9 ideas
17606 | Axioms reveal the underlying assumptions, and reveal relationships between different areas [Kline] |
Full Idea: The axiomatic method ....revealed precisely what assumptions underlie each branch [of mathematics] and made possible the comparison and clarification of the relationships of various branches. | |
From: Morris Kline (Mathematical Thought from Ancient to Modern Times [1972], p.1027), quoted by Penelope Maddy - Defending the Axioms 1.3 | |
A reaction: I take this to be the 'fruitfulness' which marks out the discovery of the essence of something. |
19347 | Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins] |
Full Idea: For individuation, substance needs three properties: independence, to separate it from other things; unity, to call it one thing, rather than an aggregate; and permanence or stability over time. Its other role is as subject for predicates. | |
From: Franklin Perkins (Leibniz: Guide for the Perplexed [2007], 3.1) | |
A reaction: Perkins is describing the Aristotelian view, which is taken up by Leibniz. 'Substance' is not a controversial idea, if we see that it only means that the world is full of 'things'. It is an unusual philosopher wholly totally denies that. |
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. |