“Canst thou by searching find out God? canst thou find out the Almighty unto perfection? It is as high as heaven; what canst thou do? deeper than hell; what canst thou know? The measure thereof is longer than the earth, and broader than the sea.”
Job 11:7-9
“Great is our Lord, and of great power: his understanding is infinite.”
Ps. 147:5
“that ye… may be able to comprehend with all saints what is the breadth, and length, and depth, and height; and to know the love of Christ, which passeth knowledge, that ye might be filled with all the fulness of God. Now unto him that is able to do exceeding abundantly above all that we ask or think, according to the power that worketh in us, unto Him be glory in the church by Christ Jesus throughout all ages, world without end. Amen.”
Eph. 3:17-21
.
.
Subsection
.
.
Order of Contents
Infinity
Divine Infinity
. Articles 12+
. Book 1
. Quotes 3
. Thomas vs. Scotus 1
. Historical 12
. Latin 10+
. Biblio 1
.
On Infinity & Infinities
.
Articles
Antiquity
Aristotle – Physics, bk. 3
“In his treatment of Zeno’s paradoxes about infinite divisibility, Aristotle (384-322 B.C.E.) made a positive step toward clarification by distinguishing two different concepts of infinity, potential infinity, and actual infinity. The latter is also called complete infinity and completed infinity. The actual infinite is not a process in time; it is an infinity that exists wholly at one time. By contrast, Aristotle spoke of the potentially infinite as a never-ending process over time, but which is finite at any specific time.
The word ‘potential’ is being used in a technical sense. A potential swimmer can learn to become an actual swimmer, but a potential infinity cannot become an actual infinity. Aristotle argued that all the problems involving reasoning with infinity are really problems of improperly applying the incoherent concept of actual infinity instead of the coherent concept of potential infinity…
For its day, this was a successful way of treating Zeno’s Achilles paradox since, if Zeno had confined himself to using only potential infinity, he would not have been able to develop his paradoxical argument. Here is why.
Zeno said that to go from the start to the finish line, the runner must reach the place that is halfway-there, then after arriving at this place he still must reach the place that is half of that remaining distance, and after arriving there he again must reach the new place that is now halfway to the goal, and so on. These are too many places to reach because there is no end to these places since for any one there is another.
Zeno made the mistake, according to Aristotle, of supposing that this infinite process needs completing when it really doesn’t; the finitely long path from start to finish exists undivided for the runner, and it is Zeno the mathematician who is demanding the completion of such a process. Without that concept of a completed infinite process there is no paradox.
Although today’s standard treatment of the Achilles paradox disagrees with Aristotle and says Zeno was correct to use the concept of a completed infinity and to imply the runner must go to an actual infinity of places in a finite time, Aristotle had so many other intellectual successes that his ideas about infinity dominated the Western world for the next two thousand years.” – Bradley Dowden
.
1900’s
Sweeney, Leo – ‘Infinity’ in New Catholic Encyclopedia VI (NY: McGraw Hill, 1967), pp. 504-8
.
2000’s
Wikipedia
‘Infinity’
‘Absolute Infinite’
‘George Cantor’
Internet Encyclopedia of Philosophy – ‘The Infinite’
“A second reason to believe humans cannot grasp infinity is that the concept must contain an infinite number of sub-concepts, which is too many for our finite minds. A counter to this reason is to defend the psychological claim that if a person succeeds in thinking about infinity, it does not follow that the person needs to have an actually infinite number of ideas in mind at one time…
Here is a simple argument that we can: If we understand negation and have the concept of finite, then the concept of infinite is merely the concept of not-finite.”
Stanford Encyclopedia of Philosophy
‘Infinity’
‘Continuity & Infinitesimals’
.
.
Books
1900’s
Rucker, Rudy – Infinity & the Mind: The Science & Philosophy of the Infinite (Princeton Univ. Press, 1995)
.
2000’s
Moore, A.W. – The Infinite 2nd ed. (Routledge, 2001)
Bell, John L.
The Continuous & the Infinitesimal in Mathematics & Philosophy (Milan: Polimetrica S.A., 2005)
The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics in The Western Ontario Series in Philosophy of Science 82 (Cham, Switzerland: Springer International Publishing, 2019)
.
.
Historical
All or Most of History
Books
Wallace, David Foster – Everything & More: A Compact History of Infinity Pre (Norton, 2004)
Maor, Eli – To Infinity & Beyond: A Cultural History of the Infinite Pre (Princeton Univ. Press, 1987)
.
On Antiquity
Book
Sweeney, Leo – Infinity in the Presocratics: A Bibliographical & Philosophical Study (Hague: Martinus Nijhoff, 1972)
.
Post-1880’s
Quote
Bradley Dowden, ‘The Infinite’ in Internet Encyclopedia of Philosophy
“There are actual infinities in the technical, post-1880s sense, which are neither endless, unlimited, nor immeasurable.
A line segment one meter long is a good example. It is not endless because it is finitely long, and it is not a process because it is timeless. It is not unlimited because it is limited by both zero and one. It is not immeasurable because its length measure is one meter.
Nevertheless, the one-meter line is infinite in the technical sense because it has an actual infinity of sub-segments, and it has an actual infinity of distinct points. So, there definitely has been a conceptual revolution.”
.
.
On Divine Infinity
.
Articles
1200’s
Aquinas – ch. 43, ‘That God is Infinite’ in Summa Contra Gentiles, bk. 1
Duns Scotus, John – distinctions 1-2 in Ordinatio, bk. 1, pp. 52-97 tr. Peter Simpson
Question 1: Whether among beings there is something existing actually infinite?
Question 2: Whether something infinite is known self-evidently?
Question 3: Whether there is only one God?
.
Anthology of the Post-Reformation
Heppe, Heinrich – sect. 6-8 in ch. 5, ‘The Attributes of God’ in Reformed Dogmatics ed. Ernst Bizer tr. G.T. Thomson (Wipf & Stock, 2007), pp. 65-67
Heppe (1820–1879), a German church historian and theologian collected a compendium of quotes from early reformed sources and organized them in the fashion of a systematic theology (many of which are inaccessible otherwise).
.
1600’s
Grotius, Hugo – On the Truth of the Christian Religion tr. T. Sedger 2nd ed. (1640; London: 1859), bk. 1
4. ‘That all perfection is in God’ 4-5
5. ‘And that, indeed, Infinite’ 5
Grotius (1583–1645) was a Dutch humanist, diplomat, lawyer, Arminian theologian, jurist, statesman, poet and playwright.
Becanus, Martin – ch. 5, ‘Concerning the Infinity of God’, pt. 1, 2 in Summa Theologiae Scolasticae tr. Michael Lynch (d. 1624; Leiden, 1683), First Tract on God & the Divine Attributes, pp. 23-24
Becanus (1563–1624) was a Dutch-born Jesuit priest, known as a theologian and controversialist.
Cheynell, Francis – pp. 3-7 of ch. 1, ‘The Godhead is Spiritual, Infinite, Incomprehensible’ in The Divine Trinunity of the Father, Son & Holy Spirit (1650)
Cheynell was a Westminster divine.
Leigh, Edward – ch. 4. ‘That God is Infinite, Omnipresent, Eternal’ in A System or Body of Divinity… (London, A.M., 1654), bk. 2, pp. 142-50
Le Blanc de Beaulieu, Louis – ‘On the Perfection & Infinity of God’ in Theological Theses Published at Various Times in the Academy of Sedan 3rd ed. tr. by AI by Colloquia Scholastica at Discord (1675; London, 1683), pp. 194-99 Latin
Le Blanc (1614-1675) was a French reformed professor of theology at Sedan.
Turretin, Francis – q. 8, ‘Is God infinite in essence? We affirm against Socinus and Vortius.’ in Institutes of Elenctic Theology, tr. George M. Giger, ed. James Dennison Jr. (1679–1685; P&R, 1992), vol. 1, 3rd Topic, pp. 194-96
van Mastricht, Peter
ch. 9, ‘The Infinity & Greatness of God’ in Theoretical-Practical Theology ed. Joel Beeke, tr: Todd Rester (RHB, 2018), vol. 2, Faith in the Triune God, pt. 1, bk. 2, pp. 181-92
The Gangrene of the Cartesian Innovations… (Amsterdam, 1677)
Section 2, the Particular Points of Cartesianism are Exhibited
13. On the Power of God, as it is able to Make an Infinite Burden 274-76
18. On the Nature of the Trinity
…
2. That communicability of an essence does not arise from infinity 326-28
19. On Creation in General
…
4. Between nothing and something there is not an infinite distance 350
20. On the Soul of the World, it being infinite and a unity 361
…
2. The world is of an indefinite quantity and is capable of being infinite 362
27. On the Intellect & Will of Man
2. About the Will, that the mode of it is infinite 451-57
.
1700’s
Howe, John – Works, vol. 1, Living Temple, pt. 1, ch. 4
De Moor, Bernard – sect. 18. ‘The Infinity & Perfection of the Divine Being’, pt. 1, 2 in Continuous Commentary, ch. 4, ‘On God’
.
1800’s
Vos, Geerhardus – questions 19-22, pp. 19-20 in Reformed Dogmatics tr. Richard B. Gaffin one vol. ed. (Lexham Press, 2020), vol. 1, ch. 2
.
1900’s
Wolter, Allan B. – Article 3, ‘On the Infinite & Finite’ in Little Summary of Metaphysics (Milwaukee: Bruce Publishing Co., 1958), pp. 73-75
Wolter was an American Scotus scholar.
Owen, H. P. – ‘Infinity in Theology & Metaphysics’ in ed. Paul Edwards, The Encyclopedia of Philosophy (1967), vol. 4, pp. 190-3
Hill, William J. – ‘In What Sense is God Infinite? A Thomistic View’ in The Thomist XLII (1978), pp. 14-27
Hill argues against the process theology of Alfred North Whitehead and his followers.
“The affirmation of God as transcending all such distinction… is not an admission that God’s being is contentless, however, but, on the contrary, the ascription to him of the very plenitude of all content.
He is this actual plenitude nonetheless in a way that remains unknown and unknowable, i.e., though affirmed by way of concepts and from a perspective provided by man’s concepts, he is not properly represented in any concept. To admit there could be a concept of God is to admit that his essence is something other than the act of being (esse)… Thus, God is what he is in a way that cannot be properly grasped in a concept because the latter expresses only a mode of being.
…
The determinateness of God, far from being exclusive of other determinations, is all-embracing in a unity transcendent to the rich diversity of the finite. All that is excluded is what pertains not to beings as such, but to their diminished or defective states, to being as
it suffers privation in its finite instances with such sequelae to
finitude as, e.g., evil. This is but to say: God is wholly infinite
and nowise finite.” – pp. 17-18
Balas, David L. – ‘A Thomist View on Divine Infinity’ in Proceedings of the American Catholic Philosophical Association, vol. 55 (1981), pp. 91-98
“The brief text… will address… the following points: 1. The historical development of infinity as a divine attribute; 2. The teaching of Thomas Aquinas on divine infinity; 3. A philosophical appraisal of this teaching; 4. An appraisal of this teaching from the point of view of Christian faith; 5. Some remarks on alternative positions – especially on process theism and a non-theistic stance – in view of a critical dialogue.” – p. 91
“both in Plato and in Aristotle infinity is associated with the realm of the ‘more-or-Iess,’ with indefiniteness and consequently with imperfection. The First Unmoved Mover is infinite only as to his power insofar as it is the cause of an endless circular motion.” – p. 91
“The most fundamental reason [for Thomas] why God’s perfection is infinite is that act is limited only insofar as it is received in a potency. ‘But God is act in no way existing in another, for neither is He a form in matter… nor does His esse inhere in some form or nature, since He is His own esse… It remains, then, that God is infinite” (prgr. 5). In other words: “…God, Who is pure act (actus purus) is infinite in His actuality (in sua actualitate)” (prgr. 6). He possesses esse, goodness, perfection not as participated, but by essence (his very esse in His goodness) and, therefore, He is infinite in goodness (prgr. 8-9).
A further argument… proceeds from the fact that our ‘intellect… extends to the infinite in understanding…. But this ordination of the intellect would be in vain unless an infinite intelligible existed” (prgr. 10).” – pp. 93-94
Thomas: “In a sense, however, both matter is limited by form and form by matter… Matter, however, is perfected by the form by which it is limited, and therefore infinity as attributed to matter means an imperfection, for it implies formless matter. Form, however, is not perfected by matter but is rather restricted by it, and therefore infinity on the part of a form not determined by matter connotes perfection.
But that which has the character of form in the highest sense (quod est maxime formale omnium) is esse itself… Therefore, since the divine esse is not received in something else but He (God) is his own subsistent esse (ipse est suum esse subsistens)… it is manifest that God is infinite and perfect.” – p. 94
.
Book
2000’s
eds. Göcke, Benedikt P. & Christian Tapp – The Infinity of God: New Perspectives in Theology & Philosophy Pre (Univ. of Notre Dame, 2019) ToC
Part 1 covers historical approaches to divine infinity. Part 2 contains chapters on systematic issues.
.
Quotes
Order of
Voet
Thomistic Theses
Wolter
.
1600’s
Gisber Voet
I. ‘Of God’ in Syllabus of Theological Problems (Utrecht, 1643), pt. 1, section 1, tract 2, 1. Whether there may be a God?, Controversies of the 2nd Kind
“Whether all being is rightly divided into finite and infinite, or created and uncreated, or whether indeed a third thing is given that is neither created nor yet God, so it may be ideas or the sephirot of the Jews, or a light that some construct, inaccessible, or an empyrean heaven? The prior is affirmed, the latter denied.”
.
1900’s
24 Thomistic Theses, thesis 23 (1914)
“The Divine Essence is well proposed to us as constituted in its metaphysical concept by its identity with the exercised actuality of its existence, or, in other terms, as the very subsisting being; and by the same token it exhibits to us the reason of its infinity in perfection.”
.
Allan Wolter
‘Allan Wolter’s Conclusions respecting Reality, Proving God’ (1958), ‘Conclusions respecting Reality’
“2. If the relatively permanent exists the absolutely permanent exists.
“Whatever can begin to be or cease to be is in itself indifferent to existing and not existing, otherwise it would either always exist or never exist. Everything thus indifferent does not, as such, have in itself the total reason for its existence or for its permanence. Therefore if such thing really is and persists, the reason not only for its beginning to be, after not being, but also for its persisting or continuing to be must be looked for in something else. Such a reason for the existence of another thing is by definition called the cause…
But what of the reason that a being persists? Either it is something that depends on another with respect to its existence and permanence or it is not. If it is independent with respect to existence and permanence it has in itself the reason of both and so cannot not exist. If it is not independent then either:
a) there is a regress to infinity, or
b) there is a circle in dependent things, or
c) there will be a stand at some being that is simply first, namely first in being independent both as to existence and as to permanence in existence.
a) An infinite series of [dependent] things existing simultaneously is impossible, because such a series would be simultaneously dependent and independent:
dependent because it would be indifferent to existing and would not have in itself a reason for existing;
independent because nothing would exist outside the series for it to depend on, otherwise it would not be an infinite series since [it would be] limited and brought to an end in the being on which it depends.
By such a series then cannot be explained why something exists. This argument is confirmed by an example. Who would say that a sufficient reason for the suspension of the whole of a chain could be found in the length itself of the chain even though it could not be found in any ring of the chain?
b) Similarly a circle of mutually dependent things involves a contradiction unless we suppose a sufficient cause outside the circle as such. Otherwise every individual cause would be the total cause of itself and so would be dependent and independent, caused and uncaused, at the same time, which is manifestly absurd.
c) If a) and b) are excluded, c) is what is left. So in every case there must be a being altogether independent as to its existence and its permanence.” pp. 34-35
…
4. An actually infinite series of simultaneously existing dependent things is impossible. [see 2]
…
8. Being is therefore divided into the transient and permanent. That the transient exists is continuously verified by experience; that the permanent exists follows from conclusion 7.
Scotus: “But in the case of disjunctive features [of being]… when the extreme that is less noble is posited of some being, the extreme that is more noble can be proved of some being – just as it follows that if some being is finite then some being is infinite, and if some being is contingent then some being is necessary. For in these cases the more imperfect extreme could not be present in some being in particular unless the more perfect extreme were present in some being on which the former would depend.” p. 21
…
16. In the same class of essentially ordered causes, the series cannot be infinite, for otherwise there would be an actually infinite series of simultaneously existing dependent things, which is impossible (from conclusion 4). Hence there cannot be an infinite series of essentially ordered efficient causes. The like must be said of final causes, or of material or formal causes.
…
48. If something accidental exists, something substantial exists.
Proof:
An accident depends essentially on its substrate. This dependence is of the same order as that which is found between formal cause and material cause. For substance is as it were the matter of accidents. Hence for any accident that actually exists there is required the simultaneous existence of another being, namely that in which the accident is. If this other is not something substantial but on the contrary an accident, then some third being is required. But there cannot be a regress to infinity, both because there would be at the same time an infinite number and because dependence in any essential order ends in some independent being in the same order.
…
Everything Finite is Caused, to an Infinite Being
[see pp. 73-74 of the Summary]
63. Everything finite, therefore, is a caused being or a being from-another.
This follows from the two previous conclusions. For a being is finite because it is constituted either from mixed perfections or from pure perfections finite in number or degree. But from conclusion 61, all mixed perfections can be reduced to pure perfections in finite degree. But, from its own definition, no pure perfection contains in itself a reason for limiting itself intensively, nor does it have a reason for excluding other pure perfections from the being in which this perfection is (from conclusion 62)
Therefore if a full and sufficient reason for the actual limitation of a finite being cannot be found in the positive being-ness of the finite being itself, it must be in some other being, namely in the cause that gives the finite being its positive being-ness. In other words, no finite thing qua finite is from-itself, but everything of this sort is from-another.
64. Conversely, no being that is altogether independent and uncausable can be finite, either intensively or extensively.
65. If there is something finite, there is something infinite.
I prove it as follows: a finite being, because it is also a caused being, involves the existence of another being, namely an uncaused being (from conclusion 23 and following). But from conclusion 64, an uncaused being is both intensively and extensively infinite.
66. An infinite being actually exists.
This follows from the fact that there exists an uncausable being (conclusion 27) or a being from-itself (conclusion 33). But it can be proved immediately as follows: There is or can be something. Such a thing is either finite or infinite. But the finite involves another infinite being (from conclusion 65). Therefore in either case, if something can be, an infinite being can be. But if an infinite being can be it must be, both because it is uncausable and because, if it lacked actual existence, it would not be infinite.
67. Being is divided into finite and infinite.
The existence of finite being is plain from experience. But it can be inferred from other things already proved, for example from the fact that being is causable. For a caused being lacks the perfection of from-itselfness. The existence of the infinite follows from conclusions 65 and 66.
.
Something is Infinite and has all Pure Perfections in the Highest Degree
[see p. 75 of the Summary]
68. When being is divided through contradictory attributes opposite to each other with respect to being, one of the dividing attributes belongs to a perfection in being and the other to imperfection.
The reason is that one extreme of the disjunction formally involves the negation of the other. But both perfections cannot formally be perfections simply or pure perfections, because, from conclusion 62, pure perfections cannot formally exclude each other.
Likewise, both extremes cannot formally be imperfections or mixed perfections, otherwise no being could be infinite (against conclusion 65). But a true disjunctive should include under one or other extreme every actual or potential being. Therefore one extreme is a perfection (a pure perfection) and the other an imperfection (a mixed perfection).
69. From this follows a general law of disjunction, namely that in disjunct properties of being, when the extreme that is less noble is posited of any being, the other more noble extreme can be deduced about some other being (see Scotus, Oxon. 1, d. 39, q. un, n. 13).
The reason is that the one extreme involves imperfection and is therefore finite, while the other involves perfection simply, or pure perfection. But from conclusion 65, if something is finite, something else is infinite and has all pure perfections in the highest degree.
.
Proof of God
Only One Infinite Being Exists, which is from Itself & Perfect
[see pp. 77-80 of the Summary]
1. Some being from-itself actually exists.
I prove this conclusion summarily as follows: if something can exist, this something is either a being from-itself, altogether independent, or a being from another and so dependent with respect to its continued existence.
If it is from another there is required at the same time a cause conserving it in existence. If this cause is not a being from-itself, there is either: a) an infinite regress in conserving causes, or b) a circle in such causes, or c) there is an ultimate stand in some being simply first, namely in a first conserver that is not conserved by anything, because it is a being from-itself.
But an infinite regress in conserving causes is impossible, for such causes must be simultaneous [see conclusions 2 & 17]. The like must be said of a circle in conserving causes.
Therefore in either case, in order that something be able to exist, there is required as a condition sine qua non [without which: nothing] some other being that exists from-itself. But if a being from-itself did not actually exist, it could not exist.
Hence in brief, if it is possible that something exist, a being from-itself must exist. But it is possible that something exist, as is plain from experience. Therefore some being from-itself actually exists.
2. Every being from-itself must have every pure perfection in the highest degree and hence is both intensively and extensively perfect.
Every finite being is from-another, because no such thing has in its positive being-ness any sufficient reason as to why it lacks any pure perfection, and indeed in the highest degree. Therefore the reason for its limitation must be found in something else, namely in its cause.
Conversely, no being from-itself can be finite either intensively or extensively.
3. Only one infinite being can exist.
This conclusion involves two things: a) that existing-from-itself belongs to only one nature, because such a being is infinite; b) that a plurality of such from-itself natures is excluded. For Scholastics admit a double unity, namely [1] essential or quidditative [whatness] unity and [2] the unity of singularity.
The first excludes a multiplicity of species within the same genus, or the sort of multiplicity found, for example, in the genus of animal, which includes several species, as man, dog, horse, insect, amoeba, etc.
The second excludes a multiplicity of individuals within the same species, or the sort of multiplicity found, for example, in Peter and Paul, who differ as individuals within the same species of man [is excluded].
Proof of the two parts:
By the first is excluded the possibility of there being several infinite beings diverse in species in this way. To only one nature does it belong to be infinite,
for if several essentially diverse natures can exist, they would have to differ by reason of some essential perfection that was pure. The independence of a being from-itself or infinite being would exclude all reason for limitation. But on this supposition one or the other nature would lack some pure perfection, namely the perfection by which it would differ from another. But the consequent is false; therefore the antecedent is too.
Secondly, one must note that this infinite nature is also of itself individual and singular. The sense is that this nature qua [as] nature is such as to be unable to be multiplied in several individuals, and so no difference contracting this nature to this individual is required. But it is not to be wondered at that this is not immediately or directly perceived in this life.
For, as we said above in the chapter on individuation [pp. 24-29], all our concepts proper to God are derived from creatures, namely by affirming or denying the perfections found in creatures; and so nothing is found in such concepts, constructed or composed of common notions, that is prima facie repugnant to existing in several individuals. Hence the human mind can indeed ask: why cannot there be several infinite beings that differ only numerically?
Nevertheless, the same reason that excludes a multiplicity of infinite species in the same genus, also prohibits a plurality of infinitely perfect individuals, for if there were two beings completely identical in positive being-ness, they would not be two but one being.
But if anything does differ from a completely perfect or infinite being, it would be because it lacks some perfection that is found in the infinite being. Hence there can be a plurality of beings precisely because all beings beside the infinite being are finite.
We can therefore prove this infinite nature to be of itself individual and singular as follows:
Now it is an empty question to ask: What is the positive perfection whereby the infinite differs from the finite and why it cannot be found in several individuals? For as long as we have to form our distinct concepts by comparison with likenesses in other things, so that such concepts, precisely as distinct, are universal or composed of universal features (as, for example, an infinite being is composed positively of the feature of being and negatively of the feature of the finite), we cannot express the ultimate positive difference of a thing distinctly and in a positive way,¹ but only indirectly and in a negative way, for example when we say that one individual must differ from another by something positive that the other lacks.
¹ [See Wolter’s discussion of individuation, pp. 24-29]
So as long as we conceive the individuating reason that is ultimate in the order of singularity, properness, and unicity, it is in vain that through concepts universal, improper, and common alone we seek for a response in some individuating reason why this reason cannot multiply in many things.
That this question is indeed vain (“a meaningless question”) surely appears from consideration of this fact. Many individuals exist and are known, as is positively clear from immediate and intuitive experience. Hence individuals are really known in some way. Not indeed distinctly, as is plain from the notion of distinct knowledge (namely through definition or common concepts), along with the fact at the same time that no individual is perfectly known, because our perfect or distinct knowledge of any individual does not point out or explain why it is precisely this and not something else.¹
¹ “…something is not perfectly known unless its opposite is known…” p. 18
Hence the strength of the argument of ours adduced above must not be judged by the difficulty, or rather impossibility, of distinctly conceiving that by virtue of which an individual is precisely this and not something else like it, but [it] must rather be judged by the light of this whole fundamental principle, namely that no individual is conceived in its individuality perfectly and distinctly (that is, by common or universal notions).
Hence, besides what it has in common with other things, one being differs from another being by something positive such that one has what the other lacks.
We can therefore prove this infinite nature to be of itself individual and singular as follows:
1) Principal argument: if this nature were not of itself a this [something in itself singular], and hence were able to exist in several individuals, these individuals would have to differ by something positive, which can be called haecceity [this-ness]. Now this haecceity would be a pure perfection [because it does not reduce to anything else]. Therefore if several individuals existed, they could not be infinitely perfect, because each would lack the haecceity [a perfection] of the other. The consequent is false, therefore also the antecedent.
2) Confirmation from Scotus (On the First Principle, ch. 4, concl. 11): A multiplicable species is of itself multiplicable infinitely; therefore if an infinite being could be multiplied, an infinite multitude of infinite beings would actually exist; for if an infinite being can exist, it must and does actually exist. The consequent is unacceptable and is admitted by no philosopher.
.
How Creatures Differ from God
Corollaries
1. Whatever besides God actually exists or can exist is: a) dependent on God as on the first cause, and b) [is] a finite or limited being. For these conclusions follow from the unicity of a being altogether independent and infinitely perfect; for if anything besides God were a being from-itself, it too would have to be infinitely perfect. But there cannot be two infinite beings.
2. No being that we now experience can be God, because everything we experience is transient, finite, etc., and so lacks the perfection that belongs to God.
…
5. If all mixed perfections are reducible to a plurality of pure perfections existing in limited degree, and if an infinite being possesses all pure perfections, the consequent is that God in some way possesses every positive perfection that is found or can be found in creatures, and indeed possesses it in unlimited degree.
Accordingly God seems to differ from creatures by something positive not possessed by creatures. Creatures, by contrast, do not seem, in the ultimate analysis, to differ from God by any positive perfection precisely, but rather because they lack some perfection that God has. This notion is also expressed in the theory of participation, according to which creatures are finite or imperfect likenesses of God insofar as any perfection possessed by them is found in God either formally or virtually or eminently.
…
16. Therefore God is personal.
“A conclusion certain enough: God loves himself.” p. 100
Proof:
…
2) Blessedness seems to be a pure perfection, and therefore it belongs to God in supreme degree. But love seems to be either the principal element in blessedness, or at any rate intimately connected with the blessedness of an intellectual being.
That blessedness is a pure perfection is clear from the notion of it; for blessedness is nothing other than an intellectual being pleased, that follows upon possession of one’s proper perfection. But God knows himself as infinitely perfect; he seems, therefore, to be blessed; therefore blessedness seems to be a pure perfection.
…
18. Whatever a finite cause can produce, God can directly produce.
This conclusion seems to be a corollary of the preceding one, for the reason there stated.
…
Conclusions Respecting Reality
…
30. Evil involves good, or evil exists in a good, for from what was said, evil is privation of good in something good.
…
Evil cannot have a material or formal cause, namely constitutive principles. If the material cause is taken in the sense of the subject-in-which, good is this cause. Evil cannot exist in itself, but [only] in some good.
But can it have a final cause?
Physical evil [as distingushed from moral evil] can be intended as a means to some end, and licitly so, provided the end is good, or indifferent, or proportionate to the evil. Moral evil can be intended only illicitly and only by a finite will.
But no evil can be desired for its own sake or as an end, save under the appearance of good. For evil as such has no appetibility in itself or because of itself. But every evil can be permitted, that is, not impeded either by God or by man, given what needs to be given.”
.
.
On the Teaching of Thomas Aquinas vs. John Duns Scotus
Article
1600’s
Macedo, Francisco – 4. ‘Thomas’s argument for proving God’s infinity’ in Collations of the Teachings of St. Thomas & Scotus, with the Differences between the Two… vol. 1 tr. AI by Vertias (Padua: Frambotti, 1671), vol. 1, bk. 1, Collation 3, pp. 142-46 A more detailed ToC is given at the beginning of the volume.
Macedo (1596-1681), known as S. Augustino, was a Portuguese Franciscan theologian. While exercising independent judgment, he tends to lean original-Scotus. He had a very good knowledge of Aquinas’s works (and of Thomists and their works) through his life (vol. 2, p. 424).
.
Historical
All or Most of History
Article
Sweeney, Leo – ‘Infinity of God’ in New Catholic Encyclopedia VI (New York: McGraw Hill, 1967), pp. 508-9
.
Books
Sweeney, Leo – Divine Infinity in Greek & Medieval Thought Ref Buy (P. Lang, 1998) 576 pp.
“This volume was inspired by Etienne Gilson’s query, made in the early 1950s, as to why medieval authors spoke of God’s being as infinite, a statement found neither in Judaeo-Christian scriptures nor in Greek philosophy… It concludes that infinity is predicated of God not only extrinsically, but also intrinsically: His very being is infinite – a predication resting on an Aristotelian theory of act/potency or on a Platonic version of participation.”
eds. Göcke, Benedikt P. & Christian Tapp – pt. 1, ‘Historical Approaches to the Infinity of God’ ToC in The Infinity of God: New Perspectives in Theology & Philosophy Pre (Univ. of Notre Dame, 2019)
.
On the Era of the Early Church
Article
Whittaker, John – ‘Philological Comments on the Neoplatonic Notion of Infinity’ in ed. R. Baine Harris, The Significance of Neoplatonism (Norfolk, VA: International Society for Neoplatonic Studies, Old Dominion University, 1976)
.
Books
Hennessy, J.E. – The Background, Sources & Meaning of Divine Infinity in St. Gregory of Nyssa PhD diss. (Fordham University, 1963)
.
Quote
David L. Balas, ‘A Thomist View on Divine Infinity’ in Proceedings of the American Catholic Philosophical Association, vol. 55 (1981), p. 92
“In spite of the fact that the Bible ‘has only a few and (at best) indirect texts on infinity,’ God’s infinity seems to be taught by Philo and by several of the early Christian Fathers.
Worthy to be mentioned in this connection are certainly Irenaeus and Clement of Alexandria… Whereas Origen is usually mentioned as a witness to the persistence of the older Greek conception of infinity as imperfection, Gregory of Nyssa has been shown – by several recent studies, independent of each other-to be the (as it seems first) Christian thinker who has not only affirmed with clarity but also elaborated the doctrine of God’s infinity.
In view of what we shall see to be the teaching of Aquinas, it is perhaps particularly interesting to point out that Gregory’s writings contain also a very clear development of the principle that all limited perfection is participated perfection (and this implies an intrinsic composition between the perfection participated and the recipient) whereas unparticipated perfection must be infinite and simple.”
.
On the Middle Ages
Articles
Sweeney, Leo – ‘Bonaventure & Aquinas on the Divine Being as Infinite’ The Southwestern Journal of Philosophy, vol. 5, no. 2 (Summer, 1974), pp. 71-91
Aquinas (c. 1225–1274); Bonaventure (1221-1274)
Goff, J. Isaac – ch. 8, ‘Divine Infinity in Bonaventure’s Disputed Questions on the Mystery of the Trinity’ Pre in Ordo et Sanctitas: The Franciscan Spiritual Journey in Theology & Hagiography (Brill, 2017), pp. 165-85
Bonaventure (1221-1274)
Maurer, Armand – ch. 16, ‘The Role of Infinity in the Thought of Francis Meyronnes’ in Being & Knowing: Studies in Thomas Aquinas & Later Medieval Philosophers (Pontifical Institute of Medieval Studies, 1990), pp. 333-61
Meyronnes (c. 1280–1328) was a French scholastic philosopher. He was a distinguished pupil of Duns Scotus, whose teaching he usually followed. He acquired a great reputation for ability in discussion at the Sorbonne, and was known as Doctor Illuminatus, Magister Acutus or Doctor Acutus, and as Magister Abstractionum.
Wass, Meldon C. – ch. 3, ‘The Infinite Sea of Substance’ in The Infinite God & the Summa Fratris Alexandri [of Brother Alexander of Hales] (Chicago, 1964), pp. 47-70
The Summa of Alexander of Hales was published in 1245. According to Leo Sweeny, it contains “a rather highly advanced theory of divine infinity”.
.
Book
Dubrule, Diane E. – Divine Infinity in the Writings of Henry of Ghent PhD diss. (Univ. of Toronto, 1968) 290 pp.
Summary: “Etienne Gilson brought the problem of the origin of the notion of divine infinity to the attention of historians of the middle ages in the early nineteen-fifties. Although research has been conducted into the meaning and sources of the negative infinity of actuality current in the second half of the thirteenth century, the doctrine of positive infinity, the forerunner of our modern concept, has not been investigated. Three basic views of infinity paved the way for the work of Henry of Ghent (d. 1293), the apparent source of this doctrine.
According to the pre-Socratics, infinity was either a subsistent material principle unlimited in extent… or a spatial, temporal, or numerical property or numeric property of some original stuff… Plato did not predicate infinity of the Ideas, but in the Philebus he semed to regard the infinite as a subsistent principle inferior to limit, as it had been for the Pythagoreans.
Aristotle gave the first technical analysis of quantitative infinity. Having proved that there could be no actually infinite magnitude or number, he held that infinity was potential and a property of a process, not a product. Aristotle also ascribed infinite power to the prime mover, as the cause of an infinite motion over an infinite time. But here also infinity remained quantitative and predicated of the prime mover only by extrinsic denomination.
A new view of infinity was introduced by Plotinus, Pseudo-Dionysius and John Damascene. According to these authors, the one, which was above being, was infinite both as transcending form (the limiting principle) and because its unity precluded its having an internal composition of form with formed… The Plotinian infinity of non-being was not applied to God in medieval Latin philosophy. In Augustine, Peter Lombard and William of Auvergne, infinity remained extrinsic and relative, as it had been for the pre-Socratics and Aristotle.
Richard Fishacre [d. 1248, a Dominican] seems to have been the first author to expound an infinity of being, according to which infinity was predicated of God absolutely, on account of the simplicity of his essence and without reference to anything extrinsic to it. This view apparently was unknown to Albert the Great until near the end of his life, but it was adopted by Bonaventure and Thomas Aquinas, both of whom argued from God’s actuality to his simplicity and then from his simplicity to his infinity. These authors generally regarded infinity as a negative divine attribute, though in one text Bonaventure said that the ‘highest position’ corresponded to it. Richard of Middleton, however, explicitly stated that ‘infinite’ does posit something in God. The work of Richard of Middleton probably postdated Henry of Ghent’s Summa, a. 44 by nearly five years.
A. 44 of Henry’s Summa, ‘On the infinity of God’, contains two questions, the first of which inquires whether God is infinite… Divine infinity must agree with the mode of being of a self-subsistent and totally actual form. It can be contrasted with creaturely infinity in three ways: (1) Divine infinity is actual, whereas creaturely infinity is only potential (as Aristotle argued); (2) God’s infinity follows upon perfection and totality, whereas potential infinity precludes both; (3) Divine infinity is formal, but creaturely infinity is material.
The form of God, unlike the forms of creatures, does not place limitations on God… Thus, the indeterminate being of God can contain the mode of being of every possible being. The manner of this comprehension… is unified (unlike the way in which the infinite quantum contains other quanta as parts) and unconfused (in contrast to the way in which the genus comprehends its differentiae). Because God comprehends all modes of being actually and not as parts, the existence of participated beings does not wound the divine totality.
Henry’s reply to the second question, which asks whether ‘infinite’ signifies positively, negatively, or privatively, seems to be directed against the thirteenth-century exponents of negative infinity. He begins his response by distinguishing three types of infinity: (1) the negation of a terminus in that which has no process, (2) the privation of a terminus in that which has a process and is naturally constituted to end, (3) the position of a perpetually extended process in that which is not naturally constituted to end.
The second cannot be predicated of God, and the first, though it makes clear God’s lack of internal and external limitations, does not express what we mean to ascribe to God by the term ‘infinite’. This is clear (1) from the nature of the negation, for we mean to ascribe a certain dignity to God by means of ‘infinite’, which a negation per se can never accomplish. It is apparent to Henry that God contains an aspect (ratio) superior to perfection and totality that is commonly expressed by ‘infinite’, which then must signify a position (2) from the nature of the thing signified. (3) From its mode of imposition, ‘infinite’ is negative, but only secondarily, inasmuch as it signifies the negation or privation of finitude, which is a real privation of further extension. Primarily it signifies the position of further extension, for the negation or privation of a privation is a real position… although perfection, totality and infinity are really identical with each other and with the divine essence, yet there is a distinction of reason between them, such that ‘infinite’ adds the higher, positive note ‘further extension’ to perfection and totality…
Henry probably gave it a positive character… because of the theory of signification expounded in a. 32, according to which divine names negative in form signify real positions.
Henry of Ghent’s contribution to the history of infinity thus appears to be restricted to a reinterpretation of the late thirteenth-century infinity of actuality. Despite its influence on Duns Scotus and the moderns, Henry’s positive infinity does not seem to reflect the new metaphysics that the introduction of infinity of non-being and the development of infinity of actuality so clearly evidence.” – pp. 1-3
.
Quote
David L. Balas, ‘A Thomist View on Divine Infinity’ in Proceedings of the American Catholic Philosophical Association, vol. 55 (1981), pp. 92-93
“Early Scholasticism — surprising as such an assertion is — seems to have ignored the question of the infinity of God’s being; what is even more surprising, a group of thirteenth century Scholastics — apparently motivated by the condemnation of the denial of the beatific vision by William of Auvergne, the Bishop of Paris, in 1241 — explicitly maintained that God’s essence is finite.
From the second half of the thirteenth century on the affirmation of the infinity of God’s very being prevailed, though it was taught with varying degrees of clarity.”
.
On the Post-Reformation
Articles
Muller, Richard
‘infinitas’ in Dictionary of Latin & Greek Theological Terms: Drawn Principally from Protestant Scholastic Theology 1st ed. (Baker, 1985), p. 154
ch. 4, sect. 4, ‘Divine Infinity, Eternity and Related Attributes’ ToC in Post-Reformation Reformed Dogmatics, vol. 3 (The Divine Essence & Attributes) 2nd ed. (Baker Books, 2003), pp. 325-65
.
Latin
*** Need to add articles from Lombard.
.
1300’s
Bradwardine, Thomas – Of the Cause of God, Against the Pelagians, & on the Power of Causes… (London, 1618), bk. 1 ToC
Ch. 1, First is premitted two suppositions, the first of which is that God is the highest perfection and the highest good, so that nothing else is able to be more perfect or better. The second is, Nothing infinite has proceeded into entities, but is in whatever genus, the first one. 1
Corollaries
…
4. Contra those who deny that God is simply of all infinite virtue and goodness whatsoever 4
…
25. Contra those who do not distinguish, but withdraw from God being simply of infinite virtue and infinite power, even intensively 19
…
Ch. 5, That God is not mutable in any way
…
2. Whether, further, He is outside the world in a place, or in an imaginary, infinite, void?
.
1500’s
Zanchi, Jerome – 6. ‘Of the Immensity & Infinity of God’ in Of the Nature of God, or of the Divine Attributes (Heidelberg, 1577), bk. 2, pp. 108-68
Q. 1, Whether God is immense and infinite, and by that everywhere present 109
Thesis: God is immense and infinite, and therefore indeed everywhere present 109
What is infinity and how manyfold 109
God is infinite in what way 110
II. Wherefore God is everywhere present and in what way
Acts 17:27
What effects that some thing is called present or absent
Heb. 4:13
III. Ps. 139:1, 11; Ex. 20:3; Isa. 66:1; Jer. 23:23; Ps. 14:2; Acts 17:27; Mt. 6:4, 6
IV. God is infinite
Ex. 3:14
V. God is everywhere present
Acts 17:28; Heb. 1:3; Jn. 1:9; Acts 17:28; Jn. 1:4; Acts 17:28; Gen. 1:2
Q. 2, In what way God being everywhere present is understood; 1 Cor. 5:30 114
Thesis: God is truly everywhere, his whole essence and by that and his power or virtue present… 115
Acts 17:28
II. God is everywhere present by his essence, not only by the virtue of power; Isa. 66:1; Jer. 23:23; Acts 17:27; Gen. 1:2; Num. 12:6
III. Testimonies of the Fathers; Jer. 23:24; Wis. 1:7; Ps. 139:7; Jer. 23:24; Eph. 3:18; Acts 17:27; Wis. 1:7; Jer. 23:24; 23:23; Acts 17:28; Gen. 1:26; Col. 2:9
IV. Use of the doctrine; Jer. 23:23; Ps. 23:4; Gen. 17:1; 5:24; Ex. 20:3
Q. 3, In what way God, in which He is everywhere, is said to be in heaven, not in the earth, to inhabit in the saints, not in the impious, and in Christ otherwise than in the saints, and to separate from us and to return? 122
Ps. 103:19; Mt. 6:9; Dt. 7:21; Num. 14:42; 1 Cor. 6:19; 3:16; 1 Jn. 4:16; Ps. 23:4; Jn. 14:23
Thesis: God is not said to be, nor is greater in Heaven than in the earth, or greater in the saints than in the ungodly by reason of essence, but by reason of operation and grace. 122
II. Why God is said to inhabit Heaven and not so on earth 123
Ps. 19:2; Hos. 2:21; Rom. 1:18; Isa. 66:1; Ps. 103:19
III. In what way God inhabits the saints and not likewise the ungodly 124
Heb. 6:4; 1 Cor. 3:16; 6:19; 2 Cor. 6:16; Gal. 4:6; Isa. 55:6; 1 Cor. 15:28
IV. In what way God is said to come to us or recede from us 125
Ps. 51:12, 14; Jn. 14:23; Ps. 22:2; 1 Sam. 18:28; 1 Cor. 12:11
V. In another much greater way God inhabits Christ than us. 125
Heb. 2:14; Col. 2:9; Isa. 66:1; 2 Kings 2:9
Q. 4, Whether it is of God alone to be everywhere, or whether such may be competent even to some creature 127
That it is proper to God that his essence be everywhere and in all things be present; thus this is able to be competent to no creature 128
1 Cor. 12:12; Jer. 33:1
IV. An explanation of places of holy Scripture for Ubiquity; From the words of the Supper Ubiquity is not able to be concluded; The Supper’s words are all figurative.
Lk. 22:20; 1 Cor. 11:25
V. From no interpretation of the words of the Supper is Ubiquity able to be proved. 137
VI. From Acts 9 Ubiquity is not evinced.
Acts 7:56; Mt. 3:17; 17:5; Acts 22:9
VII. From Eph. 4 Ubiquity is not proved.
Acts 1:9; 3:21; Mt. 25:31; Heb. 4:14; Isa. 66:1; Ps. 139:8; Phil. 2:10; Col. 3:2; Joel 2:29; Jn. 16:7; 7:39; 12:32; Ps. 68:19; Acts 1:26; 13:2; 1 Tim. 2:4; Phil. 2:10; Mt. 15:24; Rom. 15:8
VIII. Refutation of Sophisms 142
Jn. 1:14
From the hypostatic union Ubiquity is not proved
Heb. 4:15; Lk. 2:52; Mt. 27:46; Acts 2:24; John 2:19; Mt. 11:27
In what way all things are given to Christ 144
2 Chron. 2:6
I. By the session at the right hand of the Father Ubiquity is not proved 148
Acts 17:28
II. Ex. 15:6; Ps. 118:16; Lk. 2:20; Phil. 2:7; Mt. 17:2; Acts 7:56; Rev. 1:16; 21:23
III. Ps. 110:1; 1 Cor. 15:25; Lk. 24:26; Eph. 1:20; Phil. 2:9; Heb. 1:13; 1 Pt. 3:22; 1 Cor. 15:28; Rev. 5:12
IV. In which things Christ reigns everywhere; it is able to be said He is everywhere even in those things 156
Heb. 1:3; Ps. 33:9; 2 Pet. 1:3; Rom. 8:9; Jn. 16:7; Acts 1:8; Ps. 2:9; Rev. 2:12; 1 Pet. 1:3; 1 Cor. 12:13; Jn. 16:14
Epilogue: in what ways He reigns everywhere 158
“Sufficiently therefore the threefold way is explained in which we concede Christ as He is man, reigns everywhere with the Father: and in the first place [in primis], in his elect. First, indeed, by the virture, power and wisdom of his deity and divine nature. Next, by his Spirit and the gifts and effects of his Spirit. Lastly, by the fellowship even of his body and blood produced through the Holy Spirit.”
V. Nor is it simply true that He is everywhere by the assumption to the right hand of God. 158
Mt. 6:9; Isa. 66:1; Heb. 1:3; 7:26; 9:24; 1 Pet. 3:22; Col. 3:1; Heb. 2:1; Isa. 66:1
Sophism 3. From omnipotence you are not able to prove Ubiquity, nor out of Mt. 28, ‘All power is given unto Me.’ 159
2 Tim. 2:13; Mt. 28:18; Phil. 2:6; Heb. 2:7; Mt. 13:58; Jn. 11:41; 17:5; Phil. 2:6; Heb. 4:15; Acts 2:36; Phil. 2:9; Mt. 28:18; 18:18; 19:17
Sophism 4. From the presence of Christ’s body in the Supper Ubiquity is not demonstrated 164
Christ’s body is not consumed so far as the wine is in the Supper, but so far as He died and thus such is offered to us; and in the same way his blood is drunk. 165
2 Pet. 3:10; Jn. 16:28; Mt. 16:15; Jn. 1:9
Use of the Doctrine 167 (4 sections)
4. Christ exists in Heaven: He feeds us by his body. 168
Goclenius, Rudolf – ch. 13. ‘Concerning Infinite & Finite’ in An Introduction to the First Philosophy of the Peripatetics & Scholastics, which is Accustomed to be called Metaphysics… (Frankfurt, 1598), pt. 1, Metaphysical Precepts, pp. 96-100
Goclenius (1547-1628) was a reformed professor of philosophy at Marburg.
.
1600’s
Sachse, Karl – A Disquisition on the Essential Attributes of God, Infinite & Uncreated, None of a Finite & Created Nature by a Participative Communication, Against Balthasar Meisner (Frankfurt, 1616)
Sachse (1558-1616) is listed as reformed by PRDL, though it is also noted there that this is uncertain. Meisner (1587-1626) was Lutheran.
Alsted, Johann Heinrich
ch. 11. ‘Of Finiteness & Infiniteness’ in A Most Concise Delineation of Metaphysics… (Herborne, 1611), pp. 41-42
“All being is either finite or infinite. The finite is that which is circumscribed by certain limits…
Infinite [Being] is that which is circumscribed by no limits. Thus the infinite is defined by the removal of finitude. By way of the order of the created intellect, the infinite is defined as that which we are not able to comprehend.”
ch. 19. ‘Of Infinity & Finiteness’ in Metaphysics Drawn out in Three Books through Methodical Precepts, Select Theorems & Clear, Short Commentaries… (Herborne, 1613), bk. 1, Of Transcendentals, pp. 160-64 This is the same as his Most Exquisite Method of Metaphysics… (1611)
Theorem 9, ‘That which is infinite is that which by no measure is able to be measured’ in A Metaphysical Disputation on Uncreated Substance (Herborne, 1615), pp. 20-22
ch. 31. ‘On Infiniteness & Finiteness’ in bk. 11 of The Encyclopedia, Propounding Metaphysics in The Encyclopedia in Seven Distinct Tomes… (Herborne, 1630), pp. 608-9
Rules:
1. One only is properly called infinite, that is God.
2. There is no proportion from the finite to the infinite.
3. The finite cannot contain the infinite.
4. The infinite is of perfection or of imperfection. [This distinguishes God, who is perfectly infinite, from other infinite things which are only imperfectly so.]
5. The infinite is often so called by reason of duration or value.
6. The finite in essence is also finite in all attributes.
Combach, Johann – ch. 14. ‘Infinite & Finite, also Illocal & Local’ in The 3rd Edition of the Metaphysics… Comprehending the Universal Doctrine of First Philosophy by the Most Brief Theorems, Illustrated with Necessary Comments… (Frankfurt, 1630), bk. 1, pp. 283-97
Combach (1585-1651) was a professor of physics at Marburg.
Crocius, Ludwig – 9. ‘Of the Infinity of God’ in A System of Sacred Theology (Bremen, 1636), bk 3, pp. 472-80
Crocius (1586-1655)
“And thus of the first attribute of God, even the absolute necessity of existing. Another surely follows: infinity, which is thus: the sum perfection of the divine essence, without any end or limit….
God is said even to be free from an end of his perfection in two ways, i.e. extensively and intensively.” – pp. 472-73
Jacchaeus, Gilbert – Institutions of the First Philosophy, or of Metaphysics… (Leiden: Elsevir, 1640), bk. 4
2. Of Infinite Being, or of God 179
3. Of Divine Perfection 183
4. Of Divine Infinity & Simplicity 187-96
Jacchaeus (c.1578-1628) was a reformed professor of philosophy at Herborn and Leiden.
Voet, Gisbert – (5) ‘On the Infinity of God’ in Syllabus of Theological Problems (Utrecht, 1643), pt. 1, section 1, tract 2, I. ‘Of God’, 4. Attributes of God in Specific, 1st Kind Abbr.
Controversies of the 1st Kind
Whether God is infinite? It is affirmed.
Whether something besides Himself may be infinite according to essence? It is denied.
Controversies according to the 2nd Kind
Whether some act is able to be infinite according to magnitude? It is denied.
Whether some act is able to be infinite according to multitude? It is denied.
Whether the human nature of Christ is infinite? It is denied.
Rutherford, Samuel – sect. 6, ‘Impossibility in the first infinite being is the origin of all impossibility in creatures’ in A Scholastic Disputation on Divine Providence (Edinburgh, 1649), Metaphysical Inquiries, that may Perhaps bring forth a Measure of Light to the Doctrine of Providence, question 4, pp. 544-45
Senguerdius, Arnold – ch. 7. ‘Of the Infinity of God’ in The Idea of General & Special Metaphysics 3rd ed. (Utrecht, 1659), Special Metaphysics, pp. 159-65
Senguerdius (1610-1667) was a reformed professor of metaphysics and physics at Utrecht when this was written, and later a professor of philosophy at Amsterdam. Senguerdius was Voet’s most recommended author on metaphysics.
Heereboord, Adrian – disp. 2, ‘On Infinite Being’ in Philosophical Outlines [Meletemata], in which Most Things in Metaphysics are Ventilated… 2nd ed. (Leiden, 1659), pt. 1, pp. 10-14
Burman, Francis – ch. 18. ‘Of the Infinity & Perfection of God’ in A Synopsis of Theology, & especially of the Economy of the Covenant of God... (Utrecht, 1671), vol. 1, Locus 2, ‘Of God’, pp. 107-8
Burman (1628-79)
Turretin, Francis – q. 8, ‘Is God infinite in essence? We affirm against Socinus and Vortius.’ in Institutes of Elenctic Theology (Geneva, 1679-1686; NY, Robert Carter, 1847), vol. 1, Locus 3, ‘God’, pp. 175-78
Turretin (1623–1687)
de Vries, Gerard – Rational Exercitations on God & the Divine Perfections, even Miscellaneous Philosophical Things new ed. (Utrecht, 1695), vol. 1, Miscellaneous Philosophical Things, or Academic Dissertations
1. The Infinite, sect. 1, Concept of Infinity 263
2. The Infinite, sect. 2, Infinite Extension 281
van Mastricht, Petrus – ch. 9. ‘Of the Infinity & Magnitude of God’ on Ps. 145:3 in Theoretical & Practical Theology… new ed. (Utrecht, 1724), bk. 2, pp. 117-21
Van Mastricht (1630-1706)
.
1700’s
Heidegger, Johann H.
sect. 24-25, ‘Of the Infinity of God’ in Locus 3, ‘Of the Existence & Divinity of God’ in The Marrow of Christian Theology (Zurich, 1713), pp. 48-49
sect. 39-40, ‘The Infinity of God as to the Essence is Explained & Proved’ in Locus 3, ‘Of the Existence & Divinity of God’ in A Body of Christian Theology, Exhibiting True Doctrine, which is according to godliness (Tigur, 1700), vol. 1, pp. 74-75
Heidegger (1633-1698)
Van Til, Salomon – B. ‘Of the Supreme Infinity of Being’ in A Compendium of Both Natural & Revealed Theology (Leiden, 1704; 1719), bk. 1, ch. 1, Section 2, ‘Of the Attributes of the Divine Essence’, pp. 17-18
Van Til (1643-1713)
“Another attribute of the most supreme Being (that is of God) is called infinity, which is the absolute possession of all absolutes.” – p. 17
Holtzfus, Barthold – 5. ‘Of the Truth, Goodness, Primacy & Independency, Infinity, Incomprehensibleness, Eternity, Immensity, & Immutability of God’ in A Theological Tract on God, Attributes & the Divine Decrees, Three Academic Dissertations (1707), pp. 40-55
Holtzfus (1659-1717) was a reformed professor of philosophy and theology at Frankfurt.
Andala, Ruard – ch. 5. ‘Of the Two Attributes of the Divine Essence & so a Sum of Perfect Consideration: the Infinity & Incomprehensibility of God’ in A System of Theological-Physical Metaphysics, containing a Compendium of Natural Theology: a Paraphrase of the Principles of the Philosophy of Renee Descartes… (Franeker, 1711), pt. 2, pp. 66-69
Andala (1665-1727) was a reformed, Cartesian professor of philosophy and theology at Franeker.
.
.
Bibliography
Article
1800’s
Malcom, Howard – ‘Infinity of God’ in Theological Index… (Boston, 1868), p. 240
.
.
.
“Great is the Lord, and greatly to be praised; and his greatness is unsearchable.”
Ps. 145:3
.
.
.
Related Pages