17 ideas
| 17950 | The logos enables us to track one particular among a network of objects [Nehamas] |
| Full Idea: The logos (the definition) is a summary statement of the path within a network of objects that one will have to follow in order to locate a particular member of that network. | |
| From: Alexander Nehamas (Episteme and Logos in later Plato [1984], p.234) | |
| A reaction: I like this because it confirms that Plato (as well as Aristotle) was interested in the particulars rather than in the kinds (which I take to be general truths about particulars). |
| 17951 | A logos may be short, but it contains reference to the whole domain of the object [Nehamas] |
| Full Idea: A thing's logos, apparently short as it may be, is implicitly a very rich statement since it ultimately involves familiarity with the whole domain to which that particular object belongs. | |
| From: Alexander Nehamas (Episteme and Logos in later Plato [1984], p.234) | |
| A reaction: He may be wrong that the logos is short, since Aristotle (Idea 12292) says a definition can contain many assertions. |
| 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. |
| 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. |
| 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] |
| 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. |
| 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. |
| 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) |
| 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'. |
| 18823 | To say there could have been people who don't exist, but deny those possible things, rejects Barcan [Stalnaker, by Rumfitt] |
| Full Idea: Stalnaker holds that there could have been people who do not actually exist, but he denies that there are things that could have been those people. That is, he denies the unrestricted validity of the Barcan Formula. | |
| From: report of Robert C. Stalnaker (Counterparts and Identity [1987]) by Ian Rumfitt - The Boundary Stones of Thought 6.2 | |
| A reaction: And quite right too, I should have thought. As they say, Jack Kennedy and Marilyn Monroe might have had a child, but the idea that we should accept some entity which might have been that child but wasn't sounds like nonsense. Except as fiction….. |
| 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) |
| 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. |
| 16412 | If counterparts exist strictly in one world only, this seems to be extreme invariant essentialism [Stalnaker] |
| Full Idea: Counterparts involve the thesis that domains of different possible worlds are disjoint: possible individuals exist in at most one possible world. This seems to suggest extreme essentialism, where nothing could differ from how it is. | |
| From: Robert C. Stalnaker (Counterparts and Identity [1987], 2) | |
| A reaction: He quotes Salmon (1981:236) as saying counterpart theory is particularly inflexible essentialism. This is a long way from my use of 'essentialism'. The problem is just the extent to which my counterpart is 'the same' as me. |
| 16409 | Unlike Lewis, I defend an actualist version of counterpart theory [Stalnaker] |
| Full Idea: I defend a version of counterpart theory that is quite different from Lewis's version, as it is tied to actualism (all that exists is part of the actual world) rather than possibilism (possible things may exist without actually existing). | |
| From: Robert C. Stalnaker (Counterparts and Identity [1987], 1) | |
| A reaction: This could be the theory I am after. I am sympathetic to both actualism and to counterpart theory. Off to the woodshed…. |
| 16411 | If possible worlds really differ, I can't be in more than one at a time [Stalnaker] |
| Full Idea: Nothing can be in two places at once. If other possible worlds are really other universes, then clearly, you and I cannot be in them if we are here in this one. | |
| From: Robert C. Stalnaker (Counterparts and Identity [1987], 2) | |
| A reaction: This can be sensibly expressed without possible worlds. I can't embody my other possibilities while I am embodying this one (I'm too busy). Insofar as possible worlds are a good framework, they are just a precise map of common sense. |
| 16410 | Extensional semantics has individuals and sets; modal semantics has intensions, functions of world to extension [Stalnaker] |
| Full Idea: Semantic values in extensional semantics are extensions, like individuals for terms, and sets for predicates. In modal semantics we have intensions, functions from worlds to appropriate extensions. | |
| From: Robert C. Stalnaker (Counterparts and Identity [1987], 2) | |
| A reaction: It seems obvious that the meaning of a word like 'giraffe' must include possible giraffes, as well as actual and deceased giraffes. |