15 ideas
| 23291 | Without truth, both language and thought are impossible [Davidson] |
| Full Idea: Without a grasp of the concept of truth, not only language, but thought itself, is impossible. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.16) | |
| A reaction: Davidson never mentions animals, but I like this idea because it points to importance of truth for animals as well. I say that truth is relevant to any mind that makes judgements - and quite small animals (e.g. ants and spiders) make judgements. |
| 23284 | Plato's Forms confused truth with the most eminent truths, so only Truth itself is completely true [Davidson] |
| Full Idea: Plato's conflation of abstract universals with entities of supreme value reinforced the confusion of truth with the most eminent truths. …The only perfect exemplar of a Form is the Form itself, …and only truth itself is completely true. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.3) | |
| A reaction: Even non-subscribers to Plato often talk as if there were some grand thing called the Truth with a capital T, quite often used in a religious context. Truth is the hallmark of successful (non-fanciful) thought. |
| 23286 | Truth can't be a goal, because we can neither recognise it nor confim it [Davidson] |
| Full Idea: Since it is neither visible as a target, nor recognisable when achieved, there is no point in calling truth a goal. We should only aim at increasing confidence in our beliefs, by collecting further evidence or checking our calculations. | |
| From: Donald Davidson (Truth Rehabilitated [1997], P.6) | |
| A reaction: This is mainly aimed at pragmatists, but Davidson obviously subscribes (as do I) to their fallibilist view of knowledge. |
| 23292 | Correspondence can't be defined, but it shows how truth depends on the world [Davidson] |
| Full Idea: Correspondence, while it is empty as a definition, does capture the thought that truth depends on how the world is. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.16) | |
| A reaction: Just don't try to give a precise account of the correspondence between two things (thoughts and facts) which are so utterly different in character. |
| 23288 | When Tarski defines truth for different languages, how do we know it is a single concept? [Davidson] |
| Full Idea: We have to wonder how we know that it is some single concept which Tarski indicates how to define for each of a number of well-behaved languages. | |
| From: Donald Davidson (Truth Rehabilitated [1997], P.11) | |
| A reaction: Davidson says that Tarski makes the assumption that it is a single concept, but fails to demonstrate the fact. This resembles Frege's Julius Caesar problem - of how you know whether your number definition has defined a number. |
| 23287 | Disquotation only accounts for truth if the metalanguage contains the object language [Davidson] |
| Full Idea: Disquotation cannot pretend to give a complete account of the concept of truth, since it works only in the special case where the metalanguage contains the object language. Neither can contain their own truth predicate. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.10) | |
| A reaction: Presumably more sophisticated and complete accounts would need a further account of translation between languages - which explains Quine's interest in that topic. […see this essay, p.12] |
| 13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
| Full Idea: Peano's axioms are categorical (any two models are isomorphic). Some conclude that the concept of natural number is adequately represented by them, but we cannot identify natural numbers with one rather than another of the isomorphic models. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 11) by Richard Cartwright - Propositions 11 | |
| A reaction: This is a striking anticipation of Benacerraf's famous point about different set theory accounts of numbers, where all models seem to work equally well. Cartwright is saying that others have pointed this out. |
| 18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
| Full Idea: Peano Arithmetic is about any system of entities that satisfies the Peano axioms. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 6.3) by David Bostock - Philosophy of Mathematics 6.3 | |
| A reaction: This doesn't sound like numbers in the fullest sense, since those should facilitate counting objects. '3' should mean that number of rose petals, and not just a position in a well-ordered series. |
| 17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
| Full Idea: Peano's premises are recommended not only by the fact that arithmetic follows from them, but also by their inherent obviousness. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
| Full Idea: Peano Arithmetic cannot derive its own consistency from within itself. But it can be strengthened by adding this consistency statement or by stronger axioms (particularly ones partially expressing soundness). These are known as Reflexion Principles. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 1.2) by Volker Halbach - Axiomatic Theories of Truth (2005 ver) 1.2 |
| 17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
| Full Idea: Peano's premises are not the ultimate logical premises of arithmetic. Simpler premises and simpler primitive ideas are to be had by carrying our analysis on into symbolic logic. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 23285 | If we try to identify facts precisely, they all melt into one (as the Slingshot Argument proves) [Davidson] |
| Full Idea: If we try to provide a serious semantics for reference to facts, we discover that they melt into one; there is no telling them apart. The relevant argument (the 'Slingshot') was credited to Frege by Alonso Church. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.5) | |
| A reaction: This sounds like good grounds for not attempting to be too precise. 'There are bluebells in my local wood' identifies a fact by words, but even an animal can distinguish this fact. Only a logician dreams of making its content precise. |
| 23289 | Knowing the potential truth conditions of a sentence is necessary and sufficient for understanding [Davidson] |
| Full Idea: It is clear that someone who knows under what conditions a sentence would be true understands that sentence, …and if someone does not know under what conditions it would be true then they do not understand it. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.13) | |
| A reaction: I've always subscribed to this view. Langauge is meaningless if you can't relate it to reality, and I don't think there could be a language without an intuitive notion of truth. |
| 23290 | It could be that the use of a sentence is explained by its truth conditions [Davidson] |
| Full Idea: It may be that sentences are used as they are because of their truth conditions, and they have the truth conditions they do because of how they are used. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.13) | |
| A reaction: I've always taken the attempt to explain meaning by use as absurd. It is similar to trying to explain mind in terms of function. In each case, what is the intrinsic nature of the thing, which makes that use or that function possible? |
| 1590 | The just man does not harm his enemies, but benefits everyone [Plato] |
| Full Idea: First, Socrates, you told me justice is harming your enemies and helping your friends. But later it seemed that the just man, since everything he does is for someone's benefit, never harms anyone. | |
| From: Plato (Clitophon [c.372 BCE], 410b) | |
| A reaction: Socrates certainly didn't subscribe to the first view, which is the traditional consensus in Greek culture. In general Socrates agreed with the views later promoted by Jesus. |