25 ideas
| 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. |
| 4444 | One moderate nominalist view says that properties and relations exist, but they are particulars [Armstrong] |
| Full Idea: There is a 'moderate' nominalism (found in G.F.Stout, for example) which says that properties and relations do exist, but that they are particulars rather than universals. | |
| From: David M. Armstrong (Universals [1995], p.504) | |
| A reaction: Both this view and the 'mereological' view seem to be ducking the problem. If you have two red particulars and a green one, how do we manage to spot the odd one out? |
| 4445 | If properties and relations are particulars, there is still the problem of how to classify and group them [Armstrong] |
| Full Idea: The view that properties exist, but are particulars rather than universals, is still left with the problem of classification. On what basis do we declare that different things have the same property? | |
| From: David M. Armstrong (Universals [1995], p.504) | |
| A reaction: This seems like a fairly crucial objection. The original problem was how we manage to classify things (group them into sets), and it looks as if this theory leaves the problem untouched. |
| 4448 | Should we decide which universals exist a priori (through words), or a posteriori (through science)? [Armstrong] |
| Full Idea: Should we decide what universals exist a priori (probably on semantic grounds, identifying them with the meanings of general words), or a posteriori (looking to our best general theories about nature to give revisable conjectures about universals)? | |
| From: David M. Armstrong (Universals [1995], p.505) | |
| A reaction: Nice question for a realist. Although the problem is first perceived in the use of language, if we think universals are a real feature of nature, we should pursue them scientifically, say I. |
| 4446 | It is claimed that some universals are not exemplified by any particular, so must exist separately [Armstrong] |
| Full Idea: There are some who claim that there can be uninstantiated universals, which are not exemplified by any particular, past, present or future; this would certainly imply that those universals have a Platonic transcendent existence outside time and space. | |
| From: David M. Armstrong (Universals [1995], p.504) | |
| A reaction: Presumably this is potentially circular or defeasible, because one can deny the universal simply because there is no particular. |
| 4440 | 'Resemblance Nominalism' finds that in practice the construction of resemblance classes is hard [Armstrong] |
| Full Idea: It is difficult for Resemblance Nominalists to construct their interconnected classes in practice. | |
| From: David M. Armstrong (Universals [1995], p.503) | |
| A reaction: Given the complexity of the world this is hardly surprising, but it doesn't seem insuperable for the theory. It is hard to decide whether an object is white, or hot, whatever your theory of universals. |
| 4439 | 'Resemblance Nominalism' says properties are resemblances between classes of particulars [Armstrong] |
| Full Idea: Resemblance Nominalists say that to have a property is to be a member of a class which is part of a network of resemblance relations with other classes of particulars. ..'Resemblance' is taken to be a primitive notion, though one that admits of degrees. | |
| From: David M. Armstrong (Universals [1995], p.503) | |
| A reaction: Intuition suggests that this proposal has good prospects, as properties are neither identical, nor just particulars, but have a lot in common, which 'resemblance' captures. Hume saw resemblance as a 'primitive' process. |
| 4431 | 'Predicate Nominalism' says that a 'universal' property is just a predicate applied to lots of things [Armstrong] |
| Full Idea: For a Predicate Nominalist different things have the same property, or belong to the same kind, if the same predicates applies to, or is 'true of', the different things. | |
| From: David M. Armstrong (Universals [1995], p.503) | |
| A reaction: This immediately strikes me as unlikely, because I think the action is at the proposition level, not the sentence level. And why do some predicates seem to be synonymous? |
| 4433 | Concept and predicate nominalism miss out some predicates, and may be viciously regressive [Armstrong] |
| Full Idea: The standard objections to Predicate and Concept Nominalism are that some properties have no predicates or concepts, and that predicates and concepts seem to be types rather than particulars, and it is types the theory is seeking to analyse. | |
| From: David M. Armstrong (Universals [1995], p.503) | |
| A reaction: The claim that some properties have no concepts is devastating if true, but may not be. The regress problem is likely to occur in any explanation of universals, I suspect. |
| 4432 | 'Concept Nominalism' says a 'universal' property is just a mental concept applied to lots of things [Armstrong] |
| Full Idea: Concept Nominalism says different things have the same property, or belong to the same kind, if the same concept in the mind is applied to different things. | |
| From: David M. Armstrong (Universals [1995], p.503) | |
| A reaction: This is more appealing than Predicate Nominalism, and may be right. Our perception of the 'properties' of a thing may be entirely dictated by human interests, not by nature. |
| 4436 | 'Class Nominalism' may explain properties if we stick to 'natural' sets, and ignore random ones [Armstrong] |
| Full Idea: Class Nominalism can be defended (by Quinton) against the problem of random sets (with nothing in common), by giving an account of properties in terms of 'natural' classes, where 'natural' comes in degrees, but is fundamental and unanalysable. | |
| From: David M. Armstrong (Universals [1995], p.503) | |
| A reaction: This still seems to beg the question, because you still have to decide whether two things have anything 'naturally' in common before you assign them to a set. |
| 4434 | 'Class Nominalism' says that properties or kinds are merely membership of a set (e.g. of white things) [Armstrong] |
| Full Idea: Class Nominalists substitute classes or sets for properties or kinds, so that being white is just being a member of the set of white things; relations are treated as ordered sets. | |
| From: David M. Armstrong (Universals [1995], p.503) | |
| A reaction: This immediately seems wrong, because it invites the question of why something is a member of a set (unless membership is arbitrary and whimsical - which it usually isn't). |
| 4435 | 'Class Nominalism' cannot explain co-extensive properties, or sets with random members [Armstrong] |
| Full Idea: Class Nominalism cannot explain co-extensive properties (which qualify the same things), and also a random (non-natural) set has particulars with nothing in common, thus failing to capture an essential feature of a general property. | |
| From: David M. Armstrong (Universals [1995], p.503) | |
| A reaction: These objections strike me as conclusive, since we can assign things to a set quite arbitrarily, so membership of a set may signify no shared property at all (except, say, 'owned by me', which is hardly a property). |
| 4437 | 'Mereological Nominalism' sees whiteness as a huge white object consisting of all the white things [Armstrong] |
| Full Idea: Mereological Nominalism views a property as the omnitemporal whole or aggregate of all the things said to have the property, so whiteness is a huge white object whose parts are all the white things. | |
| From: David M. Armstrong (Universals [1995], p.503) | |
| A reaction: A charming proposal, in which bizarre and beautiful unities thread themselves across the universe, but white objects may also be soft and warm. |
| 4438 | 'Mereological Nominalism' may work for whiteness, but it doesn't seem to work for squareness [Armstrong] |
| Full Idea: Mereological Nominalism has some plausibility for a case like whiteness, but breaks down completely for other universals, such as squareness. | |
| From: David M. Armstrong (Universals [1995], p.503) | |
| A reaction: A delightful request that you attempt a hopeless feat of imagination, by seeing all squares as parts of one supreme square. A nice objection. |
| 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. |
| 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. |
| 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. |