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9. Objects / F. Identity among Objects / 8. Leibniz's Law

[identical objects must have identical features or truths]

18 ideas
Only if two things are identical do they have the same attributes [Aristotle]
     Full Idea: It is only to things which are indistinguishable and one in essence [ousia] that all the same attributes are generally held to belong.
     From: Aristotle (Sophistical Refutations [c.331 BCE], 179a37)
     A reaction: This simply IS Leibniz's Law (to which I shall from now on quietly refer to as 'Aristotle's Law'). It seems that it just as plausible to translate 'ousia' as 'being' rather than 'essence'. 'Indistinguishable' and 'one in ousia' are not the same.
Two things are different if something is true of one and not of the other [Duns Scotus]
     Full Idea: If this is, and that is not, then they are not the same entity in being.
     From: John Duns Scotus (Ordinatio [1302], IV.11.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 25.3
     A reaction: This is the contrapositive of the indiscernibility of identicals, expressed in terms of what is true about a thing, rather than what properties pertain to it.
Two bodies differ when (at some time) you can say something of one you can't say of the other [Hobbes]
     Full Idea: Two bodies are said to differ from one another, when something may be said of one of them, which cannot be said of the other at the same time.
     From: Thomas Hobbes (De Corpore (Elements, First Section) [1655], 2.11.02)
     A reaction: Note the astute addition of 'at the same time'. Note also that it is couched in terms of what is true, rather than in terms of 'properties' or 'accidents'.
Two substances can't be the same if they have different attributes [Spinoza]
     Full Idea: Two substances having different attributes have nothing in common with one another.
     From: Baruch de Spinoza (The Ethics [1675], I Pr 02)
     A reaction: This is the contrapositive of Leibniz's Law (i.e of the Indiscernibility of Identicals). Same things must have same attributes, so if the attributes differ they can't be the same things.
Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman]
     Full Idea: Geach rejects the standard formulation of Leibniz's Law as incomplete, since it includes a non-relativized identity predicate.
     From: report of Peter Geach (Reference and Generality (3rd ed) [1980]) by Ryan Wasserman - Material Constitution 6
     A reaction: Not many people accept Geach's premiss that identity is a relative matter. I agree with Wiggins on this, that identity is an absolute (and possibly indefinable). The problem with the Law is what you mean by a 'property'.
The indiscernibility of identicals is as self-evident as the law of contradiction [Kripke]
     Full Idea: It seems to me that the Leibnizian principle of the indiscernibility of identicals (not to be confused with the identity of indiscernibles) is as self-evident as the law of contradiction.
     From: Saul A. Kripke (Naming and Necessity preface [1980], p.03)
     A reaction: This seems obviously correct, as it says no more than that a thing has whatever properties it has. If a difference is discerned, either you have made a mistake, or it isn't identical.
Do both 'same f as' and '=' support Leibniz's Law? [Wiggins]
     Full Idea: Is Leibniz's Law as true for 'is the same as' as it is for '='?
     From: David Wiggins (Sameness and Substance Renewed [2001], 1.2)
     A reaction: [By Leibniz's Law he means if they are the same, they support the same truths]
Substitutivity, and hence most reasoning, needs Leibniz's Law [Wiggins]
     Full Idea: Leibniz's Law underwrites the substitutivity of identity and this is a principle not long dispensable in any form of reasoning.
     From: David Wiggins (Sameness and Substance Renewed [2001], 2.7)
     A reaction: Thus the modern fashion of deriving our metaphysics from our logic. Presumably we can derive it from our epistemology too, or even from our intuitions, if we thought they were good enough as evidence.
Two identical things must share properties - including creation and destruction times [Gibbard]
     Full Idea: For two things to be strictly identical, they must have all properties in common. That means, among other things, that they must start to exist at the same time and cease to exist at the same time.
     From: Allan Gibbard (Contingent Identity [1975], I)
     A reaction: I don't accept that coming into existence at time t is a 'property' of a thing. Coincident objects give you the notion of 'existing as' something, which complicates the whole story.
Leibniz's Law isn't just about substitutivity, because it must involve properties and relations [Gibbard]
     Full Idea: As a general law of substitutivity of identicals, Leibniz's Law is false. It is a law about properties and relations, that if two things are identical, they have the same properties and relations. It only works in contexts which attribute those.
     From: Allan Gibbard (Contingent Identity [1975], V)
     A reaction: I'm not convinced about relations, which are not intrinsic properties. Under different descriptions, the relations to human minds might differ.
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.
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 says 'x = y iff for all P, Px iff Py' [McGinn]
     Full Idea: Leibniz's Law says 'x = y iff for all P, Px iff Py'.
     From: Colin McGinn (Logical Properties [2000], Ch.1)
     A reaction: That is, two things are the same if when we say that one thing (x) has a property (P), then we are saying that the other thing (y) also has the property. A usefully concise statement of the Law.
Leibniz's Law presupposes the notion of property identity [McGinn]
     Full Idea: Leibniz's Law presupposes the notion of property identity.
     From: Colin McGinn (Logical Properties [2000], Ch.1)
     A reaction: A very important observation, because it leads to recognition of the way in which basic concepts and categories of thought interconnect. Which is more metaphysically basic, identity or properties? It is not easy to say…
Leibniz's Law is so fundamental that it almost defines the concept of identity [McGinn]
     Full Idea: Leibniz's Law, which a defender of relative identity might opt to reject, is so fundamental to the notion of identity that rejecting it amounts to changing the subject.
     From: Colin McGinn (Logical Properties [2000], Ch.1 n8)
     A reaction: The Law here is the 'indiscernibility of identicals'. I agree with McGinn, and anyone who loses their grip on this notion of identity strikes me as losing all grip on reality, and threatening their own sanity (well, call it their 'philosophical sanity').
Leibniz's Law is an essentialist truth [Oderberg]
     Full Idea: Leibniz's Law is an essentialist truth.
     From: David S. Oderberg (Real Essentialism [2007], 1.1)
     A reaction: That is, if two things must have identical properties because they are the same thing, this is because those properties are essential to the thing. Otherwise two things could be the same, even though one of them lacked a non-identifying property.
If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity [Sider]
     Full Idea: If someone is in pain at t1 and not at t2, we might restrict Leibniz's Law so as not to apply to 'timebound' properties, ..but this is deeply unsatisfying, ...and forfeits one's claim to be discussing identity. The demands of identity are high.
     From: Theodore Sider (Four Dimensionalism [2001], 5.5)
     A reaction: [on Myro 1986] Sider's response is unsatisfying. It means a thing loses its identity (with itself?) if it has even a tiny fluctuating in its properties. Quantum changes then destroy all notions of identity. English-speakers don't use 'identity' like that.
If two things might be identical, there can't be something true of one and false of the other [Hawley]
     Full Idea: We can call the 'transference principle' the claim that if it is indeterminate whether two objects are identical, then nothing determinately true of one can be determinately false of the other.
     From: Katherine Hawley (How Things Persist [2001], 4.9)
     A reaction: The point is that Leibniz's Law could immediately be invoked to show there is no possibility of their identity.