5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
| Full Idea: Anaximander was the first to produce a philosophical book (later conventionally titled 'On Nature'), if not the first to produce a book at all. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by István Bodnár - Anaximander | |
| A reaction: Wow! Presumably there were Egyptian 'books', but this still sounds like a stupendous claim to fame. |
| 10468 | A metaphysics has an ontology (objects) and an ideology (expressed ideas about them) [Oliver] |
| Full Idea: A metaphysical theory hs two parts: ontology and ideology. The ontology consists of the entities which the theory says exist; the ideology consists of the ideas which are expressed within the theory using predicates. Ideology sorts into categories. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §02.1) | |
| A reaction: Say 'what there is', and 'what we can say about it'. The modern notion remains controversial (see Ladyman and Ross, for example), so it is as well to start crystalising what metaphysics is. I am enthusiastic, but nervous about what is being said. |
| 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. |
| 1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
| Full Idea: Something which is established in the centre and has equality in relation to the extremes has no more reason to move up than it has down or to the sides (so the earth is stationary) | |
| From: report of Anaximander (fragments/reports [c.570 BCE], A26) by Aristotle - On the Heavens 295b11 |
| 10471 | Ockham's Razor has more content if it says believe only in what is causal [Oliver] |
| Full Idea: One might give Ockham's Razor a bit more content by advising belief in only those entities which are causally efficacious. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §03) | |
| A reaction: He cites Armstrong as taking this line, but I immediately think of Shoemaker's account of properties. It seems to me to be the only account which will separate properties from predicates, and bring them under common sense control. |
| 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. |
| 10749 | Necessary truths seem to all have the same truth-maker [Oliver] |
| Full Idea: The definition of truth-makers entails that a truth-maker for a given necessary truth is equally a truth-maker for every other necessary truth. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §24) | |
| A reaction: Maybe we could accept this. Necessary truths concern the way things have to be, so all realities will embody them. Are we to say that nothing makes a necessary truth true? |
| 10750 | Slingshot Argument: seems to prove that all sentences have the same truth-maker [Oliver] |
| Full Idea: Slingshot Argument: if truth-makers work for equivalent sentences and co-referring substitute sentences, then if 'the numbers + S1 = the numbers' has a truth-maker, then 'the numbers + S2 = the numbers' will have the same truth-maker. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §24) | |
| A reaction: [compressed] Hence every sentence has the same truth-maker! Truth-maker fans must challenge one of the premises. |
| 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. |
| 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) |
| 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) |
| 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? |
| 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. |
| 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. |
| 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) |
| 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) |
| 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). |
| 14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
| Full Idea: Anaximander discovers the contradictory character of our world: it perishes from its own qualities. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by Friedrich Nietzsche - Unpublished Notebooks 1872-74 19 [239] | |
| A reaction: A lovely gloss on Anaximander, though I am not sure that I understand what Nietzsche means. |
| 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. |
| 10747 | Accepting properties by ontological commitment tells you very little about them [Oliver] |
| Full Idea: The route to the existence of properties via ontological commitment provides little information about what properties are like. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §22) | |
| A reaction: NIce point, and rather important, I would say. I could hardly be committed to something for the sole reason that I had expressed a statement which contained an ontological commitment. Start from the reason for making the statement. |
| 10748 | Reference is not the only way for a predicate to have ontological commitment [Oliver] |
| Full Idea: For a predicate to have a referential function is one way, but not the only way, to harbour ontological commitment. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §22) | |
| A reaction: Presumably the main idea is that the predicate makes some important contribution to a sentence which is held to be true. Maybe reference is achieved by the whole sentence, rather than by one bit of it. |
| 10719 | There are four conditions defining the relations between particulars and properties [Oliver] |
| Full Idea: Four adequacy conditions for particulars and properties: asymmetry of instantiation; different particulars can have the same property; particulars can have many properties; two properties can be instantiated by the same particulars. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §09) | |
| A reaction: The distinction between particulars and universals has been challenged (e.g. by Ramsey and MacBride). There are difficulties in the notion of 'instantiation', and in the notion of two properties being 'the same'. |
| 10721 | If properties are sui generis, are they abstract or concrete? [Oliver] |
| Full Idea: If properties are sui generis entities, one must decide whether they are abstract or concrete. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §09) | |
| A reaction: A nice basic question! I take the real properties to be concrete, but we abstract from them, especially from their similarities, and then become deeply confused about the ontology, because our language doesn't mark the distinctions clearly. |
| 10716 | There are just as many properties as the laws require [Oliver] |
| Full Idea: One conception of properties says there are only as many properties as are needed to be constituents of laws. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §03) | |
| A reaction: I take this view to the be precise opposite of the real situation. The properties are what lead to the laws. Properties are internal to nature, and laws are imposed from outside, which is ridiculous unless you think there is an active deity. |
| 10720 | We have four options, depending whether particulars and properties are sui generis or constructions [Oliver] |
| Full Idea: Both properties and particulars can be taken as either sui generis or as constructions, so we have four options: both sui generis, or both constructions, or one of each. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §09) | |
| A reaction: I think I favour both being sui generis. God didn't make the objects, then add their properties, or make the properties then create some instantiations. There can't be objects without properties, or objectless properties (except in thought). |
| 10714 | The expressions with properties as their meanings are predicates and abstract singular terms [Oliver] |
| Full Idea: The types of expressions which have properties as their meanings may vary, the chief candidates being predicates, such as '...is wise', and abstract singular terms, such as 'wisdom'. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §02) | |
| A reaction: This seems to be important, because there is too much emphasis on predicates. If this idea is correct, we need some account of what 'abstract' means, which is notoriously tricky. |
| 10715 | There are five main semantic theories for properties [Oliver] |
| Full Idea: Properties in semantic theory: functions from worlds to extensions ('Californian'), reference, as opposed to sense, of predicates (Frege), reference to universals (Russell), reference to situations (Barwise/Perry), and composition from context (Lewis). | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §02 n12) | |
| A reaction: [compressed; 'Californian' refers to Carnap and Montague; the Lewis view is p,67 of Oliver]. Frege misses out singular terms, or tries to paraphrase them away. Barwise and Perry sound promising to me. Situations involve powers. |
| 10738 | Tropes are not properties, since they can't be instantiated twice [Oliver] |
| Full Idea: I rule that tropes are not properties, because it is not true that one and the same trope of redness is instantiated by two books. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
| A reaction: This seems right, but has very far-reaching implications, because it means there are no properties, and no two things have the same properties, so there can be no generalisations about properties, let alone laws. ..But they have equivalence sets. |
| 10739 | The property of redness is the maximal set of the tropes of exactly similar redness [Oliver] |
| Full Idea: Using the predicate '...is exactly similar to...' we can sort tropes into equivalence sets, these sets serving as properties and relations. For example, the property of redness is the maximal set of the tropes of redness. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
| A reaction: You have somehow to get from scarlet and vermilion, which have exact similarity within their sets, to redness, which doesn't. |
| 10740 | The orthodox view does not allow for uninstantiated tropes [Oliver] |
| Full Idea: It is usual to hold an aristotelian conception of tropes, according to which tropes are present in their particular instances, and which does not allow for uninstantiated tropes. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
| A reaction: What are you discussing when you ask what colour the wall should be painted? Presumably we can imagine non-existent tropes. If I vividly imagine my wall looking yellow, have I brought anything into existence? |
| 10741 | Maybe concrete particulars are mereological wholes of abstract particulars [Oliver] |
| Full Idea: Some trope theorists give accounts of particulars. Sets of tropes will not do because they are always abstract, but we might say that particulars are (concrete) mereological wholes of the tropes which they instantiate. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
| A reaction: Looks like a non-starter to me. How can abstract entities add up to a mereological whole which is concrete? |
| 10742 | Tropes can overlap, and shouldn't be splittable into parts [Oliver] |
| Full Idea: More than one trope can occupy the same place at the same time, and a trope occupies a place without having parts which occupy parts of the place. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
| A reaction: This is the general question of the size of a spatial trope, or 'how many red tropes in a tin of red paint?' |
| 10472 | 'Structural universals' methane and butane are made of the same universals, carbon and hydrogen [Oliver] |
| Full Idea: The 'structural universals' methane and butane are each made up of the same universals, carbon and hydrogen. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §07) | |
| A reaction: He cites Lewis 1986, who is criticising Armstrong. If you insist on having universals, they might (in this case) best be described as 'patterns', which would be useful for structuralism in mathematics. They reduce to relations. |
| 10724 | Located universals are wholly present in many places, and two can be in the same place [Oliver] |
| Full Idea: So-called aristotelian universals have some queer features: one universal can be wholly present at different places at the same time, and two universals can occupy the same place at the same time. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
| A reaction: If you want to make a metaphysical doctrine look ridiculous, stating it in very simple language will often do the job. Belief in fairies is more plausible than the first of these two claims. |
| 7963 | Aristotle's instantiated universals cannot account for properties of abstract objects [Oliver] |
| Full Idea: Properties and relations of abstract objects may need to be acknowledged, but they would have no spatio-temporal location, so they cannot instantiate Aristotelian universals, there being nowhere for such universals to be. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11), quoted by Cynthia Macdonald - Varieties of Things | |
| A reaction: Maybe. Why can't the second-order properties be in the same location as the first-order ones? If the reply is that they would seem to be in many places at once, that is only restating the original problem of universals at a higher level. |
| 10730 | If universals ground similarities, what about uniquely instantiated universals? [Oliver] |
| Full Idea: If universals are to ground similarities, it is hard to see why one should admit universals which only happen to be instantiated once. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
| A reaction: He is criticising Armstrong, who holds that universals must be instantiated. This is a good point about any metaphysics which makes resemblance basic. |
| 10727 | Uninstantiated universals seem to exist if they themselves have properties [Oliver] |
| Full Idea: We may have to accept uninstantiated universals because the properties and relations of abstract objects may need to be acknowledged. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
| A reaction: This is the problem of 'abstract reference'. 'Courage matters more than kindness'; 'Pink is more like red than like yellow'. Not an impressive argument. All you need is second-level abstraction. |
| 7962 | Uninstantiated properties are useful in philosophy [Oliver] |
| Full Idea: Uninstantiated properties and relations may do some useful philosophical work. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11), quoted by Cynthia Macdonald - Varieties of Things | |
| A reaction: Their value isn't just philosophical; hopes and speculations depend on them. This doesn't make universals mind-independent. I think the secret is a clear understanding of the word 'abstract' (which I don't have). |
| 10722 | Instantiation is set-membership [Oliver] |
| Full Idea: One view of instantiation is that it is the set-membership predicate. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §10) | |
| A reaction: This cuts the Gordian knot rather nicely, but I don't like it, if the view of sets is extensional. We need to account for natural properties, and we need to exclude mere 'categorial' properties. |
| 10744 | Nominalism can reject abstractions, or universals, or sets [Oliver] |
| Full Idea: We can say that 'Harvard-nominalism' is the thesis that there are no abstract objects, 'Oz-nominalism' that there are no universals, and Goodman's nominalism rejects entities, such as sets, which fail to obey a certain principle of composition. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §15 n46) | |
| A reaction: Personally I'm a Goodman-Harvard-Oz nominalist. What are you rebelling against? What have you got? We've been mesmerized by the workings of our own minds, which are trying to grapple with a purely physical world. |
| 10726 | Things can't be fusions of universals, because two things could then be one thing [Oliver] |
| Full Idea: If a particular thing is a bundle of located universals, we might say it is a mereological fusion of them, but if two universals can be instantiated by more than one particular, then two particulars can have the same universals, and be the same thing. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
| A reaction: This and Idea 10725 pretty thoroughly demolish the idea that objects could be just bundles of universals. The problem pushes some philosophers back to the idea of 'substance', or some sort of 'substratum' which has the universals. |
| 10725 | Abstract sets of universals can't be bundled to make concrete things [Oliver] |
| Full Idea: If a particular thing is a bundle of located universals, we might say that it is the set of its universals, but this won't work because the thing can be concrete but sets are abstract. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
| A reaction: This objection applies just as much to tropes (abstract particulars) as it does to universals. |
| 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! |
| 10745 | Science is modally committed, to disposition, causation and law [Oliver] |
| Full Idea: Natural science is up to its ears in modal notions because of its use of the concepts of disposition, causation and law. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §15) | |
| A reaction: This is aimed at Quine. It might be possible for an auster physicist to dispense with these concepts, by merely describing patterns of observed behaviour. |
| 10746 | Conceptual priority is barely intelligible [Oliver] |
| Full Idea: I find the notion of conceptual priority barely intelligible. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §19 n48) | |
| A reaction: I don't think I agree, though there is a lot of vagueness and intuition involved, and not a lot of hard argument. Can you derive A from B, but not B from A? Is A inconceivable without B, but B conceivable without A? |
| 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? |
| 405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
| Full Idea: The essential nature, whatever it is, of the non-limited is everlasting and ageless. | |
| From: Anaximander (fragments/reports [c.570 BCE], B2), quoted by (who?) - where? |
| 13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
| Full Idea: Those thinkers are in error who postulate ...a single matter, for this cannot exist without some 'perceptible contrariety': this Boundless, which they identify with the 'original real', must be either light or heavy, either hot or cold. | |
| From: comment on Anaximander (fragments/reports [c.570 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 329a10 | |
| A reaction: A dubious objection, I would say. If there has to be a contrasting cold thing to any hot thing, what happens when the cold thing is removed? |
| 404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
| Full Idea: The non-limited is the original material of existing things; their source is also that to which they return after destruction, according to necessity; they give justice and make reparation to each other for injustice, according to the arrangement of Time. | |
| From: Anaximander (fragments/reports [c.570 BCE], B1), quoted by Simplicius - On Aristotle's 'Physics' 24.13- | |
| A reaction: Simplicius is quoting Theophrastus |
| 1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
| Full Idea: Anaximander said that the first principle and element of existing things was the boundless; it was he who originally introduced this name for the first principle. | |
| From: report of Anaximander (fragments/reports [c.570 BCE], A09) by Simplicius - On Aristotle's 'Physics' 9.24.14- | |
| A reaction: Simplicius is quoting Theophrastus |
| 1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |
| Full Idea: The parts of all things are susceptible to change, but the whole is unchangeable. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.An.2 |