12 ideas
| 6806 | Do not multiply entities beyond necessity [William of Ockham] |
| Full Idea: Do not multiply entities beyond necessity. | |
| From: William of Ockham (works [1335]) | |
| A reaction: This is the classic statement of Ockham's Razor, though it is not found in his printed works. It appears to be mainly aimed at Plato's Theory of Forms. It is taken to refer to types of entities, not numbers. One seraph is as bad as a hundred. |
| 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) |
| 22132 | Species and genera are individual concepts which naturally signify many individuals [William of Ockham] |
| Full Idea: In his mature nominalism, species and genera are identified with certain mental qualities called concepts or intentions of the mind. Ontologically they are individuals too, like everthing else, ...but they naturally signify many different individuals. | |
| From: William of Ockham (works [1335]), quoted by Claude Panaccio - William of Ockham p.1056 | |
| A reaction: 'Naturally' is the key word, because the concepts are not fictions, but natural responses to encountering individuals in the world. I am an Ockhamist. |
| 19381 | The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham] |
| Full Idea: Time is composed of non-entities, because it is composed of the past which does not exist now, although it did exist, and of the future, which does not yet exist; therefore time does not exist. | |
| From: William of Ockham (works [1335], 6:496), quoted by Richard T.W. Arthur - Leibniz 7 'Nominalist' | |
| A reaction: I've a lot of sympathy with this! I favour Presentism, so the past is gone and the future is yet to arrive. But we have no coherent concept of a present moment of any duration to contain reality. We are just completely bogglificated by it all. |
| 8010 | William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham] |
| Full Idea: The most notable philosopher who makes God's commandment the basis of goodness, rather than God's goodness a reason for obeying him, is William of Occam. | |
| From: William of Ockham (works [1335]), quoted by Alasdair MacIntyre - A Short History of Ethics Ch.9 | |
| A reaction: Either view has problems. Why choose God to obey? Obey anyone who is powerful? But how do you decide that God is good? How do we know the nature of God's commands, or the nature of God's goodness? Etc. |
| 20695 | God's eternal power and deity are clearly seen in what has been created [Paul] |
| Full Idea: From the creation of the world God's invisible nature, namely his eternal power and deity, are clearly perceived in the things that have been made. | |
| From: St Paul (06: Romans [c.55], 19-21), quoted by Brian Davies - Introduction to the Philosophy of Religion | |
| A reaction: St Paul says that for this reason the Gentiles are 'without excuse' for not believing (which means they are in trouble if Christians ever gain political power). Davies says it is unusual to find an argument for God's existence in the Bible. |
| 16679 | Even an angel must have some location [William of Ockham, by Pasnau] |
| Full Idea: Ockham dismisses the possibility of non-location out of hand, remarking that even an angel has some location. | |
| From: report of William of Ockham (works [1335]) by Robert Pasnau - Metaphysical Themes 1274-1671 14.4 |