27 ideas
| 13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
| Full Idea: The two best understood conceptions of set are the Iterative Conception and the Limitation of Size Conception. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2) |
| 13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
| Full Idea: There are set theories that countenance exceptions to the Principle of Separation in exchange for a universal set. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2) |
| 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. |
| 13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
| Full Idea: The possibility of unrestricted quantification does not immediately presuppose the existence of an all-inclusive domain. One could deny an all-inclusive domain but grant that some quantifications are sometimes unrestricted. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1) | |
| A reaction: Thus you can quantify over anything you like, but only from what is available. Eat what you like (in this restaurant). |
| 13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
| Full Idea: There are doubts about whether absolute generality is possible, if there are certain concepts which are indefinitely extensible, lacking definite extensions, and yielding an ever more inclusive hierarchy. Sets and ordinals are paradigm cases. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.1) |
| 13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
| Full Idea: If one thought of second-order quantification as quantification over first-level Fregean concepts [note: one under which only objects fall], talk of domains might be regimented as talk of first-level concepts, which are not objects. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2) | |
| A reaction: That is (I take it), don't quantify over objects, but quantify over concepts, but only those under which known objects fall. One might thus achieve naïve comprehension without paradoxes. Sound like fun. |
| 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. |
| 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. |
| 13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |
| Full Idea: We generally take an assertion's domain of discourse to be implicitly restricted by context. [Note: the standard approach is that this restriction is a semantic phenomenon, but Kent Bach (2000) argues that it is a pragmatic phenomenon] | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1) | |
| A reaction: I think Kent Bach is very very right about this. Follow any conversation, and ask what the domain is at any moment. The reference of a word like 'they' can drift across things, with no semantics to guide us, but only clues from context and common sense. |
| 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? |
| 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) |
| 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) |