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9874
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Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
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Full Idea:
The contradiction in Frege's system is due to the presence of second-order quantification, ..and Frege's explanation of the second-order quantifier, unlike that which he provides for the first-order one, appears to be substitutional rather than objectual.
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From:
comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], §25) by Michael Dummett - Frege philosophy of mathematics Ch.17
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A reaction:
In Idea 9871 Dummett adds the further point that Frege lacks a clear notion of the domain of quantification. At this stage I don't fully understand this idea, but it is clearly of significance, so I will return to it.
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18252
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Real numbers are ratios of quantities, such as lengths or masses [Frege]
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Full Idea:
If 'number' is the referent of a numerical symbol, a real number is the same as a ratio of quantities. ...A length can have to another length the same ratio as a mass to another mass.
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From:
Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], III.1.73), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's'
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A reaction:
This is part of a critique of Cantor and the Cauchy series approach. Interesting that Frege, who is in the platonist camp, is keen to connect the real numbers with natural phenomena. He is always keen to keep touch with the application of mathematics.
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9190
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A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
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Full Idea:
In later Frege, a concept could be taken as a particular case of a function, mapping every object on to one of the truth-values (T or F), according as to whether, as we should ordinarily say, that object fell under the concept or not.
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From:
report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Michael Dummett - The Philosophy of Mathematics 3.5
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A reaction:
As so often in these attempts at explanation, this sounds circular. You can't decide whether an object truly falls under a concept, if you haven't already got the concept. His troubles all arise (I say) because he scorns abstractionist accounts.
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8412
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A causal interaction is when two processes intersect, and correlated modifications persist afterwards [Salmon]
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Full Idea:
When two processes intersect, and they undergo correlated modifications which persist after the intersection, I shall say that the intersection is a causal interaction. I take this as a fundamental causal concept.
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From:
Wesley Salmon (Causality: Production and Propagation [1980], §4)
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A reaction:
There may be a problem individuating processes, just as there is for events. I like this approach to causation, which is ontologically sparse, and fits in with the scientific worldview. Change of properties sounds precise, but isn't. Stick to processes.
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8413
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Cause must come first in propagations of causal interactions, but interactions are simultaneous [Salmon]
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Full Idea:
In a typical cause-effect situation (a 'propagation') cause must precede effect, for propagation over a finite time interval is an essential feature. In an 'interaction', an intersection of processes resulting in change, we have simultaneity.
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From:
Wesley Salmon (Causality: Production and Propagation [1980], §8)
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A reaction:
This takes the direction of time as axiomatic, and quite right too. Salmon isn't addressing the real difficulty, though, which is that the resultant laws are usually held to be time-reversible, which is a bit of a puzzle.
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8411
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Instead of localised events, I take enduring and extended processes as basic to causation [Salmon]
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Full Idea:
I propose to approach causality by taking processes rather than events as basic entities. Events are relatively localised in space and time, while processes have much greater temporal duration, and, in many cases, much greater spatial extent.
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From:
Wesley Salmon (Causality: Production and Propagation [1980], §2)
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A reaction:
This strikes me as an incredibly promising proposal, not just in our understanding of causation, but for our general metaphysics and understanding of nature. See Idea 4931, for example. Vague events and processes blend into one another.
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