Combining Philosophers

Ideas for Roger Penrose, David Hume and David H. Sanford

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

display all the ideas for this combination of philosophers

---

2 ideas

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle

8649	Two numbers are equal if all of their units correspond to one another [Hume]
	Full Idea: When two numbers are so combin'd, as that the one has always a unit answering to every unit of the other, we pronounce them equal.
	From: David Hume (Treatise of Human Nature [1739], I.III.1)
	A reaction: This became known as Hume's Principle after Frege made use of it for logicism (Foundations §63). It reduces equality to something fairly simple and visual (one-to-one correspondence). But we also say that two logicians or musicians are 'equal' in ability.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

2197	Reason assists experience in discovering laws, and in measuring their application [Hume]
	Full Idea: Abstract reasonings are employed, either to assist experience in the discovery of natural laws, or to determine their influence in particular instances, where it depends upon any precise degree of distance or quantity.
	From: David Hume (Enquiry Conc Human Understanding [1748], IV.I.27)