The prompt said, “Explain the core arguments using formal logic:”, and contained the full text of this dialogue.

Below is a reconstructive formalization of the main argumentative moves in the dialogue. I’ll use (i) first-order logic with identity, (ii) a light modal layer for Leibniz’s “necessary/possible,” and (iii) explicit definitions (since Leibniz’s strategy is: replace troublesome words with their meanings).

0) Notation (minimal “language”)

Individuals: agents (x,y); God $g$; events/acts $e$; states $s$. Predicates / relations:

$God(g)$
$Omni(g)$: omniscient (enough for the early proof)
$Just(x)$
$Loves(x,y)$
$Happy(y)$
$Harmony(s)$
$HasHappyState(y,s)$
$Knows(x,s)$
$Exper(x,s)$: $x$ “experiences” $s$ (as harmony)
$Del(x,s)$: $x$ is delighted by $s$
$Sin(e)$
$PartOf(e,B)$: event $e$ is part of world-series $B$
$Will(x,e)$, $NotWill(x,e)$, $Permit(x,e)$
$Cause(x,e)$, $Author(x,e)$

Modal operators (Leibniz’s “in itself”):

$\Box p$: $p$ is necessary (its negation implies contradiction)
$\Diamond p$: $p$ is possible (conceivable without contradiction)

1) “God is just” via definitions (justice → universal love)

Definitions (as in the dialogue)

Justice: $$ Just(x) \; \overset{def}{\leftrightarrow}\; \forall y, Loves(x,y) $$
Love: $$ Loves(x,y) \;\overset{def}{\leftrightarrow}\; \exists s,(HasHappyState(y,s)\wedge Del(x,s)) $$ (Informally: loving $y$ is being delighted by $y$’s happiness-state.)
Delight: $$ Del(x,s)\;\overset{def}{\leftrightarrow}\; Exper(x,s)\wedge Harmony(s) $$
Happiness is harmonic: $$ Happy(y)\to \exists s,(HasHappyState(y,s)\wedge Harmony(s)) $$ (This encodes the earlier sub-argument that happiness is a maximally harmonious mind-state.)
Omniscience “covers” harmony: $$ Omni(x)\to \forall s,(Harmony(s)\to Knows(x,s)) $$
Knowing harmony yields experiencing it (a substantive bridge the dialogue relies on): $$ \forall x\forall s,((Knows(x,s)\wedge Harmony(s))\to Exper(x,s)) $$

Target claim

$$ God(g)\wedge Omni(g)\;\to\; Just(g) $$

Derivation sketch

Let $y$ be arbitrary.

Assume $God(g)\wedge Omni(g)$.
Suppose $Happy(y)$. Then by (4) pick (s) with ($asHappyState(y,s)\wedge Harmony(s)$.
From $Omni(g)$ and $Harmony(s)$, get $Knows(g,s)$ by (5).
From $Knows(g,s)\wedge Harmony(s)$, get $Exper(g,s)$ by (6).
Then $Del(g,s)$ by (3).
So $Loves(g,y)$ by (2).
Since $y$ was arbitrary, $\forall y, Loves(g,y)$.
Hence $Just(g)$ by (1).

So the early “God is just” proof is essentially: definitions + (Happiness ⊆ Harmony) + (God knows all Harmony) + (knowing harmony = experiencing it).

2) Principle of Sufficient Reason (PSR) ⇒ God is the ultimate reason for the world-series

Core PSR axiom

$$ \forall p,(Exists(p)\to \exists r,SR(r,p)) $$ $(SR(r,p)$ = “$r$ is a sufficient reason for $p$”)

“Sufficient reason entails” principle

$$ SR(r,p)\to (Exists(r)\to Exists(p)) $$ (If $r$ is sufficient for $p$, then $r$’s existence guarantees $p$’s.)

Leibniz’s key move: let $A$ be God, $B$ be the actual world-series

Let $A := Exists(g)$ and $B := Exists(WorldSeries)$.

Assume: $$ SR(g,WorldSeries) $$ Then: $$ Exists(g)\to Exists(WorldSeries) $$ i.e. $$ A\to B $$

By classical contraposition: $$ \neg B \to \neg A $$

That is the “if this series were removed/changed, God would be removed/changed” move in formal clothing: given “this God” as the sufficient reason of “this world-series,” you don’t get the same God with a different series.

3) “God is cause of sin” but “not author of sin” (will vs understanding; whole vs parts)

Definitions he later insists on

To will: $Will(x,e)$ = “$x$ is delighted by $e$’s existence” (we can model it as) $$ Will(x,e)\;\overset{def}{\leftrightarrow}\; Del(x,Exists(e)) $$
To not-will: $$ NotWill(x,e)\;\overset{def}{\leftrightarrow}\; Del(x,\neg Exists(e)) \;\;\vee\;\; Pain(x,Exists(e)) $$
To permit: $$ Permit(x,e)\;\overset{def}{\leftrightarrow}\; Knows(x,e)\wedge \neg Will(x,e)\wedge \neg NotWill(x,e) $$
Author: (explicitly stated in the text) $$ Author(x,e)\;\overset{def}{\leftrightarrow}\; Will(x,e)\wedge Cause(x,e) $$

The “whole does not distribute to parts” point

Let $B$ be the whole world-series. Leibniz wants:

God wills the whole series: $$ Will(g,B) $$
Sins are parts of the whole: $$ Sin(e)\to PartOf(e,B) $$
But it does not follow that God wills each sinful part: $$ Will(g,B)\wedge PartOf(e,B)\;\not\vdash\; Will(g,e) $$

Formally, Leibniz blocks an invalid inference schema: $$ \forall x\forall B\forall e,\big((Will(x,B)\wedge PartOf(e,B))\to Will(x,e)\big) $$ He rejects that schema.

What he does keep

God is (in a grounding/“physical”) sense the cause of anything in the series: $$ PartOf(e,B)\to Cause(g,e) $$
But sins are not willed “in themselves”: $$ Sin(e)\to \neg Will(g,e) $$
Therefore: $$ Sin(e)\to \neg Author(g,e) $$ since $Author(g,e)$ requires $Will(g,e)$.

So the structure is:

Grounding: $Cause(g,e)$ for all $e\in B$
Non-authorship: $Sin(e)\to \neg Will(g,e)$
Therefore: God is not the “author” of sin though he is ultimate reason/cause of the existence of the series in which sin occurs.

4) The “fatalism” objection and Leibniz’s modal fix: necessity-in-itself vs necessity-by-hypothesis

Leibniz’s explicit definition

$$ \Box p \;\overset{def}{\leftrightarrow}\; \neg \Diamond \neg p $$ (“Necessary = opposite implies contradiction.”)

Then “contingent in itself” is: $$ Cont(p) \;:=\; \Diamond p \wedge \Diamond\neg p $$

His key denial

He rejects the unrestricted rule: $$ (\Box A \wedge (A\to p))\to \Box p $$ in the intended reading of “follows.” (He treats the relevant “follows” as hypothetical/certainty from the actual series, not as metaphysical entailment.)

So he separates:

Absolute necessity: $\Box p$ (contradiction if not-$p$)
Certainty given the actual harmony: think “given $H$”: $$ \Box(H\to p)\quad \text{and}\quad H $$ which yields $p$, but not $\Box p$.

This matches his line: Judas’s non-salvation is certain/foreseen/“necessary by accident” (given the actual series), while not contradictory to conceive Judas saved: $$ \Diamond(Saved(Judas)) $$ even though (in the actual world-series) ( \neg Saved(Judas)).

The reduplication point (“whatever is, necessarily is”)

He interprets “Whatever is, necessarily is” as the tautology: $$ \Box(Exists(e)\to Exists(e)) $$ not as: $$ Exists(e)\to \Box Exists(e) $$ So he’s dissolving fatalistic slogans by expanding them into what they actually mean.

5) Freedom under PSR: reject “libertarian indifference,” keep spontaneity + rational choice

PSR applied to willing

$$ Will(x,e)\to \exists r,SR(r,Will(x,e)) $$

His definitional chain (compressed)

Willing tracks what appears good/harmonious: $$ Will(x,e)\leftrightarrow AppearsGood(x,e) $$
Appearing good depends on agent+object+medium: $$ AppearsGood(x,e)=F(Temperament(x),Object(e),Context) $$ So (holding fixed the full state), will is not “up to” a further will: $$ \neg \exists w ,(Will(x,w)\wedge SR(w,Will(x,e))) $$ on pain of regress.

The criticized definition of free will

The target is roughly:

able to act or not act with all requisites equal.

If “all requisites” includes the complete sufficient conditions for acting, then:

Let $Req(x,e)$ be the conjunction of requisites for $Do(x,e)$, and define action as: $$ Do(x,e)\leftrightarrow Req(x,e) $$ Then: $$ Req(x,e)\to Do(x,e) $$ So the libertarian demand $$ Req(x,e)\wedge \neg Do(x,e) $$ is inconsistent.

Leibniz’s positive definition (Aristotelian)

He keeps:

Spontaneity: source of action in agent
Freedom: spontaneity + choice (improved by knowledge)

You can model the “degree of freedom” idea as: $$ FreedomDegree(x)\uparrow \text{ as } Knowledge(x)\uparrow \text{ and } PassionNoise(x)\downarrow $$ Not a single clean FOL axiom, but the logical point is:

no “reasonless toggling” is needed for freedom;
freedom is compatible with PSR because the relevant explanation is: the agent acts from their own reasons/character/intellect, not from external compulsion alone.

6) Damnation as self-caused: hatred of God → maximal pain → “always damnable”

Definitions paralleling the love argument

Love: delight at another’s happiness
Hatred: pain at another’s happiness $$ Hates(x,y) \;\overset{def}{\leftrightarrow}\; PainAt(x,Happy(y)) $$
God as maximal happiness: $$ MaxHappy(g) $$
Max pain (= damnation) arises from hating maximal happiness: $$ (Hates(x,g)\wedge MaxHappy(g))\to Damned(x) $$

Persistence post mortem (a substantive premise)

He assumes: after death, no new sensory inputs, so the “last dominant orientation” persists/escalates: $$ Dies(x)\wedge LastStateIsHatred(x,g)\to \forall t>death, Hates(x,g) $$ Then: $$ \forall t>death,Damned(x) $$ But he rhetorically reframes this as: they are never “statically damned,” always “damning themselves” (an “always re-instantiating” state).

“No just complaint” structure

His complaint-blocking move is basically:

If a person is shown the consequence and has the (internal) route to avoid it conditional on willing it, then responsibility attaches to the will-state: $$ (SeesConsequence(x)\wedge CanAvoidIfWills(x))\to \neg JustifiedComplaint(x) $$ Even if the will-state itself has an explanation, punishment is keyed to the present resolved wicked will, not to tracing an infinite regress of causes.

7) “Why this soul?” dissolves into individuation-by-place-and-time

He treats “thisness” (haecceity) as fixed by spatiotemporal determination in cases of maximal similarity.

A clean way to capture the punchline:

Let $Origin(x)$ be the ordered pair $\langle t,place\rangle$.

Principle (for the “maximally similar eggs/souls” case): $$ (Origin(x)=Origin(y)\wedge Intrinsic(x)=Intrinsic(y))\to x=y $$

Then the question:

Why is this soul in these circumstances?

becomes:

Why does $x$ have $Origin(x)$?

But if you “move” the origin, you are no longer talking about the same individual: $$ Origin(x)\neq Origin(y)\to x\neq y $$ So “Why am I not born elsewhere/otherwise?” reduces to “Why am I not someone else?”, which is not a substantive complaint about justice on his view.

What ties these arguments together (one meta-schema)

Leibniz is repeatedly doing this:

Replace loaded terms by definitions (justice, love, will, permission, necessity).
Block invalid distribution rules (whole → parts, “follows” → “necessary in itself”).
Distinguish kinds of explanation:
- grounding/physical cause vs moral authorship,
- absolute necessity vs certainty under the actual harmony,
- freedom as rational self-determination vs “reasonless indifference.”

If you want, I can rewrite the above into a single compact “axiom set + theorems” presentation (like a mini formal system) or do a Fitch-style proof for one thread (e.g., the anti-fatalism move) in full detail.

Thiago’s ChatGPT Blog

Friday, February 27, 2026

Philosopher’s Confession (Leibniz), formalized