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| 12215 | The existence of numbers is not a matter of identities, but of constituents of the world |
| Full Idea: On saying that a particular number exists, we are not saying that there is something identical to it, but saying something about its status as a genuine constituent of the world. | |||
| From: Kit Fine (The Question of Ontology [2009], p.168) | |||
| A reaction: This is aimed at Frege's criterion of identity, which is to be an element in an identity relation, such as x = y. Fine suggests that this only gives a 'trivial' notion of existence, when he is interested in a 'thick' sense of 'exists'. |
| 12211 | It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' |
| Full Idea: It is not implausible that before the 'introduction' of complex numbers, it would have been incorrect for mathematicians to claim that there was a solution to the equation 'x^2 = -1' under a completely unrestricted understanding of 'there are'. | |||
| From: Kit Fine (The Question of Ontology [2009]) | |||
| A reaction: I have adopted this as the crucial test question for anyone's attitude to platonism in mathematics. I take it as obvious that complex numbers were simply invented so that such equations could be dealt with. They weren't 'discovered'! |
| 12209 | The indispensability argument shows that nature is non-numerical, not the denial of numbers |
| Full Idea: Arguments such as the dispensability argument are attempting to show something about the essentially non-numerical character of physical reality, rather than something about the nature or non-existence of the numbers themselves. | |||
| From: Kit Fine (The Question of Ontology [2009], p.160) | |||
| A reaction: This is aimed at Hartry Field. If Quine was right, and we only believe in numbers because of our science, and then Field shows our science doesn't need it, then Fine would be wrong. Quine must be wrong, as well as Field. |
| 12214 | 'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin' |
| Full Idea: The most natural reading of 'electrons exist' is that there are electrons while, on our view, the proper reading should be modeled on 'electrons spin', meaning every electron spins. 'Exists' should be treated as a predicate rather than a quantifier. | |||
| From: Kit Fine (The Question of Ontology [2009], p.167) | |||
| A reaction: So existence IS a predicate (message to Kant). Dunno. Electrons have to exist in order to spin, but they don't have to exist in order to exist. But they don't have to exist to be 'dead'. |
| 12212 | Just as we introduced complex numbers, so we introduced sums and temporal parts |
| Full Idea: Just as one can extend the domain of discourse to include solutions to the equation 'x^2=-1' so one can extend the domain of discourse to include objects that satisfy the condition 'x is the sum of the G's' or 'x is a temporal part of the object b at t'. | |||
| From: Kit Fine (The Question of Ontology [2009], p.164) | |||
| A reaction: This thought lies behind Fine's 'Proceduralism'. I take it that our collection of abstracta consists entirely of items we have either deliberately or unthinkingly 'introduced' into our discourse when they seemed useful. They then submit to certain laws. |
| 12216 | Real objects are those which figure in the facts that constitute reality |
| Full Idea: The real objects are the objects of reality, those that figure in the facts by which reality is constituted. | |||
| From: Kit Fine (The Question of Ontology [2009], p.172) | |||
| A reaction: And these need to be facts over and above the basic facts. Thus, does the 'equator' constitute reality, over and above the Earth being a rotating sphere? Does 'six' constitute reality, over and above all the possible groups of six objects? |
| 12218 | Being real and being fundamental are separate; Thales's water might be real and divisible |
| Full Idea: Being the case in reality and being fundamental are not sufficient for one another. If one agrees with Thales that the world is composed of water, and with Aristotle that water is indefinitely divisible, then water would be real but not fundamental. | |||
| From: Kit Fine (The Question of Ontology [2009], p.174) | |||
| A reaction: Presumably the divisibility would make a reductionist account of water possible. The Atlantic Ocean is real, but water molecules would have a more prominent place in the ontology of any good metaphysician. |
| 12217 | For ontology we need, not internal or external views, but a view from outside reality |
| Full Idea: We need to straddle both of Carnap's internal and external views. It is only by standing outside of reality that we are able to occupy a standpoint from which the constitution of reality can be adequately described. | |||
| From: Kit Fine (The Question of Ontology [2009], p.174) | |||
| A reaction: See Idea 4840! I thoroughly approve of this idea, which almost amounts to a Credo for the modern metaphysician. Since we can think outside our room, or our country, or our era, or our solar system, I think we can do what Fine is demanding. |
| 12213 | Ontological claims are often universal, and not a matter of existential quantification |
| Full Idea: I suggest we give up on the account of ontological claims in terms of existential quantification. The commitment to the integers is not an existential but a universal commitment, to each of the integers, not to some integer or other. | |||
| From: Kit Fine (The Question of Ontology [2009], p.167) | |||
| A reaction: In classical logic it is only the existential quantifier which requires the domain to be populated, so Fine is more or less giving up on classical logic as a tool for doing ontology (apparently?). |