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14212
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A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those [Lewis]
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Full Idea:
A consistent theory is, by definition, one satisfied by some model; an isomorphic image of a model satisfies the same theories as the original model; to provide the making of an isomorphic image of any given model, a domain need only be large enough.
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From:
David Lewis (Putnam's Paradox [1984], 'Why Model')
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A reaction:
This is laying out the ground for Putnam's model theory argument in favour of anti-realism. If you are chasing the one true model of reality, then formal model theory doesn't seem to offer much encouragement.
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8748
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Logical positivists incorporated geometry into logicism, saying axioms are just definitions [Carnap, by Shapiro]
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Full Idea:
The logical positivists brought geometry into the fold of logicism. The axioms of, say, Euclidean geometry are simply definitions of primitive terms like 'point' and 'line'.
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From:
report of Rudolph Carnap (Empiricism, Semantics and Ontology [1950]) by Stewart Shapiro - Thinking About Mathematics 5.3
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A reaction:
If the concept of 'line' is actually created by its definition, then we need to know exactly what (say) 'shortest' means. If we are merely describing a line, then our definition can be 'impredicative', using other accepted concepts.
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13933
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Existence questions are 'internal' (within a framework) or 'external' (concerning the whole framework) [Carnap]
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Full Idea:
We distinguish two kinds of existence questions: first, entities of a new kind within the framework; we call them 'internal questions'. Second, 'external questions', concerning the existence or reality of the system of entities as a whole.
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From:
Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 2)
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A reaction:
This nicely disposes of many ontological difficulties, but at the price of labelling most external questions as meaningless, so that the internal answers have very little commitment, and the external (big) questions are now banned. Not for me.
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14213
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Anti-realists see the world as imaginary, or lacking joints, or beyond reference, or beyond truth [Lewis]
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Full Idea:
Anti-realists say the only world is imaginary, or only has the parts or classes or relations we divide it into, or doubt that reference to the world is possible, or doubt that our interpretations can achieve truth.
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From:
David Lewis (Putnam's Paradox [1984], 'Why Anti-R')
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A reaction:
[compression of a paragraph on anti-realism] Lewis is a thoroughgoing realist. A nice example of the rhetorical device of ridiculing an opponent by suggesting that they don't even know what they themselves believe.
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13935
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We only accept 'things' within a language with formation, testing and acceptance rules [Carnap]
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Full Idea:
To accept the thing world means nothing more than to accept a certain form of language, in other words, to accept rules for forming statements and for testing, accepting, or rejecting them.
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From:
Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 2)
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A reaction:
If you derive your metaphysics from your language, then objects are linguistic conventions. But why do we accept conventions about objects?
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14210
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A gerrymandered mereological sum can be a mess, but still have natural joints [Lewis]
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Full Idea:
The mereological sum of the coffee in my cup, the ink in this sentence, a nearby sparrow, and my left shoe is a miscellaneous mess of an object, yet its boundaries are by no means unrelated to the joints of nature.
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From:
David Lewis (Putnam's Paradox [1984], 'What Might')
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A reaction:
In that case they do, but if there are no atoms at the root of physics then presumably their could also be thoroughly jointless assemblages, involving probability distributions etc. Even random scattered atoms seem rather short of joints.
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13932
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Empiricists tend to reject abstract entities, and to feel sympathy with nominalism [Carnap]
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Full Idea:
Empiricists are in general rather suspicious with respect to any kind of abstract entities like properties, classes, relations, numbers, propositions etc. They usually feel more sympathy with nominalists than with realists (in the medieval sense).
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From:
Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 1)
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A reaction:
The obvious reason is that you can't have sense experiences of abstract entities. I like the question 'what are they made of?' rather than the question 'how can I experience them?'.
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13937
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New linguistic claims about entities are not true or false, but just expedient, fruitful or successful [Carnap]
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Full Idea:
The acceptance of new linguistic forms about entities cannot be judged as being either true or false because it is not an assertion. It can only be judged as being more or less expedient, fruitful, conducive to the aim for which the language is intended.
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From:
Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 3)
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A reaction:
The obvious problem seems to be that a complete pack of lies might be successful for a very long time, if it plugged a critical hole in a major theory. Is success judged financially? How do we judge success without mentioning truth?
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14209
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Descriptive theories remain part of the theory of reference (with seven mild modifications) [Lewis]
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Full Idea:
Description theories of reference are supposed to have been well and truly refuted. I think not: ..it is still tenable with my seven points, and part of the truth of reference [7: rigidity, egocentric, tokens, causal, imperfect, indeterminate, families].
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From:
David Lewis (Putnam's Paradox [1984], 'Glob Desc')
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A reaction:
(The bit at the end refers to his seven points, on p.59). He calls his basic proposal 'causal descriptivism', incorporating his seven slight modifications of traditional descriptivism about reference.
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