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| 13939 | No possible evidence could decide the reality of numbers, so it is a pseudo-question |
| Full Idea: I cannot think of any possible evidence that would be regarded as relevant by both nominalists and realists about numbers, and would decide the controversy, or make one side more probable. Hence I regard the external questions as pseudo-questions. | |||
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 4) |
| 13936 | Questions about numbers are answered by analysis, and are analytic, and hence logically true |
| Full Idea: For the internal question like 'is there a prime number greater than a hundred?' the answers are found by logical analysis based on the rules for the new expressions. The answers here are analytic, i.e., logically true. | |||
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 2) |
| 8748 | Logical positivists incorporated geometry into logicism, saying axioms are just definitions |
| 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'. | |||
| From: report of Rudolph Carnap (Empiricism, Semantics and Ontology [1950]) by Stewart Shapiro - Thinking About Mathematics 5.3 | |||
| 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. |
| 8960 | Internal questions about abstractions are trivial, and external ones deeply problematic |
| Full Idea: Carnap's verdict is that questions regarding the existence of abstracta tend to be trivial when taken as internal and deeply problematic when taken as external. | |||
| From: report of Rudolph Carnap (Empiricism, Semantics and Ontology [1950]) by Zoltán Gendler Szabó - Nominalism 6 | |||
| A reaction: If the internal aspect of the problem is 'trivial', this would put Carnap in league with fictionalists, who are only committed to entities while playing the current game. What is the status of the theory? Carnap wanted flowers to bloom. |
| 13933 | Existence questions are 'internal' (within a framework) or 'external' (concerning the whole framework) |
| 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. | |||
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 2) | |||
| 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. |
| 13934 | To be 'real' is to be an element of a system, so we cannot ask reality questions about the system itself |
| Full Idea: To be real in the scientific sense means to be an element of the system; hence this concept cannot be meaningfully applied to the system itself. | |||
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 2) |
| 13938 | A linguistic framework involves commitment to entities, so only commitment to the framework is in question |
| Full Idea: If someone accepts a framework for a kind of entities, then he must admit the entities as possible designata. Thus the question of the admissibility of entities is reduced to the question of the acceptability of the linguistic framework for the entities. | |||
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 4) | |||
| A reaction: Despite the many differences of opinion between Quine and Carnap, this appears to be a straight endorsement by Carnap of the Quinean conception of ontological commitment. |
| 13935 | We only accept 'things' within a language with formation, testing and acceptance rules |
| 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. | |||
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 2) | |||
| A reaction: If you derive your metaphysics from your language, then objects are linguistic conventions. But why do we accept conventions about objects? |
| 13932 | Empiricists tend to reject abstract entities, and to feel sympathy with nominalism |
| 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). | |||
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 1) | |||
| 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?'. |
| 13937 | New linguistic claims about entities are not true or false, but just expedient, fruitful or successful |
| 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. | |||
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 3) | |||
| 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? |
| 13940 | All linguistic forms in science are merely judged by their efficiency as instruments |
| Full Idea: The acceptance or rejection of abstract (or any other) linguistic forms in any branch of science will finally be decided by their efficiency as instruments. | |||
| From: Rudolph Carnap (Empiricism, Semantics and Ontology [1950], 5) |