35 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. |
| 8166 | Truth is part of semantics, since valid inference preserves truth [Dummett] |
| Full Idea: The concept of truth belongs to semantics, since after all truth is what must be preserved by a valid deductive inference. | |
| From: Michael Dummett (Thought and Reality [1997], 2) | |
| A reaction: Does this conclusion follow? Compare 'nice taste belongs to cooking, since that is what cooking must preserve'. I don't like this. I take 'truth' to be a relevant concept to a discussion of a dog's belief that it is going to be taken for a walk. |
| 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. |
| 8173 | Language can violate bivalence because of non-referring terms or ill-defined predicates [Dummett] |
| Full Idea: Two features of natural languages cause them to violate bivalence: singular terms (or proper names) which have a sense but fail to denote an object ('the centre of the universe'); and predicates which are not well defined for every object. | |
| From: Michael Dummett (Thought and Reality [1997], 4) | |
| A reaction: If we switch from sentences to propositions these problems might be avoided. If there is no reference, or a vague predicate, then there is (maybe) just no proposition being expressed which could be evaluated for truth. |
| 8179 | The law of excluded middle is the logical reflection of the principle of bivalence [Dummett] |
| Full Idea: The law of excluded middle is the reflection, within logic, of the principle of bivalence. It states that 'For any statement A, the statement 'A or not-A' is true'. | |
| From: Michael Dummett (Thought and Reality [1997], 5) | |
| A reaction: True-or-not-true is an easier condition to fulfil than true-or-false. The second says that 'false' is the only alternative, but the first allows other alternatives to 'true' (such as 'undecidable'). It is hard to challenge excluded middle. Somewhat true? |
| 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. |
| 8184 | Philosophers should not presume reality, but only invoke it when language requires it [Dummett] |
| Full Idea: The philosopher's task is not to make a prior commitment for or against realism, but to discover how far realist considerations must be invoked in order to describe our understanding of our language: they may be invoked only if they must be invoked. | |
| From: Michael Dummett (Thought and Reality [1997], 6) | |
| A reaction: I don't see why the default position should be solipsism, or a commitment to Ockham's Razor. This is the Cartesian 'Enlightenment Project' approach to philosophy - that everything has to be proved. There is more to ontology than language. |
| 8185 | We can't make sense of a world not apprehended by a mind [Dummett] |
| Full Idea: We can make no clear sense of there being a world that is not apprehended by any mind. | |
| From: Michael Dummett (Thought and Reality [1997], 8) | |
| A reaction: I find Dummett's view quite baffling. It is no coincidence that Dummett is a theist, along (it seems) Berkeleian lines. I see no more problem with imagining such worlds than with imagining ships sunken long ago which will never be found. |
| 8163 | Since 'no bird here' and 'no squirrel here' seem the same, we must talk of 'atomic' facts [Dummett] |
| Full Idea: What complex of objects constitutes the fact that there is no bird on the bough, and how is that distinct from no squirrel on the bough? This drives us to see the world as composed of 'atomic' facts, making complexes into compounds, not reality itself. | |
| From: Michael Dummett (Thought and Reality [1997], 1) | |
| A reaction: [He cites early Wittgenstein as an example] But 'no patch of red here' (or sense-datum) seems identical to 'no patch of green here'. I suppose you could catalogue all the atomic facts, and note that red wasn't among them. But you could do that for birds. |
| 8161 | We know we can state facts, with true statements [Dummett] |
| Full Idea: One thing we know about facts, namely that we can state them. Whenever we make some true statement, we state some fact. | |
| From: Michael Dummett (Thought and Reality [1997], 1) | |
| A reaction: Then facts become boring, and are subsumed within the problem of what 'true' means. Personally I have a concept of facts which includes unstatable facts. The physical basis of melancholy I take to be a complex fact which is beyond our powers. |
| 8180 | 'That is red or orange' might be considered true, even though 'that is red' and 'that is orange' were not [Dummett] |
| Full Idea: A statement of the form 'that is red or orange', said of something on the borderline between the two colours, might rank as true, although neither 'that is red' nor 'that is orange' was true. | |
| From: Michael Dummett (Thought and Reality [1997], 5) | |
| A reaction: It seems to me that the problem here would be epistemological rather than ontological. One of the two is clearly true, but sometimes we can't decide which. How can anyone say 'It isn't red and it isn't orange, but it is either red or orange'? |
| 8178 | Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale [Dummett] |
| Full Idea: Our sentences cannot be divided into two classes, empirical and a priori, the truth of one to be decided by observation, the other by ratiocination. They lie on a scale, with observational sentences at one end, and mathematical ones at the other. | |
| From: Michael Dummett (Thought and Reality [1997], 5) | |
| A reaction: The modern post-Kantian dissolution of the rationalist-empiricist debate. I would say that mathematical sentences require no empirical evidence (for their operation, rather than foundation), but a bit of reasoning is involved in observation. |
| 17499 | Theoretical models can represent, by mapping onto the data-models [Portides] |
| Full Idea: The semantic approach contends that theoretical models ...are candidates for representing physical systems by virtue of the fact that they stand in mapping relations to corresponding data-models. | |
| From: Demetris Portides (Models [2008], 'Current') | |
| A reaction: Sounds like a neat and satisfying picture. |
| 17498 | In the 'received view' models are formal; the 'semantic view' emphasises representation [Portides, by PG] |
| Full Idea: The 'received view' of models is that they are Tarskian formal axiomatic calculi interpreted by meta-mathematical models. The 'semantic' view of models gives equal importance to their representational capacity. | |
| From: report of Demetris Portides (Models [2008], 'background') by PG - Db (ideas) | |
| A reaction: The Tarskian view is the one covered in my section on Model Theory. Portides favours the semantic account, and I am with him all the way. Should models primarily integrate with formal systems, or with the world? Your choice... |
| 17501 | Representational success in models depends on success of their explanations [Portides] |
| Full Idea: Models are representational, independently of the strength of their relation to theory, depending on how well they achieve the purpose of providing explanations for what occurs in physical systems. | |
| From: Demetris Portides (Models [2008], 'Current') | |
| A reaction: This doesn't sound quite right. It seems possible to have a perfect representation of a system which remains quite baffling (because too complex, or with obscure ingredients). Does the stylised London tube map explain well but represent badly? |
| 17502 | The best model of the atomic nucleus is the one which explains the most results [Portides] |
| Full Idea: The unified model can be considered a better representation of the atomic nucleus in comparison to the liquid-drop and shell models, because it explains most of the known results about the nucleus. | |
| From: Demetris Portides (Models [2008], 'Current') | |
| A reaction: The point here is that models are evaluated not just by their accuracy, but by their explanatory power. Presumably a great model is satisfying and illuminating. Do the best models capture the essence of a thing? |
| 17496 | 'Model' belongs in a family of concepts, with representation, idealisation and abstraction [Portides] |
| Full Idea: A better understanding of 'model', as used in science, could be achieved if we examine it as a member of the triad of concepts of representation, idealisation and abstraction. | |
| From: Demetris Portides (Models [2008], 'Intro') | |
| A reaction: Abstraction seems to have a bad name in philosophy, and yet when you come to discuss things like models, you can't express it any other way. |
| 17497 | Models are theory-driven, or phenomenological (more empirical and specific) [Portides] |
| Full Idea: 'Theory-driven' models are constructed in a systematic theory-regulated way by supplementing the theoretical calculus with locally operative hypotheses. 'Phenomenological' models deploy semi-empirical results, with ad hoc hypotheses, and extra concepts. | |
| From: Demetris Portides (Models [2008], 'Intro') | |
| A reaction: [compressed] I am not at all clear about this distinction, even after reading his whole article. The first type of model seems more general, while the second seems tuned to particular circumstances. He claims the second type is more explanatory. |
| 17500 | General theories may be too abstract to actually explain the mechanisms [Portides] |
| Full Idea: If theoretical models are highly abstract and idealised descriptions of phenomena, they may only represent general features, and fail to explain the specific mechanisms at work in physical systems. | |
| From: Demetris Portides (Models [2008], 'Current') | |
| A reaction: [compressed] While there may be an ideal theory that explains everything, it sounds right capturing the actual mechanism (such as the stirrup bone in the ear) is not at all theoretical. |
| 8175 | A theory of thought will include propositional attitudes as well as propositions [Dummett] |
| Full Idea: A comprehensive theory of thought will include such things as judgement and belief, as well as the mere grasp of propositions. | |
| From: Michael Dummett (Thought and Reality [1997], 4) | |
| A reaction: This seems to make any theory of thought a neat two-stage operation. Beware of neatness. While propositions might be explained using concepts, syntax and truth, the second stage looks faintly daunting. See Idea 2209, for example. |
| 8174 | The theories of meaning and understanding are the only routes to an account of thought [Dummett] |
| Full Idea: For the linguistic philosopher, the theory of meaning, and the theory of understanding that is built upon it, form the only route to a philosophical account of thought. | |
| From: Michael Dummett (Thought and Reality [1997], 4) | |
| A reaction: I am of the party that thinks thought is prior to language (esp. because of animals), but Dummett's idea does not deny this. He may well be right that this is the 'only route'. We can only hope to give an account of human thought. |
| 8165 | To 'abstract from' is a logical process, as opposed to the old mental view [Dummett] |
| Full Idea: The phrase 'abstracted from' does not refer to the mental process of abstraction by disregarding features of concrete objects, in which many nineteenth century thinkers believed; it is a logical (not mental) process of concept-formation. | |
| From: Michael Dummett (Thought and Reality [1997], 1) | |
| A reaction: I take Frege's attack on 'psychologism' to be what dismissed the old view (Idea 5816). Could one not achieve the same story by negating properties in quantified logical expressions, instead of in the mind? |
| 8168 | To know the truth-conditions of a sentence, you must already know the meaning [Dummett] |
| Full Idea: You can know the condition for a sentence to be true only when you know what the sentence means. | |
| From: Michael Dummett (Thought and Reality [1997], 3) | |
| A reaction: This makes the truth-conditions theory of meaning circular, and is Dummett's big objection to Davidson's view. The composition of a sentence creates a model of a world. Truth-conditions may only presuppose knowledge of concepts. |
| 8181 | A justificationist theory of meaning leads to the rejection of classical logic [Dummett] |
| Full Idea: If we adopt a justificationist theory of meaning, we must reject the universal law of excluded middle, and with it classical logic (which rests on the two-valued semantics of bivalence). We admit only intuitionist logic, which preserves justifiability. | |
| From: Michael Dummett (Thought and Reality [1997], 5) | |
| A reaction: This is Dummett's philosophy in a very neat nutshell. He seems to have started by accepting Brouwer's intuitionism, and then working back to language. It all implies anti-realism. I don't buy it. |
| 8182 | Verificationism could be realist, if we imagined the verification by a superhuman power [Dummett] |
| Full Idea: There is a possible route to realism, which has been called 'ideal verificationism', if we base our grasping the understanding and truth of a range of sentences on the procedure that would be available to an imagined being with superhuman powers. | |
| From: Michael Dummett (Thought and Reality [1997], 5) | |
| A reaction: This is actually a slippery slope for verificationists, as soon as they allow that verification could be done by other people. A verifier might turn up who had telepathy, or x-ray vision, or could see quarks... |
| 8183 | If truths about the past depend on memories and current evidence, the past will change [Dummett] |
| Full Idea: If justificationists succumb to the temptation for statements in the past, we shall view their senses as given by present memories and present traces of past events; but this will force us into a view of the past as itself changing. | |
| From: Michael Dummett (Thought and Reality [1997], 6) | |
| A reaction: Obviously Dummett attempts to sidestep this problem, but it strikes me as powerful support for the realist view about the past. How can we not be committed to the view that there are facts about the past quite unconnected to our verifying abilities? |
| 8176 | We could only guess the meanings of 'true' and 'false' when sentences were used [Dummett] |
| Full Idea: Even if we guessed that the two words denoted the two truth-values, we should not know which stood for the value 'true' and which for the value 'false' until we knew how the sentences were in practice used. | |
| From: Michael Dummett (Thought and Reality [1997], 4) | |
| A reaction: These types of problem are always based on the idea that some one item must have logical priority in the process, but there is a lot of room for benign circularity in the development of mental and linguistic functions. |
| 8170 | Sentences are the primary semantic units, because they can say something [Dummett] |
| Full Idea: While words are semantic atoms, sentences remain the primary semantic units, in the sense of the smallest bits of language by means of which it is possible to say anything. | |
| From: Michael Dummett (Thought and Reality [1997], 3) | |
| A reaction: Syncategorematic terms (look it up!) may need sentences, but most nouns and verbs can communicate quite a lot on their own. Whether words or sentences come first may not be a true/false issue. |
| 8169 | We can't distinguish a proposition from its content [Dummett] |
| Full Idea: No distinction can be drawn between a proposition and its content; no two distinct propositions can have the same content. | |
| From: Michael Dummett (Thought and Reality [1997], 3) | |
| A reaction: And one proposition cannot have two possible contents (ambiguity). Are we to say that a proposition supervenes on its content, or that proposition and content are identical? Ockham favours the latter. |
| 8186 | Time is the measure of change, so we can't speak of time before all change [Dummett] |
| Full Idea: Time is the measure of change, and it makes no sense to speak of how things were before there was anything that changed. | |
| From: Michael Dummett (Thought and Reality [1997], 8) | |
| A reaction: Something creating its own measure sounds like me marking my own exam papers. If an object appears, then inverts five seconds later, how can the inversion create the five seconds? How does that differ from inverting ten seconds later? |
| 8167 | If Presentism is correct, we cannot even say that the present changes [Dummett] |
| Full Idea: If Presentism is correct - the doctrine that there is nothing at all, save what holds good at the present moment - then we cannot even say that the present changes, because that requires that things are not now as they were some time ago. | |
| From: Michael Dummett (Thought and Reality [1997], 2) | |
| A reaction: Presumably we can compare our present memory with our present experience. See Idea 6668. The logic (very ancient!) is that the present has not duration at all, and so no experiences can occur during it. |