Combining Texts

All the ideas for 'Lectures on the History of Philosophy', 'On the Foundations of Logic and Arithmetic' and 'Theory of Knowledge (2nd ed 1977)'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

4 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined

21757	Philosophy is the conceptual essence of the shape of history [Hegel]
	Full Idea: Philosophy is the supreme blossom - the concept - of the entire shape of history, the consciousness and the spiritual essence of the whole situation, the spirit of the age as the spirit present and aware of itself in thought.
	From: Georg W.F.Hegel (Lectures on the History of Philosophy [1830], p.25), quoted by Stephen Houlgate - An Introduction to Hegel 01
	A reaction: This sees philosophy as intrinsically historical, which is a founding idea for 'continental' philosophy. Analysis is tied to science, in which the history of the subject is seen as irrelevant to its truth. Does this mean we can't go back to Aristotle?

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.

11. Knowledge Aims / A. Knowledge / 5. Aiming at Truth

19569	We have a basic epistemic duty to believe truth and avoid error [Chisholm, by Kvanvig]
	Full Idea: Chisholm says our fundamental epistemic duties arise from the fundamental duty to (do one's best to) believe the truth and avoid error.
	From: report of Roderick Chisholm (Theory of Knowledge (2nd ed 1977) [1966]) by Jonathan Kvanvig - Truth is not the Primary Epistemic Goal 'Epistemic'
	A reaction: Since it strikes me as impossible to perceive something as being true, and yet still not believe it (except in moments of shock), I don't see why we need to introduce dubious claims about 'duty' here. Stupidity isn't a failure of duty.