Combining Texts

All the ideas for 'Identity and Spatio-Temporal Continuity', 'Sententia on 'Posterior Analytics'' and 'Science and Hypothesis'

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3 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10180 Mathematicians do not study objects, but relations between objects [Poincaré]
     Full Idea: Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter.
     From: Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6
     A reaction: This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well.
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
13128 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins]
     Full Idea: 'Ultimate sortals' are said to be non-subordinated, disjoint from one another, and uniquely paired with each object. Because of this, the ultimate sortal cannot be a satisfactory explication of the notion of an ontological category.
     From: comment on David Wiggins (Identity and Spatio-Temporal Continuity [1971], p.75) by Jan Westerhoff - Ontological Categories §26
     A reaction: My strong intuitions are that Wiggins is plain wrong, and Westerhoff gives the most promising reasons for my intuition. The simplest point is that objects can obviously belong to more than one category.
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
22109 The fullest knowledge places a conclusion within an accurate theory [Aquinas, by Kretzmann/Stump]
     Full Idea: Having 'scientia' is the fullest possible human cognition, by which one situates the fact expressed by a conclusion in an explanatory theory that accurately maps metaphysical or physical reality.
     From: report of Thomas Aquinas (Sententia on 'Posterior Analytics' [1269], 1.2.9, 1.5.7) by Kretzmann/Stump - Aquinas, Thomas 11
     A reaction: That is a perfect statement of my concept of knowledge. Explanatory theories must specify the essential natures of the entities involved. We don't aim for 'knowledge', we aim for the 'fullest possible cognition'. This account extend's Aristotle's.