Combining Texts

Ideas for 'From an Ontological Point of View', 'The Principles of Mathematics' and 'Ecce Homo'

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5 ideas

18. Thought / C. Content / 6. Broad Content
Externalism is causal-historical, or social, or biological [Heil]
     Full Idea: Some externalists focus on causal-historical connections, others emphasise social matters (especially thinkers' linguistic communities), still others focus on biological function.
     From: John Heil (From an Ontological Point of View [2003], 18.5 n6)
     A reaction: Helpful. The social view strikes me as the one to take most seriously (allowing for contextual views of justification, and for the social role of experts). The problem is to combine the social view with realism and a robust view of truth.
18. Thought / C. Content / 7. Narrow Content
Intentionality is based in dispositions, which are intrinsic to agents, suggesting internalism [Heil]
     Full Idea: I suggest that intentionality is grounded in the dispositionalities of agents. Dispositions are intrinsic to agents, so this places me on the side of the internalists and against the externalists.
     From: John Heil (From an Ontological Point of View [2003], 18.4)
     A reaction: I think this is a key idea, and the right view. The key question is whether we see intentionality as active or passive. The externalist view seems to see the brain as a passive organ which the world manipulates. If the brain is active, what is it doing?
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstraction principles identify a common property, which is some third term with the right relation [Russell]
     Full Idea: The relations in an abstraction principle are always constituted by possession of a common property (which is imprecise as it relies on 'predicate'), ..so we say a common property of two terms is any third term to which both have the same relation.
     From: Bertrand Russell (The Principles of Mathematics [1903], §157)
     A reaction: This brings out clearly the linguistic approach of the modern account of abstraction, where the older abstractionism was torn between the ontology and the epistemology (that is, the parts of objects, or the appearances of them in the mind).
The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell]
     Full Idea: The principle of Abstraction says that whenever a relation with instances is symmetrical and transitive, then the relation is not primitive, but is analyzable into sameness of relation to some other term. ..This is provable and states a common assumption.
     From: Bertrand Russell (The Principles of Mathematics [1903], §157)
     A reaction: At last I have found someone who explains the whole thing clearly! Bertrand Russell was wonderful. See other ideas on the subject from this text, for a proper understanding of abstraction by equivalence.
A certain type of property occurs if and only if there is an equivalence relation [Russell]
     Full Idea: The possession of a common property of a certain type always leads to a symmetrical transitive relation. The principle of Abstraction asserts the converse, that such relations only spring from common properties of the above type.
     From: Bertrand Russell (The Principles of Mathematics [1903], §157)
     A reaction: The type of property is where only one term is applicable to it, such as the magnitude of a quantity, or the time of an event. So symmetrical and transitive relations occur if and only if there is a property of that type.