15 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. |
| 13804 | A property is essential iff the object would not exist if it lacked that property [Forbes,G] |
| Full Idea: A property P is an essential property of an object x iff x could not exist and lack P, that is, as they say, iff x has P at every world at which x exists. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 1) | |
| A reaction: This immediately places the existence of x outside the normal range of its properties, so presumably 'existence is not a predicate', but that dictum may be doubted. As it stands this definition will include trivial and vacuous properties. |
| 13805 | Properties are trivially essential if they are not grounded in a thing's specific nature [Forbes,G] |
| Full Idea: Essential properties may be trivial or nontrivial. It is characteristic of P's being trivially essential to x that x's possession of P is not grounded in the specific nature of x. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 2) | |
| A reaction: This is where my objection to the modal view of essence arises. How is he going to explain 'grounded' and 'specific nature' without supplying an entirely different account of essence? |
| 13808 | A relation is essential to two items if it holds in every world where they exist [Forbes,G] |
| Full Idea: A relation R is essential to x and y (in that order) iff Rxy holds at every world where x and y both exist. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 2) | |
| A reaction: I find this bizarre. Not only does this seem to me to have nothing whatever to do with essence, but also the relation might hold even though it is a purely contingent matter. All rabbits are a reasonable distance from the local star. Essence of rabbit? |
| 13806 | Trivially essential properties are existence, self-identity, and de dicto necessities [Forbes,G] |
| Full Idea: The main groups of trivially essential properties are (a) existence, self-identity, or their consequences in S5; and (b) properties possessed in virtue of some de dicto necessary truth. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 2) | |
| A reaction: He adds 'extraneously essential' properties, which also strike me as being trivial, involving relations. 'Is such that 2+2=4' or 'is such that something exists' might be necessary, but they don't, I would say, have anything to do with essence. |
| 13807 | A property is 'extraneously essential' if it is had only because of the properties of other objects [Forbes,G] |
| Full Idea: P is 'extraneously essential' to x iff it is possessed by x at any world w only in virtue of the possession at w of certain properties by other objects. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 2) | |
| A reaction: I would say that these are the sorts of properties which have nothing to do with being essential, even if they are deemed to be necessary. |
| 13809 | One might be essentialist about the original bronze from which a statue was made [Forbes,G] |
| Full Idea: In the case of artefacts, there is an essentialism about original matter; for instance, it would be said of any particular bronze statue that it could not have been cast from a totally different quantity of bronze. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 3) | |
| A reaction: Forbes isn't endorsing this, and it doesn't sound convincing. He quotes the thought 'I wish I had made this pot from a different piece of clay'. We might corrupt a statue by switching bronze, but I don't think the sculptor could do so. |
| 13810 | The source of de dicto necessity is not concepts, but the actual properties of the thing [Forbes,G] |
| Full Idea: It is widely held that the source of de dicto necessity is in concepts, ..but I deny this... even with simple de dicto necessities, the source of the necessity is to be found in the properties to which the predicates of the de dicto truth refer. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 3) | |
| A reaction: It is normal nowadays to say this about de re necessities, but this is more unusual. |
| 22868 | The value and truth of knowledge are measured by success in activity [Dewey] |
| Full Idea: What measures knowledge's value, its correctness and truth, is the degree of its availability for conducting to a successful issue the activities of living beings. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 4:180), quoted by David Hildebrand - Dewey 2 'Critique' | |
| A reaction: Note that this is the measure of truth, not the nature of truth (which James seemed to believe). Dewey gives us a clear and perfect statement of the pragmatic view of knowledge. I don't agree with it. |
| 22865 | Habits constitute the self [Dewey] |
| Full Idea: All habits are demands for certain kinds of activity; and they constitute the self. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 14:22), quoted by David Hildebrand - Dewey 1 'Acts' | |
| A reaction: Not an idea I have encountered elsewhere. He emphasises that habits are not repeated actions, but are dispositions. I'm not clear whether these habits must be conscious. |
| 22871 | The good people are those who improve; the bad are those who deteriorate [Dewey] |
| Full Idea: The bad man is the man who no matter how good he has been is beginning to deteriorate, to grow less good. The good man is the man who no matter how morally unworthy he has been is moving to become better. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 12:181), quoted by David Hildebrand - Dewey 3 'Reconstruct' | |
| A reaction: Although a slightly improving rat doesn't sound as good as a slightly deteriorating saint, I have some sympathy with this thought. The desire to improve seems to be right at the heart of what makes good character. |
| 22876 | Democracy is the development of human nature when it shares in the running of communal activities [Dewey] |
| Full Idea: Democracy is but a name for the fact that human nature is developed only when its elements take part in directing things which are common, things for the sake of which men and women form groups. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 12:199), quoted by David Hildebrand - Dewey 4 'Democracy' | |
| A reaction: It is hard to prove that human nature develops when it particpates in groups. If people are excluded from power, their loyalty tends to switch to sub-groups, such as friends in a pub, or a football team. Powerless nationalists baffle me. |
| 22875 | Democracy is not just a form of government; it is a mode of shared living [Dewey] |
| Full Idea: A democracy is more than a form of government; it is primarily a mode of associated living, of conjoint communicated experience | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 9:93), quoted by David Hildebrand - Dewey 4 'Democracy' | |
| A reaction: This precisely pinpoints the heart of the culture wars in 2021. A huge swathe of western populations believe in Dewey's idea, but a core of wealthy right-wingers and their servants only see democracy as the mechanism for obtaining power. |
| 22874 | Individuality is only developed within groups [Dewey] |
| Full Idea: Only in social groups does a person have a chance to develop individuality. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 15:176), quoted by David Hildebrand - Dewey 4 'Individuals' | |
| A reaction: This is a criticism of both Rawls and Nozick. Rawls's initial choosers don't consult, or have much social background. Nozick's property owners ignore everything except contracts. |