The tradition calls God *infinite*: unlimited, unbounded, without measure. Quantitative infinity is always infinity along a magnitude, number, degree, or intensity. Classical divine infinity is offered instead as non-quantitative absence of ontological limitation, so the section must assess that analogical sense rather than assume the quantitative one exhausts the term. In its familiar uses, infinity is a fact about a magnitude with no greatest, a series that does not terminate, a scale that runs on without end. The classical God, though, has no magnitude (it is immaterial), no number (it is one and simple), no parts to be many, no degrees of more-and-less (simplicity admits no composition of intensities). Strip away every dimension along which a thing could be unbounded, and the question presses: infinite in *what*?

*What the tradition holds.* Classical theology makes infinity a divine perfection: God is *infinitus*, without limit, and the tradition is careful about the sense. God is not infinite in magnitude or quantity: Aquinas follows Aristotle in holding an actual infinite magnitude impossible, so divine infinity is neither spatial nor numerical bulk (Aquinas, *ST* -(Aquinas, Thomas, (1265–1274) 1947), I.7.1–4; cf. Aristotle, *Physics* -(Aristotle, (4th c. BCE) 1984), III). Divine infinity is infinity *of being*: God's act of existing (*esse*) is unlimited because it is not received in, and so not contracted by, any matter or essence that would bound it, a form unlimited by reception. Where a finite being's existing is limited by the essence that receives it, God's existing is its essence and is subject to no such limit; God holds the whole perfection of being without restriction. Infinity, so understood, is the negative face of the divine fullness: *in-finite*, not-bounded, because there is nothing outside God to bound God. The doctrine keeps the believer's intuition that God exceeds every creature without measure, and binds it to the unlimited perfection of being rather than to any quantity.

*What cannot be answered.* Four questions leave the doctrine without an answer once *infinite* has to specify what it is the infinity of. What presses beneath them is that unboundedness has content only relative to a dimension, and the classical God is defined to have none.

**Q1.** *If God has no magnitude, no number, and no degree, what is God infinite in?* To be infinite is to be unbounded along a dimension: a magnitude with no greatest, a count with no last, a scale with no ceiling. The classical God has no magnitude (immaterial), no number (simple, one), no parts and so no quantity, no degrees of intensity (simplicity excludes more-and-less). With every dimension of unboundedness removed, *infinite* has no variable to range over. If no positive account of unlimited *esse* is supplied, the predicate risks becoming merely negative. That is a determinacy burden, not yet a category mistake, because the Thomist explicitly denies that divine infinity is a magnitude.

**Q2.** *If God's infinity is unlimited being rather than unlimited size, what is the more-and-less of being along which God is the maximum?* The tradition's best move relocates infinity from quantity to *esse*, and refuses to concede that this names a scale at all. Infinity of being, on the Thomist account, is a *negative* determination: God's *esse* is unlimited not because it tops some dimension of intensity but because it is unreceived, not contracted by an essence that would bound it (*ST* -(Aquinas, Thomas, (1265–1274) 1947), I.7.1). Unboundedness here is the *absence* of a limiting receiver, not a maximal rung on a ladder of more-and-less, so the demand "unbounded along what?" is said to misfire. It is the strongest reply the doctrine has, and [§6.2.1](<6.2.1 Simplicity.md>) has already run it to its end. *Esse* unreceived by any essence is *ipsum esse subsistens*, and [§6.2.1](<6.2.1 Simplicity.md>) fixes what that construal delivers: an act of existing with no receiving essence has no determinate kind-content, no what-it-is, nothing but the bare that-it-is. Press the infinity-claim through that result. Either the unreceived *esse* has determinate content (it is *this* plenitude and not another, full in *these* respects rather than those) and that content is contrastive, a being thus-and-not-otherwise, which reinstates the very differentiation a scale records and seats divine infinity back inside the order of more-and-less; or it has no determinate content, and then its property-list is the property-list [§2.7](<2.7 Nothing to Consider.md>) assigns the Null State, so "infinite being" names not the maximum of being but ∅. The negative determination does not slip the fork; it inherits it. What is genuinely unbounded (limited by nothing outside because there is no outside) is not an unreceived *esse* standing beyond the order but the structural conditions within which bound and measure are defined at all.

**Q3.** *If no completed actual infinite is possible, how is God an actual infinite, and if God's is merely potential or qualitative, in what does it exceed the finite?* The theistic tradition that presses the impossibility of a completed actual infinite to argue for a beginning of the world (William Lane Craig, 1979) cannot then help itself to a completed actual infinite in the divine being without strain. The charge must be stated precisely or it equivocates: what that tradition forbids is an actual infinite *magnitude or multitude* (an infinite of quantity) and [§5.1.2](<5.1.2 Cosmological Argument.md>) defends the actual infinite on exactly that quantitative terrain against the Kalām. Divine infinity, the Thomist rightly answers, was never quantitative (the first question), so the prohibition does not reach it directly. The remaining question is whether "unlimited being" has intelligible non-scalar content; failure to provide it would make the predicate obscure, but it would not revive the mathematics of completed multitudes. If it is merely potential, it is a never-completed limit, the infinity of a process rather than of a perfect being. And if it is "qualitative," the second question returns unanswered: qualitative along what?

**Q4.** *If God's infinity just is God's simple essence, what tells it apart from finitude?* On simplicity ([§6.2.1](<6.2.1 Simplicity.md>)), infinity is not a feature added to the essence but the essence itself. Yet the marks by which the infinite is told from the finite (the finite can be exceeded, added to, bounded; the infinite cannot) are all marks along a dimension, and a partless essence standing on no dimension of more-and-less bears none of them. Where there is no scale at all, *infinite* and *finite* lose their contrast together, exactly as [§6.2.1](<6.2.1 Simplicity.md>) finds a simple essence admitting no internal differentiation losing the contrasts identity needs. An infinity that differs from finitude in no specifiable respect is *infinite* in name only.

*What is required.* Taken in order, the four pressures settle what *infinite* depends on. Infinity is unboundedness along a dimension; remove every dimension and the predicate has nothing to range over. Relocating infinity from magnitude to being does not escape this: *more-and-less of esse* is itself a scale, and the negative-determination reply forks, by [§6.2.1](<6.2.1 Simplicity.md>), into scale or ∅. The tradition's own anti-infinitism forbids a completed actual divine infinite of quantity, and the retreats to potential or qualitative infinity either reintroduce process or reopen the demand for a dimension. And an infinity identical with a partless, scaleless essence loses its contrast with finitude altogether. What *infinite* survives as, once the pressures have run, is not a perfection a simple being could hold but unboundedness along the dimensions there are, which are the structural ones.

*What is inverted.* Infinity is the limitlessness of the structural conditions themselves. *Infinite*, in the sense that comes through intact, names what has no outer bound, and what has no outer bound is not a being among beings but the structure within which bound and measure are defined. The structural roles do not by themselves establish that physical space is spatially unbounded or that time has no first or last moment. Cosmological boundary questions remain distinct from the claim that any boundary is represented within a broader structural description; the structural conditions admit no *outside* by which they could be bounded, because *outside* is itself a structural notion. □(T∧S∧Φ), if established, is unrestricted in modal scope. Calling that "infinite" in Aquinas's sense is an analogy that requires care, not a direct consequence of the absence of a spatial or temporal exterior. The tradition reaches for *infinite* to say that God is limited by nothing outside; traced honestly, what is limited by nothing outside is Nature, since only the condition of all limits can fail to stand under one. The infinite God is Nature's own limitlessness, named as though it belonged to something beyond Nature, when *beyond Nature* is the one place that cannot be.


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← [6.2.2 Unity](<6.2.2 Unity.md>) | [6.2.4 Perfection](<6.2.4 Perfection.md>) →
