Combining Texts

Ideas for 'Defending the Axioms', 'In Defense of Absolute Essentialism' and 'Identity'

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14 ideas

9. Objects / D. Essence of Objects / 6. Essence as Unifier
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.
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?
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
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?
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
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.
9. Objects / D. Essence of Objects / 9. Essence and Properties
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.
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
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.
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
I could have died at five, but the summation of my adult stages could not [Noonan]
     Full Idea: Persons have different modal properties from the summations of person-stages. …I might have died when I was five. But the maximal summation of person-stages which perdurantists say is me could not have had a temporal extent of a mere five years.
     From: Harold Noonan (Identity [2009], §5)
     A reaction: Thus the summation of stages seems to fail Leibniz's Law, since truths about a part are not true of the whole. But my foot might be amputated without me being amputated. The objection is the fallacy of composition?
9. Objects / E. Objects over Time / 5. Temporal Parts
Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan]
     Full Idea: Stage theorists, accepting the ontology of perdurance, modify the semantics to secure the result that fatness is a property of a cat. Every temporal part of a cat (such as Tabby-on-Monday) is a cat. …(but they pay a price over the counting of cats).
     From: Harold Noonan (Identity [2009], §5)
     A reaction: [Noonan cites Hawley and Sider for this view. The final parenthesis compresses Noonan] I would take the difficulty over counting cats to be fatal to the view. It produces too many cats, or too few, or denies counting altogether.
9. Objects / F. Identity among Objects / 2. Defining Identity
Problems about identity can't even be formulated without the concept of identity [Noonan]
     Full Idea: If identity is problematic, it is difficult to see how the problem could be resolved, since it is difficult to see how a thinker could have the conceptual resources with which to explain the concept of identity whilst lacking that concept itself.
     From: Harold Noonan (Identity [2009], §1)
     A reaction: I don't think I accept this. We can comprehend the idea of a mind that didn't think in terms of identities (at least for objects). I suppose any relation of a mind to the world has to distinguish things in some way. Does the Parmenidean One have identity?
Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan]
     Full Idea: Numerical identity is usually defined as the equivalence relation (or: the reflexive relation) satisfying Leibniz's Law, the indiscernibility of identicals, where everything true of x is true of y.
     From: Harold Noonan (Identity [2009], §2)
     A reaction: Noonan says this must include 'is identical to x' among the truths, and so is circular
Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan]
     Full Idea: Identity can be circularly defined, as 'the relation everything has to itself and to nothing else', …or as 'the smallest equivalence relation'.
     From: Harold Noonan (Identity [2009], §2)
     A reaction: The first one is circular because 'nothing else' implies identity. The second is circular because it has to quantify over all equivalence relations. (So says Noonan).
Identity can only be characterised in a second-order language [Noonan]
     Full Idea: There is no condition in a first-order language for a predicate to express identity, rather than indiscernibility within the resources of the language. Leibniz's Law is statable in a second-order language, so identity can be uniquely characterised.
     From: Harold Noonan (Identity [2009], §2)
     A reaction: The point is that first-order languages only refer to all objects, but you need to refer to all properties to include Leibniz's Law. Quine's 'Identity, Ostension and Hypostasis' is the source of this idea.
9. Objects / F. Identity among Objects / 8. Leibniz's Law
Indiscernibility is basic to our understanding of identity and distinctness [Noonan]
     Full Idea: Leibniz's Law (the indiscernibility of identicals) appears to be crucial to our understanding of identity, and, more particularly, to our understanding of distinctness.
     From: Harold Noonan (Identity [2009], §2)
     A reaction: True, but indiscernibility concerns the epistemology, and identity concerns the ontology.
Leibniz's Law must be kept separate from the substitutivity principle [Noonan]
     Full Idea: Leibniz's Law must be clearly distinguished from the substitutivity principle, that if 'a' and 'b' are codesignators they are substitutable salva veritate.
     From: Harold Noonan (Identity [2009], §2)
     A reaction: He gives a bunch of well-known problem cases for substitutivity. The Morning Star, Giorgione, and the number of planets won't work. Belief contexts, or facts about spelling, may not be substitutable.