Notes for 9/29/2026
9/29/2026
[Philosophy Club every Wednesday, 5-6 pm, in the Buchtel College of Arts and Sciences room 436 ("The Cave")
Bioethics Club Tuesdays from 4:30-5:30 in CAS 436.]
Do you think everything happens for a reason?
Is Leibniz harder to understand than Spinoza?
Leibniz agrees with Descartes and Spinoza that God somehow implies maximal reality. But L disagrees with S that this all has to be possessed by God.
S thought there could only be one maximally real substance.
Leibniz (and also Anne Conway) thought maximal reality implies a maximal number of substances, and that this number = infinite.
So, whereas S thought there was one substance, L thought there were infinitely many substances.
For L, substances are not in space. Here’s his argument:
1. Substances must be indivisible.
2. Anything that is in space is extended.
3. Anything that is extended is divisible.
4. Therefore, substances must not be in space.
This means that for L, substances are not material.
But, the material world exists, and L also accepts this (as did everyone else, except Berkeley):
Reality must be grounded in substance(s).
So,
The material world must be grounded in substance(s).
This initially seems to conflict with:
There are no material substances.
We’ll come back to how L tries to resolve the tension here.
L’s philosophy mostly follows from a number of principles, some of which end up being explicitly named.
One of these is the principle of plenitude, which we already encountered (the principle of maximality), which he thinks follows from God’s maximal perfection and God’s nature as creator (God as the ultimate originator of all things).
Another is the principle of identity / the law of identity
X = X
X = Y = (Z^2 + 12)
Two dimensions of the principle of identity:
First is Leibniz’s Law
- Principle of identity of indiscernibles: if x and y have no properties to differentiate one from the other, then they are identical (all difference is difference in properties)
- Principle of the indiscernibility of identicals: If x = y then there are no properties belonging to x that don’t belong to y and vice-versa
LL = x =y if and only if x and y have all and only the same properties
Second is L’s doctrine that all truth is (somehow) analytic.
A priori truths are those that can be understood by concepts alone.
A posteriori truths are those that require experience to understand.
An analytic truth is one that can be known to be true just by properly understanding the concepts involved – if you analyze the subject concept, you can find the predicate concept contained in that analysis.
D thought only some truths are analytic, and this is what underwrites his truth rule (his “inspectional account of knowledge).
Examples:
All vixens are female (subject = vixens, predicate = being female)
All bachelors are unmarried
All triangles are trilateral
All triangles have internal angles that sum to 180 degrees
Leibniz thinks that ALL truth turns out to be analytic, and this follows from God’s omniscience (details later).
“Contained predicate doctrine of truth” or “analytic doctrine of truth” or “containment view of truth”
The second great foundational principle of rational thought Leibniz thinks is the Principle of Sufficient Reason (PSR):
For every positive truth, there is a reason why it is true rather than not.
PSR means there are and cannot be any “brute facts”
A brute fact is something that just plain is as it is without any reason why it is.
1=1
PSR implies that reality has to make sense. (It is impossible for reality to lack an intelligible structure.)
However complex, there is a rule that represents every state of affairs. Leibniz uses math as an example: There is a function that describes any possible line, however apparently random.
PSR implies the “Principle of the Best” = God not only has a reason for creating the world exactly as it is, but this must be the best of reasons, and so, this is the best of all possible worlds.
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