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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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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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13764
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Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
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Full Idea:
Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? Are they non-truth-functional, like 'because' or 'before'? Do the values of A and B, in some cases, leave open the value of 'If A,B'?
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From:
Dorothy Edgington (Conditionals [2001], 17.1)
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A reaction:
I would say they are not truth-functional, because the 'if' asserts some further dependency relation that goes beyond the truth or falsity of A and B. Logical ifs, causal ifs, psychological ifs... The material conditional ⊃ is truth-functional.
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13765
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'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
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Full Idea:
If it were possible to have A true, B false, and If A,B true, it would be unsafe to infer B from A and If A,B: modus ponens would thus be invalid. Hence 'If A,B' must entail ¬(A & ¬B).
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From:
Dorothy Edgington (Conditionals [2001], 17.1)
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A reaction:
This is a firm defence of part of the truth-functional view of conditionals, and seems unassailable. The other parts of the truth table are open to question, though, if A is false, or they are both true.
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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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6213
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A man cannot will to will, or will to will to will, so the idea of a voluntary will is absurd [Hobbes]
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Full Idea:
The will is not voluntary: for a man can no more say he will will, than he will will will, and so make an infinite repetition of the word 'will', which is absurd and insignificant.
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From:
Thomas Hobbes (Human Nature [1640], Ch.XII.5)
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A reaction:
A nice simple point, allied to Nietzsche's notion that thoughts are uncontrollable (Idea 2291). Even Aquinas, who is quite a fan of free will, spotted the problem (Idea 1854). Personally I agree with Hobbes. Free will is a shibboleth.
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6210
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Life has no end (not even happiness), because we have desires, which presuppose a further end [Hobbes]
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Full Idea:
For an utmost end, in which the ancient philosophers have placed felicity, there is no such thing in this world, nor way to it: for while we live, we have desires, and desire presupposeth a further end.
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From:
Thomas Hobbes (Human Nature [1640], Ch.VII.6)
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A reaction:
Kant's definition of happiness (Idea 1452) seems to be the underlying idea, and hence with the same implication (of impossibility). However, an alcoholic locked in a brewery would seem to have all that Hobbes requires for happiness.
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6212
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Lust involves pleasure, and also the sense of power in pleasing others [Hobbes]
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Full Idea:
Lust consists of two appetites together, to please, and to be pleased, and the delight men take in delighting is not sensual, but a pleasure or joy of the mind consisting in the imagination of the power they have so much to please.
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From:
Thomas Hobbes (Human Nature [1640], Ch.IX)
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A reaction:
Hobbes would rather burst a blood-vessel than admit any altruism. If you take pleasure in pleasing someone else, why can't that simply be because of the other person's pleasure, with which we sympathise, rather than relishing our own 'power'?
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