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16252
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Metaphysics uses empty words, or just produces pseudo-statements [Carnap]
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Full Idea:
Since metaphysics doesn't want to assert analytic propositions, nor fall within the domain of physical science, it is compelled to employ words for which no criteria of application are specified, ..or else combine meaningful words..into pseudo-statements.
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From:
Rudolph Carnap (Elimination of Metaphysics by Analysis of Language [1959]), quoted by Tim Maudlin - The Metaphysics within Physics 2.4
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A reaction:
A classic summary of the logical positivist rejection of metaphysics. I incline to treat metaphysics as within the domain of science, but at a level of generality so high that practising scientists become bewildered and give up.
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13342
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Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap]
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Full Idea:
Carnap proposed to define consequence as 'sentence X follows from the sentences K iff the sentences K and the negation of X are contradictory', but 1) this is intuitively impossible, and 2) consequence would be changed by substituting objects.
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From:
comment on Rudolph Carnap (The Logical Syntax of Language [1934], p.88-) by Alfred Tarski - The Concept of Logical Consequence p.414
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A reaction:
This seems to be the first step in the ongoing explicit discussion of the nature of logical consequence, which is now seen by many as the central concept of logic. Tarski brings his new tool of 'satisfaction' to bear.
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13251
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Each person is free to build their own logic, just by specifying a syntax [Carnap]
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Full Idea:
In logic, there are no morals. Everyone is at liberty to build his own logic, i.e. his own form of language. All that is required is that he must state his methods clearly, and give syntactical rules instead of philosophical arguments.
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From:
Rudolph Carnap (The Logical Syntax of Language [1934], §17), quoted by JC Beall / G Restall - Logical Pluralism 7.3
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A reaction:
This is understandable, but strikes me as close to daft relativism. If I specify a silly logic, I presume its silliness will be obvious. By what criteria? I say the world dictates the true logic, but this is a minority view.
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13949
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All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
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Full Idea:
Peano's axioms are categorical (any two models are isomorphic). Some conclude that the concept of natural number is adequately represented by them, but we cannot identify natural numbers with one rather than another of the isomorphic models.
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From:
comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 11) by Richard Cartwright - Propositions 11
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A reaction:
This is a striking anticipation of Benacerraf's famous point about different set theory accounts of numbers, where all models seem to work equally well. Cartwright is saying that others have pointed this out.
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5897
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0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew]
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Full Idea:
1) 0 is a number; 2) The successor of any number is a number; 3) No two numbers have the same successor; 4) 0 is not the successor of any number; 5) If P is true of 0, and if P is true of any number n and of its successor, P is true of every number.
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From:
report of Giuseppe Peano (works [1890]) by Antony Flew - Pan Dictionary of Philosophy 'Peano'
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A reaction:
Devised by Dedekind and proposed by Peano, these postulates were intended to avoid references to intuition in specifying the natural numbers. I wonder if they could define 'successor' without reference to 'number'.
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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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14305
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In the truth-functional account a burnt-up match was soluble because it never entered water [Carnap]
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Full Idea:
If a wooden match was completely burned up yesterday, and never placed in water at any time, is it not the case, therefore, that the match is soluble (in the truth-functional view). This follows just from the antecedent being false.
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From:
Rudolph Carnap (Testability and Meaning [1937], I.440), quoted by Stephen Mumford - Dispositions
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A reaction:
This, along with Edgington's nice example of the conditional command (Idea ) seems conclusive against the truth-functional account. The only defence possible is some sort of pragmatic account about implicature.
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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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13048
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Good explications are exact, fruitful, simple and similar to the explicandum [Carnap, by Salmon]
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Full Idea:
Carnap's four criteria for giving a good explication are similarity to the explicandum, exactness, fruitfulness and simplicity.
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From:
report of Rudolph Carnap (Logical Foundations of Probability [1950], Ch.1) by Wesley Salmon - Four Decades of Scientific Explanation 0.1
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A reaction:
[compressed] Salmon's view is that this represents the old attitude, that the contribution of philosophy to explanation is the clarification of the key concepts. Carnap is, of course, a logical empiricist.
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20239
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Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche]
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Full Idea:
Hesiod reckons envy among the effects of the good and benevolent Eris, and there was nothing offensive in according envy to the gods. ...Likewise the Greeks were different from us in their evaluation of hope: one felt it to be blind and malicious.
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From:
report of Hesiod (works [c.700 BCE]) by Friedrich Nietzsche - Dawn (Daybreak) 038
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A reaction:
Presumably this would be understandable envy, and unreasonable hope. Ridiculous envy can't possibly be good, and modest and sensible hope can't possibly be bad. I suspect he wants to exaggerate the relativism.
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