بسم الله الرحمن الرحيم

الحمد لله الباقي القديم، المتوحد ذي الفضل العظيم.

أما بعد

The belief in Allāh being the Necessary Existent is one of the most pivotal points of creed held by orthodox Sunnī theologians. Anything that breaks the necessity of God breaks the belief in the Ultimate Creator, therefore disproving His Existence, opening the doors to atheism. There are various arguments that detail the necessity of a creator, such as Burhān al-Ḥudūth, Burhān al-ʾImkān and others. This article isn’t for that purpose. Instead we will be looking at the entailments of such a belief. What does it mean for God to be Necessary? One of the entailments of God being necessary is that contingent existences cannot occur within His Essence.

As a definition, necessary is something whose non-existence is impossible to occur. Contingent is something whose existence was preceded by non-existence. The definitions by their very nature contradict one another, as necessary is something that never ceases to exist, whereas contingent is something that didn’t exist at one point, which makes the two concepts, if they were to converge in one entity, to violate the law of non-contradiction, which is rationally impossible.

Now the first argument may not satisfy some as they may limit contingency to just dependency. Let us unpack what it really means to be contingent, to get a better idea.

(As a note, I will be utilising modal logic notation in this article so below is my framework for the symbols I use:)

Modes. □ = wājib (necessary), ◇ = mumkin (possible), □¬ = mumtaniʿ (impossible). Two-sided contingency, al-ʾimkān al-khāṣṣ, is defined: Cx ↔ (◇Ex ∧ ◇¬Ex) — “x is contingent iff it can exist and can fail to exist.”

Predicates. Ax accident (ʿaraḍ) · Jx atom (jawhar) · Dx depends on a locus (muftaqir ʾilā maḥall) · Dep(x) depends on a cause/preponderator (the genus of which Dx is a species) · Hx contingent (ḥādith) · Qx pre-eternal (qadīm) · Ex exists · Cx contingent · g = Allāh.

Background system: S5 — chosen because the modalities are ʿalā al-ʾiṭlāq (absolute) and dhātī (essential). The S5 collapse of iterated modalities just is the claim that these statuses don’t themselves vary.

What Consists in Contingency?

Contingency is marked by two qualities, which the later arguments will rely on:

1. (μ1) Dependence — iftiqār: Cx → Dep(x). “Every contingent leans on an external preponderator (murajjiḥ).” Locus-dependence Dx is its species.
2. (μ2) Possible non-existence — ʾimkān al-ʿadam: Cx → ◇¬Ex. This falls straight out of the definition of ʾimkān khāṣṣ. An accident’s perishing (lā yabqā zamānayn) is its temporal realisation.

Now, when it comes to anything beyond accidents, the reason they may be contingent, too, lies on the receptivity proof (a qiyās murakkab):

1. Nisbaħ wāḥidaħ: R(s,φ) ↔ R(s,φ*) — receptivity to an attribute is receptivity to its contrary; the capacity comes as a matched pair.
2. Plenitude / no-void: □ ∀t ∃φ inheres(φ, s, t) — “necessarily, at every moment some determinate of the range inheres in s.” The substrate can never sit bare.
3. ∀φ Hφ — each such determinate is contingent.
4. ∴ □ (s is never free of ḥawādith).
5. Major (the article’s own thesis): ∀x ( “never free of ḥawādith” → Hx ).
6. ∴ Hs — the substrate is itself originated.

Contingency propagates upwards from accidents to whatever bears them. This is still why an atom is contingent.

The Contrast Class: God’s Necessity

1. (G1) □Eg — “Allāh necessarily exists” (wājib al-wujūd bi-dhātihi); hence ¬◇¬Eg.
2. (G2) ¬Dep(g) — “He leans on nothing” (ghanī, qāʾim bi-nafsihi); in particular □¬Dg.
3. (Q) ∀x ( Qx → □Ex ) — the maxim mā thabata qidamuhu istaḥāla ʿadamuhu: “whatever’s pre-eternity is established, its non-existence is impossible.” With Qg this delivers G1.

Dissimilarity to Accidents

Both are qiyās istithnāʾī by rafʿ at-tālī (denying the consequent).

B1 — dependence.

• Major: ∀x(Ax → □Dx) — “every accident necessarily depends on a locus” (by its ḥaqīqaħ).
• Sharṭīyyaħ: Ag → □Dg. Istithnāʾ: □¬Dg (G2). ∴ ¬Ag.
• The one technical line, ◇□Dx → □Dx (S5), lifts this to □¬Ag: impossible, not merely false —istaḥālaħ mumāthalatuhu.

B2 — permanence.

• From the accident’s perishing: ◇¬Ex; by the contrapositive of (Q), ¬Qx — “the accident is not pre-eternal.”
• Sharṭīyyaħ: Ag → ◇¬Eg. Istithnāʾ: ¬◇¬Eg (G1). ∴ ¬Ag, lifting to □¬Ag.

B3 — a fortiori (qiyās al-ʾawlā). By Layer I (What Consists in Contingency?) the atom’s contingency is grounded in the accident’s. So if resemblance to an atom would entail Cg, resemblance to the accident entails it more strongly (ʾaqwā), and the accident carries the extra disqualifiers B1 and B2 on top, leaving the case overdetermined.

The Generalisation: Dissimilarity to Every Contingent

B1 was reasoned through the fact that accidents are locus-dependent, and B2 via perishing. They were reasoned via species. We can lift these arguments to their genus and the whole result generalises as below:

• (μ1) Cx → Dep(x) and (μ2) Cx → ◇¬Ex.
• Allāh: ¬Dep(g) (G2) and ¬◇¬Eg (G1) — both marks excluded at once.
• Modus tollens on either: ¬Cg, lifting in S5 to □¬Cg — “it is impossible that Allāh be contingent.”
• Exhaustive dichotomy: every existent is wājib ʾaw mumkin, no third (the mumtaniʿ does not exist). There is exactly one wājib. ∴ Allāh is, of necessity, dissimilar to every existent other than Himself.

This is what we call Mukhālafaħ lil-Ḥawādith (Dissimilarity from Contingent Existences), derived as a theorem. Layer III (Dissimilarity to Accidents) is now subsumed and not discarded. B1 is the μ1-instance (Dx ⊂ Dep), B2 the μ2-instance (perishing ⊂ ◇¬E), the atom one further instance.

The Two Hinges

The argument runs on two different frames, yet they still converge on the same conclusion: God is Dissimilar to Every Contingent, however they rest on different premises:

• Ḥudūth route: the hinge is (Q), qidam → wujūb — pre-eternity entails necessity of existence.
• ʾImkān route: the hinge is (μ1), the murajjiḥ premise: that contingency genuinely requires an external preponderator; together with the exhaustive wājib/mumkin division.

What Does the Formalism Earn?

The three rational judgements map directly onto the operators (wājib=□, mumkin=¬□p ∧ ¬□¬p, mumtaniʿ=□¬), so the vocabulary was already modal in all but notation. What the symbolisation into modal logic demonstrates is three things:

1. Layer I’s (What Consists in Contingency?) premise is a necessity (□¬ of a bare substrate, not a mere observation).
2. The impossible verdicts in Layers III–IV (Dissimilarity to Accidents and The Generalisation: Dissimilarity to Every Contingent) require S5-strength to be earned from categorical premises.
3. The accident-proofs stand to the general proof as species to genus.

Inherence of Contingent Existences (Ḥulūl al-Ḥawādith)

Now, anyone who believes in a spatio-temporal God, a God who speaks in time, acts in time, or anything of the sort fall into this, as all of these require some form of ḥudūth arising in the Essence of Allāh, hence violating His Necessity, making their belief redundant.

We can dive deeper into this by looking at the necessary consequence (ʾilzām) of these beliefs is to attribute God with contingent existences. To say God is receptive to these things is to say His Essence is a locus in which contingent existences inhere. However, the receptivity proof establishes two things:

1. whatever is receptive to a temporal attribute is receptive to its contrary, and the relation is one,
   so it is never free of the pair, and
2. whatever is not free of contingent things is itself contingent

Adding these together within God would require that He would be contingent too, and by virtue of that, He would require a creator/cause too. This is a negation of the belief of Him being the Necessary Existent.

Now the specific positions the claimants of this belief hold, and that I want to focus on for now, can be summarised into the following categories:

1. Motion
2. Speech in letters and sounds
3. Acting in time
4. Existing in time

As for motion, anything receptive to movement is receptive to stillness. Motion has a contradictory to it, being stillness. We’ve already provided the proof of Allāh being dissimilar from accidents, and to all bodies. Motion also entails occupying a place and changing it. This entails direction, extension and composition. All of these are signs of contingency. When it comes to terms like these mentioned in the Qurʾān, we either relegate the meaning to Allāh (tafwīḍ) or interpret it in light of His Being Necessary (taʾwīl), however we do not interpret it literally.

As for speaking in time, if His Speech is a succession of contingent, originated sounds and letters subsisting in Him, His Essence again would be a locus to contingent existences. We do have a way to understand the Speech of Allāh in the split between His Kalām Nafsī (Essential Speech) and Kalām Lafẓī (Perceptible Speech) but this isn’t the place to delve into them.

Acting in time requires dependence on a preponderator, and dependence is a sign of contingency. If one argues that He has always been acting with successive contingent acts, then a beginningless chain of contingent events would occur, which can easily be refuted by the impossibility of actual infinity (which there will be an article for this in the future ان شاء الله).

As for existing in time, then this is also impossible for Allāh. If He were to, time would encompass and measure Him. He would have a before and after. All of this entails change, and change entails He could have been otherwise. If He could have been otherwise He would not be necessary. God is Transcendent to time, and not an infinite duration within it.

All of these collapse to the same point: change means a thing can be another way than it is, which is the very definition of the contingency mark μ2, plus the dependence of μ1. We have proved □¬Cg: it is impossible that God be contingent. A mutable, temporal, moving god is a mumkin god, and “necessary being that is contingent” is a flat contradiction. So the position isn’t merely wrong; it is incoherent on its own terms once you grant that He exists necessarily.

وما علينا إلا البلاغ المبين