13 ideas
| 16014 | It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan] |
| Full Idea: 'Numerical identity' implies the controversial view that it is the only identity relation in accordance with which we can properly count (or number) things: x and y are to be properly counted as one just in case they are numerically identical. | |
| From: Harold Noonan (Identity [2009], §1) | |
| A reaction: Noonan cites Geach, presumably to remind us of relative identity, where two things may be one or two, depending on what they are relative to. The one 'guard on the gate' may actually be two men. |
| 16024 | 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? |
| 16023 | 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. |
| 16015 | 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? |
| 16017 | 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 |
| 16016 | 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). |
| 16020 | 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. |
| 16018 | 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. |
| 16019 | 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. |
| 9216 | Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K] |
| Full Idea: The three sources of necessity - the identity of things, the natural order, and the normative order - have their own peculiar forms of necessity. The three main areas of human enquiry - metaphysics, science and ethics - each has its own necessity. | |
| From: Kit Fine (The Varieties of Necessity [2002], 6) | |
| A reaction: I would treat necessity in ethics with caution, if it is not reducible to natural or metaphysical necessity. Fine's proposal is interesting, but I did not find it convincing, especially in its view that metaphysical necessity doesn't intrude into nature. |
| 19699 | A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington] |
| Full Idea: A Gettier case contains a belief which is true and well justified without being knowledge. Its justificatory support is also fallible, ...and there is considerable luck in how the belief combnes being true with being justified. | |
| From: Stephen Hetherington (The Gettier Problem [2011], 5) | |
| A reaction: This makes luck the key factor. 'Luck' is a rather vague concept, and so the sort of luck involved must first be spelled out. Or the varieties of luck that can produce this outcome. |
| 9214 | Unsupported testimony may still be believable [Fine,K] |
| Full Idea: I may have good reason to believe some testimony, for example, even though the person providing the testimony has no good reason for saying what he does. | |
| From: Kit Fine (The Varieties of Necessity [2002], 5) | |
| A reaction: Thus small children, madmen and dreamers may occasionally get things right without realising it. I take testimony to be merely one more batch of evidence which has to be assessed in building the most coherent picture possible. |
| 9215 | Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K] |
| Full Idea: It would be harder to break P-and-Q implying P than the connection between cause and effect. This difference in strictness means it is more plausible that natural necessities include metaphysical necessities, than vice versa. | |
| From: Kit Fine (The Varieties of Necessity [2002], 6) | |
| A reaction: I cannot see any a priori grounds for the claim that causation is more easily disrupted than logic. It seems to be based on the strategy of inferring possibilities from what can be imagined, which seems to me to lead to wild misunderstandings. |