18 ideas
6806 | Do not multiply entities beyond necessity [William of Ockham] |
Full Idea: Do not multiply entities beyond necessity. | |
From: William of Ockham (works [1335]) | |
A reaction: This is the classic statement of Ockham's Razor, though it is not found in his printed works. It appears to be mainly aimed at Plato's Theory of Forms. It is taken to refer to types of entities, not numbers. One seraph is as bad as a hundred. |
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'. |
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. |
3644 | Two things being joined together doesn't prove they are the same [Descartes] |
Full Idea: The fact that we often see two things joined together does not license the inference that they are one and the same. | |
From: René Descartes (Reply to Sixth Objections [1641], 444) | |
A reaction: Correct. The problem comes when they are never ever apart, and you begin to suspect that they are conjoined in all possible worlds. Why might this be so? It can only be identity or a causal link. |
22132 | Species and genera are individual concepts which naturally signify many individuals [William of Ockham] |
Full Idea: In his mature nominalism, species and genera are identified with certain mental qualities called concepts or intentions of the mind. Ontologically they are individuals too, like everthing else, ...but they naturally signify many different individuals. | |
From: William of Ockham (works [1335]), quoted by Claude Panaccio - William of Ockham p.1056 | |
A reaction: 'Naturally' is the key word, because the concepts are not fictions, but natural responses to encountering individuals in the world. I am an Ockhamist. |
3621 | Only judgement decides which of our senses are reliable [Descartes] |
Full Idea: Sense alone does not suffice to correct visual error: we also need a degree of reason to tell us that we should believe the judgement based on touch rather than vision. Since we don't have this power in infancy, it must be attributed to the intellect. | |
From: René Descartes (Reply to Sixth Objections [1641], 439) |
19381 | The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham] |
Full Idea: Time is composed of non-entities, because it is composed of the past which does not exist now, although it did exist, and of the future, which does not yet exist; therefore time does not exist. | |
From: William of Ockham (works [1335], 6:496), quoted by Richard T.W. Arthur - Leibniz 7 'Nominalist' | |
A reaction: I've a lot of sympathy with this! I favour Presentism, so the past is gone and the future is yet to arrive. But we have no coherent concept of a present moment of any duration to contain reality. We are just completely bogglificated by it all. |
8010 | William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham] |
Full Idea: The most notable philosopher who makes God's commandment the basis of goodness, rather than God's goodness a reason for obeying him, is William of Occam. | |
From: William of Ockham (works [1335]), quoted by Alasdair MacIntyre - A Short History of Ethics Ch.9 | |
A reaction: Either view has problems. Why choose God to obey? Obey anyone who is powerful? But how do you decide that God is good? How do we know the nature of God's commands, or the nature of God's goodness? Etc. |
3637 | Ideas in God's mind only have value if he makes it so [Descartes] |
Full Idea: It is impossible to imagine that anything is thought of in the divine intellect as good or true, or worthy of belief or action or omission, prior to the decision of the divine will to make it so. | |
From: René Descartes (Reply to Sixth Objections [1641], 432) |
16679 | Even an angel must have some location [William of Ockham, by Pasnau] |
Full Idea: Ockham dismisses the possibility of non-location out of hand, remarking that even an angel has some location. | |
From: report of William of Ockham (works [1335]) by Robert Pasnau - Metaphysical Themes 1274-1671 14.4 |