19 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. |
| 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. |
| 15091 | Restrict 'logical truth' to formal logic, rather than including analytic and metaphysical truths [Shoemaker] |
| Full Idea: I favour restricting the term 'logical truth' to what logicians would count as such, excluding both analytic truths like 'Bachelors are unmarried' and Kripkean necessities like 'Gold is an element'. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], I) | |
| A reaction: I agree. There is a tendency to splash the phrases 'logical truth' and 'logical necessity around in vague ways. I take them to strictly arise out of the requirements of formal systems of logic. |
| 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. |
| 15095 | A property's causal features are essential, and only they fix its identity [Shoemaker] |
| Full Idea: The view I now favour says that the causal features of a property, both forward-looking and backward-looking, are essential to it. And it says that properties having the same causal features are identical. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], III) | |
| A reaction: In this formulation we have essentialism about properties, as well as essentialism about the things which have the properties. |
| 15097 | I claim that a property has its causal features in all possible worlds [Shoemaker] |
| Full Idea: The controversial claim of my theory is that the causal features of properties are essential to them - are features that they have in all possible worlds. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], III) | |
| A reaction: One problem is that a property can come in degrees, so what degree of the property is necessary to it? It is better to assign this claim to the fundamental properties (which are best called 'powers'). |
| 15094 | I now deny that properties are cluster of powers, and take causal properties as basic [Shoemaker] |
| Full Idea: I now reject the formulation of the causal theory which says that a property is a cluster of conditional powers. That has a reductionist flavour, which is a cheat. We need properties to explain conditional powers, so properties won't reduce. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], III) | |
| A reaction: [compressed wording] I agree with Mumford and Anjum in preferring his earlier formulation. I think properties are broad messy things, whereas powers can be defined more precisely, and seem to have more stability in nature. |
| 15099 | If something is possible, but not nomologically possible, we need metaphysical possibility [Shoemaker] |
| Full Idea: If it is possible that there could be possible states of affairs that are not nomologically possible, don't we therefore need a notion of metaphysical possibility that outruns nomological possibility? | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], VI) | |
| A reaction: Shoemaker rejects this possibility (p.425). I sympathise. So there is 'natural' possibility (my preferred term), which is anything which stuff, if it exists, could do, and 'logical' possibility, which is anything that doesn't lead to contradiction. |
| 15101 | Once you give up necessity as a priori, causal necessity becomes the main type of necessity [Shoemaker] |
| Full Idea: Once the obstacle of the deeply rooted conviction that necessary truths should be knowable a priori is removed, ...causal necessity is (pretheoretically) the very paradigm of necessity, in ordinary usage and in dictionaries. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], VII) | |
| A reaction: The a priori route seems to lead to logical necessity, just by doing a priori logic, and also to metaphysical necessity, by some sort of intuitive vision. This is a powerful idea of Shoemaker's (implied, of course, in Kripke). |
| 15098 | Empirical evidence shows that imagining a phenomenon can show it is possible [Shoemaker] |
| Full Idea: We have abundant empirical evidence that when we can imagine some phenomenal situation, e.g., imagine things appearing certain ways, such a situation could actually exist. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], VI) | |
| A reaction: There seem to be good reasons for holding the opposite view too. We can imagine gold appearing to be all sorts of colours, but that doesn't make it possible. What does empirical evidence really tell us here? |
| 15100 | Imagination reveals conceptual possibility, where descriptions avoid contradiction or incoherence [Shoemaker] |
| Full Idea: Imaginability can give us access to conceptual possibility, when we come to believe situations to be conceptually possible by reflecting on their descriptions and seeing no contradiction or incoherence. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], VI) | |
| A reaction: If take the absence of contradiction to indicate 'logical' possibility, but the absence of incoherence is more interesting, even if it is a bit vague. He is talking of 'situations', which I take to be features of reality. A priori synthetic? |
| 15096 | 'Grue' only has causal features because of its relation to green [Shoemaker] |
| Full Idea: Perhaps 'grue' has causal features, but only derivatively, in virtue of its relation to green. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], III) | |
| A reaction: I take grue to be a behaviour, and not a property at all. The problem only arises because the notion of a 'property' became too lax. Presumably Shoemaker should also mention blue in his account. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 15093 | We might say laws are necessary by combining causal properties with Armstrong-Dretske-Tooley laws [Shoemaker] |
| Full Idea: One way to get the conclusion that laws are necessary is to combine my view of properties with the view of Armstrong, Dretske and Tooley, that laws are, or assert, relations between properties. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], I) | |
| A reaction: This is interesting, because Armstrong in particular wants the necessity to arise from relations between properties as universals, but if we define properties causally, and make them necessary, we might get the same result without universals. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |