16 ideas
| 13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
| Full Idea: Statements of the form '"it is snowing" is true if and only if it is snowing' and '"the world war will begin in 1963" is true if and only if the world war will being in 1963' can be regarded as partial definitions of the concept of truth. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.404) | |
| A reaction: The key word here is 'partial'. Truth is defined, presumably, when every such translation from the object language has been articulated, which is presumably impossible, given the infinity of concatenated phrases possible in a sentence. |
| 9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
| Full Idea: Logic is part of a normative theory of thinking, not a substitute for thinking. | |
| From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.13) | |
| A reaction: There is some sort of logicians' dream, going back to Leibniz, of a reasoning engine, which accepts propositions and outputs inferences. I agree with this idea. People who excel at logic are often, it seems to me, modest at philosophy. |
| 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
| Full Idea: For a language, we must enumerate the primitive terms, and the rules of definition for new terms. Then we must distinguish the sentences, and separate out the axioms from amng them, and finally add rules of inference. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.402) | |
| A reaction: [compressed] This lays down the standard modern procedure for defining a logical language. Once all of this is in place, we then add a semantics and we are in business. Natural deduction tries to do without the axioms. |
| 13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
| Full Idea: Semantics is the totality of considerations concerning concepts which express connections between expressions of a language and objects and states of affairs referred to by these expressions. Examples are denotation, satisfaction, definition and truth. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.401) | |
| A reaction: Interestingly, he notes that it 'is not commonly recognised' that truth is part of semantics. Nowadays truth seems to be the central concept in most semantics. |
| 13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
| Full Idea: People have not been aware that the language about which we speak need by no means coincide with the language in which we speak. ..But the language which contains its own semantics must inevitably be inconsistent. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.402) | |
| A reaction: It seems that Tarski was driven to propose the metalanguage approach mainly by the Liar Paradox. |
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
| Full Idea: Here is a partial definition of the concept of satisfaction: John and Peter satisfy the sentential function 'X and Y are brothers' if and only if John and Peter are brothers. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.405) | |
| A reaction: Satisfaction applies to open sentences and truth to closed sentences (with named objects). He uses the notion of total satisfaction to define truth. The example is a partial definition, not just an illustration. |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
| Full Idea: It has been found useful in defining semantical concepts to deal first with the concept of satisfaction; both because the definition of this concept presents relatively few difficulties, and because the other semantical concepts are easily reduced to it. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.406) | |
| A reaction: See Idea 13339 for his explanation of satisfaction. We just say that a open sentence is 'acceptable' or 'assertible' (or even 'true') when particular values are assigned to the variables. Then sentence is then 'satisfied'. |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
| Full Idea: Using the definition of truth we are in a position to carry out the proof of consistency for deductive theories in which only (materially) true sentences are (formally) provable. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.407) | |
| A reaction: This is evidently what Tarski saw as the most important first fruit of his new semantic theory of truth. |
| 9389 | Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt] |
| Full Idea: Vagueness in respect of membership is consistency with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of a concept. | |
| From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.5) | |
| A reaction: I find this view of sets much more appealing than the one that identifies a set with its members. The empty set is less of a problem, as well as non-existents. Logicians prefer the extensional view because it is tidy. |
| 19718 | Indefeasibility does not imply infallibility [Grundmann] |
| Full Idea: Infallibility does not follow from indefeasibility. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Significance') | |
| A reaction: If very little evidence exists then this could clearly be the case. It is especially true of historical and archaeological evidence. |
| 19717 | Can a defeater itself be defeated? [Grundmann] |
| Full Idea: Can the original justification of a belief be regained through a successful defeat of a defeater? | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Defeater-Defs') | |
| A reaction: [Jäger 2005 addresses this] I would have thought the answer is yes. I aspire to coherent justifications, so I don't see justifications as a chain of defeat and counter-defeat, but as collective groups of support and challenge. |
| 19716 | Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann] |
| Full Idea: An unmodified reliabilism does not accommodate defeaters, and surely there can be defeaters against reliably produced beliefs? | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Defeaters') | |
| A reaction: [He cites Bonjour 1980] Reliabilism has plenty of problems anyway, since a generally reliable process can obviously occasionally produce a bad result. 20:20 vision is not perfect vision. Internalist seem to like defeaters. |
| 19715 | You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann] |
| Full Idea: There are 'rebutting' defeaters against the truth of a previously justified belief, 'undercutting' defeaters against the power of the evidence, and 'reason-defeating' defeaters against the truth of the reason for the belief. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'How') | |
| A reaction: That is (I think) that you can defeat the background, the likelihood, or the truth. He cites Pollock 1986, and implies that these are standard distinctions about defeaters. |
| 19713 | Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann] |
| Full Idea: Advocates of the defeasibility theory have tried to exclude true pieces of information that are misleading defeaters. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'What') | |
| A reaction: He gives as an example the genuine news of a claim that the suspect has a twin. |
| 19714 | Knowledge requires that there are no facts which would defeat its justification [Grundmann] |
| Full Idea: The 'defeasibility theory' of knowledge claims that knowledge is only present if there are no facts that - if they were known - would be genuine defeaters of the relevant justification. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'What') | |
| A reaction: Something not right here. A genuine defeater would ensure the proposition was false, so it would simply fail the truth test. So we need a 'defeater' for a truth, which must therefore by definition be misleading. Many qualifications have to be invoked. |
| 19719 | 'Moderate' foundationalism has basic justification which is defeasible [Grundmann] |
| Full Idea: Theories that combine basic justification with the defeasibility of this justification are referred to as 'moderate' foundationalism. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Significance') | |
| A reaction: I could be more sympathetic to this sort of foundationalism. But it begins to sound more like Neurath's boat (see Quine) than like Descartes' metaphor of building foundations. |