11 ideas
| 10153 | In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski] |
| Full Idea: In everyday language it seems impossible to define the notion of truth or even to use this notion in a consistent manner and in agreement with the laws of logic. | |
| From: Alfred Tarski (works [1936]), quoted by Feferman / Feferman - Alfred Tarski: life and logic Int III | |
| A reaction: [1935] See Logic|Theory of Logic|Semantics of Logic for Tarski's approach to truth. |
| 19141 | Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson] |
| Full Idea: Tarski preferred an explicit definition of truth to axioms. He says axioms have a rather accidental character, only a definition can guarantee the continued consistency of the system, and it keeps truth in harmony with physical science and physicalism. | |
| From: report of Alfred Tarski (works [1936]) by Donald Davidson - Truth and Predication 2 n2 | |
| A reaction: Davidson's summary, gleaned from various sources in Tarski. A big challenge for modern axiom systems is to avoid inconsistency, which is extremely hard to do (given that set theory is not sure of having achieved it). |
| 10048 | There is no clear boundary between the logical and the non-logical [Tarski] |
| Full Idea: No objective grounds are known to me which permit us to draw a sharp boundary between the two groups of terms, the logical and the non-logical. | |
| From: Alfred Tarski (works [1936]), quoted by Alan Musgrave - Logicism Revisited §3 | |
| A reaction: Musgrave is pointing out that this is bad news if you want to 'reduce' something like arithmetic to logic. 'Logic' is a vague object. |
| 10694 | Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall] |
| Full Idea: Tarski's 1936 definition of logical consequence is that in any model in which the premises are true, the conclusion is true too (so that no model can make the conclusion false). | |
| From: report of Alfred Tarski (works [1936]) by JC Beall / G Restall - Logical Consequence 3 | |
| A reaction: So the general idea is that a logical consequence is distinguished by being unstoppable. Sounds good. But then we have monotonic and non-monotonic logics, which (I'm guessing) embody different notions of consequence. |
| 10479 | Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W] |
| Full Idea: Tarski's definition of logical consequence (1936) is that in a fully interpreted formal language an argument is valid iff under any allowed interpretation of its nonlogical symbols, if the premises are true then so is the conclusion. | |
| From: report of Alfred Tarski (works [1936]) by Wilfrid Hodges - Model Theory 3 | |
| A reaction: The idea that you can only make these claims 'under an interpretation' seems to have had a huge influence on later philosophical thinking. |
| 10157 | Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman] |
| Full Idea: Tarski found an elegant new axiom system for Euclidean geometry that improved Hilbert's earlier version - and he formulated it without the use of set-theoretical notions. | |
| From: report of Alfred Tarski (works [1936]) by Feferman / Feferman - Alfred Tarski: life and logic Ch.9 |
| 19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
| Full Idea: A proposition about an item exists only if that item exists... how could something be the proposition that that dog is barking in circumstances in which that dog does not exist? | |
| From: Timothy Williamson (Necessary Existents [2002], p.240), quoted by Trenton Merricks - Propositions | |
| A reaction: This is a view of propositions I can't make sense of. If I'm under an illusion that there is a dog barking nearby, when there isn't one, can I not say 'that dog is barking'? If I haven't expressed a proposition, what have I done? |
| 23896 | We see our character as a restricting limit, but also as an unshakable support [Weil] |
| Full Idea: Our character appears to us as a limit by which we do not want to be imprisoned, …but also as a support that we want to believe is unshakable. | |
| From: Simone Weil (On the Concept of Character [1941], p.100) | |
| A reaction: A nice perception. It is fairly easy to criticise, or even laugh at, one's own actions, but extremely hard to criticise our own character. Maybe we all wish we were more determined in our projects, but not much else. |
| 23894 | The concept of character is at the centre of morality [Weil] |
| Full Idea: We cannot pose a moral problem without putting the concept of character at its centre. | |
| From: Simone Weil (On the Concept of Character [1941], p.98) | |
| A reaction: The question for Aristotle (which I derive from Philippa Foot) is whether moral goodness simply is good character, or whether it is the actions (or even the consequences). Weil is close to modern virtue theory here. |
| 23893 | We don't see character in a single moment, but only over a period of time [Weil] |
| Full Idea: Character is constant over a period of time; the way a person is at a single moment does not at all reflect the character of this person. We do, however, concede that character changes. | |
| From: Simone Weil (On the Concept of Character [1941], p.98) | |
| A reaction: I do think, though, that there are moments in behaviour which are hugely revealing of character, even in a single remark. But I agree that most single moments do not show much. |
| 23895 | We modify our character by placing ourselves in situations, or by attending to what seems trivial [Weil] |
| Full Idea: We can modify our character, by putting ourselves in circumstances that will act on us from the outside, …or by the orientation of our attention in the moments that appear most insignificant or indifferent in our lives. | |
| From: Simone Weil (On the Concept of Character [1941], p.99) | |
| A reaction: I've never seen anyone address this question (apart from Aristotle's emphasis on training habits). Choosing your source for current affairs information strikes me as very important. What you read, what you watch, who you spend time with… |