Combining Texts

All the ideas for 'Causality: Production and Propagation', 'Explanation in Mathematics' and 'Letters to Frege'

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8 ideas

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell]
     Full Idea: Russell's Paradox is a stripped-down version of Cantor's Paradox.
     From: comment on Bertrand Russell (Letters to Frege [1902]) by Graham Priest - The Structure of Paradoxes of Self-Reference §2
Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell]
     Full Idea: Russell's paradox showed that we cannot consistently assume what is sometimes called the 'naïve comprehension principle', namely that every property is collectivizing.
     From: comment on Bertrand Russell (Letters to Frege [1902]) by Michael Potter - Set Theory and Its Philosophy 03.6
8. Modes of Existence / B. Properties / 11. Properties as Sets
Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen]
     Full Idea: Russell refuted Frege's principle that there is a set for each property.
     From: report of Bertrand Russell (Letters to Frege [1902], 1904.12.12) by Roy Sorensen - Vagueness and Contradiction 6.1
     A reaction: This is the principle stumbling block to any attempt to explain properties purely in terms of sets. I would say that Russell proved there couldn't be a set for each predicate. You can't glibly equate proper properties with predicates.
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu]
     Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties).
     From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1)
     A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it.
18. Thought / C. Content / 6. Broad Content
We don't assert private thoughts; the objects are part of what we assert [Russell]
     Full Idea: I believe Mont Blanc itself is a component part of what is actually asserted in the proposition 'Mont Blanc is more than 4000 metres high'; we do not assert the thought, which is a private psychological matter, but the object of the thought.
     From: Bertrand Russell (Letters to Frege [1902], 1904.12.12), quoted by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4
     A reaction: This would appear to be pretty much externalism about concepts, given that Russell would accept that other people know much more about Mont Blanc than he does, and their knowledge is included in what he asserts.
26. Natural Theory / C. Causation / 4. Naturalised causation
A causal interaction is when two processes intersect, and correlated modifications persist afterwards [Salmon]
     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.
     From: Wesley Salmon (Causality: Production and Propagation [1980], §4)
     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.
26. Natural Theory / C. Causation / 5. Direction of causation
Cause must come first in propagations of causal interactions, but interactions are simultaneous [Salmon]
     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.
     From: Wesley Salmon (Causality: Production and Propagation [1980], §8)
     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.
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Instead of localised events, I take enduring and extended processes as basic to causation [Salmon]
     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.
     From: Wesley Salmon (Causality: Production and Propagation [1980], §2)
     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.