23 ideas
| 13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
| Full Idea: There are four 'perfect syllogisms': Barbara (every M is P, every S is M, so every S is P); Celarent (no M is P, every S is M, so no S is P); Darii (every M is P, some S is M, so some S is P); Ferio (no M is P, some S is M, so some S is not P). | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
| A reaction: The four names are mnemonics from medieval universities. |
| 13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
| Full Idea: It has often been claimed (e.g. by Leibniz) that a single rule governs all syllogistic validity, called 'dictum de omni et null', which says that what is affirmed or denied of any whole is affirmed or denied of any part of that whole. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
| A reaction: This seems to be the rule which is captured by Venn Diagrams. |
| 13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
| Full Idea: Three common kinds of sentence cannot be put into syllogistic ('categorical') form: ones using singular terms ('Mars is red'), ones using relational terms ('every painter owns some brushes'), and compound sentences. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) |
| 13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
| Full Idea: Term logic begins with expressions and two 'term functors'. Any simple letter is a 'term', any term prefixed by a minus ('-') is a 'negative term', and any pair of terms flanking a plus ('+') is a 'compound term'. Parenthese are used for grouping. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
| A reaction: [see Engelbretsen and Sayward for the full formal system] |
| 13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
| Full Idea: One of the key ideas of modern formal logic is that all formally valid inferences can be specified in strictly syntactic terms. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Ch.2) |
| 13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
| Full Idea: Classical logic rests on the concepts of truth and falsity (and usually makes use of a semantic theory based on models), whereas constructivist logic accounts for inference in terms of defense and refutation. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Intro) | |
| A reaction: My instincts go with the classical view, which is that inferences do not depend on the human capacity to defend them, but sit there awaiting revelation. My view isn't platonist, because I take the inferences to be rooted in the physical world. |
| 13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |
| Full Idea: Unlike ∨, →, ↔, and ∀, the sign = is not eliminable from a logic. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Ch.3) |
| 13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
| Full Idea: A set of axioms is said to be ω-incomplete if, for some universal quantification, each of its instances is derivable from those axioms but the quantification is not thus derivable. | |
| From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 7) |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |