28 ideas
| 8250 | So-called 'free logic' operates without existence assumptions [Meinong, by George/Van Evra] |
| Full Idea: Meinong has recently been credited with inspiring 'free logic': a logic without existence assumptions. | |
| From: report of Alexius Meinong (The Theory of Objects [1904]) by George / Van Evra - The Rise of Modern Logic 8 | |
| A reaction: This would appear to be a bold escape from the quandries concerning the existential implications of quantifiers. I immediately find it very appealing. It seems to spell disaster for the Quinean program of deducing ontology from language. |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| Full Idea: The empty set is usually derived via Zermelo's axiom of separation. But the axiom of separation is conditional: it requires the existence of a set in order to generate others as subsets of it. The original set has to come from the axiom of infinity. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: They charge that this leads to circularity, as Infinity depends on the empty set. |
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| Full Idea: Some authors need to be told loud and clear: if there is an empty set, it is something, not nothing. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: I'm inclined to think of a null set as a pair of brackets, so maybe that puts it into a metalanguage. |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| Full Idea: The empty set is said to be useful to express non-existence, but saying 'there are no Us', or ¬∃xUx are no less concise, and certainly less roundabout. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| Full Idea: Suppose we introduce Ω not as a term standing for a supposed empty set, but as a paradigm of an empty term, not standing for anything. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: This proposal, which they go on to explore, seems to mean that Ω (i.e. the traditional empty set symbol) is no longer part of set theory but is part of semantics. |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| Full Idea: Thomason says with no unit sets we couldn't call {1,2}∩{2,3} a set - but so what? Why shouldn't the intersection be the number 2? However, we then have to distinguish three different cases of intersection (common subset or member, or disjoint). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 2.2) |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| Full Idea: A 'singularist', who refers to objects one at a time, must resort to the language of sets in order to replace plural reference to members ('Henry VIII's wives') by singular reference to a set ('the set of Henry VIII's wives'). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: A simple and illuminating point about the motivation for plural reference. Null sets and singletons give me the creeps, so I would personally prefer to avoid set theory when dealing with ontology. |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| Full Idea: Plurals earn their keep in set theory, to answer Skolem's remark that 'in order to treat of 'sets', we must begin with 'domains' that are constituted in a certain way'. We can speak in the plural of 'the objects', not a 'domain' of objects. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: [Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it. |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| Full Idea: Logical truths should be true no matter what exists, so true even if nothing exists. The classical predicate calculus, however, makes it logically true that something exists. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| Full Idea: If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) | |
| A reaction: Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application. |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| Full Idea: Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2) | |
| A reaction: Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated. |
| 8719 | There can be impossible and contradictory objects, if they can have properties [Meinong, by Friend] |
| Full Idea: Meinong (and Priest) leave room for impossible objects (like a mountain made entirely of gold), and even contradictory objects (such as a round square). This would have a property, of 'being a contradictory object'. | |
| From: report of Alexius Meinong (The Theory of Objects [1904]) by Michèle Friend - Introducing the Philosophy of Mathematics 6.8 | |
| A reaction: This view is only possible with a rather lax view of properties. Personally I don't take 'being a pencil' to be a property of a pencil. It might be safer to just say that 'round squares' are possible linguistic subjects of predication. |
| 8971 | There are objects of which it is true that there are no such objects [Meinong] |
| Full Idea: There are objects of which it is true that there are no such objects. | |
| From: Alexius Meinong (The Theory of Objects [1904]), quoted by Peter van Inwagen - Existence,Ontological Commitment and Fictions p.131 | |
| A reaction: Van Inwagen say this idea is 'infamous', but Meinong is undergoing a revival, and commitment to non-existent objects may be the best explanation of some ways of talking. |
| 8718 | Meinong says an object need not exist, but must only have properties [Meinong, by Friend] |
| Full Idea: Meinong distinguished between 'existing objects' and 'subsisting objects', and being an object does not imply existence, but only 'having properties'. | |
| From: report of Alexius Meinong (The Theory of Objects [1904]) by Michèle Friend - Introducing the Philosophy of Mathematics 6.8 | |
| A reaction: Meinong is treated as a joke (thanks to Russell), but this is good. "Father Christmas does not exist, but he has a red coat". He'd better have some sort of existy aspect if he is going to have a property. So he's 'an object'. 'Insubstantial'? |
| 7756 | Meinong said all objects of thought (even self-contradictions) have some sort of being [Meinong, by Lycan] |
| Full Idea: Meinong insisted (à la Anselm) that any possible object of thought - even a self-contradictory one - has being of a sort even though only a few such things are so lucky as to exist in reality as well. | |
| From: report of Alexius Meinong (The Theory of Objects [1904]) by William Lycan - Philosophy of Language Ch.1 | |
| A reaction: ['This idea gave Russell fits' says Lycan]. In the English-speaking world this is virtually the only idea for which Meinong is remembered. Russell (Idea 5409) was happy for some things to merely 'subsist' as well as others which could 'exist'. |
| 15781 | The objects of knowledge are far more numerous than objects which exist [Meinong] |
| Full Idea: The totality of what exists, including what has existed and what will exist, is infinitely small in comparison with the totality of Objects of knowledge. | |
| From: Alexius Meinong (The Theory of Objects [1904]), quoted by William Lycan - The Trouble with Possible Worlds 01 | |
| A reaction: This is rather profound, but the word 'object' doesn't help. I would say 'What we know concerns far more than what merely exists'. |
| 4761 | The 'error theory' of morals says there is no moral knowledge, because there are no moral facts [Mackie, by Engel] |
| Full Idea: Mackie's 'error theory' of ethics says that if a fact is something that corresponds to a true proposition, there are actually no moral facts, hence no knowledge of what moral statements are about. | |
| From: report of J.L. Mackie (Ethics: Inventing Right and Wrong [1977]) by Pascal Engel - Truth §4.2 | |
| A reaction: Personally I am inclined to think that there are moral facts (about what nature shows us constitutes a good human being), based on virtue theory. Mackie is a good warning, though, against making excessive claims. You end up like a bad scientist. |
| 8337 | Some says mental causation is distinct because we can recognise single occurrences [Mackie] |
| Full Idea: It is sometimes suggested that our ability to recognise a single occurrence as an instance of mental causation is a feature which distinguishes mental causation from physical or 'Humean' causation. | |
| From: J.L. Mackie (Causes and Conditions [1965], §9) | |
| A reaction: Hume says regularities are needed for mental causation too. Concentrate hard on causing a lightning flash - 'did I do that?' Gradually recovering from paralysis; you wouldn't just move your leg once, and know it was all right! |
| 8342 | Mackie tries to analyse singular causal statements, but his entities are too vague for events [Kim on Mackie] |
| Full Idea: In spite of Mackie's announced aim of analysing singular causal statements, it is doubtful that the entities that he is concerned with can be consistently interpreted as spatio-temporally bounded individual events. | |
| From: comment on J.L. Mackie (Causes and Conditions [1965]) by Jaegwon Kim - Causes and Events: Mackie on causation §3 | |
| A reaction: This is because Mackie mainly talks about 'conditions'. Nearly every theory I encounter in modern philosophy gets accused of either circular definitions, or inadequate individuation conditions for key components. A tough world for theory-makers. |
| 8343 | Necessity and sufficiency are best suited to properties and generic events, not individual events [Kim on Mackie] |
| Full Idea: Relations of necessity and sufficiency seem best suited for properties and for property-like entities such as generic states and events; their application to individual events and states is best explained as derivative from properties and generic events. | |
| From: comment on J.L. Mackie (Causes and Conditions [1965]) by Jaegwon Kim - Causes and Events: Mackie on causation §4 | |
| A reaction: This seems to suggest that necessity must either derive from laws, or from powers. It is certainly hard to see how you could do Mackie's assessment of necessary and sufficient components, without comparing similar events. |
| 8385 | A cause is part of a wider set of conditions which suffices for its effect [Mackie, by Crane] |
| Full Idea: The details of Mackie's analysis are complex, but the general idea is that the cause is part of a wider set of conditions which suffices for its effect. | |
| From: report of J.L. Mackie (Causes and Conditions [1965]) by Tim Crane - Causation 1.3.3 | |
| A reaction: Helpful. Why does something have to be 'the' cause? Immediacy is a vital part of it. A house could be a 'fire waiting to happen'. Oxygen is an INUS condition for a fire. |
| 8335 | Necessary conditions are like counterfactuals, and sufficient conditions are like factual conditionals [Mackie] |
| Full Idea: A necessary causal condition is closely related to a counterfactual conditional: if no-cause then no-effect, and a sufficient causal condition is closely related to a factual conditional (Goodman's phrase): since cause-here then effect. | |
| From: J.L. Mackie (Causes and Conditions [1965], §4) | |
| A reaction: The 'factual conditional' just seems to be an assertion that causation occurred (dressed up with the logical-sounding 'since'). An important distinction for Lewis. Sufficiency doesn't seem to need possible-worlds talk. |
| 8336 | The INUS account interprets single events, and sequences, causally, without laws being known [Mackie] |
| Full Idea: My account shows how a singular causal statement can be interpreted, and how the corresponding sequence can be shown to be causal, even if the corresponding complete laws are not known. | |
| From: J.L. Mackie (Causes and Conditions [1965], §9) | |
| A reaction: Since the 'complete' laws are virtually never known, it would be a bit much to require that to assert causation. His theory is the 'INUS' account of causal conditions - see Idea 8333. |
| 8333 | A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition [Mackie] |
| Full Idea: If a short-circuit causes a fire, the so-called cause is, and is known to be, an Insufficient but Necessary part of a condition which is itself Unnecessary but Sufficient for the result. Let us call this an INUS condition. | |
| From: J.L. Mackie (Causes and Conditions [1965], §1) | |
| A reaction: I'm not clear why it is necessary, given that the fire could have started without the short-circuit. The final situation must certainly be sufficient. If only one situation can cause an effect, then the whole situation is necessary. |
| 8395 | Mackie has a nomological account of general causes, and a subjunctive conditional account of single ones [Mackie, by Tooley] |
| Full Idea: For general causal statements Mackie favours a nomological account, but for singular causal statements he argued for an analysis in terms of subjunctive conditionals. | |
| From: report of J.L. Mackie (Causes and Conditions [1965]) by Michael Tooley - Causation and Supervenience 5.2 | |
| A reaction: These seem to be consistent, by explaining each by placing it within a broader account of reality. Personally I think Ducasse gives the best account of how you get from the particular to the general (via similarity and utility). |
| 8334 | The virus causes yellow fever, and is 'the' cause; sweets cause tooth decay, but they are not 'the' cause [Mackie] |
| Full Idea: We may say not merely that this virus causes yellow fever, but also that it is 'the' cause of yellow fever; but we could only say that sweet-eating causes dental decay, not that it is the cause of dental decay (except in an individual case). | |
| From: J.L. Mackie (Causes and Conditions [1965], §3) | |
| A reaction: A bit confusing, but there seems to be something important here, concerning the relation between singular causation and law-governed causation. 'The' cause may not be sufficient (I'm immune to yellow fever). So 'the' cause is the only necessary one? |
| 1472 | The propositions that God is good and omnipotent, and that evil exists, are logically contradictory [Mackie, by PG] |
| Full Idea: There is a contradiction between the propositions that God is wholly good, God is omnipotent, and evil exists, and one of them has got to give way (assuming good eliminates evil, and omnipotence has no limit). | |
| From: report of J.L. Mackie (Evil and Omnipotence [1955], Pref.) by PG - Db (ideas) |
| 1473 | Is evil an illusion, or a necessary contrast, or uncontrollable, or necessary for human free will? [Mackie, by PG] |
| Full Idea: Perhaps evil is an illusion, or it is necessary for good to exist, or in humans it is required because we have free will, or God lacks the full power to control it, but none of these looks convincing. | |
| From: report of J.L. Mackie (Evil and Omnipotence [1955], §B) by PG - Db (ideas) |