15 ideas
| 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. |
| 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) |
| 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. |
| 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'. |
| 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. |
| 19405 | Substances are in harmony, because they each express the one reality in themselves [Leibniz] |
| Full Idea: Every substance expresses the whole sequence of the universe in accordance with its own viewpoint or relationship to the rest, so that all are in perfect correspondence with one another. | |
| From: Gottfried Leibniz (Identity in Substances and True Propositions [1686], p.98) | |
| A reaction: Thus 'expression' (something like mapping what is exterior) is the mechanism through which God achieves harmony in the universe. Instants of time are said to be successive moments of perfect harmony. |
| 6451 | Visual sense data are an inner picture show which represents the world [Blackburn] |
| Full Idea: In the case of vision, sense data are a kind of inner picture show which itself only indirectly represents aspects of the external world. | |
| From: Simon Blackburn (Oxford Dictionary of Philosophy [1994], p.347) | |
| A reaction: I'm unsure whether this is correct. Russell says the 'roughness' of the table is the sense datum. If it is even a possibility that there are unsensed sense-data, then they cannot be an aspect of the mind, as Blackburn is suggesting they are. |
| 2866 | A true belief might be based on a generally reliable process that failed on this occasion [Blackburn] |
| Full Idea: Reliabilism is open to the counterexample that a belief may be the result of some generally reliable process (a pressure gauge) which was in fact malfunctioning on this occasion, when we would be reluctant to attribute knowledge to the subject. | |
| From: Simon Blackburn (Oxford Dictionary of Philosophy [1994], p.327) | |
| A reaction: Russell's stopped clock that tells the right time twice a day. A good objection. Coming from a reliable source is very good criterion for good justification, but it needs critical assessment. |
| 2864 | The main objection to intuitionism in ethics is that intuition is a disguise for prejudice or emotion [Blackburn] |
| Full Idea: Critics say that intuitionism in ethics explains nothing, but may merely function as a disguise for prejudice or passion. | |
| From: Simon Blackburn (Oxford Dictionary of Philosophy [1994], p.198) | |
| A reaction: If someone claims to have an important moral intuition about something, you should carefully assess the person who has the intuition. I would trust some people a lot. |
| 2865 | Critics of prescriptivism observe that it is consistent to accept an ethical verdict but refuse to be bound by it [Blackburn] |
| Full Idea: Critics of prescriptivism have noted the problem that whilst accepting a command seems tantamount to setting oneself to obey it, accepting an ethical verdict is, unfortunately, consistent with refusing to be bound by it. | |
| From: Simon Blackburn (Oxford Dictionary of Philosophy [1994], p.300) | |
| A reaction: We nearly all of us accept that our behaviour should be better than it actually is, so we accept the oughts but fail to act. Actually 'refusing', though, sounds a bit contradictory. |