Accidents

Replies to Objections on Form

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This post replies to the objections raised in the last post.

Reply 1. I do not define form as “many relations”, in part for this very reason. Rather, I say that it is a network, and thus is one thing tied together, so to speak.

Nonetheless, the objection seems to wish to find something absolutely one which is in no way many and which causes unity in other things which are in some way lacking in unity. This does not fit with the idea of giving an account, which necessarily involves many words and thus reference to many aspects of a thing. And thus it also does not fit with the idea of form as that which makes a thing what it is, because it is evident that when we ask what a thing is, we are typically asking about things that have many aspects, as a human being has many senses and many body parts and so on.

In other words, form makes a thing one, but it also makes it what it is, which means that it also makes a thing many in various ways. And so form is one in some way, and thus called a “network,” but it also contains various relations that account for the many aspects of the thing.

Someone might extend this objection by saying that if a form contains many relations, there will need to be a form of form, uniting these relations. But there is a difference between many material parts, which might need a form in order to be one, and relations, which bind things together of themselves. To be related to something, in this sense, is somewhat like being attached to it in some way, while a number of physical bodies are not attached to each other simply in virtue of being a number of bodies. It is true that this implies a certain amount of complexity in form, but this is simply the result of the fact that there is a certain amount of complexity in what things actually are.

Reply 2. “Apt to make something one” is included in the definition in order to point to the relationships and networks of relationships that we are concerned with. For example, one could discuss the idea of a mereological sum, for example the tree outside my window together with my cell phone, and talk about a certain network of relationships intrinsic to that “sum.” This network would have little share in the idea of form, precisely because it is not apt to make anything one thing in any ordinary sense. However, I say “little share” here rather than “no share”, because this is probably a question of degree and kind. As I said here, “one thing” is said in many ways and with many degrees, and thus also form exists in many ways and with many degrees. In particular, there is no reason to suppose that “one” has one true sense compared to which the other senses would be more false than true.

Reply 3. A network of relationships could be an accidental form. Thus the form that makes a blue thing blue would normally be an accidental form. But there will be a similar network of relationships that make a thing a substance. If something is related to other things as “that in which other things are present,” and is not related to other things as “that which is present in something else,” then it will exist as substance, and precisely because it is related to things in these ways. So the definition is in fact general in comparison to both substance and accident.

Reply 4. This objection could be understood as asserting that everything relative depends on something prior which is absolute. Taken in this sense, the objection is simply mistaken. The existence of more than one thing proves conclusively that relationship as such does not need to depend on anything absolute.

Another way to understand the objection would be as asserting that whatever we may say about the thing in relation to other things, all of this must result from what the thing is in itself, apart from all of this. Therefore the essence of the thing is prior to anything at all that we say about it. And in this way, there is a truth here and an error here, namely the Kantian truth and the Kantian error. Certainly the thing is the cause of our knowledge, and not simply identical with our knowledge. Nonetheless, we possess knowledge, not ignorance, of the thing, and we have this knowledge by participation in the network of relationships that defines the thing.

Reply 5. The objection gratuitously asserts that our definition is reductionist, and this can equally well be gratuitously denied. In fact, this account includes the rejection of both reductionist and anti-reductionist positions. Insofar as people suppose that these positions are the only possible positions, if they see that my account implies the rejection of their particular side of the argument, they will naturally suppose that my account implies the acceptance of the other side. This is why the 10th objection claims the opposite: namely that my account is mistaken because it seems to be anti-reductionist.

Reply 6. I agree, in fact, that we are mostly ignorant of the nature of “blue,” and likewise of the natures of most other things. But we are equally ignorant of the network of relationships that these things share in. Thus in an earlier post about Mary’s Room, I noted that we do not even come close to knowing everything that can be known about color. Something similar would be true about pretty much everything that we can commonly name. We have some knowledge of what blue is, but it is a very imperfect knowledge, and similarly we have some knowledge of what a human being is, but it is a very imperfect knowledge. This is one reason why I qualified the claim that the essences of things are not hidden: in another way, virtually all essences are hidden from us, because they are typically too complex for us to understand exhaustively.

An additional problem, also mentioned in the case of “blue,” is that the experience of blue is not the understanding of blue, and these would remain distinct even if the understanding of blue were perfect. But again, it would be an instance of the Kantian error to suppose that it follows that one would not understand the nature of blue even if one understood it (thus we make the absurdity evident.)

Reply 7. God is not an exception to the claim about hidden essences, nor to this account of form, and these claims are not necessarily inconsistent with Christian theology.

The simplicity of God should not be understood as necessarily being opposed to being a network of relationships. In particular, the Trinity is thought to be the same as the essence of God, and what is the Trinity except a network of relations?

Nor does the impossibility of knowing the essence of God imply that God’s essence is hidden in the relevant sense. Rather, it is enough to say that it is inaccessible for “practical” reasons, so to speak. For example, consider St. Thomas’s argument that no one knows all that God can do:

The created intellect, in seeing the divine essence, does not see in it all that God does or can do. For it is manifest that things are seen in God as they are in Him. But all other things are in God as effects are in the power of their cause. Therefore all things are seen in God as an effect is seen in its cause. Now it is clear that the more perfectly a cause is seen, the more of its effects can be seen in it. For whoever has a lofty understanding, as soon as one demonstrative principle is put before him can gather the knowledge of many conclusions; but this is beyond one of a weaker intellect, for he needs things to be explained to him separately. And so an intellect can know all the effects of a cause and the reasons for those effects in the cause itself, if it comprehends the cause wholly. Now no created intellect can comprehend God wholly, as shown above (Article 7). Therefore no created intellect in seeing God can know all that God does or can do, for this would be to comprehend His power; but of what God does or can do any intellect can know the more, the more perfectly it sees God.

St. Thomas argues that if anyone knew all that God can do, i.e. everything that can be God’s effect, he would not only know the essence of God, but know it perfectly. This actually supports our position precisely: if you have an exhaustive account of the network of relationships between God and the world, actual and potential, according to St. Thomas, this is to know the essence of God exhaustively.

Reply 8. I concede the objection, but simply note that the error is on the part of Christian theology, not on the part of this account.

In this case, someone might ask why I included this objection, along with the previous, where even if I consider the theology defensible, I do not consider it authoritative. The reason is that I included objections that I expected various readers to hold in one form or another, and these are two of them. But what is the use of addressing them if I simply reject the premise of the objection?

There is at least one benefit to this. There is an important lesson here. Religious doctrines are typically defined in such a way that they have few or no undue sensible implications, as I said for example about the Real Presence. But philosophy is more difficult, and shares in much of the same distance from the senses that such religious claims have. Consequently, even if you manage to avoid adopting religious doctrines that have false scientific implications (and many don’t manage to avoid even this), if you accept any religious doctrines at all, it will be much harder to avoid false philosophical implications.

In fact, the idea of an immortal soul probably has false scientific consequences as well as false philosophical consequences, at least taken as it is usually understood. Thus for example Sean Carroll argues that the mortality of the soul is a settled issue:

Adam claims that “simply is no controlled, experimental[ly] verifiable information” regarding life after death. By these standards, there is no controlled, experimentally verifiable information regarding whether the Moon is made of green cheese. Sure, we can take spectra of light reflecting from the Moon, and even send astronauts up there and bring samples back for analysis. But that’s only scratching the surface, as it were. What if the Moon is almost all green cheese, but is covered with a layer of dust a few meters thick? Can you really say that you know this isn’t true? Until you have actually examined every single cubic centimeter of the Moon’s interior, you don’t really have experimentally verifiable information, do you? So maybe agnosticism on the green-cheese issue is warranted. (Come up with all the information we actually do have about the Moon; I promise you I can fit it into the green-cheese hypothesis.)

Obviously this is completely crazy. Our conviction that green cheese makes up a negligible fraction of the Moon’s interior comes not from direct observation, but from the gross incompatibility of that idea with other things we think we know. Given what we do understand about rocks and planets and dairy products and the Solar System, it’s absurd to imagine that the Moon is made of green cheese. We know better.

We also know better for life after death, although people are much more reluctant to admit it. Admittedly, “direct” evidence one way or the other is hard to come by — all we have are a few legends and sketchy claims from unreliable witnesses with near-death experiences, plus a bucketload of wishful thinking. But surely it’s okay to take account of indirect evidence — namely, compatibility of the idea that some form of our individual soul survives death with other things we know about how the world works.

Claims that some form of consciousness persists after our bodies die and decay into their constituent atoms face one huge, insuperable obstacle: the laws of physics underlying everyday life are completely understood, and there’s no way within those laws to allow for the information stored in our brains to persist after we die. If you claim that some form of soul persists beyond death, what particles is that soul made of? What forces are holding it together? How does it interact with ordinary matter?

Everything we know about quantum field theory (QFT) says that there aren’t any sensible answers to these questions. Of course, everything we know about quantum field theory could be wrong. Also, the Moon could be made of green cheese.

Among advocates for life after death, nobody even tries to sit down and do the hard work of explaining how the basic physics of atoms and electrons would have to be altered in order for this to be true. If we tried, the fundamental absurdity of the task would quickly become evident.

Even if you don’t believe that human beings are “simply” collections of atoms evolving and interacting according to rules laid down in the Standard Model of particle physics, most people would grudgingly admit that atoms are part of who we are. If it’s really nothing but atoms and the known forces, there is clearly no way for the soul to survive death. Believing in life after death, to put it mildly, requires physics beyond the Standard Model. Most importantly, we need some way for that “new physics” to interact with the atoms that we do have.

Very roughly speaking, when most people think about an immaterial soul that persists after death, they have in mind some sort of blob of spirit energy that takes up residence near our brain, and drives around our body like a soccer mom driving an SUV. The questions are these: what form does that spirit energy take, and how does it interact with our ordinary atoms? Not only is new physics required, but dramatically new physics. Within QFT, there can’t be a new collection of “spirit particles” and “spirit forces” that interact with our regular atoms, because we would have detected them in existing experiments. Ockham’s razor is not on your side here, since you have to posit a completely new realm of reality obeying very different rules than the ones we know.

There are certainly different ways to think about this, but this is in fact a common way of thinking about the soul in relation to the body. For example, consider this discussion by James Chastek:

Objection: Conservation laws require that outcomes be already determined. By your own admission, life has to be able to “alter what would happen by physical causes alone” and therefore violates conservation laws.

Response: Again, laws and initial conditions do not suffice to explain the actual world. Life only “alters” physical causes under the counterfactual supposition that physical causes could act alone, i.e. in a way that could suffice to explain outcomes in the actual world.

Objection: It is meaningless to describe life acting on physical laws and conditions when we can’t detect this. Life-actions are vacuous entities about which we can say nothing at all. What’s their Hamiltonian?

Response: Physical laws and conditions as physical are instrumental or partial accounts of the actual world. The interactive mechanisms and measurement devices appropriate to establishing the existence of physical causes are not appropriate tools for describing all causes of the actual world.

Chastek is deliberately ignoring the question that he poses himself. But we know his opinion of the matter from previous discussions. What physics would calculate would be one thing; what the human being will do, according to Chastek, is something different.

This almost certainly does imply a violation of the laws of physics in the sense of the discussion in Chastek’s post, as well as in the sense that concerns Sean Carroll. In fact, it probably would imply a violation of conservation of energy, very possibly to such a degree that it would be possible in principle to exploit the violation to create a perpetual motion machine, somewhat along the lines of this short story by Scott Alexander. And these violations would detectable in principle, and very likely in practice as well, at least at some point.

Nonetheless, one might think about it differently, without suggesting these things, but still suppose that people have immortal souls. And one might be forgiven for being skeptical of Sean Carroll’s arguments, given that his metaphysics is wrong. Perhaps there is some implicit dependence of his argument on this mistaken metaphysics. The problem with this response is that even the correct metaphysics has the same implications, even without considering Carroll’s arguments from physics.

It is easy to see that there still loopholes for someone who wishes to maintain the immortality of the soul. But such loopholes also indicate an additional problem with the idea. In particular, the idea that the soul is subsistent implies that it is a substantial part of a human being: that a human is a whole made of soul and body much as the body is a whole made of various parts such as legs and arms. If this were the case, the soul might not be material in a quantitative sense, but it would be “matter” in the sense that we have argued that form is not matter. In this case, it would be reasonable to suppose that an additional substantial form would be necessary to unify soul and body, themselves two substantial parts.

Reply 9. There in fact is an implicit reference to matter in the definition. “Apt to make something one” refers to what is made, but it also refers to what it is made out of, if there is anything out of which it is made. The form of a chair makes the chair one chair, but it also makes the stuff of the chair into one chair.

There is more to say about matter, but my intention for now was to clarify the concept of form.

Reply 10. The network of relationships is most certainly not a construct of the mind, if one places this in opposition to “real thing.” You cannot trace back relationships to causes that do not include any relationships, if only because “cause” is in itself relative.

I have argued against reductionism in many places, and do not need to repeat those arguments here, but in particular I would note that the objection implies that “mind” is a construct of the mind, and this implies circular causality, which is impossible.

Reply 11. The objection is not really argued, and this is mainly because there cannot be a real argument for it. There is however a rough intuition supporting it, which is that applying this idea of form to immaterial things seems unfair to reality, as though we were trying to say that the limits of reality are set by the limits of the human mind. Once again, however, this is simply a case of the usual Kantian error, mixed together with choosing something that would be especially unknown to us. An immaterial thing could not exist without having some relationship with everything else. As we have suggested elsewhere, “there is an immaterial thing,” cannot even be assigned a meaning without the implied claim that I stand in some relation with it, and that it stands in some relation to me. But evidently I know very little about it. This does not mean that we need some new definition of what it is to be something; it simply means I do not know much of what that thing is, just as I do not know much of anything about it at all.

 

Form and the Goodness of God

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In his commentary on the Sentences of Peter Lombard, St. Thomas says:

Loquendo autem de necessitate quae est ex suppositione divini propositi, quo propter benevolentiam suae bonitatis voluit unicuique eam communicare secundum suam capacitatem, necessarium est quod cuilibet materiae praeparatae forma infundatur. Non tamen eodem modo est in omnibus formis; quia formae quae mediantibus secundis agentibus in materia producuntur, necessario in materia disposita recipiuntur necessitate conditionata in comparatione ad Deum, cujus virtute cetera agentia agunt; sed necessitate absoluta per comparationem ad agentia proxima, quae necessitate naturae agunt propter ordinem divinitus eis impositum, quem praeterire non possunt. Formae autem quae immediate a Deo inducuntur, non habent necessitatem absolutam ex parte agentis, sed quaedam ex parte recipientis, sicut in perfectionibus quae sunt de esse naturae, ut est anima rationalis. Formae autem quae non debentur naturae, sicut gratia et virtutes, immediate a Deo productae, nihil habent de necessitate absoluta, sed solum de necessitate ex suppositione divini ordinis, ut dictum est.

Which is, more or less:

But speaking of the necessity which is on the supposition of the divine intention, by which on account of the benevolence of his [God’s] goodness, he wished to share with each thing according to its capacity, it is necessary that form be infused into every prepared matter. But nevertheless not in the same way in all forms; since forms which are produced in matter through the mediation of secondary agents are necessarily received into matter with a conditional necessity in comparison with God, by the power of whom other agents act, but with an absolute necessity in comparison to the proximate agents, which act by necessity of nature on account of the order divinely imposed on them, which they cannot omit. But forms which are immediately imposed by God, do not have an absolute necessity on the part of the agent, but a certain necessity on the part of the recipient, as in perfections which are of the being of nature, as is the rational soul. And forms which are not owed to nature, like grace and the virtues, produced immediately by God, have nothing of absolute necessity, but only of the necessity on the supposition of the divine order, as was said.

St. Thomas’s overall point is that every disposed matter receives its corresponding form, and that this happens on account of the goodness of God. He asserts that there are three ways in which this happens:

(1) With respect to forms produced through secondary causes, the things involved cannot naturally fail to produce the form in disposed matter, although this is taken to be conditional in comparison with God, presumably in the sense that if God wanted things to happen otherwise, they could happen otherwise, just as St. Thomas asserts that in the Eucharist accidents can exist without substance, by the divine will.

This first case seems intended to cover all natural changes, with one exception (we will get to the exception in a few moments.) So for example, according to St. Thomas, if you dispose matter to be a certain color, it will necessarily be that color; if you dispose matter to be living matter, it will necessarily be living; and so on. Just as we saw with lines and squares, properly disposed matter always has the corresponding form.

(2) Second, there are forms that are “immediately imposed by God,” but which have a certain natural necessity on the part of the recipient. He mentions the rational soul as though it were an example here, but in fact it seems to be the only thing which is meant to fall into this category rather than the third category.

This happens because St. Thomas considers the human soul to be something exceptional and unique in nature, as we can see from his discussion of the human soul as subsistent:

I answer that, It must necessarily be allowed that the principle of intellectual operation which we call the soul, is a principle both incorporeal and subsistent. For it is clear that by means of the intellect man can have knowledge of all corporeal things. Now whatever knows certain things cannot have any of them in its own nature; because that which is in it naturally would impede the knowledge of anything else. Thus we observe that a sick man’s tongue being vitiated by a feverish and bitter humor, is insensible to anything sweet, and everything seems bitter to it. Therefore, if the intellectual principle contained the nature of a body it would be unable to know all bodies. Now every body has its own determinate nature. Therefore it is impossible for the intellectual principle to be a body. It is likewise impossible for it to understand by means of a bodily organ; since the determinate nature of that organ would impede knowledge of all bodies; as when a certain determinate color is not only in the pupil of the eye, but also in a glass vase, the liquid in the vase seems to be of that same color.

Therefore the intellectual principle which we call the mind or the intellect has an operation “per se” apart from the body. Now only that which subsists can have an operation “per se.” For nothing can operate but what is actual: for which reason we do not say that heat imparts heat, but that what is hot gives heat. We must conclude, therefore, that the human soul, which is called the intellect or the mind, is something incorporeal and subsistent.

Elsewhere he says that the human soul alone is special in this way. Thus in the next article he specifically denies subsistence in regard to the souls of other animals:

I answer that, The ancient philosophers made no distinction between sense and intellect, and referred both a corporeal principle, as has been said. Plato, however, drew a distinction between intellect and sense; yet he referred both to an incorporeal principle, maintaining that sensing, just as understanding, belongs to the soul as such. From this it follows that even the souls of brute animals are subsistent. But Aristotle held that of the operations of the soul, understanding alone is performed without a corporeal organ. On the other hand, sensation and the consequent operations of the sensitive soul are evidently accompanied with change in the body; thus in the act of vision, the pupil of the eye is affected by a reflection of color: and so with the other senses. Hence it is clear that the sensitive soul has no “per se” operation of its own, and that every operation of the sensitive soul belongs to the composite. Wherefore we conclude that as the souls of brute animals have no “per se” operations they are not subsistent. For the operation of anything follows the mode of its being.

As a result of this special account of the human soul, St. Thomas asserts that natural agents do not have the capacity, considered in themselves, to produce a human soul. Consequently he says that there is not an absolute necessity on the part of the agents, meaning that there is no necessity because there is not even the possibility, considered on the part of the agents in themselves. But he says there is a necessity on the part of the recipient, meaning that nature would be lacking its appropriate perfection if e.g. the union of human seed and egg did not result in a human soul. And on account of the goodness of God, such a lack will never be permitted. Consequently every matter that is disposed to be human, will actually be human, just as in the case of the forms of the first kind.

(3) Finally, there are forms which are not “owed” to nature in the way that other natural forms are, and in the way in which even the human soul is owed. Here St. Thomas speaks of grace and “the virtues,” by which he means supernatural virtues, not natural virtues.

In order to understand this case, we can imagine a situation where we construct many shapes: squares, circles, triangles and so on. We paint all of them white, with one exception: whenever we have squares, we paint them red. In essence, we have invented a rule: we consider squares, and no other shapes, disposed to be red, and we cause them actually to be so.

In our example, there is nothing about being square that would actually make a thing red. But there is a certain order there, imposed by ourselves, whereby being square is effectively a disposition to be red. In a similar way, St. Thomas asserts that there are dispositions that God considers to be dispositions for grace, even though in themselves they would not be sufficient to make a thing have grace, or even to make a thing need grace. But St. Thomas says that on account of the goodness of God, he considers “doing as well as one can” to be the disposition for grace, and thus God always gives grace to one who does their best, even if they are merely doing their best on a natural level.

While it is not the point of this post, it is because of this account of God’s goodness in relation to form and disposed matter that St. Thomas is fundamentally opposed to any kind of rigid understanding of the doctrine of extra ecclesiam nulla salus. According to St. Thomas, whether there is a natural necessity for it or not, every disposed matter receives its appropriate form, on account of the goodness of God.

 

Mixing Water and Wine

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St. Thomas discusses what happens if you mix consecrated wine with another liquid:

I answer that, The truth of this question is evident from what has been said already. For it was said above (3; 5, ad 2) that the species remaining in this sacrament, as they acquire the manner of being of substance in virtue of the consecration, so likewise do they obtain the mode of acting and of being acted upon, so that they can do or receive whatever their substance could do or receive, were it there present. But it is evident that if the substance of wine were there present, then some other liquid could be mingled with it.

Nevertheless there would be a different effect of such mixing both according to the form and according to the quantity of the liquid. For if sufficient liquid were mixed so as to spread itself all through the wine, then the whole would be a mixed substance. Now what is made up of things mixed is neither of them, but each passes into a third resulting from both: hence it would result that the former wine would remain no longer. But if the liquid added were of another species, for instance, if water were mixed, the species of the wine would be dissolved, and there would be a liquid of another species. But if liquid of the same species were added, of instance, wine with wine, the same species would remain, but the wine would not be the same numerically, as the diversity of the accidents shows: for instance, if one wine were white and the other red.

But if the liquid added were of such minute quantity that it could not permeate the whole, the entire wine would not be mixed, but only part of it, which would not remain the same numerically owing to the blending of extraneous matter: still it would remain the same specifically, not only if a little liquid of the same species were mixed with it, but even if it were of another species, since a drop of water blended with much wine passes into the species of wine (De Gener. i).

Now it is evident that the body and blood of Christ abide in this sacrament so long as the species remain numerically the same, as stated above (4; 76, 6, ad 3); because it is this bread and this wine which is consecrated. Hence, if the liquid of any kind whatsoever added be so much in quantity as to permeate the whole of the consecrated wine, and be mixed with it throughout, the result would be something numerically distinct, and the blood of Christ will remain there no longer. But if the quantity of the liquid added be so slight as not to permeate throughout, but to reach only a part of the species, Christ’s blood will cease to be under that part of the consecrated wine, yet will remain under the rest.

Given the doctrine of transubstantiation, at least as St. Thomas understands it, so that it implies the existence of accidents without a subject, it is very difficult to understand how such a mixing would be possible at all. But his general position here is that a process analogous to substantial change necessarily happens if you mix anything into the consecrated wine, either according to a part of the wine, or according to the whole. He explains this kind of change in article five of the same question:

I answer that, Since “the corruption of one thing is the generation of another” (De Gener. i), something must be generated necessarily from the sacramental species if they be corrupted, as stated above (Article 4); for they are not corrupted in such a way that they disappear altogether, as if reduced to nothing; on the contrary, something sensible manifestly succeeds to them.

Nevertheless, it is difficult to see how anything can be generated from them. For it is quite evident that nothing is generated out of the body and blood of Christ which are truly there, because these are incorruptible. But if the substance, or even the matter, of the bread and wine were to remain in this sacrament, then, as some have maintained, it would be easy to account for this sensible object which succeeds to them. But that supposition is false, as was stated above (75, 2,4,8).

Hence it is that others have said that the things generated have not sprung from the sacramental species, but from the surrounding atmosphere. But this can be shown in many ways to be impossible. In the first place, because when a thing is generated from another, the latter at first appears changed and corrupted; whereas no alteration or corruption appeared previously in the adjacent atmosphere; hence the worms or ashes are not generated therefrom. Secondly, because the nature of the atmosphere is not such as to permit of such things being generated by such alterations. Thirdly, because it is possible for many consecrated hosts to be burned or putrefied; nor would it be possible for an earthen body, large enough to be generated from the atmosphere, unless a great and, in fact, exceedingly sensible condensation of the atmosphere took place. Fourthly, because the same thing can happen to the solid bodies surrounding them, such as iron or stone, which remain entire after the generation of the aforesaid things. Hence this opinion cannot stand, because it is opposed to what is manifest to our senses.

And therefore others have said that the substance of the bread and wine returns during the corruption of the species, and so from the returning substance of the bread and wine, ashes or worms or something of the kind are generated. But this explanation seems an impossible one. First of all, because if the substance of the bread and wine be converted into the body and blood of Christ, as was shown above (75, 2,4), the substance of the bread and wine cannot return, except the body and blood of Christ be again changed back into the substance of bread and wine, which is impossible: thus if air be turned into fire, the air cannot return without the fire being again changed into air. But if the substance of bread or wine be annihilated, it cannot return again, because what lapses into nothing does not return numerically the same. Unless perchance it be said that the said substance returns, because God creates anew another new substance to replace the first. Secondly, this seems to be impossible, because no time can be assigned when the substance of the bread returns. For, from what was said above (4; 76, 6, ad 3), it is evident that while the species of the bread and wine remain, there remain also the body and blood of Christ, which are not present together with the substance of the bread and wine in this sacrament, according to what was stated above (Question 75, Article 2). Hence the substance of the bread and wine cannot return while the sacramental species remain; nor, again, when these species pass away; because then the substance of the bread and wine would be without their proper accidents, which is impossible. Unless perchance it be said that in the last instant of the corruption of the species there returns (not, indeed, the substance of bread and wine, because it is in that very instant that they have the being of the substance generated from the species, but) the matter of the bread and wine; which, matter, properly speaking, would be more correctly described as created anew, than as returning. And in this sense the aforesaid position might be held.

However, since it does not seem reasonable to say that anything takes place miraculously in this sacrament, except in virtue of the consecration itself, which does not imply either creation or return of matter, it seems better to say that in the actual consecration it is miraculously bestowed on the dimensive quantity of the bread and wine to be the subject of subsequent forms. Now this is proper to matter; and therefore as a consequence everything which goes with matter is bestowed on dimensive quantity; and therefore everything which could be generated from the matter of bread or wine, if it were present, can be generated from the aforesaid dimensive quantity of the bread or wine, not, indeed, by a new miracle, but by virtue of the miracle which has already taken place.

This is rather strange, because he seems to be saying that the subsequent substantial forms inhere in quantity as in a subject, and that there is no matter there. But if this is possible in any way, and in particular if things remain in this state permanently, as he seems to suggest, then there seems to be little reason not to adopt Descartes’s view of material substance in general, and say that quantity is always the subject of substantial forms, rather than saying that some parts of the world have matter as a subject, and other parts quantity. The account might be more reasonable if he were to accept that when a new substance is generated, matter again comes to be, not by being “created anew,” but because the being of matter in general is from substantial form.

As we can see, this discussion is especially complex on account of the doctrine of transubstantiation and St. Thomas’s account of that doctrine. But if we simply consider the mixing of two liquids in general, various difficulties will remain. Suppose we have a glass of water and a glass of wine, and mix the two together. What exactly will happen?

It is manifest to the senses that when we do this, there is a period of time when parts of the resulting liquid are water, just as it was, and parts are wine, just as it was, without any mixture. But what about the surface where the two are in contact? What is happening there?

According to St. Thomas, there will be a quantitative part which shares in the qualities of each. And this is pretty reasonable. Just as we can see that part is wine and part is water, at a certain point we can see that part is watery wine. But how exactly did that watery part get that way? If it is a certain size, was there a sudden transition of a part which was water into the watery wine? Or the like with the wine becoming watery? Or was there a continuous process with an expanding mixed region? The last possibility seems most consistent with what we see, but it might be difficult to analyze this in terms of substantial change, as St. Thomas does, because such a continuous process would have no first moment when the mixed substance came to be. For if it did, it would come to be with a definite size, and thus the process would not be continuous, but would imply that some part suddenly went from not being watery wine to being watery wine.

Of course, it is one thing to say there are difficulties. It is quite another to say that they mean that the thing cannot happen. So none of this proves that the mixing of liquids is not a substantial change. Nonetheless, many of the ancient naturalists were moved by such considerations to adopt some form of atomic theory. If water and wine are each composed of atoms, the mixing process is easily understood — it is simply the movement in place of these atoms. Each part of the water remains as it was even qualitatively, and likewise each part of the wine, but the resulting mixture has different sensible qualities because one cannot distinguish the diverse qualities of each, just as mixing two very fine sands of different color may appear to result in a third color, even though the grains of sand are not changing qualitatively.

Modern atomic theory, of course, has far stronger arguments for it, but they are in principle, or at least were in the 18th and 19th centuries, of a very similar kind: atomic theory simply does a good job of explaining many of the things that we see happen in the world.

This is closely related to the discussion in the last post. When we construct a bicycle out of parts, it is manifest to the senses that the parts look just like they did before they were parts. And this is necessary, if it is true that those parts are governed by the same natural laws after they become parts that they were before they became parts. For however the parts “look,” they look this way because of how they act on the senses. So if their action does not change, the “way they look” will not change. Similarly, when we mix liquids, if the water parts and the wine parts do not change how they behave, the account one gives of the mixture must be an atomic theory or something very like it. That is, there must remain very small parts that act like water, and very small parts that act like wine. Or, given that wine and water are not in fact elements, at least the basic elemental parts must continue to act like those elemental parts.