Notes for 10/8/2026

  

10/8/2026

 

[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.]

 

Have you ever been a cactus?

 

 

 

 

I left off with the worry that Leibniz’s Complete Concept Doctrine (CCD) creates a problem for God’s freedom.

 

 

 

Here’s how:

      Taylor married Travis.

 

 

This means Taylor’s CC includes marrying Travis.

This means God could not have created Taylor without also creating Travis.

What holds true of Taylor and Travis also holds true of any pair of substances in the entire universe.

So, God cannot create any one substance in a possible world without also creating every other substance belonging to that possible world.

 

Arnauld thought this was an objectionable limitation on divine freedom.

 

 

Leibniz’s response was to remind Arnauld of the distinction between absolute and hypothetical necessity.

 

 

A world in which Taylor does not marry Travis because Travis does not exist would be a world in which Taylor also did not exist, either. Rather, there might be someone with many similarities to Taylor, and who might be called ‘Taylor, etc., but this would not be “our Taylor.”

 

 

 

This creates a new problem of counterfactuals, though:

 

It looks like,

      “If Eric had stayed home today, he would not be in class” turns out to be false, because if Eric had stayed home today he would not have existed.

 

That is, lots of intuitively true counterfactuals turn out to be false.

 

 

Even worse, though:

 

Suppose it is true that:

(CP) For any predicate P that is true of some substance S, P is contained in S’s CC.

 

 

 

Now consider the following true statements:

      God chose to create me.

      God chose the best possible world.

I have the property of having been chosen by God to be created.

 

Since these are true, it must be, by CP, that God has a complete concept that includes his creating me and his creating the BPW.

 

If each substance has one and only one complete concept, this looks like God’s CC includes all his choices, which seems to lead back to Spinozistic necessitarianism.

 

Leibniz could avoid this by denying the CCD applies to God, but since the CCD is motivated by his theory of truth (and PSR), it isn’t clear how he can do this. (I used to think this was what he would say, but I’ve changed my mind.)

 

 

I think L’s response would be this:

Even though a CC contains all true predicates of a substance and would not exist without having all of them, some of these predicates are only virtually contained.

 

This replies on a distinction L draws between explicit and virtual containment:

A predicate P is contained explicitly in a CC iff P can be derived by a terminating (finite) analysis of CC.

 

A predicate P is contained virtually in a CC iff P can only be derived by a non-terminating (infinite) analysis of CC.

 

This is Leibniz’s “infinite analysis” theory of contingency:

A proposition is necessarily true iff its truth can be ascertained by a finite analysis.

 

A proposition is contingently true iff its truth can only be ascertained by an infinite analysis.

 

 

 

 

On its surface, this theory is baffling (ironically, especially for Leibniz, since he invented calculus, which consists of necessary truths).

 

 

 

My view:

      In order for God to carry out the analysis of any contingent truth, he needs to survey the pre-existing field of possible truths and then choose the best among them. That is, the infinite analysis doctrine presupposes that possibility is wider than actuality. Actuality depends on divine choice, which is contingent because other possibilities exist.

 

 

This is woefully unsatisfactory.

 

God could have chosen differently because his choices are contingent, and they are contingent because God could have chosen differently.

 

 

 

In Leibniz’s later metaphysics, he seems to decentralize logical relationships in favor of phenomena (= perceptions).

 

This is because if only mental substances exist, then the most basic properties of mental substances must also belong to the category of mentality. For Leibniz, the most basic class of mental properties is perception.

 

 

L endorses unconscious perceptions, which distinguishes him from Descartes.

 

Instead of focusing on the CCD and God’s knowledge of substances, L holds that each substance (= “monad”) “perceives the entire universe from its own point of view.”

 

 

That is, the relation of each monad to every other is not indirect (dependent on divine omniscience) but is found internally within each monad. (Old doctrine, new emphasis.)