20 ideas
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong. | |
| From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1 |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory. | |
| From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2 | |
| A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this. |
| 16665 | There are entities, and then positive 'modes', modifying aspects outside the thing's essence [Suárez] |
| Full Idea: Beyond the entities there are certain real 'modes', which are positive, and in their own right act on those entities, giving them something that is outside their whole essence as individuals existing in reality. | |
| From: Francisco Suárez (Disputationes metaphysicae [1597], 7.1.17), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.3 | |
| A reaction: Suárez is apparently the first person to formulate a proper account of properties as 'modes' of a thing, rather than as accidents which are separate, or are wholly integrated into a thing. A typical compromise proposal in philosophy. Can modes act? |
| 16666 | A mode determines the state and character of a quantity, without adding to it [Suárez] |
| Full Idea: The inherence of quantity is called its mode, because it affects that quantity, which serves to ultimately determine the state and character of its existence, but does not add to it any new proper entity, but only modifies the preexisting entity. | |
| From: Francisco Suárez (Disputationes metaphysicae [1597], 7.1.17), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.3 | |
| A reaction: He seems to present mode as a very active thing, like someone who gives it a coat of paint, or hammers it into a new shape. I don't see how a 'mode' can have any ontological status at all. To exist, there has to be some way to exist. |
| 16667 | Substances are incomplete unless they have modes [Suárez, by Pasnau] |
| Full Idea: In the view of Suárez, substances are radically incomplete entities that cannot exist at all until determined in various ways by things of another kind, modes. …Modes are regarded as completers for their subjects. | |
| From: report of Francisco Suárez (Disputationes metaphysicae [1597]) by Robert Pasnau - Metaphysical Themes 1274-1671 13.3 | |
| A reaction: This is correct. In order to be a piece of clay it needs a shape, a mass, a colour etc. Treating clay as an object independently from its shape is a misunderstanding. |
| 17007 | Forms must rule over faculties and accidents, and are the source of action and unity [Suárez] |
| Full Idea: A form is required that, as it were, rules over all those faculties and accidents, and is the source of all actions and natural motions of such a being, and in which the whole variety of accidents and powers has its root and unity. | |
| From: Francisco Suárez (Disputationes metaphysicae [1597], 15.1.7), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.4 | |
| A reaction: Pasnau emphasises that this is scholastics giving a very physical and causal emphasis to forms, which made them vulnerable to doubts among the new experiment physicists. Pasnau says forms are 'metaphysical', following Leibniz. |
| 16780 | Partial forms of leaf and fruit are united in the whole form of the tree [Suárez] |
| Full Idea: In a tree the part of the form that is in the leaf is not the same character as the part that is in the fruit., but yet they are partial forms, and apt to be united ….to compose one complete form of the whole. | |
| From: Francisco Suárez (Disputationes metaphysicae [1597], 15.10.30), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 26.6 | |
| A reaction: This is a common scholastic view, the main opponent of which was Aquinas, who says each thing only has one form. Do leaves have different DNA from the bark or the fruit? Presumably not (since I only have one DNA), which supports Aquinas. |
| 16758 | The best support for substantial forms is the co-ordinated unity of a natural being [Suárez] |
| Full Idea: The most powerful arguments establishing substantial forms are based on the necessity, for the perfect constitution of a natural being, that all the faculties and operations of that being are rooted in one essential principle. | |
| From: Francisco Suárez (Disputationes metaphysicae [1597], 15.10.64), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.4 | |
| A reaction: Note Idea 15756, that this stability not only applies to biological entities (the usual Aristotelian examples), but also to non-living natural kinds. We might say that the drive for survival is someone united around a single entity. |
| 16743 | We can get at the essential nature of 'quantity' by knowing bulk and extension [Suárez] |
| Full Idea: We can say that the form that gives corporeal bulk [molem] or extension to things is the essential nature of quantity. To have bulk is to expel a similar bulk from the same space. | |
| From: Francisco Suárez (Disputationes metaphysicae [1597], 40.4.16), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 539 | |
| A reaction: This is one step away from asking why, once we knew the bulk and extension of the thing, we would still have any interest in trying to grasp something called its 'quantity'. |
| 16742 | We only know essences through non-essential features, esp. those closest to the essence [Suárez] |
| Full Idea: We can almost never set out the essences of things, as they are in things. Instead, we work through their connection to some non-essential feature, and we seem to succeed well enough when we spell it out through the feature closest to the essence. | |
| From: Francisco Suárez (Disputationes metaphysicae [1597], 40.4.16), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 23.5 | |
| A reaction: It is a common view that with geometrical figures we can actually experience the essence itself. So has science broken through, and discerned actual essences of things? |
| 22143 | Identity does not exclude possible or imagined difference [Suárez, by Boulter] |
| Full Idea: To be really the same excludes being really other, but does not exclude being other modally or mentally. | |
| From: report of Francisco Suárez (Disputationes metaphysicae [1597], 7.65) by Stephen Boulter - Why Medieval Philosophy Matters 4 | |
| A reaction: So the statue and the clay are identical, but they could become separate, or be imagined as separate. |
| 22144 | Real Essential distinction: A and B are of different natural kinds [Suárez, by Boulter] |
| Full Idea: The Real Essential distinction says if A and B are not of the same natural kind, then they are essentially distinct. This is the highest degree of distinction. | |
| From: report of Francisco Suárez (Disputationes metaphysicae [1597], Bk VII) by Stephen Boulter - Why Medieval Philosophy Matters 4 | |
| A reaction: Boulter says Peter is essentially distinct from a cabbage, because neither has the nature of the other. |
| 22146 | Minor Real distinction: B needs A, but A doesn't need B [Suárez, by Boulter] |
| Full Idea: The Minor Real distinction is if A can exist without B, but B ceases to exist without A. | |
| From: report of Francisco Suárez (Disputationes metaphysicae [1597], Bk VII) by Stephen Boulter - Why Medieval Philosophy Matters 4 | |
| A reaction: This is one-way independence. Boulter's example is Peter and Peter's actual weight. |
| 22145 | Major Real distinction: A and B have independent existences [Suárez, by Boulter] |
| Full Idea: The Major Real distinction is if A can exist in the real order without B, and B can exist in the real order without A. | |
| From: report of Francisco Suárez (Disputationes metaphysicae [1597], Bk VII) by Stephen Boulter - Why Medieval Philosophy Matters 4 | |
| A reaction: Boulter's example is the distinction between Peter and Paul, where their identity of kind is irrelevant. This is two-way independence. |
| 22147 | Conceptual/Mental distinction: one thing can be conceived of in two different ways [Suárez, by Boulter] |
| Full Idea: The Conceptual or Mental distinction is when A and B are actually identical but we have two different ways of conceiving them. | |
| From: report of Francisco Suárez (Disputationes metaphysicae [1597], Bk VII) by Stephen Boulter - Why Medieval Philosophy Matters 4 | |
| A reaction: This is the Morning and Evening Star. I bet Frege never read Suarez. This seems to be Spinoza's concept of mind/body. |
| 22148 | Modal distinction: A isn't B or its property, but still needs B [Suárez, by Boulter] |
| Full Idea: The Modal distinction is when A is not B or a property of B, but still could not possibly exist without B. | |
| From: report of Francisco Suárez (Disputationes metaphysicae [1597], Bk VII) by Stephen Boulter - Why Medieval Philosophy Matters 4 | |
| A reaction: Duns Scotus proposed in, Ockham rejected it, but Suarez supports it. Suarez proposes that light's dependence on the Sun is distinct from the light itself, in this 'modal' way. |
| 22149 | Scholastics assess possibility by what has actually happened in reality [Suárez, by Boulter] |
| Full Idea: The scholastic view is that Actuality is our only guide to possibility in the real order. One knows that it is possible to separate A and B if one knows that A and B have actually been separated or are separate. | |
| From: report of Francisco Suárez (Disputationes metaphysicae [1597], Bk VII) by Stephen Boulter - Why Medieval Philosophy Matters 4 | |
| A reaction: It may be possible to separate A and B even though it has never happened, but it is hard to see how we could know that. (But if I put my pen down where it has never been before, I know I can pick it up again, even though this has not previously happened). |
| 16682 | Other things could occupy the same location as an angel [Suárez] |
| Full Idea: An angelic substance could be penetrated by other bodies in the same location. | |
| From: Francisco Suárez (Disputationes metaphysicae [1597], 40.2.21), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 15.3 | |
| A reaction: So am I co-located with an angel right now? |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |