11103
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We aren't stuck with our native conceptual scheme; we can gradually change it [Quine]
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Full Idea:
We must not leap to the fatalistic conclusion that we are stuck with the conceptual scheme that we grew up in. We can change it bit by bit, plank by plank.
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From:
Willard Quine (Identity, Ostension, and Hypostasis [1950], 5)
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A reaction:
This is an interesting commitment to Strawson's 'revisionary' metaphysics, rather than its duller cousin 'descriptive' metaphysics. Good for Quine. Remember, though, Davidson's 'On the Very Idea of Conceptual Scheme'.
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10529
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If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
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Full Idea:
Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)
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A reaction:
This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers.
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10530
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Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
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Full Idea:
The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312)
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A reaction:
I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition.
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11092
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A river is a process, with stages; if we consider it as one thing, we are considering a process [Quine]
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Full Idea:
A river is a process through time, and the river stages are its momentary parts. Identification of the river bathed in once with the river bathed in again is just what determines our subject matter to be a river process as opposed to a river stage.
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From:
Willard Quine (Identity, Ostension, and Hypostasis [1950], 1)
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A reaction:
So if we take a thing which has stages, but instead of talking about the stages we talk about a single thing that endures through them, then we are talking about a process. Sounds very good to me.
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11093
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We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape [Quine]
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Full Idea:
'Red' is surely not going to be opposed to 'Cayster' [name of a river], as abstract to concrete, merely because of discontinuity in geometrical shape?
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From:
Willard Quine (Identity, Ostension, and Hypostasis [1950], 2)
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A reaction:
I've been slow to grasp the truth of this. However, Quine assumes that 'red' is concrete because 'Cayster' is, but it is perfectly arguable that 'Cayster' is an abstraction, despite all that water.
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11101
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General terms don't commit us ontologically, but singular terms with substitution do [Quine]
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Full Idea:
The use of general terms does not commit us to admitting a corresponding abstract entity into our ontology, but an abstract singular term, including the law of putting equals for equals, flatly commits us to an abstract entity named by the term.
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From:
Willard Quine (Identity, Ostension, and Hypostasis [1950], 4)
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A reaction:
Does this mean that in 'for the sake of the children', I have to believe in 'sakes' if I can find a synonym which will substitute for it?
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17595
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To unite a sequence of ostensions to make one object, a prior concept of identity is needed [Quine]
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Full Idea:
The concept of identity is central in specifying spatio-temporally broad objects by ostension. Without identity, n acts of ostension merely specify up to n objects. ..But when we affirm identity of object between ostensions, they refer to the same object.
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From:
Willard Quine (Identity, Ostension, and Hypostasis [1950], 1)
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A reaction:
Quine says that there is an induction involved. On the whole, Quine seems to give a better account of identity than Geach or Wiggins can offer.
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10527
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An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
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Full Idea:
If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307)
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A reaction:
I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects.
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