17 ideas
3067 | A philosopher should have principles ready for understanding, like a surgeon with instruments [Aurelius] |
Full Idea: As physicians have always their instruments and knives ready for cases which suddenly require their skill, so should you have principles ready for the understanding of things divine and human. | |
From: Marcus Aurelius (The Meditations (To Himself) [c.170], 3.13) | |
A reaction: Nice. Philosophy is the training ground where wisdom and good living are made possible, but it cannot be a substitute for living. |
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. |
3072 | Everything is changing, including yourself and the whole universe [Aurelius] |
Full Idea: All things are changing; and you yourself are in continuous mutation and in a manner in continuous destruction, and the whole universe too. | |
From: Marcus Aurelius (The Meditations (To Himself) [c.170], 9.19) |
19000 | Read 'all ravens are black' as about ravens, not as about an implication [Belnap] |
Full Idea: 'All ravens are black' might profitably be read as saying not that being a raven 'implies' being black, but rather something more like 'Consider the ravens: each one is black'. | |
From: Nuel D. Belnap (Conditional Assertion and Restricted Quantification [1970], p.7), quoted by Stephen Yablo - Aboutness 04.5 | |
A reaction: Belnap is more interested in the logic than in the paradox of confirmation, since he evidently thinks that universal generalisations should not be read as implications. I like Belnap's suggestion. |
3066 | Nothing is evil which is according to nature [Aurelius] |
Full Idea: Nothing is evil which is according to nature. | |
From: Marcus Aurelius (The Meditations (To Himself) [c.170], 2.17) | |
A reaction: A bit hopeful. Sounds tautological. I.e. anything which is agreed to be evil is probably immediately labelled as 'unnatural'. What would he agree was evil? |
3071 | Justice has no virtue opposed to it, but pleasure has temperance opposed to it [Aurelius] |
Full Idea: In the constitution of the rational animal I see no virtue which is opposed to justice; but I see a virtue which is opposed to pleasure, and that is temperance. | |
From: Marcus Aurelius (The Meditations (To Himself) [c.170], 8.39) | |
A reaction: There are plenty of hideous things opposed to justice, but presumably that immediately disqualifies them from being virtues. |
3069 | The art of life is more like the wrestler's than the dancer's [Aurelius] |
Full Idea: The art of life is more like the wrestler's than the dancer's. | |
From: Marcus Aurelius (The Meditations (To Himself) [c.170], 7.61) |
3065 | Humans are naturally made for co-operation [Aurelius] |
Full Idea: We are made for cooperation, like feet, like hands, like eyelids, like the rows of upper and lower teeth. To act against one another, then, is contrary to nature. | |
From: Marcus Aurelius (The Meditations (To Himself) [c.170], 2.1) |