22 ideas
| 8996 | If if time is money then if time is not money then time is money then if if if time is not money... [Quine] |
| Full Idea: If if time is money then if time is not money then time is money then if if if time is not money then time is money then time is money then if time is money then time is money. | |
| From: Willard Quine (Truth by Convention [1935], p.95) | |
| A reaction: Quine offers this with no hint of a smile. I reproduce it for the benefit of people who hate analytic philosophy, and get tired of continental philosophy being attacked for its obscurity. |
| 8995 | Definition by words is determinate but relative; fixing contexts could make it absolute [Quine] |
| Full Idea: A definition endows a word with complete determinacy of meaning relative to other words. But we could determine the meaning of a new word absolutely by specifying contexts which are to be true and contexts which are to be false. | |
| From: Willard Quine (Truth by Convention [1935], p.89) | |
| A reaction: This is the beginning of Quine's distinction between the interior of 'the web' and its edges. The attack on the analytic/synthetic distinction will break down the boundary between the two. Surprising to find 'absolute' anywhere in Quine. |
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3) | |
| A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough. |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.3) |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) | |
| A reaction: [He cites Fagin and Halpern 1988 for this] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
| From: Melvin Fitting (Intensional Logic [2007], §1) |
| 10064 | Quine quickly dismisses If-thenism [Quine, by Musgrave] |
| Full Idea: Quine quickly dismisses If-thenism. | |
| From: report of Willard Quine (Truth by Convention [1935], p.327) by Alan Musgrave - Logicism Revisited §5 | |
| A reaction: [Musgrave quotes a long chunk of Quine which is hard to compress!] Effectively, he says If-thenism is cheating, or begs the question, by eliminating whole sections of perfectly good mathematics, because they cannot be derived from axioms. |
| 20296 | Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey] |
| Full Idea: Quine argues that logic could not be established by conventions, since the logical truths, being infinite in number, must be given by general conventions rather than singly; and logic is needed in the meta-theory, to apply to individual cases. | |
| From: report of Willard Quine (Truth by Convention [1935]) by Georges Rey - The Analytic/Synthetic Distinction 3.4 | |
| A reaction: A helpful insight into Quine's claim. If only someone would print these one sentence summaries at the top of classic papers, we would all get far more out of them at first reading. Assuming Rey is right! |
| 8998 | Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine] |
| Full Idea: If logic and mathematics being true by convention says the primitives can be conventionally described, that works for anything, and is empty; if the conventions are only for those fields, that's uninteresting; if a general practice, that is false. | |
| From: Willard Quine (Truth by Convention [1935], p.102) | |
| A reaction: This is Quine's famous denial of the traditional platonist view, and the new Wittgensteinian conventional view, preparing the ground for a more naturalistic and empirical view. I feel more sympathy with Quine than with the other two. |
| 8999 | Logic isn't conventional, because logic is needed to infer logic from conventions [Quine] |
| Full Idea: If logic is to proceed mediately from conventions, logic is needed for inferring logic from the conventions. Conventions for adopting logical primitives can only be communicated by free use of those very idioms. | |
| From: Willard Quine (Truth by Convention [1935], p.104) | |
| A reaction: A common pattern of modern argument, which always seems to imply that nothing can ever get off the ground. I suspect that there are far more benign circles in the world of thought than most philosophers imagine. |
| 9000 | If a convention cannot be communicated until after its adoption, what is its role? [Quine] |
| Full Idea: When a convention is incapable of being communicated until after its adoption, its role is not clear. | |
| From: Willard Quine (Truth by Convention [1935], p.106) | |
| A reaction: Quine is discussing the basis of logic, but the point applies to morality - that if there is said to be a convention at work, the concepts of morality must already exist to get the conventional framework off the ground. What is it that comes first? |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
| From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
| A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
| 8994 | If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine] |
| Full Idea: Geometry can be brought into line with logicism simply by identifying figures with arithmetical relations with which they are correlated thought analytic geometry. | |
| From: Willard Quine (Truth by Convention [1935], p.87) | |
| A reaction: Geometry was effectively reduced to arithmetic by Descartes and Fermat, so this seems right. You wonder, though, whether something isn't missing if you treat geometry as a set of equations. There is more on the screen than what's in the software. |
| 8997 | There are four different possible conventional accounts of geometry [Quine] |
| Full Idea: We can construe geometry by 1) identifying it with algebra, which is then defined on the basis of logic; 2) treating it as hypothetical statements; 3) defining it contextually; or 4) making it true by fiat, without making it part of logic. | |
| From: Willard Quine (Truth by Convention [1935], p.99) | |
| A reaction: [Very compressed] I'm not sure how different 3 is from 2. These are all ways to treat geometry conventionally. You could be more traditional, and say that it is a description of actual space, but the multitude of modern geometries seems against this. |
| 8993 | If mathematics follows from definitions, then it is conventional, and part of logic [Quine] |
| Full Idea: To claim that mathematical truths are conventional in the sense of following logically from definitions is the claim that mathematics is a part of logic. | |
| From: Willard Quine (Truth by Convention [1935], p.79) | |
| A reaction: Quine is about to attack logic as convention, so he is endorsing the logicist programme (despite his awareness of Gödel), but resisting the full Wittgenstein conventionalist picture. |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
| Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.4) | |
| A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others. |
| 9757 | A person viewed as an agent makes no sense without its own future [Korsgaard] |
| Full Idea: In forming a particular plan of life, you need to identify with your future in order to be what you are even now. When the person is viewed as an agent, no clear content can be given to the idea of a merely present self. | |
| From: Christine M. Korsgaard (Intro to 'Creating the Kingdom of Ends' [1996], §2) | |
| A reaction: I certainly like the notion that we should treat persons primarily as agents, since I take personhood to be more like a process than an existent entity. If a large brick is about to hit you, you actually have no future, though you think you have. |
| 9758 | To make sense of personal identity, focus on agency rather than experience [Korsgaard] |
| Full Idea: A focus on agency makes more sense of personal identity than a focus on experience. | |
| From: Christine M. Korsgaard (Intro to 'Creating the Kingdom of Ends' [1996], §2) | |
| A reaction: This strikes me as eminently sensible advice for the beginning of any discussion of personal identity. Her personal bęte noir is Parfit, who focuses on what we are conscious of. |
| 9759 | Theory of action focuses on explanation and prediction; practical action on justification and choice [Korsgaard] |
| Full Idea: When we look at our actions from the theoretical standpoint our concern is with their explanation and prediction. When we view them from the practical standpoint our concern is with their justification and choice. | |
| From: Christine M. Korsgaard (Intro to 'Creating the Kingdom of Ends' [1996], §4) | |
| A reaction: A nice distinction, which invites us to further subdivide action theory into two branches, with entirely different concerns. |
| 9760 | Self-concern may be a source of pain, or a lack of self-respect, or a failure of responsibility [Korsgaard] |
| Full Idea: For utilitarians, self-concern causes needless pain; for Kantians, it evinces a lack of respect for one's own humanity; for the religious moralist, it is a failure of responsibility for what has been placed in one's special care. | |
| From: Christine M. Korsgaard (Intro to 'Creating the Kingdom of Ends' [1996], §5) | |
| A reaction: Worryingly, given my heathenish views, I find the third one the most congenial. If we don't take responsibility for our own selves (e.g. for having a great talent), then no one (even parents) will take responsibility for anything. |
| 9761 | Personal concern for one's own self widens out into concern for the impersonal [Korsgaard] |
| Full Idea: The personal concern which begins with one's life in a particular body finds its place in ever-widening spheres of agency and enterprise, developing finally into a personal concern for the impersonal. | |
| From: Christine M. Korsgaard (Intro to 'Creating the Kingdom of Ends' [1996], §5) | |
| A reaction: I am very struck by this nice thought, which comes from a very committed Kantian. It seems to me to capture the modern orthodoxy in ethical thinking - that concern for one's self, rather than altruism, is central, but altruism should follow from it. |