21 ideas
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 7720 | Two things can only resemble one another in some respect, and that may reintroduce a universal [Lowe] |
| Full Idea: A problem for resemblance nominalism is that in saying that two particulars 'resemble' one another, it is necessary to specify in what respect they do so (e.g. colour, shape, size), and this threatens to reintroduce what appears to be talk of universals. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
| A reaction: We see resemblance between faces instantly, long before we can specify the 'respects' of the resemblance. This supports the Humean hard-wired view of resemblance, rather than some appeal to Platonic universals. |
| 7712 | On substances, Leibniz emphasises unity, Spinoza independence, Locke relations to qualities [Lowe] |
| Full Idea: Later philosophers emphasised different strands of Aristotle's concept of substances: Leibniz (in his theory of monads) emphasised their unity; Spinoza emphasised their ontological independence; Locke emphasised their role in relation to qualities. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.4) | |
| A reaction: Note that this Aristotelian idea had not been jettisoned in the late seventeenth century, unlike other Aristotelianisms. I think it is only with the success of atomism in chemistry that the idea of substance is forced to recede. |
| 7710 | Perception is a mode of belief-acquisition, and does not involve sensation [Lowe] |
| Full Idea: According to one school of thought, perception is simply a mode of belief-acquisition,and there is no reason to suppose that any element of sensation is literally involved in perception. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.3) | |
| A reaction: Blindsight would be an obvious supporting case for this view. I think this point is crucial in understanding what is wrong with Jackson's 'knowledge argument' (involving Mary, see Idea 7377). Sensation gives knowledge, so it can't be knowledge. |
| 7711 | Science requires a causal theory - perception of an object must be an experience caused by the object [Lowe] |
| Full Idea: Only a causal theory of perception will respect the facts of physiology and physics ...meaning a theory which maintains that for a subject to perceive a physical object the subject should enjoy some appropriate perceptual experience caused by the object. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.3) | |
| A reaction: If I hallucinate an object, then presumably I am not allowed to say that I 'perceive' it, but that seems to make the causal theory an idle tautology. If we are in virtual reality then there aren't any objects. |
| 5303 | For the proletariate, law, morality and religion are just expressions of bourgeois interests [Marx/Engels] |
| Full Idea: Law, morality, religion are to the proletarian so many bourgeois prejudices, behind which lurk in ambush just as many bourgeois interests. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §1) | |
| A reaction: This Marxist idea has been the main driving force in spreading relativist views through modern culture. There is a lot of truth here, but philosophy is plausibly the search for truths which both the bourgeois and the proletarian will accept. |
| 7714 | Personal identity is a problem across time (diachronic) and at an instant (synchronic) [Lowe] |
| Full Idea: There is the question of the identity of a person over or across time ('diachronic' personal identity), and there is also the question of what makes for personal identity at a time ('synchronic' personal identity). | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.5) | |
| A reaction: This seems to me to be the first and most important distinction in the philosophy of personal identity, and they regularly get run together. Locke, for example, has an account of synchronic identity, which is often ignored. It applies to objects too. |
| 7715 | Mentalese isn't a language, because it isn't conventional, or a means of public communication [Lowe] |
| Full Idea: 'Mentalese' would be neither conventional nor a means of public communication so that even to call it a language is seriously misleading. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
| A reaction: It is, however, supposed to contain symbolic representations which are then used as tokens for computation, so it seems close to a language, if (for example) symbolic logic or mathematics were accepted as languages. But who understands it? |
| 7722 | If meaning is mental pictures, explain "the cat (or dog!) is NOT on the mat" [Lowe] |
| Full Idea: If meaning is a private mental picture, what does 'the cat is NOT on the mat' mean, and how does it differ from 'the dog is not on the mat?'. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
| A reaction: Not insurmountable. We picture an empty mat, combined with a cat (or whatever) located somewhere else. A mental 'picture' of something shouldn't be contrued as a single image in a neat black frame. |
| 21998 | Bourgeois interests create our morality, law and religion [Marx/Engels] |
| Full Idea: Morality, law and religion are bourgeois prejudices, behind which lurk in ambush just as many bourgeois interests. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], p.230), quoted by Peter Singer - Marx 9 | |
| A reaction: The obvious question is whether this creation of values is conscious or unconscious. Personally I believe in conspiracies. Some cynical conversations go on behind the scenes, of which historians will never hear. |
| 5302 | Modern governments are just bourgeois management committees [Marx/Engels] |
| Full Idea: The executive of the modern State is but a committee for managing the common affairs of the whole bourgeoisie. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §1) | |
| A reaction: In Britain the Labour Party and the Trade Unions have appeared since 1848, but bourgeoisie control of the media has pushed us a long way back towards Marx's time. Government will always be someone's management committee. |
| 5304 | Communism aims to abolish not all property, but bourgeois property [Marx/Engels] |
| Full Idea: The distinguishing feature of Communism is not the abolition of property generally, but the abolition of bourgeois property. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §2) | |
| A reaction: This is a sinister remark which has led to huge numbers of murders in the Soviet Union and China. People resent having their property 'abolished', especially if they have worked hard for it. But most of our wealth is owned by about 2% of our people. |
| 5307 | Many of the bourgeois rights grievances are a form of self-defence [Marx/Engels] |
| Full Idea: A part of the bourgeoisie is desirous of redressing social grievances, in order to secure the continued existence of bourgeois society. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §3.II) | |
| A reaction: …so don't try being nice to us. No TRUE bourgeois would actually want to help the proletariate… Nevertheless, he is probably largely right. Do we want the poor to suffer? No. Do we want them to be as rich as us? No! |
| 5306 | The free development of each should be the condition for the free development of all [Marx/Engels] |
| Full Idea: In a communist society we shall have an association, in which the free development of each is the condition for the free development of all. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §2) | |
| A reaction: This ringing slogan is remarkably close to John Stuart Mill's defence of liberalism, where liberty is an absolute, as long as it avoids the liberty of others. Personally I think freedom is marginal in political philosophy, like food and shelter. |
| 5305 | Communists want to rescue education from the ruling class [Marx/Engels] |
| Full Idea: Communists seek to rescue education from the influence of the ruling class. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §2) | |
| A reaction: Someone has to control education, and I would personally prefer it if the controllers were well educated themselves. Neutral education is an idle dream. We must educate for democracy, if we really want democracy. |
| 5301 | The history of all existing society is the history of class struggles [Marx/Engels] |
| Full Idea: The history of all existing society is the history of class struggles. | |
| From: K Marx / F Engels (The Communist Manifesto [1848], §1) | |
| A reaction: This seems to make, say, the English Peasants' Revolt of 1481 crucial, and the building of Lincoln Cathedral fairly minor. Where does the advent of the telephone figure? Etc. Still, we must concede his point. Most medieval history is about power. |