Combining Texts

All the ideas for 'Changes in Events and Changes in Things', 'Paradoxes of the Infinite' and 'Punctual and segmentive Hopi verbs'

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5 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

9987	An aggregate in which order does not matter I call a 'set' [Bolzano]
	Full Idea: An aggregate whose basic conception renders the arrangement of its members a matter of indifference, and whose permutation therefore produces no essential difference, I call a 'set'.
	From: Bernard Bolzano (Paradoxes of the Infinite [1846], §4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX
	A reaction: The idea of 'sets' was emerging before Cantor formalised it, and clarified it by thinking about infinite sets. Nowadays we also have 'ordered' sets, which rather contradicts Bolzano, and we also expect the cardinality to be determinate.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

10856	A truly infinite quantity does not need to be a variable [Bolzano]
	Full Idea: A truly infinite quantity (for example, the length of a straight line, unbounded in either direction) does not by any means need to be a variable.
	From: Bernard Bolzano (Paradoxes of the Infinite [1846]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable §10
	A reaction: This is an important idea, followed up by Cantor, which relegated to the sidelines the view of infinity as simply something that could increase without limit. Personally I like the old view, but there is something mathematically stable about infinity.

7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact

15201	That Queen Anne is dead is a 'general fact', not a fact about Queen Anne [Prior,AN]
	Full Idea: The fact that Queen Anne has been dead for some years is not, in the strict sense of 'about', a fact about Queen Anne; it is not a fact about anyone or anything - it is a general fact.
	From: Arthur N. Prior (Changes in Events and Changes in Things [1968], p.13), quoted by Robin Le Poidevin - Past, Present and Future of Debate about Tense 1 b
	A reaction: He distinguishes 'general facts' (states of affairs, I think) from 'individual facts', involving some specific object. General facts seem to be what are expressed by negative existential truths, such as 'there is no Loch Ness Monster'. Useful.

13. Knowledge Criteria / E. Relativism / 5. Language Relativism

3914	Language arranges sensory experience to form a world-order [Whorf]
	Full Idea: Language first of all is a classification and arrangement of the stream of sensory experience which results in a certain world-order.
	From: Benjamin Lee Whorf (Punctual and segmentive Hopi verbs [1936], p.55)
	A reaction: This is only true to a limited degree. See Davidson's 'On the very idea of a conceptual scheme'. All humans share a world-order, to some extent.

27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series

22899	'Thank goodness that's over' is not like 'thank goodness that happened on Friday' [Prior,AN]
	Full Idea: One says 'thank goodness that is over', ..and it says something which it is impossible which any use of any tenseless copula with a date should convey. It certainly doesn't mean the same as 'thank goodness that occured on Friday June 15th 1954'.
	From: Arthur N. Prior (Changes in Events and Changes in Things [1968]), quoted by Adrian Bardon - Brief History of the Philosophy of Time 4 'Pervasive'
	A reaction: [Ref uncertain] This seems to be appealing to ordinary usage, in which tenses have huge significance. If we take time (with its past, present and future) as primitive, then tenses can have full weight. Did tenses mean anything at all to Einstein?