Combining Texts

All the ideas for 'Lectures on the History of Philosophy', 'On the Reality of Accidents' and 'Counting and the Natural Numbers'

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5 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 / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers

17423	The essence of natural numbers must reflect all the functions they perform [Sicha]
	Full Idea: What is really essential to being a natural number is what is common to the natural numbers in all the functions they perform.
	From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2)
	A reaction: I could try using natural numbers as insults. 'You despicable seven!' 'How dare you!' I actually agree. The question about functions is always 'what is it about this thing that enables it to perform this function'.

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17425	To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha]
	Full Idea: A knowledge of 'how many' cannot be inferred from the equinumerosity of two collections; a numerical quantifier statement is needed.
	From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 3)

17424	Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha]
	Full Idea: Counting is the activity of putting an initial segment of a serially ordered string in 1-1 correspondence with some other collection of entities.
	From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2)

8. Modes of Existence / E. Nominalism / 4. Concept Nominalism

19382	Abstracta are abbreviated ways of talking; there are just substances, and truths about them [Leibniz]
	Full Idea: I consider abstracta not as real things but as abbreviated ways of talking ...and to that extent I am a nominalist, at least provisionally ...It suffices to posit only substances as real things, and, to assert truths about these.
	From: Gottfried Leibniz (On the Reality of Accidents [1688]), quoted by Richard T.W. Arthur - Leibniz
	A reaction: I am a modern nominalist, in my hostility to a serious ontological commitment to abstracta. You get into trouble, though, if you say there are only objects or substances. Physics says reality may all be 'fields', or something.... 'Truths' is good.