Combining Texts

All the ideas for 'Sententia on 'De Caelo'', 'works' and 'Set Theory and the Continuum Hypothesis'

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3 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy aims to know the truth about the way things are [Aquinas]
     Full Idea: The study of philosophy has as its purpose to know not what people have thought, but rather the truth about the way things are.
     From: Thomas Aquinas (Sententia on 'De Caelo' [1268], I.22.228), quoted by Kretzmann/Stump - Aquinas, Thomas 05
     A reaction: I agree with this deeply unfashionable opinion. Of course, modern investigations must be more sensitive to biases built into language, culture and conceptual schemes. But I am one of those sad old folks who still think truths can be stated.
1. Philosophy / H. Continental Philosophy / 5. Critical Theory
Horkheimer's critical theory was interdisciplinary, and aware of its own context and function [Horkheimer, by Finlayson]
     Full Idea: Horkheimer was chiefly responsible for developing 'critical theory' during the 1930s. ...It was interdisciplinary, reflective, dialectical, and critical. It reflected on the social context that gave rise to it, and its own function within that society.
     From: report of Max Horkheimer (works [1950]) by James Gordon Finlayson - Habermas Ch.1:02
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
We could accept the integers as primitive, then use sets to construct the rest [Cohen]
     Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities.
     From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?
     A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world.