21 ideas
| 18270 | Choice suggests that intensions are not needed to ensure classes [Coffa] |
| Full Idea: The axiom of choice was an assumption that implicitly questioned the necessity of intensions to guarantee the presence of classes. | |
| From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 7 'Log') | |
| A reaction: The point is that Choice just picks out members for no particular reason. So classes, it seems, don't need a reason to exist. |
| 18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
| Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1) | |
| A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark. |
| 18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
| Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise. |
| 18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
| Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea. |
| 18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
| Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting. |
| 16066 | Additional or removal of any part changes a thing, so people are never the same person [Epicharmus] |
| Full Idea: If you add or take away a pebble, the same number does not remain. If you add to a length or cut off from it, the former measure does not remain. So human beings grow or waste away. Both you and I were, and shall be, other men. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B02), quoted by Diogenes Laertius - Lives of Eminent Philosophers 03.12 | |
| A reaction: [The original is in dialogue form from a play. The context is a joke about not paying a debt.] Note the early date for this metaphysical puzzle. My new favourite reply is Chrysippus's Idea 16059; identity actually requires change. |
| 18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
| Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory. |
| 18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
| Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions. |
| 18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
| Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular). |
| 18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
| Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds. |
| 18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
| Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5) | |
| A reaction: They accept lots of successes in modelling necessity and time. |
| 18263 | The semantic tradition aimed to explain the a priori semantically, not by Kantian intuition [Coffa] |
| Full Idea: The semantic tradition's problem was the a priori; its enemy, Kantian pure intuition; its purpose, to develop a conception of the a priori in which pure intuition played no role; its strategy, to base that theory on a development of semantics. | |
| From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 2 Intro) | |
| A reaction: It seems to me that intuition, in the modern sense, has been unnecessarily demonised. I would define it as 'rational insights which cannot be fully articulated'. Sherlock Holmes embodies it. |
| 18272 | Platonism defines the a priori in a way that makes it unknowable [Coffa] |
| Full Idea: The trouble with Platonism had always been its inability to define a priori knowledge in a way that made it possible for human beings to have it. | |
| From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 7 'What') | |
| A reaction: This is the famous argument of Benacerraf 1973. |
| 436 | A dog seems handsome to another a dog, and even a pig to another pig [Epicharmus] |
| Full Idea: Dog seems very handsome to dog, and ox to ox, and donkey very handsome to donkey, and even pig to pig. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B05), quoted by (who?) - where? |
| 18266 | Mathematics generalises by using variables [Coffa] |
| Full Idea: The instrument of generality in mathematics is the variable. | |
| From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 4 'The conc') | |
| A reaction: I like the idea that there are variables in ordinary speech, pronouns being the most obvious example. 'Cats' is a variable involving quantification over a domain of lovable fluffy mammals. |
| 442 | Pleasures are like pirates - if you are caught they drown you in a sea of pleasures [Epicharmus] |
| Full Idea: Pleasures for mortals are like impious pirates, for the man who is caught by pleasures is immediately drowned in a sea of them. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B44), quoted by (who?) - where? | |
| A reaction: Not all slopes are slippery. Plenty of people hold themselves to strict rules about alcohol or gambling. People have occasional treats. |
| 440 | Hands wash hands; give that you may get [Epicharmus] |
| Full Idea: The hand washes the hand; give something and you may get something. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B30), quoted by (who?) - where? |
| 441 | Against a villain, villainy is not a useless weapon [Epicharmus] |
| Full Idea: Against a villain, villainy is not a useless weapon. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B32), quoted by (who?) - where? |
| 18279 | Relativity is as absolutist about space-time as Newton was about space [Coffa] |
| Full Idea: If the theory of relativity might be thought to support an idealist construal of space and time, it is no less absolutistic about space-time than Newton's theory was about space. | |
| From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991]) | |
| A reaction: [He cites Minkowski, Weyl and Cartan for this conclusion] Coffa is clearly a bit cross about philosophers who draw naive idealist and relativist conclusions from relativity. |
| 439 | God knows everything, and nothing is impossible for him [Epicharmus] |
| Full Idea: Nothing escapes the divine, this you must realise. God himself is our overseer, and nothing is impossible for him. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B23), quoted by (who?) - where? |
| 443 | Human logos is an aspect of divine logos, and is sufficient for successful living [Epicharmus] |
| Full Idea: Man has calculation, but there is also the divine logos. But human logos is sprung from the divine logos, and it brings to each man his means of life, and his maintenance. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B57), quoted by (who?) - where? |