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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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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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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7669
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We cannot attain all the ideals of every culture, so there cannot be a perfect life [Herder, by Berlin]
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Full Idea:
For Herder, we cannot attain to the highest ideals of all the centuries and all the places at once, and since we cannot do that, the whole notion of the perfect life collapses.
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From:
report of Johann Gottfried Herder (works [1784]) by Isaiah Berlin - The Roots of Romanticism Ch.3
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A reaction:
Herder seems to be the father of modern cultural relativism. The idea is hard to challenge, but the ideals of some cultures should be ignored, if they diminish rather than enhance the good life for all.
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7668
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Herder invented the idea of being rooted in (or cut off from) a home or a group [Herder, by Berlin]
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Full Idea:
The whole notion of being at home, or being cut off from one's natural roots, the whole idea of roots, the whole idea of belonging to a group, a sect, a movement, was largely invented by Herder.
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From:
report of Johann Gottfried Herder (works [1784], Ch.3) by Isaiah Berlin - The Roots of Romanticism
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A reaction:
Hm. Broad generalisations are an awful temptation in the history of ideas. As a corrective to this, trying reading the two Anglo-Saxon poems 'The Wanderer' and 'The Seafarer'. Very Germanic, I suppose. Interesting, though. Leads to Hegel's politics.
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