Combining Texts

Ideas for 'Walking the Tightrope of Reason', 'Critique of the Gotha Program' and 'Essay Conc Human Understanding (2nd Ed)'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts


2 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
The idea of 'one' is the simplest, most obvious and most widespread idea [Locke]
     Full Idea: Among all the ideas we have, as there is none suggested to the mind by more ways, so there is none more simple than that of unity, or one; ..every idea in our understanding, every thought of our minds brings this idea along with it.
     From: John Locke (Essay Conc Human Understanding (2nd Ed) [1694], 2.16.01)
     A reaction: What does Locke mean by 'suggested' to the mind? I take it that this phenomenon of psychology (or of reality, if you like) is the foundation of mathematics, making one clearly prior to zero.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
If there were real infinities, you could add two together, which is ridiculous [Locke]
     Full Idea: If a man had a positive idea of infinite, either duration or space, he could add two infinities together; nay, make one Infinite infinity bigger than another, absurdities too gross to be confuted.
     From: John Locke (Essay Conc Human Understanding (2nd Ed) [1694], 2.17.20)
     A reaction: A beautifully heartfelt objection to everything Cantor stood for, two hundred years before Cantor got round to it.