19 ideas
| 3653 | My Meditations are the complete foundation of my physics [Descartes] |
| Full Idea: My six Meditations contain all the foundations of my physics, …and their principles destroy those of Aristotle. | |
| From: René Descartes (Letters to Mersenne [1640], 1641.01.28) |
| 4736 | Truth is such a transcendentally clear notion that it cannot be further defined [Descartes] |
| Full Idea: Truth is such a transcendentally clear notion that it cannot be further defined. | |
| From: René Descartes (Letters to Mersenne [1640], 1642), quoted by Pascal Engel - Truth Intro | |
| A reaction: This is the view endorsed by Davidson. It is tempting to take basic concepts as axiomatic, but philosophers can't make that move every time they are in trouble. I have to say, though, that truth is a good candidate. |
| 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. |
| 12066 | Aristotelian and Kripkean essentialism are very different theories [Witt] |
| Full Idea: The differences between Aristotelian essentialism and Kripke's essentialism are so fundamental and pervasive that it is a serious distortion of both views to think of essentialism as a single theory. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], Intro) | |
| A reaction: This seems to me to be very important, because there is a glib assumption that when essentialism is needed for modal logic, that we must immediately have embraced what Aristotle was saying. Aristotle was better than Kripke. |
| 12067 | An Aristotelian essence is a nonlinguistic correlate of the definition [Witt] |
| Full Idea: An Aristotelian essence is a nonlinguistic correlate of the definition of the entity in question. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], Intro) | |
| A reaction: This is a simple and necessity corrective to the simplistic idea that Aristotle thought that essences just were definitions. Aristotle believes in real essences, not linguistic essences. |
| 12082 | If unity is a matter of degree, then essence may also be a matter of degree [Witt] |
| Full Idea: By holding that the most unified beings have essences in an unqualified sense, while allowing that other beings have them in a qualified sense - we can think of unity as a matter of degree. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], 4.3) | |
| A reaction: This is Witt's somewhat unorthodox view of how we should read Aristotle. I am sympathetic, if essences are really explanatory. That means they are unstable, and would indeed be likely to come in degrees. |
| 12089 | Essences mainly explain the existence of unified substance [Witt] |
| Full Idea: The central function of essence is to explain the actual existence of a unified substance. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], 5 n1) | |
| A reaction: She is offering an interpretation of Aristotle. Since existence is an active and not a passive matter, the identity of the entity will include its dispositions etc., I presume. |
| 12102 | Essential properties of origin are too radically individual for an Aristotelian essence [Witt] |
| Full Idea: The radical individuality of essential properties of origin makes them unsuitable for inclusion in an Aristotelian essence. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], 6.2) | |
| A reaction: Nevertheless, Aristotle believes in individual essences, though these seem to be fixed by definitions, which are composed of combinations of universals. The uniqueness is of the whole definition, not of its parts. |
| 12085 | Reality is directional [Witt] |
| Full Idea: Reality is directional. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], 4.5) | |
| A reaction: [Plucked from context! She attributes the view to Aristotle] This slogan beautifully summarises the 'scientific essentialist' view of reality, based not on so-called 'laws', but on the active powers of the stuffs of reality. |
| 3652 | I can't prove the soul is indestructible, only that it is separate from the mortal body [Descartes] |
| Full Idea: I don't know how to demonstrate that God cannot annihilate the soul, but only that it is entirely distinct from the body, and consequently that it is not naturally subject to die with it, which is all that is required to establish religion. | |
| From: René Descartes (Letters to Mersenne [1640], 1640.02.24) |