2. There must be simple substances because there are compound substances; for the compound is nothing else than a collection or aggregatum of simple substances.
Gottfried W. Leibniz, Monadology
Crazy how a “father” of calculus was so illogical in his seminal work of 1714.
- The existence of compound things does not imply the existence of partless atoms.
- He asserts, doesn’t prove, that a compound is “nothing more than" a collection of simple substances. (atoms)
I’ve collected a few tidbits about non-wellfoundedness on
- the opposite of the idea of “indivisible atoms" at the "bottom" of everything
- turtles all the way down
- (infinite regress is OK)
- a > b > c > a
- (so the two options I can think of for non-wellfounded sets are either an infinite straight line or a circle—which biject by stereographic projection)
as well as examples of irreducible things:
- if you take away one Borromean ring
then the whole is no longer interlinked
- Twisted products in K-theory are different to straight products.
A Möbius band is different to a wedding band.
Yet 100% of the difference is in how two 1-D lines are put together. The parts in the recipe are the same, it’s the way they’re combined (twisted or straight product) that makes the difference.
So Leibnitz’s assertions are not only unsupported, but wrong. (Markov, causality, St Anselm’s argument, conservation of mass, etc. in Monadology 4, 5, 22, 44, 45.)
tl,dr: Leibniz, like Spinoza, uses the word “therefore” to mean “and here’s another thing I’m assuming”.