Combining Texts

All the ideas for 'The Value of Science', 'Mathematical Explanation' and 'Improvement of Understanding'

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6 ideas

2. Reason / D. Definition / 2. Aims of Definition
All the intrinsic properties of a thing should be deducible from its definition [Spinoza]
     Full Idea: The definition of a thing should be such that all the properties of that thing, in so far as it is considered by itself, and not in conjunction with other things, can be deduced from it.
     From: Baruch de Spinoza (Improvement of Understanding [1675], p.35), quoted by E.J. Lowe - What is the Source of Knowledge of Modal Truths? 6
     A reaction: This is exactly what Locke requires of a real essence (though he is pessimistic about ever achieving it). Spinoza is talking of an Aristotelian real definition, which may be complex, and not a lexicographer's short verbal explication.
9. Objects / D. Essence of Objects / 3. Individual Essences
Particular essence is often captured by generality [Steiner,M]
     Full Idea: Generality is often necessary for capturing the essence of a particular.
     From: Mark Steiner (Mathematical Explanation [1978], p.36)
     A reaction: The most powerful features of an entity are probably those which are universal, like intelligence or physical strength in a human. Those characteristics are powerful because they compete with the same characteristic in others (perhaps?).
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M]
     Full Idea: Maybe to deduce a theorem as an instance of a generalization is more explanatory than to deduce it correctly.
     From: Mark Steiner (Mathematical Explanation [1978], p.32)
     A reaction: Steiner eventually comes down against this proposal, on the grounds that some proofs are too general, and hence too far away from the thing they are meant to explain.
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
To understand the properties we must know the essence, as with a circle [Spinoza]
     Full Idea: If a circle is defined as a figure in which lines from centre to circumference are equal, such definitions do not explain the essence of a circle, but only a property. The properties of a thing are not understood as long as their essences are not known.
     From: Baruch de Spinoza (Improvement of Understanding [1675], §95), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 1.2.1
     A reaction: This is the traditional Aristotelian view of essence, and the example of a circle is nice, though I am not sure what the essence of a circle might be. Presumably ALL the properties of a circle must flow from it.
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]
     Full Idea: My proposal is that an explanatory proof makes reference to the 'characterizing property' of an entity or structure mentioned in the theorem, where the proof depends on the property. If we substitute a different object, the theory collapses.
     From: Mark Steiner (Mathematical Explanation [1978], p.34)
     A reaction: He prefers 'characterizing property' to 'essence', because he is not talking about necessary properties, since all properties are necessary in mathematics. He is, in fact, reverting to the older notion of an essence, as the core power of the thing.
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré]
     Full Idea: In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose.
     From: report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2
     A reaction: I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts.