I am using a method which I call logical algebra or Leibnizian algebra since it appears that Leibniz was the first one to understand this, although it appears that he didn’t grasp the importance of it since he doesn’t use this tool much in the Metaphysics or in the Monadology. Essentially: x means y if x can be substituted for y without changing the truth value. So what we do is set up a equation:
x defines y = y must have x
Then we substitute the same words for x and y on both sides of the equation and the truth value should be the same. E.g. Two hydrogen and one oxygen defines water means water must have two hydrogen and one oxygen. The truth value is the same on both sides of the equation. So let’s now try to understand what it means for x to cause y.
has, exist, and, not are indefinable. Decrease and more can be defined but for the sake of brevity I chose not to define them, along with a few other words.
x has a probability means x is very possible or not very possible. (very cannot be defined. Possible is defined in terms of necessary so: x is necessary means it is not possible that x does not exist. And necessary cannot be defined.)
x causes y means the non-existence of x decreases the probability of y more than any other thing z.
E.g. Hitler caused WWII means if Hitler had not existed, then probability of WWII would have decreased more than had any other thing not existed. Oswald caused the assassination of JFK on 11/22/63 means had Oswald not existed then the probability of JFK being assassinated on 11/22/63 would have decreased more than the non-existence of any other thing.
x allows y to cause z means the non-existence of x decreases the probability of y causing z more than any other thing. EOR - permit = allow
E.g. The German people, German unemployment in the early 30s, German inflation in the early 20s, Chamberlain, the Anschluss with Austria among others allowed Hitler to cause WWII means had all those things not existed then the probability of Hitler causing WWII would have decreased more than any other thing. JFK’s decision to ride in an open car allowed Oswald to shoot him on 11/22/63 means had JFK decided to not ride an open car then the probability of Oswald causing the assassination of JFK would have decreased more than the non-existence of any other thing.
x is more responsible for y than z means the non-existence of x decreases the probability of y more than z.
x is not responsible for y means if x did not exist then the probability of y would be mostly identical.
E.g. Because several things can cause one event we need a word that distinguishes those that decrease the probability of the event more than others and this is where “responsible” comes in. Hitler was more responsible for WWII than Goebbels even though Goebbels did a lot to make WWII happen means if Hitler did not exist than the probability of WWII would have decreased more than if Goebbels did not exist. The American desire for land was more responsible for the Revolution than a hatred of taxation seeing as there was only a nominal tax on tea in 1776 means if Americans did not desire to own the land that the British were owning (for example, Washington had land which the British voided and gave to higher-ups in the government) then the probability of the Revolution would have decreased more than if the nominal tax (a very minor tax) on tea had not existed.
Now there is one major counterexample that I know of to this theory:
Marilyn Monroe committed suicide in 1964 and it just so happens that the night before she killed herself LBJ decided to not press the nuclear button which could have malfunctioned and landed in LA since the Russians couldn’t hit the US at that time. So:
The absence of a nuclear explosion caused the suicide of Marilyn Monroe means had the absence of the nuclear explosion not existed (meaning the nuclear explosion existed) then Marilyn Monroe would not have committed suicide.
We can handle this counterexample by showing that: “the absence of a nuclear explosion caused the suicide of Marilyn Monroe” is a contradiction.
Natural is a property of a thing x means x causes some facts.
Abstract is a property of a thing x means x does not cause and relates all things.
E.g. The Earth has one moon does not cause anything and it relates the Earth to the moon and to the number one, means abstract is a property of “The Earth has one moon does not cause anything and it relates the Earth to the moon and to the number one.” Natural is a property of hydrogen atom means a hydrogen causes some facts, most notably: the atomic mass of 1.
There was an absence of a nuclear explosion the night before MM committed suicide relates “absence” to a nuclear explosion means abstract is a property of “absence of a nuclear explosion the night before MM committed suicide.”
Abstract things do not cause anything.
Therefore, the absence of a nuclear explosion caused the suicide of Marilyn Monroe is a contradiction.
Only natural things (things composed of atoms) cause things.
The only natural thing that could have caused a nuclear explosion in 1964 was LBJ. Let’s now plug LBJ into our equation for cause and see if we can plausibly say that LBJ caused MM’s suicide.
Had LBJ not existed then the probability of a nuclear explosion would have decreased more than any other thing. That’s a false statement. If LBJ had not existed then some other person would have been president and the probability of a nuclear explosion would not have changed. Therefore, LBJ did not cause MM’s suicide which matches our intuitions about causation.