Molnar&#039;s metaphysics of properties

Auxiliary Definitions
1. ontological dependence
  1. (1) if A ontologically depends on B, then it is impossible for A to exist without B existing (29)
  2. (2) A ontologically depends on B iff it is impossible for A to exist without B existing, and the impossibility is due to the nature (essence) of A. (29)
2. Molnar's view of objects
  1. Simple
    1. An object is simple iff it has no (spatially extended) parts (33).
  2. Complex
    1. An object is complex iff it has (spatially extended) parts (33).
3. foundationism
  1. the doctrine that all relations are founded in non-relational, intrinsic properties of objects, and that therefore we do not have to include Relation among the irreducibly different categories to which all existents belong (51)
Sample Object: Yasmine the oval
1. 1st-order, fully determinate property #1: being of fully determinate shape so-n-so (31-33)
  1. 2nd-order property, a determinable: having some shape or other
    1. 3rd-order property, a determinable: being oval
      1. 4th-order property, a determinable: being a regular shape
      2. ...
2. 1st-order, fully determinate property #2: being of fully determinate size such-n-such
  1. 2nd-order property, a determinable: having some positive size
3. 1st-order, fully determinate relation: being at such-n-such a point in space
  1. an irreducible, non-power property
  2. the relation does not satisfy Directedness, Independence, nor Intrinsicality (161-2)
Sample Object: Ellie the electron
1. 1st-order, fully determinate, basic property #1: having unit electric charge (143)
2. 1st-order, fully determinate, basic property #1: having spin 1/2 (143)
3. 1st-order, fully determinate, derived property: being an electron
Sample Complex Object
1. Complex Part A
  1. Simple Part A1
    1. 1st-order, fully determinate, basic (=ultimate) property
      1. 2nd-order determinable property
      2. Higher-order properties are neither basic nor derived
      3. Because it's a basic property of a simple object, it's also an ultimate property
    2. 1st-order, fully determinate, derived property
      1. Because it's a simple part, the derived property must be derived from the basic (ultimate) property above
    3. ...
  2. Complex Part A2
    1. ...
    2. 1st-order, fully determinate, derived property
      1. Because it's a simple part, the derived property must be derived from the basic (ultimate) property above
    3. ...
  3. ...
2. Complex Part B
  1. ...
  2. 1st-order, fully determinate, basic (=emergent) property
  3. ...
3. ...
4. 1st-order, fully determinate, basic (=emergent) property
5. 1st-order, fully determinate, derived property
6. 1st-order, fully determinate derived property
7. ...
May 31, 2013
Distinctions & classifications
1. Derivative/basic
  1. Basic
    1. Properties which are ontologically independent of any other properties, either of the whole or properties of the object's parts
      1. DEF: F is a basic property of a iff a has the property F and a's having F does not ontologically depend on any properties of any parts of a, and a's having F does not ontologically depend on any other properties of a (29).
  2. Derivative
    1. Properties which are ontologically dependent either on properties of an object's parts or on other properties of the whole object
      1. DEF: F is a derivative property of a iff a has the property F and a's having F ontologically depends on some properties of some parts of a, or a's having F ontologically depends on some other properties of a (29).
      2. DEF: A power is derivative if the presence of this power in the object depends on the powers that its constituents have and the special relations in which the constituents stand to each other (144).
  3. Note: This distinction only applies to first-order properties (32)
2. First-/second- order
  1. First-order
    1. Properties of objects
    2. All first-order properties are fully determinate (32)
  2. Second-order
    1. Properties of properties
3. Basic/iterated powers
  1. Basic power
    1. The power of an object to bring about some manifestation (32)
    2. Example: being magnetized
  2. Iterated power
    1. The power to gain/lose some further power (32)
    2. Example: being magnetizable
  3. Note: All powers, basic and iterated, are first-order properties (i.e. properties of objects) (33)
4. Determinate/determinable
  1. Determinate
    1. Are genuine, sparse properties
  2. Determinable
    1. Are genuine, sparse properties
    2. Determinable properties are always higher-order (31)
5. Simple/complex
  1. Simple
  2. Complex (1): conjunctive
    1. Armstrong: If a has the property, P, and also the distinct property, Q, then, I maintain, it has the conjunctive property P&Q.
    2. Molnar rejects conjunctive universals on the grounds that, because 'they are nothing over and above their conjuncts', there is in fact no reason to posit them.
  3. Complex (2): structural
    1. Properties had by a whole in virtue of a set of (non-identical) properties being possessed by the whole's parts (36)
      1. DEF: A property, S, is structural if and only if proper parts of particulars having S have some property or properties, T, … not identical with S, and this state of affairs is, in part at least, constitutive of S. It will be seen that a structural property must be complex.
    2. The examples usually given of structural properties can be understood as derivative (mereologically simple) properties (36). Structural properties in the sense of properties which have parts are rejected (147).
6. Essential/necessary
  1. Accidental
  2. Necessary
    1. DEF: F is a necessary property of a iff a has F in all possible worlds that include a (39).
  3. Essential
    1. DEF: F is an essential property of a iff being F is constitutive of the identity of a (39).
7. Intrinsic/extrinsic
  1. Intrinsic
    1. Properties the (non) having of which in no way depends on distinct objects
      1. DEF: F is an intrinsic property of a iff a's having the property F is ontologically independent of the existence, and of the non-existence, of any contingent b such that a is wholly distinct from b; and a's not having the property F is ontologically independent of the existence, and of the nonexistence, of any contingent b such that a is wholly distinct from b (39-40).
  2. Extrinsic
    1. A non-intrinsic property
      1. DEF: F is an extrinsic property of a iff F is a property of a and F is not an intrinsic property of a.
  3. Note 1: Molnar's definition of intrinsic, unlike the Lewis/Langton definition, ranges over both impure and haecceistic properties (40).
  4. Note 2: Molnar's definition, unlike the Lewis/Langton definition, does not range over disjunctive properties because there are excluded from the domain of sparse properties (41).
8. Relation/non-relation
  1. Relation
    1. DEF: R is a relation iff R is an n-adic property and n >= 2 (42).
  2. Relational property
    1. DEF: FR is a relational property of a iff FR is a property of a and it is essetial to a's having FR that there exists some x and some y and some relation φ such that φ(x,y).
  3. Non-relation
  4. Note 1: Predicates exist which exhibit any combination of the intrinsic/extrinsic & relational/non-relational distinction.
  5. Note 2: All extrinsic properties are relation.
9. (Non-)Transferability
  1. Whether a trope can(not) be transfered to a distinct object
  2. Non-transferability
    1. DEF: F1 is a non-transferable property of a iff if a has F1, then if any thing, x, has the very trope F1 that a has, then x = a.
10. Homogenous properties
  1. properties of complex objects which are properties of the object's constituents (143)
11. Collective properties
  1. properties of complex objects as a whole; not possessed by any of the complex object's constituents (143)
  2. derivative
    1. ultimately derived from properties of the object's constituents (143)
  3. basic
    1. such properties would be emergent properties (143)
Fundamental categories
1. Objects
  1. the primary bearers of spatiotemporal location (160)
2. Properties (tropes)
  1. particular, non-abstract, non-repeatable properties
  2. bear spatiotemporal location derivatively (160)
3. Relations