Individuation is a question of the formal cause

When scholastic philosophers discuss individuation, their basic question is this: which of a thing's constituents make it the individual that it is? This question deserves some comment. As the schoolmen see it, we are looking for what they call the 'formal cause', not the 'efficient cause'.

The efficient cause is the agent that brings the effect in question into being. For instance, when a sculptor makes a statue, the sculptor is the efficient cause here, for the sculptor is the person/agent who effectively brings the statue into being. In short, the efficient cause is the producer of the effect.

The formal cause, on the other hand, is some feature or constituent of the product itself that explains why it is the sort of thing it is. For instance, the formal cause of a statue being a statue is the shape of the statue. Without it's shape, it wouldn't be a statue, so that very shape is the 'formal cause' of the statue being a statue.

When the schoolmen talk about individuation, everybody agrees that the efficient cause of the individual is its producer. But that seems perfectly obvious. If you want to know who produced this particular statue, the answer is the sculptor who actually produced it.

But when it comes to the formal cause, the schoolmen disagree. Again, here they are looking for some feature or constituent (or combination thereof) in the individual itself that explains why it is the individual it is.

More precisely: here we are looking for some set of features or constituents that cannot exist in some other individual. Suppose I ask every member of a group to take a side on capital punishment. Some will be for it, others will be against it, but in this case, taking the 'for' or 'against' side will separate these individuals into distinct groups, for nobody can be 'for' and 'against' capital punishment at the same time.

Taking the 'for' or 'against' side here would be an example of something that is the 'formal cause' of distinction: it's the sort of thing that cannot exist in more than one individual at the same time, and so when individuals take the 'for' or 'against' side of capital punishment, they necessarily get separated into groups. So also when it comes to individuals. The schoolmen are looking for some feature that cannot exist in more than one individual at a time, much like how being 'for' or 'against' capital punishment cannot exist in one and the same individual at the same time.

One argument of Scotus against Henry of Ghent (translation)

From the Lectura

‘According to the Philosopher in Physics 5, a change belongs to the same species as its end-point, just as [the act of] whitewashing [a log] belongs to the species of whiteness, not the species of “white-log”, which is only one “thing” incidentally’.

[Scotus, Lect. 1.5.2.un., n. 72 (Vat. 16: 437.2-4): ‘quia secundum Philosophum V Physicorum [224b6-8] mutatio est eadem specie cum termino, ut dealbatio cum albedine, et non cum ligno albo, quod est unum per acccidens’.]

From the Ordinatio

‘A production is placed in a genus or a species from its formal end-point, as is clear from the Philosopher in Physics V [224a26-30]. For instance, a change in quality is placed in the genus of quality, for here there is a [qualitative] form which is the formal end-point of the change in quality. Therefore, if the formal end-point of some such production were a relation, that production would be placed in the genus of relation, and it would not be a generation’.

[Scotus, Ord. 1.5.2.un., n. 69 (Vat. 4: 49.8-13): ‘productio ponitur in genere vel specie ex suo termino formali, sicut patet per Philosophum V Physicorum, — sicut alteratio ponitur in genere qualitatis, qua ibi est forma quae est formalis terminus alterationis; ergo si formalis terminus huiusmodi productionis esset relatio, ista productio poneretur in genere relationis et non esset generatio’.]


From the Reportatio

‘Change and every per se production is placed per se in the genus of the end-point to which [the change or production is directed], and [it is placed] precisely in the genus of the formal end-point, according to Physics V, where examples are given from each [kind of] per se motion or change, namely generation, alteration [i.e., change in quality], and growth [i.e., change in size]. If, then, the formal end-point of the Son’s production were a relation [i.e., the Son’s unique property of sonship] rather than the [divine] essence, then the Son’s production would not be a generation, but more a change in relationship’.

[Scotus, Rep. 1.5.2.un., n. 63 (Wolter, 275): ‘mutatio et omnis per se productio ponitur per se in genere termini ad quem et praecipue in genere termini formalis, V Physicorum, ubi exemplificatur de omnibus per se motu et mutatione, scilicet generatione et alteratione et augmentatione. Si igitur formalis terminus productionis Filii non est essentia sed relatio, tunc productio Filii non esset generatio, sed magis adaliquatio erit’.]

Scotus on how the divine essence and a personal property 'combine' to make a person (translation)

‘But how is it that the nature of a real relation [viz., a personal property such as sonship] does not have the same formal nature as the divine essence, but nevertheless the two do not constitute a composite together? The reason for this is that the nature of the one is perfectly the same as the nature of the other, for on account of the infinity of the one nature, whatever can be [compresent] with it is perfectly the same with it. Therefore, the perfection of this identity excludes any composition or quasi-composition, and that identity holds because of the infinity [of the divine essence]. Still, that infinity does not destroy the formal natures [of the things contained in it], so this one [viz., sonship] is formally distinct from that one [viz., the divine essence]’.

[Scotus, Ord. 1.5.2.un., n. 117 (Vat. 4: 69.6-13): ‘Qualiter autem stat quod ratio relationis [e.g., filiationis] in re non sit formaliter eadem rationi [divinae] essentiae et tamen in eodem concurrentes non constituunt compositum, — hoc ideo est, quia illa ratio est perfecte eadem illi: propter infinitatem enim unius rationis, quidquid potest esse cum ea, est perfecte idem sibi. Perfectio ergo identitatis excludit omnem compositionem et quasi-compositionem, quae identitas est propter infinitatem, — et tamen infinitas non tollit formales rationes quin haec formaliter non sit illa’.]

‘Now, [to say “deity is in the Father”] is true insofar as [deity or the divine essence] is a nature in the person, for that person has its “being” and “whatness” through that nature (for this belongs to a “whatness” insofar as it is a “whatness”), but this is not because the form informs the person, and this is true even in creatures. But [to say “fatherhood is in the Father”] is true insofar [fatherhood] is an individual form in the individual, but [again] not by informing it’.

[Scotus, Ord. 1.5.2.un., nn. 121-122 (Vat. 4: 71.8-13): ‘Nam prima [viz., “deitas est in Patre”, cf. n. 120] est vera ut natura est in supposito, habente “esse” quiditativum ea (quia hoc convenit quiditati unde quiditas est), sed non propter hoc est forma informans suppositum, etiam in creaturis. Secunda [viz., “paternitas est in Patre”, cf. n. 120] est vera ut forma hypostatica est in hypostasi, – sed nec informat ipsam’.]


‘I concede that the relation [viz., a unique personal property like sonship] contributes to the actuality of the [divine] person, but it does not contribute actuality to the “whatness” [of that person], for the relation distinguishes that person “personally” rather than in terms of its “whatness”. However, the essence contributes actuality to the “whatness” [of the person], and by that “whatness”, it distinguishes [the person from other things with a different “whatness”]’.

[Scotus, Ord. 1.5.2.un., n. 127 (Vat. 4: 72.16-19): ‘Concedo relationem esse actum personalem, non actum quiditativum, – quia personaliter distinguit et non quiditative. Essentia autem est actus quiditativus et quiditative distinguens’.]

‘So although the “whatness” [in a person] is the form of that person just as much as its individual form is (as it also is in creatures), it is not an informing form. For in creatures, the “whatness” is a part [of a person], so to speak, but in a divine person it is [present] as one formal nature, as it were, formally concurring with another to [constitute] one simple thing that has within itself many formal natures’.

[Scotus, Ord. 1.5.2.un., n. 122 (Vat. 4: 71.13-17): ‘Tam enim quiditas quam forma hypostatica, etiam in creaturis, licet sit forma suppositi, non tamen est forma informans, sed ibi quasi pars, hic autem quasi una ratio formalis concurrens cum alia, formaliter, ad idem simplex sed habens in se plures rationes formales’.]

Scotus on generation without matter

From the Reportatio

‘Insofor as it implies production, generation as such does not require matter or quasi-matter, and where it happens without matter, generation is said to be perfect and without any imperfection. Therefore, this is how it has to be ascribed to God, for in no way can generation be conceived without imperfection if it is understood to presuppose matter’.

[Scotus, Rep. 1.5.2.un., n. 74 (Wolter, 279): ‘generatio ut importat productionem, quae ut sic non requirit materiam nec quasi materiam et ut sic dicit perfectionem sine imperfectione; ergo ut sic habet attribui Deo. Sed nullo modo concipitur sine imperfectione ut intelligitur praesupponere materiam’.]


From the Ordinatio

‘The reason that a “generated creature” is not [produced] from nothing is that something in it (such as matter) pre-exists. Therefore, . . . if the form of something were to pre-exist and the matter were newly added to it so that it were informed by the pre-existent form, that very product would not be [produced] from nothing, for something in it pre-existed [the production] . . . . Therefore, if someone [like Henry] were to say that the Son is not [produced] from nothing “because his essence existed in the Father prior in the order of origin”, and if [they said that] the essence is the matter, so to speak, in the Son’s generation, then how much more would it be the case that the Son is not [produced] from nothing if the [divine] essence that “exists in the Father prior in origin” is a quasi-form shared with the Son?’

[Scotus, Ord. 1.5.2.un., n. 103 (Vat. 4: 64.3-13): ‘quia “creatura genita” non est de nihilo, quia aliquid eius praeexsistit, ut materia. Ergo . . . si forma alicuius praeexsisteret et materia de novo adveniret et informaretur illa forma iam praeexsistente, ipsum productum non esset de nihilo, quia aliquid eius praeexstitisset . . . . Ergo si Filius non diceretur esse de nihilo “quia essentia eius secundum ordinem originis praefuit in Patre”, et hoc si illa essentia esset quasi-materia generationis Fili, multo magis nec Filius erit de nihilo si illa essentia “prius origine exsistens in Patre” sit quasi-forma communicata Filio’.]


From the Reportatio

‘It is impossible for the numerically same [lump of] matter to remain under the form of the generator and the generated [at the same time], whatever sort of thing the generator or the generated is, for the same [lump of] matter cannot be simultaneously perfected by two ultimate forms which give complete being to the matter. Nevertheless, the same form can give being to many [lumps of] matter simultaneously, or to one [lump of] matter to which it did not give being before. This is clear in growth, for where the form of food has corrupted into flesh, the [already existing] form of the flesh newly perfects the matter of the food, because the [body’s] flesh converts the food into flesh and perfects the matter of the food insofar as it is flesh pre-existing in the food’.

[Scotus, Rep. 1.5.2.un., n. 80 (Wolter, 282): ‘impossibile est eandem materiam numero manere sub forma generantis et geniti, quodcumque sit generans vel genitum, quia non potest eadem materia simul perfici duabus formis ultimis quae dant esse completum materiae; potest tamen eadem forma dare esse pluribus materiis simul, sive uni materiae cui non dabat prius. Patet in augmentatione ubi, corrupta forma alimenti in carnem, forma carnis de novo perficit materiam alimenti, quia caro convertit alimentum in carnem et perficit materiam alimenti ut carnem praeexsistentem in alimento’.]


From the Lectura

‘This can also be shown with an example. If something were to grow in itself without anything being added to it (as it happens in rarefaction), here the form of the growable thing would be changed and it would receive some new perfection. But suppose that there is some growth that occurs by something more being added to it, and that the soul (which havs the capacity and power to perfect the whole organic body) only perfects one part (like the heart) [first], and afterwards when other parts of the body are added to it, the soul — without any change to itself — perfects those other organic parts without being perfected in some other way. Similarly, the divine essence is supremely perfect in the first instant of nature, and afterwards the relations spring forth and come onto it, as it were, and then the essence makes itself intimate to them, giving them every perfection that they have and making them God by deity. For this reason, in no way does the essence have a passive capacity to be perfected by them’.

[Scotus, Lect. 1.5.2.un., n. 105 (Vat. 16: 451.10-21): ‘Hoc etiam declaratur in exemplo: si alquid augmentetur in se sine alio adveniente, ut est in rarefactione, ibi forma rei augmentabilis mutatur et recipit novam perfectionem. Sed ponamus quod augmentatio fiat aliquo extra adveniente, isto modo, quod anima habens potentiam et virtutem perficiendi totum corpus organicum tantum perficiat unam partem, ut cor, et quod postea aliae partes corporis addantur, tunc anima — sine ulla mutatione sui — absque hoc quod aliunde perficitur perficit alias partes organicas. — Sic essentia divina, in primo signo naturae est perfectissima; postea, quasi superveniant relationes pullulantes, essentia intimat se eis, dans eis quidquid perfectionis habent et quod sint Deus deitate, — et ideo nullo modo habet potentiam passivam ut perficiatur eis’.]


From the Ordinatio

‘An example of this can be taken from creatures, by postulating a certain counterpossible situation. [We know that] growth happens when food [that’s been eaten] comes to be corrupted in the body, and its matter receives the form of flesh, and [thereby being new flesh added to the body], in this way it becomes informed by the soul. Here we are supposing that the same matter which remains throughout is apt to receive another part of the [soul’s] form (just as it is thought to happen in rarefaction), so the matter remains one, though it was first informed [by the form of food], but is now informed by a new form. This is formally a real change, because the matter goes from being deprived of to having a form. Now let’s look at this from the side of the soul. Suppose that the same soul perfects first one part of the body (such as the heart), and then later, when another part of the organic body which is perfectible by the soul is added to it [such as some food that is converted into flesh], the soul perfects that newly added part. In this case, the soul is not changed by this because it is not first deprived of and then comes to have a form. Deprivation is a lack in something that is naturally apt to receive, but [in our example here], the soul is first not-informing [the acquired part] and afterwards it is informing [it], and the soul is not apt to receive something, but rather to give’.

[Scotus, Ord. 1.5.2.un., n. 133 (Vat. 4: 76.1-15): ‘Exemplum istius potest accipi in creaturis, ponendo ibi quaedam “per impossibile”. Augmentatio modo fit per hoc quod alimentum adveniens corpori corrumpitur, et materia eius recipit formam carnis, et sic informatur ab anima. Ponatur quod eadem materia manens nata sit recipere aliam partem formae (sicut ponitur in rarefactione), materia manet una, quae prius fuit formata et nunc nova forma formatur, — ipsa tamen formaliter est vere mutata, quia de privatione transit ad formam. — Ponamus, ex alia parte, quod anima eadem perficeret primo unam partem corporis (ut cor), postea adveniret alia pars corporis organici, perfectibilis ab anima, anima perficeret illam partem advenientem de novo, — et ipsa tamen non mutaretur, quia non esset in ea primo privatio et postmodum forma. Privatio enim est carentia, in apto nato recipere; anima autem primo non-informans et postea informans non est nata aliquid recipere sed dare’.]

‘In each of these cases, there is a real production of some product, but in the first case, there is a change, and in the second case, there is not’.

[Scotus, Ord. 1.5.2.un., n. 134 (Vat. 4: 76.16-17): ‘In utroqe extremorum istorum vere esset productio alicuius producti, sed in primo mutatio, in secundo non’.]
‘A more apt example can be seen if we suppose that the matter of the animated heart could remain the same and be shared with diverse forms — say, that of a hand and a foot — so that by the [hypothetical] active power of the animated heart, it would produce those composites [namely, the hand and the foot] from its matter that it shares with them and their forms. Here there would be a true production of the composite wholes, and they would have the same matter, though this would happen through a change in the matter. Now let’s look at this from the side of the soul. Let’s suppose that the soul [which first exists in and so animates the heart] is unlimited with respect to its actuality as a form, such that it could be shared with many things, so that by the power of that soul in the heart, it could share itself with a hand and a foot which the animated heart produces. If that happened, there would here be a true production of many things that are consubstantial in their form, without any change in that form’.

[Scotus, Ord. 1.5.2.un., n. 135 (Vat. 4: 76.18-77.4): ‘Aptius videtur exemplum, si ponamus materiam cordis animati posse eandem communicari diversis formis — puta manus et pedis — et hoc virtute activa cordis animati, producentis composita ista ex materia sua communicata et ex formis istis, hic vere esset productio totorum habentium eandem materiam, et esset cum mutatione illius materiae; sed si, ex alia parte, ponamus animam — propter sui illimitationem in ratione actus et formae — posse communicari multis et virtute animae in corde ipsam communicari manui et pedi, productis a corde animato, hic vere esset productio multorum consbustantialium in forma, absque mutatione illius formae’.]

‘In each example, it is proposed that some being is produced which is subsistent by itself (rather than proposing that some parts are produced that belong to the same thing, because to be a part is an imperfection). These cases being posed, the second case in each example (which is about a form being shared with the product) perfectly represents production in God, while the first case in each example (which is about matter being shared) does not. Let’s modify this example even further, namely by supposing that although the soul is in the heart and the hand and the foot, it is not an informing form (for being a component of a composite is an imperfection), but is rather a whole form which is those subsistent things [viz., the heart, the hand, and the foot] and which animates them. Similarly, deity is understood to be shared with the relational subsistences (assuming that the persons are relative subsistences) not like quasi matter, but rather as a form, and not by informing them but rather as that by which each relation or the relative subsistent is God’.

[Scotus, Ord. 1.5.2.un., n. 136 (Vat. 4: 77.5-16): ‘In utroque exemplo ponantur producta esse per se subsistentia, non partes eisdem, quia esse partem est imperfectionis. Hoc posito, secundus modus in utroque exemplo, qui est de communicatione formae ipsi producto, perfecte repraesentat productionem in Deo, non primus, qui est de communicatione materiae, — et hoc, adhuc addendo in positione, quod anima in corde et manu et pede non sit forma informans, quia componibilitas includit imperfectionem, sed sit forma totalis qua illa subsistentia sint et animata sint: ita quod intelligitur deitas non communicari quasi-materia, sed relationibus subsistentibus — si personae ponantur relativae — communicatur deitas per modum formae, non informantis sed qua relatio vel relativum subsistens est Deus’.] [See also, Rep. 1.5.2.un., nn. 77-79 (Wolter, 280-281).]

Scotus on the formal end-point of production (translation)

From the Lectura

‘I say that in creatures, there is something that is produced, and that’s the primary end-point of production — it is the whole composite that is primarily produced or generated, just as the Philosopher proves in Metaphysics VII [1033b16-18]. Similarly, there is something that’s formally in the product which is produced, and this is the formal nature under which the production ends. This is the formal end-point of production, and it is the form of the product. So in one sense, the form truly ends the production . . . . the form truly is an end-point of production, even though the primary and adequate end-point is the composite itself’.

[Scotus, Lect. 1.5.1.un., nn. 27-28 (Vat. 16: 420.8-22): ‘dico quod in creaturis est aliquid quod producitur, quod est primus terminus productionis, — et est totum compositum quod primo producitur et generatur, sicut probatur VII Metaphysicae; similiter, est aliquid formale in producto quod producitur, quod est formalis ratio sub qua terminat productionem, et est formalis terminus productionis, et haec est forma producti. Et quod sic forma uno modo vere terminat productionem . . . . forma vere est terminus productionis, sed tamen terminus primus adaequatus est ipsum compositum’.]


From the Ordinatio

‘I say that a production has the product for its primary end-point, and I call this “primary end-point” here an adequate end-point. In this way, the Philosopher says in Metaphysics VII [1033b16-18] that the whole composite is what is primarily produced or generated, for it is what primarily gets its existence from the production, and this is adequate [for there to be a production]. Nevertheless, the form in the composite is the formal end-point of generation, but this is not an incidental end-point, as is apparent from the Philosopher’s comment in Physics II [193b12-18] where he proves that a form is a nature: “generation is natural because it is the way into nature, but since it is the way into form, etc.” That argument would mean nothing if the form were only an incidental end-point of generation’.

[Scotus, Ord. 1.5.1.un., nn. 27-29 (Vat. 4: 25.13-26.9): ‘dico quod productio habet productum pro termino suo primo, et dico hic “primum terminum” terminum adaequatum; et hoc modo dicit Philosophus VII Metaphysicae quod compositum primo generatur, quia est quod primo habet esse per productionem, hoc est adaequatum. In composito tamen forma est formalis terminus generationis, non autem terminus per accidens, sicut apparet per Philosophum II Physicorum, ubi probat formam esse naturam per hoc quod “generatio est naturalis quia est via in naturam, est autem via in formam, ergo etc.”, — quae ratio nulla esset si forma tantum esset terminus per accidens generationis’.]

Aquinas on what kind of opposites the Son and Spirit are

In the last post, I talked about Aquinas's claim that all distinct spirits are opposites. He wants to use this to show that the Son and Spirit are distinct by opposites too. To do so, he goes through Aristotle's four kinds of opposites (see my earlier posts on that), and he argues that of Aristotle’s four kinds of opposites, only the first (viz., correlatives) applies to the Son and Spirit. To see this, let’s start with contradictions and work our way backwards.

(d) First then, are contradictions. Aquinas claims that the Son and Spirit are not opposites by contradiction. That is, the Son and Spirit are not opposites in the way that ‘Socrates is sitting’ and ‘Socrates is not sitting’ are. Why not? One obvious reason is this: the Son and Spirit are not sentences, and contradictions only apply to sentences. But that’s not what Aquinas says. Instead, he says that a contradiction distinguishes ‘beings’ from ‘non-beings’.

By ‘beings’ and ‘non-beings’, Aquinas has in mind the beings that affirmative and negative statements describe. An affirmative statement asserts that some state of affairs exists. A negative statement, by contrast, asserts that some state of affairs does not exist. Thus, affirmative statements describe ‘being(s)’, and negative statements describe ‘non-being(s)’.

Okay, so affirmative and negative statements describe states of affairs that do and do not exist. But why should that mean the Son and Spirit can’t be distinguished by contradiction? Unfortunately, Aquinas says no more than what I’ve already said, namely that the Son and Spirit aren’t distinguished by contradiction because contradiction distinguishes ‘beings’ and ‘non-beings’. Apparently, he thinks the conclusion is obvious, but it takes some explaining (it does for me, anyways).

Consider the following. Can’t I say that ‘the Son is begotten by the Father’ and ‘the Spirit is not begotten by the Father’? Wouldn’t that be enough to distinguish them? Similarly, if I said ‘George Bush Jr. is the President of the United States’ and ‘I am not the President of the United States’, wouldn’t that be enough to distinguish myself from the President?

Well, the problem here is that these are faux contradictions. Both pairs of statements are true, so they don’t count as contradictions, strictly speaking. As I explained in my previous post, contradictions are such that one of the sentences must be true and the other false. If two sentences are true, then there’s really no contradiction there.

Indeed, Bush Jr. really is the President, and I’m really not the President, and there’s nothing contradictory about that. Likewise, the Son really is begotten by the Father, and the Spirit really isn’t (he’s spirated, not begotten), and there’s nothing contradictory about that either.

A genuine contradiction would be this: ‘the Son is begotten by the Father’ and ‘the Son is not begotten by the Father’. Those two sentences are opposites by contradiction, not ‘the Son is begotten by the Father’ and ‘the Spirit is not begotten by the Father’. But the genuine contradiction can’t apply to the Son, for the false sentence is simply false. The Son is begotten, and that’s all we can say. But the Son being begotten says nothing about the Spirit. So genuine contradictions don’t really help us distinguish two things.

(c) Second, Aquinas says that the Son and Spirit are not distinguished by possession and deprivation. The reason is that possession and deprivation distinguish the perfect from the imperfect. Again, Aquinas says no more than this, for he assumes that the conclusion is obvious. And for me anyways, this time it is a little more obvious.

In this context, ‘perfection’ refers to fully realized potential, so something is ‘perfect’ only when it fully realizes its potential, and it’s ‘imperfect’ until its potential is fully realized. Possession and deprivation imply this sort of perfection and imperfection. A blind animal can’t realize its capacity to see, so it’s ‘imperfect’ with respect to sight. A seeing animal, on the other hand, is fully realizing its capacity for sight, so it’s ‘perfect’ with respect to sight.

In the Godhead, of course, nothing can be imperfect. There is no unrealized potential in God, so every divine person has everything it has the capacity for. Thus, there simply is no ‘deprivation’ in God, and therefore, there can’t be opposition between ‘possession’ and ‘deprivation’ in the Trinity. This kind of opposition is simply not possible in the divine case, so it can’t distinguish the Son and Spirit.

(b) Third, Aquinas says the Son and Spirit are not distinguished by contraries. As I explained above, contaries are non-relational features like ‘hot’ and ‘cold’ or ‘white’ and ‘black’. For Aquinas (and for Aristotle), these sorts of features are forms. Something is hot, for example, because it has the form of ‘heat’, and that form is what makes it hot.

Consequently, a difference between contraries amounts to a difference between forms. A hot thing and a cold thing differ with respect to hot and cold because one of them has the form of ‘heat’, and the other has the contrary form of ‘cold’.

For Aquinas though, there is just one form in God, and that’s the divine essence. The three persons all share that one divine-essence-form. Thus, the persons cannot differ by having different forms, and so the Son and Spirit cannot be opposites by having contrary forms.

(a) That leaves only correlatives. The Son and Spirit must, then, differ by having correlative features. As I explained above, correlatives are relational features that are reciprocal, like ‘double’ and ‘half’. So the Son and Spirit must each have a relational feature that is reciprocal with respect to the other’s relational feature.

However, there are lots of different kinds of correlatives, and so Aquinas still needs to show which kind of correlative the Son and Spirit differ by.

Aquinas on the distinction of spirits

In the Summa Contra Gentiles, book 4, chapter 24, Aquinas provides a number of arguments for the filioque (i.e., the claim that the Spirit is produced by two divine persons, namely the Father and the Son). In one of those arguments (n. 8 in the Taurini 1961 edition), he makes the following claim:

In things where the material distinction is removed (and a material distinction cannot have any place in the divine persons), no two things are found to be distinguished unless by some opposition.

Here Aquinas is saying that when it comes to non-material things (let’s just call them spirits), the only distinction is one between opposites. That is, any two distinct spirits are opposites in some way. Let's formulate this claim like so:

(A1) For any spirits x and y, x and y are distinct iff x and y are opposites.

Right away, I’m skeptical. A1 states that all spirits are opposites, but why should we believe that? You and I are distinct, but we’re certainly not opposites. Why can’t two spirits be distinct like we are, without being opposites? The angels Gabriel and Michael are distinct, but are they opposites? If so, in what way?

To explain why spirits are always distinguished by opposition, Aquinas says the following:

Those things that have no opposition to each other can be in the same thing at the same time. Hence, no distinction can be caused by them. Whiteness and triangularity are diverse, but they’re not opposites, so they can belong to the same thing.

This requires some unpacking. There are three points here, and each needs to be separated. That way, we can more clearly see what Aquinas is actually saying here.

(a) The first point to clarify is based on the comment that whiteness and triangularity can exist together in the same thing. The assumption is that some features can simultaneously exist in the same thing, but others cannot. Some features have no disagreement and are perfectly happy to be together, but others just can’t be in the same room, so to speak. Let’s say that the former type are ‘compatible’, and the latter type are ‘incompatible’:

(A2) For any x and y, x and y are compatible iff x and y can exist simultaneously in some z.

(A3) For any x and y, x and y are incompatible iff there is no z in which x and y can exist simultaneously.

To use Aquinas’s own example, whiteness and triangularity are compatible because one and the same thing can be both white and triangular. And indeed, we see white triangles all the time, so whiteness and triangularity are clearly compatible in this way.

Incompatible things, on the other hand, aren’t like this. If I ask a group of people to take sides on capital punishment, that will break up the group: some will be for the death penalty, and others will be against it. These are incompatible viewpoints, so they have to be held by different individuals/groups.

(b) The second point to clarify is based on Aquinas’s comment that compatible features cannot be the cause of distinction. The claim here is that incompatible features can, but compatible features cannot, be the cause of distinction. What does Aquinas mean by ‘cause’ here? To answer this, we need to distinguish between what Aquinas calls an ‘efficient cause’ and a ‘formal cause’.

The efficient cause explains how something comes to exist, while the formal cause explains how something is the particular kind of thing it is. Thus, the efficient cause of some x is the agent that brings x into being, but the formal cause of x is x’s defining characteristics (or ‘formal characteristics’, as the medievals put it), for those are the characteristics that make x the sort of thing it is.

For example, the efficient cause of a clay statue is the sculptor, for that’s who made it. Without the sculptor’s activity, the statue wouldn’t exist. But the formal cause of the statue is its statue-shape, for that’s what makes it a statue. After all, if the sculptor gave the clay a vase-shape, that’d make it a vase, not a statue.

So does Aquinas think incompatible features are efficient or formal causes of distinction? Surely he doesn’t think they’re efficient causes. Taking sides on capital punishment divides people into two groups, but the viewpoints themselves don’t literally twist people’s arms and force them into two groups. As the saying goes, viewpoints don’t kill people, people kill people.

But the ‘for’ and ‘against’ viewpoints are formal causes of division. Their formal/defining characteristics are such that one and the same individual can’t hold both viewpoints simultaneously. Thus, they require separate advocates: one to take the ‘for’ side, and another to take the ‘against’ side.

Besides, features depend on the things they belong to, not the other way around. A sports car has the feature of being red, but its red color depends on the car for its existence; the car doesn't depend on its red color. After all, I could re-paint my car, and the car would still exist, but if I destroyed the car, any color it might have would cease to exist too.

Consequently, features can't be the efficient cause of distinction. Features come on the scene too late, as it were, to cause any distinctions. For this reason alone, incompatible features can’t be the efficient cause of distinction (though they can be the formal cause of distinction).
I take it, then, that Aquinas thinks incompatible features are the formal cause, not the efficient cause, of distinction. When he says that two incompatible features F and G are the ‘cause’ of distinction, he means F and G formally require distinct things. He doesn’t mean that F and G efficiently cause distinct things to come into being.

(Note that this seems to be a priori or ‘self evident’ in the sense that the consequence is included in the antecedent. Here, incompatible features are defined as features that can’t exist in the same thing (A3 above). But to say that incompatible features are the ‘formal cause’ of distinction is just to say that incompatible features can only exist in distinct things.)

(c) The third point that needs clarification focuses on Aquinas’s claim that two features are compatible so long as they’re not opposites. We need to be careful here. How wide is Aquinas casting this net? He’s supposed to be talking only about spirits, but his example of whiteness and triangularity is taken from the material world. So is Aquinas talking about any two features (be they spiritual or material), or is he only talking about spirit features? If it’s the former, then Aquinas is saying this:

(A4) For any features F and G, F and G are compatible iff F and G are not opposites.

But if it’s the latter, Aquinas is saying this:

(A4*) For any spirit features F and G, F and G are compatible iff F and G are not opposites.

These are very different claims. The fact that Aquinas talks about whiteness and triangularity makes it tempting to think that he is affirming the former claim (namely, A4). After all, spirits are neither white nor triangular, so it certainly appears as if Aquinas is thinking that this rule applies to more than just spirits.

The problem is, Aquinas thinks A4 isn’t always true. Individual material substances are incompatible according to A3, but they’re not opposites. Socrates and Plato, for example, obviously can’t exist in the same thing, but they’re not opposites. Thus, Aquinas should reject A4.

Perhaps he holds A4* instead. That would support his initial claim (A1 above) that all spirits are distinct because they’re opposites. But if that’s right, I still wonder why Aquinas uses whiteness and triangularity as an example. Maybe it’s just a bad example, and that’s all there is to it.

Now, it’s well known that for Aquinas, material beings are distinct because they occur in different lumps of matter, but angels are distinct because they belong to different species. For Aquinas, a species gets divided up into different individuals when its instantiated in different lumps of matter, roughly similar to the way a cookie cutter’s shape gets replicated when it’s stamped into different lumps of cookie dough. (So Socrates is the human-species ‘stamped’ into this lump of tissue, and Plato is the human-species ‘stamped’ into that lump of tissue.) But angels don’t have any matter, so any given angel-species can’t be replicated by being ‘stamped’ into different lumps of matter. Thus, each angel is the sole member of its species. Moreover, each angel just is its species, much like how there’s nothing but the cookie cutter’s shape if there aren’t any lumps of cookie dough to take on that shape.

Given this, we might think that Aquinas believes that although distinct material beings (in the same species) aren’t opposites, distinct species are opposites. That would support the initial claim (A1), for although Aquinas is willing to accept that material things are distinct without being opposites, there is no matter in the realm of angels, so the only distinction there is one between species, and species are distinct only because they’re opposites.

But if that’s right, then what is it that makes species opposites? Every species is a complex of a shared genus and a unique specific difference. For example, the human species is composed of animality (the genus that humans share with other animals), and rationality (the specific difference that belongs uniquely to humans, and so distinguishes humans from other animals). Thus, any opposition between species would have to occur between the specific differences. After all, the genus is shared, and shared things can’t be opposites. But does Aquinas really think that specific differences are opposites?

That seems to be the moral of the story here. Consider the human- and brute-species. These are distinct because the former has rationality and the latter does not. Rationality and irrationality seem to be opposites, so perhaps that makes sense. Maybe, then, Aquinas is using opposition to explain how species themselves are distinct.

Still, this leaves many questions unanswered. If specific differences are opposites, what, exactly, are opposites? How does one define ‘opposites’? Are there different kinds of opposites? If so, which kind do specific differences fall under?

In any case, now that we’ve gone through all that, we’re in a better place to summarize Aquinas’s argument. As I hope is clear by now, Aquinas argues that non-opposing features are compatible, so they’re perfectly happy to exist in the same thing. (Well, in the material world, material substances can be incompatible without being opposites, but we’re talking about the realm of spirits here.) Consequently, non-opposing features can’t be the formal cause of distinction between spirits, for there’s nothing about such features which demands that they exist in distinct things.

Opposite features, on the other hand, are incompatible, so they cannot exist in the same thing. On the contrary, opposite features can only exist in distinct things. Thus, opposite features must be the formal cause of distinction for spirits.

Unfortunately, A4/A4* are contentious. Neither A4 nor A4* are universally agreed-upon claims. Ockham, for example, thinks that angels are individuals just like Socrates and Plato, and all individuals are primitively distinct (without being opposites). So Aquinas’s argument is only as successful as A4/A4*, and not everybody buys A4/A4*.