29 ideas
| 13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
| Full Idea: Quine ends up with the logic that is maximally justified by experience, ...but a large number of the core principles of logic will have to be used to select the logic that is maximally justified by experience. | |
| From: comment on Willard Quine (Carnap and Logical Truth [1954]) by Paul Boghossian - Knowledge of Logic p.233 | |
| A reaction: In order to grasp some core principles of logic, you will probably need a certain amount of experience. I take logic to be an abstracted feature of reality (unless it is extended by pure fictions). Some basic logic may be hard wired in us. |
| 9002 | Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine] |
| Full Idea: Elementary logic, as commonly systematized nowadays, comprises truth-function theory (involving 'or', 'and', 'not' etc.), quantifiers (and their variables), and identity theory ('='). In addition, set theory requires classes among values of variables. | |
| From: Willard Quine (Carnap and Logical Truth [1954], II) | |
| A reaction: Quine is famous for trying to squeeze properties out of the picture, which would then block higher-order logics (which quantify over properties). Quine's list gives a nice programme for a student of the philosophy of logic to understand. |
| 13681 | Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider] |
| Full Idea: Quine's view of logical consequence is that it is when there is no way of uniformly substituting nonlogical expressions in the premises and consequences so that the premises all remain true but the consequence now becomes false. | |
| From: report of Willard Quine (Carnap and Logical Truth [1954], p.103) by Theodore Sider - Logic for Philosophy 1.5 | |
| A reaction: One might just say that the consequence holds if you insert consistent variables for the nonlogical terms, which looks like Aristotle's view of the matter. |
| 13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
| Full Idea: Quine said a logical truth is a truth in which only logical constants occur essentially, ...but then a fruitful definition of 'logical constant' is called for. | |
| From: comment on Willard Quine (Carnap and Logical Truth [1954]) by Ian Hacking - What is Logic? §02 |
| 15590 | It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that [Fine,K] |
| Full Idea: Once Frege had provided a clear syntactic account of variables and once Tarski had supplemented this with a rigorous semantic account, it would appear that there was nothing more of significance to be said. | |
| From: Kit Fine (Semantic Relationism [2007], 1) | |
| A reaction: He later remarks that there are now three semantic accounts: the Tarskian, the instantial, and the algebraic [see xref ideas]. He offers a fourth account in his Semantic Relationism. This grows from his puzzles about variables. |
| 15591 | In separate expressions variables seem identical in role, but in the same expression they aren't [Fine,K] |
| Full Idea: When we consider the semantic role of 'x' and 'y' in two distinct expressions x>0 and y>0, their semantic roles seems the same. But in the same expression, such as x>y, their roles seem to be different. | |
| From: Kit Fine (Semantic Relationism [2007], 1.A) | |
| A reaction: [compressed] This new puzzle about variables leads Fine to say that the semantics of variables, and other expressions, is not intrinsic to them, but depends on their external relations. Variables denote any term - unless another variable got there first. |
| 15595 | The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K] |
| Full Idea: In the 'algebraic' approach to variables, we move from a quantified sentence to the term specifying a property (the λ-term), and then reducing to the algebraic operations for atomic formulas. | |
| From: Kit Fine (Semantic Relationism [2007], 1.C) | |
| A reaction: [Bealer is a source for this view] Fine describes it as an 'algebra of operations'. I presume this is a thoroughly formalist approach to the matter, which doesn't seem to get to the heart of the semantic question. |
| 15594 | 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K] |
| Full Idea: According to the 'instantial' approach to variables, a closed quantified sentence is to be understood on the basis of one of its instances; from an understanding of an instance we understand satisfaction by an arbitrary individual. | |
| From: Kit Fine (Semantic Relationism [2007], 1.D) | |
| A reaction: Fine comments that this is intuitively plausible, but not very precise, because it depends on 'abstraction' of the individual from the expression. |
| 15592 | The usual Tarskian interpretation of variables is to specify their range of values [Fine,K] |
| Full Idea: The usual Tarskian way of indicating how a variable is to be interpreted is to simply specify its range of values. | |
| From: Kit Fine (Semantic Relationism [2007], 1.B) |
| 15593 | Variables can be viewed as special terms - functions taking assignments into individuals [Fine,K] |
| Full Idea: The alternative Tarskian way of indicating how a variable is to be interpreted is that a variable x will be a special case of the semantic value of the term; it will be a function which takes each assignment into the individual which it assigns to x. | |
| From: Kit Fine (Semantic Relationism [2007], 1.B) |
| 15599 | Cicero/Cicero and Cicero/Tully may differ in relationship, despite being semantically the same [Fine,K] |
| Full Idea: There may be a semantic relationship between 'Cicero' and 'Cicero' that does not hold between 'Cicero' and 'Tully', despite the lack of an intrinsic semantic difference between the names themselves. | |
| From: Kit Fine (Semantic Relationism [2007], 2.E) | |
| A reaction: This is the key idea of Fine's book, and a most original and promising approach to a rather intractable problem in reference. He goes on to distinguish names which are 'strictly' coreferential (the first pair) from those that are 'accidentally' so. |
| 9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
| Full Idea: Unlike elementary logic, the truths of set theory are not obvious. Set theory was straining at the leash of intuition ever since Cantor discovered higher infinites; and with the added impetus of the paradoxes of set theory the leash snapped. | |
| From: Willard Quine (Carnap and Logical Truth [1954], II) | |
| A reaction: This problem seems to have forced Quine into platonism about sets, because he felt they were essential for mathematics and science, but couldn't be constructed with precision. So they must be real, but we don't quite understand them. |
| 9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
| Full Idea: We might say that set theory is not really logic, but a branch of mathematics. This would deprive 'includes' of the status of a logical word. Frege's derivation of arithmetic would then cease to count as a derivation from logic: for he used set theory. | |
| From: Willard Quine (Carnap and Logical Truth [1954], II) | |
| A reaction: Quine has been making the point that higher infinities and the paradoxes undermine the status of set theory as logic, but he decides to continue thinking of set theory as logic. Critics of logicism frequently ask whether the reduction is to logic. |
| 9006 | Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine] |
| Full Idea: One's hypothesis as to there being universals is at bottom just as arbitrary or pragmatic a matter as one's adoption of a new brand of set theory or even a new system of bookkeeping. | |
| From: Willard Quine (Carnap and Logical Truth [1954], x) | |
| A reaction: This spells out clearly the strongly pragmatist vein in Quine's thinking. |
| 15603 | I can only represent individuals as the same if I do not already represent them as the same [Fine,K] |
| Full Idea: I can only represent two individuals as being the same if I do not already represent them as the same. | |
| From: Kit Fine (Semantic Relationism [2007], 3.A) | |
| A reaction: A very nice simple point. If I say 'Hesperus is Hesperus' I am unable to comment on the object, but 'Hesperus is Phosphorus' has a different expressive power. Start from contexts where it is necessary to say that two things are actually one. |
| 15604 | If Cicero=Tully refers to the man twice, then surely Cicero=Cicero does as well? [Fine,K] |
| Full Idea: 'Cicero=Cicero' and 'Cicero=Tully' are both dyadic predications. It is unnatural to suppose that the use of the same name converts a dyadic predicate into a reflexive predicate, or that there is one reference to Cicero in the first and two in the second. | |
| From: Kit Fine (Semantic Relationism [2007], 3.A) | |
| A reaction: I am deeply suspicious of the supposed 'property' of being self-identical, but that may not deny that it could be a genuine truth (shorthand for 'the C you saw is the same as the C I saw'). Having an identity makes equality with self possible. |
| 9001 | Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine] |
| Full Idea: When Kant's arithmetical examples of a priori synthetic judgements were sweepingly disqualified by Frege's reduction of arithmetic to logic, attention moved to the less tendentious and logically prior question 'How is logical certainty possible?' | |
| From: Willard Quine (Carnap and Logical Truth [1954], I) | |
| A reaction: A nice summary of the story so far, from someone who should know. This still leaves the question open of whether any synthetic truths can be derived from the logical certainties which are available. |
| 14286 | In nearby worlds where A is true, 'if A,B' is true or false if B is true or false [Stalnaker] |
| Full Idea: Consider a possible world in which A is true and otherwise differs minimally from the actual world. 'If A, then B' is true (false) just in case B is true (false) in that possible world. | |
| From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1 | |
| A reaction: This is the first proposal to give a possible worlds semantics for conditional statements. Edgington observes that worlds which are nearby for me may not be nearby for you. |
| 14285 | A possible world is the ontological analogue of hypothetical beliefs [Stalnaker] |
| Full Idea: A possible world is the ontological analogue of a stock of hypothetical beliefs. | |
| From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1 | |
| A reaction: Sounds neat and persuasive. What is the ontological analogue of a stock of hopes? Heaven! |
| 9005 | Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine] |
| Full Idea: In trying to make sense of the role of convention in a priori knowledge, the very distinction between a priori and empirical begins to waver and dissolve. | |
| From: Willard Quine (Carnap and Logical Truth [1954], VI) | |
| A reaction: This is the next stage in the argument after Wittgenstein presents the apriori as nothing more than what arises from truth tables. The rationalists react by taking us back to the original 'natural light of reason' view. Then we go round again... |
| 15602 | Mental files are devices for keeping track of basic coordination of objects [Fine,K] |
| Full Idea: Mental files should be seen as a device for keeping track of when objects are coordinated (represented as-the-same) and, rather than understand coordination in terms of mental files, we should understand mental files in terms of coordination. | |
| From: Kit Fine (Semantic Relationism [2007], 3.A) | |
| A reaction: Personally I think that the metaphor of a 'label' is much closer to the situation than that of a 'file'. Thus my concept of Cicero is labelled 'Tully', 'Roman', 'orator', 'philosophical example'... My problem is to distinguish the concept from its labels. |
| 15588 | You cannot determine the full content from a thought's intrinsic character, as relations are involved [Fine,K] |
| Full Idea: There is no determining the full content of what someone thinks or believes from the individual things that he thinks or believes; we must also look at the threads that tie the contents of these thoughts or beliefs together. | |
| From: Kit Fine (Semantic Relationism [2007], Intro) | |
| A reaction: I'm not sure what 'full' content could possibly mean. Does that include all our background beliefs which we hardly ever articulate. Content comes in degrees, or needs an arbitrary boundary? |
| 15596 | The standard aim of semantics is to assign a semantic value to each expression [Fine,K] |
| Full Idea: The aim of semantics, as standardly conceived, is to assign a semantic value to each (meaningful) expression of the language under consideration. | |
| From: Kit Fine (Semantic Relationism [2007], 1.G) | |
| A reaction: Fine is raising the difficulty that these values can get entangled with one another. He proposes 'semantic connections' as a better aim. |
| 15587 | That two utterances say the same thing may not be intrinsic to them, but involve their relationships [Fine,K] |
| Full Idea: In my 'Semantic Relationism' the fact that two utterances say the same thing is not entirely a matter of their intrinsic semantic features; it may also turn on semantic relationships among the utterances of their parts not reducible to those features. | |
| From: Kit Fine (Semantic Relationism [2007], Intro) | |
| A reaction: You'll need to read the book slowly several times to get the hang of this, but at least it allows that two different utterances might say the same thing (express the same proposition, I would say). |
| 15589 | The two main theories are Holism (which is inferential), and Representational (which is atomistic) [Fine,K] |
| Full Idea: For holists a proper theory will be broadly inferential, while for their opponents it will be representational in character, describing relations between expressions and reality. Representational semantics is atomist, holist semantics inferential. | |
| From: Kit Fine (Semantic Relationism [2007], Intro) | |
| A reaction: Fine presents these as the two main schools in semantics. His own theory then proposes a more holistic version of the Representational view. He seeks the advantages of Frege's position, but without 'sense'. |
| 15598 | We should pursue semantic facts as stated by truths in theories (and not put the theories first!) [Fine,K] |
| Full Idea: A 'semantics' is a body of semantic facts, and a 'semantic theory' is a body of semantic truths. The natural order is a theory being understood as truths, which state facts. Davidson, alas, reversed this order, with facts understood through theories. | |
| From: Kit Fine (Semantic Relationism [2007], 2.C) | |
| A reaction: [compressed; he cites Davidson 1967, and calls it 'one of the most unfortunate tendencies in modern philosophy of language, ..as if chemistry were understood in terms of formulae rather than chemical facts']. |
| 15600 | Referentialist semantics has objects for names, properties for predicates, and propositions for connectives [Fine,K] |
| Full Idea: The standard referentialist semantics for a language with names is that the semantic value of the name is the object, the content of a predicate is a property, and the content of a logical connective is an operation on propositions. | |
| From: Kit Fine (Semantic Relationism [2007], 2.F) | |
| A reaction: My particular bęte noire is the idea that every predicate names a property. It is the tyranny of having to have a comprehensive semantic theory that drives this implausible picture. And I don't see how an object can be a semantic value… |
| 15601 | Fregeans approach the world through sense, Referentialists through reference [Fine,K] |
| Full Idea: Fregeans emphasise an orientation towards the speaker: possession of sense makes language meaningful, and language relates to the world through sense. For the Referentialist its representational relationships make it meaningful, and relate it to the world | |
| From: Kit Fine (Semantic Relationism [2007], 2.G) | |
| A reaction: The Referentialist approach is for Kripkean fans of direct reference, rather than the Fregean reference through descriptions. I am inclined to favour the old-fashioned, deeply discredited, much mocked Fregean approach. |
| 15605 | I take indexicals such as 'this' and 'that' to be linked to some associated demonstration [Fine,K] |
| Full Idea: Demonstrative uses of an indexical such as 'this' or 'that' should be taken to be anaphoric on an associated demonstration. It is a semantic requirement on the use of the indexical that it be coreferential with the demonstration. | |
| From: Kit Fine (Semantic Relationism [2007], Post 'Indexicals') | |
| A reaction: Similarly 'now' must connect to looking at a clock, and 'I' to pointing at some person. The demonstration could be of a verbal event, as much as a physical one. |