Combining Texts

All the ideas for 'works', 'On the Foundations of Logic and Arithmetic' and 'Improvement of Understanding'

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5 ideas

2. Reason / D. Definition / 2. Aims of Definition

16541	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.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17697	The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
	Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment.
	From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130)
	A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17698	Logic already contains some arithmetic, so the two must be developed together [Hilbert]
	Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required.
	From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131)
	A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher.

14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence

13073	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.

22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature

22086	The most important aspect of a human being is not reason, but passion [Kierkegaard, by Carlisle]
	Full Idea: Kierkegaard insisted that the most important aspect of a human being is not reason, but passion.
	From: report of Søren Kierkegaard (works [1845]) by Clare Carlisle - Kierkegaard: a guide for the perplexed Intro
	A reaction: Hume comes to mind for a similar view, but in character Hume was far more rational than Kierkegaard.