Key ideas: Gottfried Leibniz (1646-1716) was one of the greatest thinkers of the 17th and 18th centuries.
Controversies are boiling these days among distinguished men over true and false ideas. This is an issue of great importance for recognizing truth - an issue on which Descartes himself is not altogether satisfactory. So I want to explain briefly what I think can be established about the distinctions and criteria that relate to ideas and knowledge....
We often mistakenly believe that we have ideas of things in our mind, assuming that we have already explained ·to ourselves· some of the terms we are using, when really we haven’t explained any of them. Some people hold that we can’t understand what we are saying about a thing unless we have an idea of it; but this is false or at least ambiguous, because we can have understanding of a sort even when our thinking is blind or symbolic and doesn’t involve ideas.
When we settle for this blind thinking, and don’t pursue the resolution of notions far enough, we may have a thought that harbours a contradiction that we don’t see because it is buried in a very complex notion....
My favourite illustrative example of this is the fastest motion, which entails an absurdity. I now show that it does:
Suppose there is a wheel turning with the fastest motion. Anyone can see that if a spoke of the wheel came to poke out beyond the rim, the end of it would then be moving faster than a nail on the rim of the wheel. So the nail’s motion is not the fastest, which is contrary to the hypothesis.
Now, we certainly understand the phrase ‘the fastest motion’, and we may think we have an idea corresponding to it; but ·we don’t, because· we can’t have an idea of something impossible.
So we have a line to draw between nominal definitions, which contain only marks that distinguish the thing from other things, and real definitions, from which the thing can be shown to be possible. And that’s my answer to Hobbes, who claimed that truths are arbitrary because they depend on nominal definitions. What he didn’t take into account was that a definition’s being real is not something we decide, and that not just any notions can be joined to one another. Nominal definitions are insufficient for perfect knowledge except when the possibility of the thing defined is established in some other way...
All this, I think, finally lets us understand that one should be cautious in claiming to have this or that idea. Many people who use this glittering title ‘idea’ to prop up certain creatures of their imagination are using it wrongly, for we don’t always have an idea corresponding to everything we consciously think of (as I showed with the example of greatest speed).