Tag Archives: Mill

December 10, 2008, 7:38 am

Leibniz on 1+1=2

From Kuo & Joe, here’s an interesting article on different philosophers’ views on what it means for 1+1 to equal 2 and how their concept of divinity plays into their ideas. Leibniz’ view seems the most compelling:

When Gottfried Wilhelm Leibniz, an inventor of the calculus, was asked by one of his students, “Why is one and one always two, and how do we know this?” Leibnitz replied, “One and one equals two is an eternal, immutable truth that would be so whether or not there were things to count or people to count them.” Numbers, numerical relationships, and mathematical laws (such as the law of addition) exist in this abstract realm and are independent of any physical existence. In Leibnitz’s view, numbers are real things that exist in a dimension outside of the physical realm and would exist even if no human existed to recognize them.

I don’t know if the exchange between Leibniz and…

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