Monday, 31 May 2010

Question 16 - Truth

Why this Question Matters.

Pontius Pilate famously asked “what is truth?” Questions such as “in what does truth subsist?” and “is truth eternal?” have always been amongst the deepest and most important questions in life. Here St. Thomas affirms that “knowledge is of truths” and, having discussed God’s knowledge previously, now enquires into the nature of truth.

The Thread of the Argument

A1: The first article considers whether truth is something that exists in things themselves or whether it exists in the intellect. Given our modern sensibilities it might be as well to remember that in neither case would Aquinas consider that truth could be subjective. Here he is concerned to locate truth as part of the enquiry as to what it is as an objective reality. The objections suggest that truth exists more in things than in the intellect. For example, it’s fairly well known that St. Augustine anticipated the “cogito ergo sum” of Descartes by over a thousand years, but less well known that he also anticipated the saying “if a tree falls in the forest and nobody is there to hear it, does it make a sound?” As with the “cogito”, St Augustine’s inference goes thoroughly against modern idealism, here concluding that absence of cognition of an event provides evidence that the truth of the event must be in the event itself. Hence “The true is what is” and therefore truth must exist in things more than in the intellect. Aquinas, in his answer, reverses the order of this conclusion: truth exists primarily in the intellect and secondarily in things themselves. However, he argues that the intellect involved may be God’s intellect rather than ours (thus overcoming the objections). The answer is careful and detailed, starting with a discussion of the analogy between the good (that towards which the appetite tends) and the true (that towards which the intellect or any cognition tends), noting that they are different in that the end towards which the appetite tends exists in the object of the appetite whereas the end of cognition exists in the intellect (in the grasping of the intellectual species of what is cognized). Aquinas then notes that the concept of the good “migrates” to the appetite from the thing desired (so we can have a good desire) and conversely that the concept of truth “migrates” from the intellect to the thing cognized. In both cases, there is a sort of conformity between subject and object. Next Aquinas notes that we can divide the relationship between things and an intellect into two classes: things that depend for their being on an intellect (a “per se” relationship) and things that do not (a “per accidens” relationship). For example, an artefact that a craftsman designs and makes depends on the intellect of the craftsman for its existence; a stone depends on the intellect of God for its existence. The key point of Aquinas’s argument is that things are judged to be true or not according to the relationship that the thing has with the intellect on which it depends for its being. Hence, truth depends primarily on an intellect (which may be ours or which may be God’s) and secondarily to the things themselves according to how they are related per se to an intellect.

A2: We tend to know things through a process of what Aquinas calls “composing and dividing”. We have to carefully consider facts and their relationships one by one, putting them together into complexes and cutting them up into simpler facts and relationships until we arrive at a positions whose truth satisfies us. Is this necessarily so? Does truth exist in our intellects only by this process? Against this idea, it might seem that we can know certain “elementary” truths (such as sense data) directly, without going through this process. Aquinas answers by appealing to the idea of truth as a conformity between the intellect and the thing concerned and, most importantly, that truth involves a cognition of this conformity. The sorts of ways in which we directly apprehend things (such as through the senses) do not have a cognition of this conformity; they exist prior to such a cognition. So, although it may be the case that the senses are true to a given thing (or, more abstractly, the intellect may directly grasp a real definition), in the sense of corresponding to how things are, they do not have a cognition of this fact, hence their “knowledge” cannot be considered true in the way that Aquinas wants us to consider truth. For Aquinas, truth involves more than just the correspondence between our intellect and things; it also involves an intellectual cognition of that conformity. Hence truth in the intellect must involve our intellect’s process of composing and dividing.

A3: Aquinas now returns to the convertibility of the trancendentals. In this case, being and truth are shown to be convertible, as each thing is knowable insofar as it has being. Of course, as we have seen before with examples of convertibility, this does not mean that as separate concepts they are redundant, rather that their underlying reality is the same. It might be objected (as it is here) that truth is prior to being as we cannot understand anything as being unless we have the concept of truth. Aquinas’s solution to this objection involves a discussion of the way that truth and being interweave in a similar way to how the concepts of being and intelligibility interweave.

A4: Having returned to the notion of the trancendentals, Aquinas now asks about the relationship between “good” and “truth”. In particular, although they must be convertible, should we say that good is conceptually prior to truth? It might appear that “good” is a more universal concept than “truth” and is thus conceptually prior to it. However, Aquinas teaches that it is the other way around: “truth” is conceptually prior to “good” because “truth” is closely related to “being” which we have seen to be conceptually prior to “good” (Question 5 Article 2). Also, in Aquinas’s psychology, cognition is prior to desire which implies that the true is conceptually prior to the good.

A5: “I am the way, the truth and the life” (John 14:6), therefore God is truth. However, Aquinas is willing to identify truth with God even prior to revelation. God’s act of understanding is creative, the cause of being in all things. But truth consists of cognition of the conformity between the intellect and what is; God’s knowledge provides a supreme example of this conformity, therefore He is the “first and highest truth”.

A6: Since God is truth and God is also supremely one, we might be tempted to think that there is only one truth by which all other truths are true. Aquinas resists such a blunt instrument by claiming that there is a sense in which this is true, but that there is also a sense in which it is false. He appeals to a difference between univocal and analogical predication, in that univocal predication among a group involves something being true in the same sense for all members of the group, whereas analogical predication involves the concept being particularly true for one member of the group and true for the other members of the group insofar as they are related to the truth of the concept in that exemplar individual. A similar distinction can be made here: from the point of view of truth as it exists in things themselves, those truths flow from the one truth in God’s intellect (so they are analogously true from God’s truth). But from the point of view of truths in intellects, they are genuinely distinct truths (univocally true as distinct truths in distinct intellects).

A7: Things like the truths of arithmetic appear to be eternal. Similarly, universals appear to be eternal and truth is a universal. Considering the truth or falsity of the proposition “truth does not exist” would seem to indicate that truth is eternal (for if it is false, then there must be some notion of truth by which it is judged to be false, which is a contradiction). If we restrict ourselves to created truths, are they eternal? Aquinas points out that the truth of a proposition is essentially (“per se”) due to it being a truth of the intellect. Hence, such truths are eternal only insofar as they correspond to an eternal intellect. So, only truths in the intellect of God (for example, arithmetic truths) are eternal. So, in this sense, created truths as truths in our intellects are not eternal as we are not eternal.

A8: Having considered the notion of truth outside of time in article 7, Aquinas now turns to the question of the immutability of truth within time. As truth exists properly in the intellect, it is seen that the question concerns the nature of the intellect. Aquinas points out that since truth in the intellect involves a conformity between the intellect and things, truth in the intellect can change in two ways. Firstly, it can change when a belief about a thing changes but the thing itself does not change. Secondly, it can change when the belief remains the same but the thing changes. In each case, there is a change between conformity and non-conformity (or vice versa). So for our intellects, where this happens all the time, we cannot claim that the truth-in-our-intellects is immutable. This does not imply that truth itself is subject to change, rather that our cognition of truth changes. God’s intellect, however, does not change and there is never a failure of conformity between what is and what is in His intellect. In God’s intellect, truth is immutable.

Handy Concepts

  • A relationship is “per se” if it involves the very being of the thing concerned. Otherwise it is a “per accidens” relationship.
  • Our intellect works by “composing” and “dividing”.
  • Truth is a transcendental convertible with all the other trancendentals.


  • One has to be careful in this question to distinguish between truth as objective and subjective (a modern concern) and truth as an absolute (in the intellect of God) and as known to our intellects.

Tuesday, 25 May 2010

Question 15 - Ideas in the Mind of God

Why this Question Matters.

As we saw in the background document on metaphysics, Plato thought that forms (which he called Ideas) exist in a realm of their own. However, Aristotle considered that forms only exist in so much as they are instantiated in the things they inform. St Augustine, taking a basically Platonic point of view, placed the realm of the Ideas in the mind of God. In this question, Aquinas attempts to reconcile the teaching of St Augustine concerning Ideas in the mind of God with an Aristotelian metaphysical framework.

The Thread of the Argument

A1: Aquinas is quite happy to affirm that there are Ideas in God's mind. In order to do this in an Aristotelian framework, he claims that forms can exist apart from the thing that they inform in two ways: as the exemplar of the thing itself, or as the means of knowing the thing. Aquinas has already covered the idea of a form existing in the mind as a means of knowing something in question 14. But also, since God's knowledge is causative, it is quite natural for Aquinas to accept both ways in which forms can exist in God's mind. Therefore, what Aquinas achieves in this article is to show that Augustine’s placing of the realm of Ideas in the mind of God can be made quite consistent with the former’s Aristotelian approach to God’s causative knowledge.

A2: Having reconciled St Augustine and Aristotle in the first article, Aquinas now faces a tricky problem. God is entirely simple, so it would seem quite natural to assert that there is only one Idea in the mind of God. But this would seem to be quite foreign to St Augustine's conception of Ideas in the mind of God, so it might seem that Aquinas's reconciliation in article 1 is in vain. In his answer, Aquinas is quick to reject an idea (due to Ibn Sina) that would give him an easy way out of this conundrum. He denies that God simply created the first being that consequently created everything else. He asserts that the plans to everything in creation must be in God's mind and therefore there must be a plurality of Ideas in God's mind. Aquinas's answer to the problem of reconciling this with divine simplicity is so disarmingly simple that it may seem like a sleight of hand. He says that “the idea of a work is in the mind of the agent as that which is known, not as the species by which there is knowledge”. In other words, Aquinas is saying that Ideas are present in the mind of God not as a multitude of individual forms facilitating the creation of individual things act by an act, but rather as a single complex facilitating the creation of all things by God's single act of being. The many ideas are in God's mind as objects of his simple knowledge.

A3: Finally, Aquinas asks whether there is an idea in the mind of God corresponding to everything that He knows. The objections list several knowable things that may be considered not to have corresponding forms. Aquinas meets these objections by going back to Plato's fundamental concept that the ideas are sources of the knowledge of things and of their coming into existence. This sits perfectly well with Aquinas's idea of God's creative knowledge and allows Aquinas to claim that ideas and things known to God correspond.

Monday, 24 May 2010

Question 14 - God's Knowledge - Texts

1.0 Introduction

Question 14 assumes that we share St Thomas’s view of Mind. St Thomas shows how what we know of Mind can also be said of God, and the ways in which God as uncaused cause must transcend what we understand of the operation of Mind.

This document takes what is said about our way of thinking, and abstracts it from the theology, so that we can approach Question 14 with a better understanding of St Thomas’s starting point, i.e. what he understands about intellect, and the human mind in particular. When we understand this, understanding the theology might be a bit easier.

Refer here to the guide to this question.

1.1 Characteristics of a “knowing” creature

The difference between a knowing and non-knowing creature (subject) is that the latter has nothing but its own form, whereas a knowing subject is one whose nature it is to have in addition the form of something else; for a species (representation) of the thing known is in the knower. Thus, the nature of a non-knowing subject is more confined and limited by comparison with knowing subjects. The latter have a greater scope and extension. As Aristotle says, ‘the soul is in a manner all things’.

Now form is limited by matter, so the freer forms are from matter the more they approach to a kind of infinity. So it is clear that something’s freedom from matter is the reason why it is able to know, and the capacity to know is in proportion to the degree of freedom from matter.

Thus we say plants have no knowledge because of their materiality. But the senses can know because they can receive the species of things without the matter. Intellect is still more capable of knowing because it is freer from matter and unmixed, as we read in Aristotle. So, since God is immaterial in the highest degree, it follows that he has knowledge in the highest degree.

Knowing is in the person who knows. It is a kind of living. Knowledge depends on the capacity of knowers; for what is known is in knowers according to the measure of their capacity.

Knowledge requires a likeness between the knower and the known.

1.2 Knowledge

Knowledge is of what is true.
Knowledge is a disposition. A disposition is intermediate between potentiality and actuality.
Knowledge is of conclusions, a kind of cognition caused by something else, namely from knowing principles.
The intelligible natures of things, as they exist in our knowledge are called ideas.
All knowledge is either universal or particular.
All knowledge comes about through a likeness.

In people different objects of knowledge imply different levels of knowledge
  • In knowing principles we speak of ourselves as having understanding
  • In knowing conclusions, science
  • In knowing the highest cause, wisdom
  • In knowing human actions, counsel or prudence

1.3 Relationship of Knowledge to what is Known

Whereas in activities which produce an external effect, the object of the activity (its end, or terminus) is something outside the agent, in activities which take place in an agent the object which is the end of the activity lies in the agent itself. The object in the agent is the activity actually taking place. Thus we find Aristotle saying that the actualisation of what is sensible is the senses while they are active, and the actualisation of what is intelligible is the intellect while it is active. We have actual sensation or actual knowledge because our intellect or senses are informed by the species of a sensible or intelligible object. Sense or intellect is different from the sensible or intelligible only to the extent that both are in a state of potentiality [with respect to the sensing (or understanding)].

We know something in two ways: in itself, or in another. We know something in itself when we know it through a species adequate to the thing itself, coterminous with the thing known, as when our eyes see someone through the species of that person. We see something in another when we see it through the species of what contains it, as when we see a part in a whole through the species of the whole, or as when we see someone in a mirror through the species of the mirror, and so of other ways in which we know one thing in another.

It is not the substance of something known that perfects a knower, but its species, by which it is in the intellect as a form and perfection. As Aristotle says, 'a stone is not in the soul; its species is'.

We do not specify understanding itself by what we understand in something else. We do so by the primary object understood, in which we understand other things. The proper object of understanding specifies understanding itself inasmuch as intelligible form is a source of understanding. For every activity is specified by the form which is the source of the activity, as heating is by heat. So, intellectual activity is specified by the intelligible form which makes the intellect to be actually knowing. And this form is the species of the principal object known.

Something is known for what it is only through its own proper idea.

To know things specifically is to know them, not merely in what they have in common, but in their differences from each other. For to know something generically and not specifically is to know it imperfectly. Hence our intellect, in passing from potentiality to actuality, attains first to a universal and confused knowledge of things, then to a knowledge of what is proper to each, thereby passing from incomplete to complete knowledge (as Aristotle makes clear in the Physics).

To know something “as it is in the knower” can be understood in two ways: (i) with “as” referring to the way the thing as known is in the knower. Taken thus it is false. For a knower does not always know something known as it exists in a knower. An eye, for example, does not know a stone as it exists in it. Rather, through the species of the stone that it has in itself, the eye knows the stone as it exists outside the eye. And if people do know the known object as it exists in knowers, they still know it as it exists outside knowers. So, the intellect, in knowing that it is knowing a stone, knows the stone in the intelligible existence it has in the intellect; but it still knows the existence which the stone has in its own nature, (ii) But if we take “as” to refer to a knower's manner of knowing, it is true that a knower knows the thing known only as it is in a knower; because the more perfectly something known is in a knower, the more perfect the degree of knowledge.

But according to Aristotle the condition of being able to call up knowledge covers many objects at the same time, while actual knowledge covers only one object.

Again, the knowable is prior to knowledge and is its measure, as we read in the Metaphysics

1.4 Understanding

To understand is a kind of passivity and movement, as Aristotle states, and knowledge is an assimilation of the thing known. Also, something known is a perfecting of the knower. However, when we call the act of understanding a kind of movement or passivity, we use the expressions “to move” and “to be passive” equivocally, as Aristotle says. For the act of knowing is not a movement in the sense of an actualisation of something incompletely actualized and passing from one subject to another. It is the act of something completely actualized, taking place within the agent itself. Similarly, for an intellect to be perfected by what is intelligible, or assimilated to it, is proper to an intellect which is at some time in a state of potentiality. For in being potential itself, it differs from the intelligible, and is assimilated to it by the intelligible species which is the likeness of the thing known, and the intellect is completed by it as a potency that is actualized.

Understanding is an activity of some sort. But an activity is normally something proceeding from an agent. All understanding is the understanding of something. Understanding is a perfection and actuality in those who understand. As I have said, understanding is not an action that goes out to something external. It remains in an agent as its actuality and perfection (just as existing perfects things that exist). As form brings existence, so the intelligible species brings understanding. Understanding is not an activity going out from an agent. It remains in it.
Moreover, something understood perfects the one who understands.

1.5 Understanding understanding

Existence in nature does not belong to prime matter, which of itself is potential, except in so far as it is brought to actuality by a form. Now, our passive intellect has, in the order of knowing, the same condition as that of prime matter in the order of natural things. It is potentially able to receive intelligible forms as prime matter is potentially able to receive natural forms. So, our passive intellect can have an activity which it can know only when it is perfected by the intelligible species of something. In that way it knows itself through an intelligible species, as it does other things: for in knowing the intelligible it obviously knows its own act of knowing, and knows the power of knowing through the act of knowing.

Our intellect does not understand itself except as it understands other things (Aristotle)

“All knowers who know their own essence are in the condition of a complete returning”. [Book of Causes] For a thing to “return on its own essence” is simply for it to be self-subsistent. A form when it perfects matter by giving it existence, in a certain sense spreads itself out over the matter. But in so far as it has existence in itself, it returns on itself. So, those powers of knowing which are not subsistent but are the acts of certain organs, do not know themselves, as is clear in the case of each of the senses. But powers of knowing which are subsistent do know themselves. Hence the statement in the Book of Causes that “knowers who know their own essence return upon their own essence”.

1.6 Degrees of Knowing

Augustine says that “that which has comprehensive knowledge of itself is finite to itself” and “Everything that knows itself has comprehensive knowledge of itself.” We say that we comprehend (have comprehensive knowledge of) something when our knowledge of it can go no further, that is, when we know it as completely as it is knowable. For example, we comprehensively know a demonstrable proposition when we know it through demonstration, but not when we know it through some merely probable reason. But something is knowable in proportion to its actuality. As we read in the Metaphysics, something is known as actual, not as potential. Strictly speaking, “to comprehend” means “to hold or enclose some¬thing else”. Taken in that sense, all that is comprehended must be finite, as all that is enclosed must be. We may quote Augustine: “The whole is comprehended by vision when it is seen in such a way that no part of it escapes the one who sees.”

Understanding gets its specific content from an intelligible object, as every other act gets its specific content from its object. So, the excellence of understanding is in proportion to that of the object known.

But if something is known perfectly, its power must be known perfectly. Now the power of a thing cannot be known perfectly unless the objects to which the power extends are known.

Whoever knows a thing perfectly must know all that can happen to it.

1.7 Discursive Knowledge

To know an effect through a cause amounts to discursive knowledge. We know created effects in created causes, and thus pass discursively from causes to effects.

In our knowledge there is a twofold discursiveness:
  • that of mere succession, as when after actually knowing one thing we turn to another thing;
  • the discursiveness that involves causality, as when we come to know conclusions through principles.
We know a number of things successively when taken one at a time, which we know all at once if we know them in a unity. Thus we can know the parts in the whole, or see different things in a mirror. The second kind of discursive knowledge presupposes the first, for when we pass from principles to conclusions we are not considering both at the same time, and this kind of discursiveness passes from known to unknown. So, it is clear that when we know the first we are still ignorant of the second. Thus we do not know the second in the first, but from the first. And the process comes to an end when the second is seen in the first and the effects are found in their causes, at which point the discursive process ceases.

Although understanding in itself is of something single, it is still possible to know many things in one thing, as I have said.

1.8 Knowledge as Cause

Knowledge either causes what is known or is caused by it.

The knowledge of artists is the cause of their products because they work through their intellects. So, the form in their intellects must be the principle of their activity, as heat is the principle of heating. But we may note that a natural form, merely as the form remaining in the thing to which it gives existence, does not indicate a principle of activity. It does so only in so far as it has an inclination towards producing an effect. Similarly, an intelligible form does not indicate a principle of activity merely as it is in the knower unless it is accompanied by an inclination, supplied by the will, towards producing an effect. An intelligible form is indifferent to opposite courses, since one and the same knowledge covers contraries. So, a form would not produce a determined effect if it were not determined to one course by desire, as we read in the Metaphysics.

1.8 Knowing things that don’t exist

Things which do not actually exist have truth corresponding to their potentiality (i.e. it is true that they are potentially existent.

Moreover, all that is known is known either through its likeness or through its opposite.

An intellect that is not in potentiality does not know privation. We should understand Aristotle's words as meaning that an intellect which is not in a state of potentiality does not know privation through a privation which it has in itself. And this agrees with what he had said just before, namely that we know a point, and every indivisible, by way of privation of division. The reason is that simple and indivisible forms are not in our intellect actually (i.e. not as known directly) but only potentially (i.e. as known indirectly); for if they were in our intellect actually they would not be known by way of privation. Substances that are not joined to matter know what is simple in that way. So, God does not know evil through a privation which he has in himself. He knows it through the contrary good.

Again, what is known not through itself but through something else is known imperfectly.

To know something only through something else is to have imperfect knowledge if the thing is knowable through itself. But evil is not knowable through itself, because evil of its very nature is the privation of good. So, it cannot be defined or known except through good.

1.9 Universals and Specifics

Our intellect does not know individuals precisely because of its freedom from matter. As Aristotle says, “the mind grasps universals; the senses grasp individuals”. Moreover, in ourselves the only powers of knowing which can grasp individuals are those which receive species which have not been freed from material conditions.

Our intellect abstracts intelligible species from individuating principles. So, an intelligible species in our intellect cannot be the likeness of the principles of individuals as such — which is why our intellect does not know individuals.

1.10 Knowing Infinity

An infinite as such is unknown. As Aristotle says, an infinite is “that of which, if one grasps a part, there is always something more to grasp”. Augustine also says that “what is comprehended by knowing is limited by the knower's comprehension”. But infinites cannot be limited.
The reason for this is that the extension of a knower's knowledge depends on the scope of the form that is its principle. Now in sense-knowledge the species is the likeness of one individual only; so only one individual can be known by means of it. But an intelligible species in our intellect is the likeness of something in its specific nature, which can be shared by an unlimited number of individuals. So, our intellect, through the intelligible species of human beings, knows in a manner an unlimited number of human beings; not, however, human beings in their distinction from one another, but in their common possession of their specific nature; for the intelligible species in our intellect is not the likeness of humans in what makes them individuals, but only in what makes the species.

As Aristotle says, “the notion of infinity coincides with that of quantity”; and the notion of quantity includes an ordering of parts. So, to know an infinite in its own nature is to know part after part; and in that way an infinite is not really known at all; for whatever number of parts is grasped, something always remains beyond.

“Going through” implies a certain succession of parts; and that is why an infinite cannot be gone through either by a finite or by an infinite. But the idea of comprehensive knowledge is satisfied if the knowledge equals the object known, for we say that something is known comprehensively when no part of it remains beyond the knower's grasp. So, it is not contrary to the notion of an infinite that it should be known comprehensively by something that is infinite. In that sense, we can say that what is infinite in itself is finite to God's knowledge (i.e. is known comprehensively by it) - though we cannot say this if we take “that which is infinite” to mean “that which can be gone through”.

1.11 Thinking about Contingent Events

To appreciate this we should note that we can think of an event as contingent in two ways.
First, we can think of it intrinsically and in so far as it is already actual. If we think of it in this way, it is not future but present, and it is not contingent with respect to different outcomes. It is determined to one outcome. As such, it can be the object of certain and infallible knowledge, as something seen is to vision (as when I see Socrates sitting down).

But we can also think of a contingent event as it exists in its cause. If we do that, we think of it as going to happen, as a contingent event not yet determined to one outcome (for a contingent cause can end up having varying effects). Considered as such, a contingent event is not something of which we have any certain knowledge. So, someone who knows a contingent effect only in its cause has no more than a conjectural knowledge of it.

We know successively things which become actual in time while God knows them in eternity, which is above time. So we cannot be certain when it comes to future contingents, for we know them precisely as future contingents.

1.12 Propositions

To know propositions is proper to our intellect in its function of putting together and separating. Since our intellect has the power to form propositions, the way they are formed is by putting together or separating their terms in our minds. We pass from one object to another because the intelligible species in our minds represents one thing without representing other things. So in understanding the nature of people we do not thereby immediately understand what else is true of them. We understand them one by one according to a certain succession. For this reason we have to reduce to unity what we understand separately, by putting together or separating concepts to form a statement.

1.13 Theoretical and Practical Knowledge

We gain theoretical knowledge through abstraction from actual things. But theoretical knowledge is more excellent than practical knowledge, as Aristotle shows. Knowledge may be speculative only or practical only. Or it may be partly speculative and partly practical. We can see this by noting that we can call knowledge speculative on three accounts.
  • First, from the nature of the things known, when they are not producible by the knower, for example, someone's knowledge of natural things or of divine things.
  • Second, with respect to the mode of knowing - as, for example, when an architect defines, analyses and examines the qualities proper to houses in general. To do all this is to consider producible things, but in a speculative way, not as producible. Something is producible by way of the application of form to matter, not by way of a resolution of a composite into its formal principles considered universally.
  • Third, knowledge can be speculative with regard to its end or purpose. As Aristotle says, 'the practical intellect differs from the speculative in the end to which it looks'. The aim of the practical intellect is production. That of the speculative intellect the consideration of truth. Thus, if builders consider how some house could be built, not with a view to building it but merely for the sake of knowing, their consideration, so far as concerns the end they look to, is speculative, though still about what could be produced.
So knowledge which is speculative from the nature of the thing known is speculative only. Knowledge which is speculative either in its mode or in the end it looks to is speculative in one respect and practical in another, and knowledge directed to production is unqualifiedly practical.

Question 14 - God's Knowledge


We've now come to a major division in what is often referred to as the “Treatise on the one God” (QQ. 2-26). Aquinas has talked about God's essence and about how we can know God and about how we can talk about God. It's now time for Aquinas to discuss in more detail the inner life of God. The rest of this treatise is divided into four sections: on God's intellect; on God’s will; on the conjunction of God’s intellect and will; and finally on God's power. This will take us up to the end of the Treatise on the One God, and will lead in to the Treatise on the Triune God.

Question 14 is a long and difficult question that contains topics that are still thoroughly controversial areas of thought in philosophical theology. To help us through this question, we thought it would be a good idea to have both the usual summary guide (this entry) as well as texts of the question concerning knowledge itself rearranged into thematic groups, so that St. Thomas explains his terminology to us in his own words.

Why this Question Matters.

God obviously knows everything. But what does it mean for Him to “know”? How does God’s knowledge differ from our knowledge? The answers for many of the inquiries included in the articles of this question seem obvious: “Yes, of course!” or “Of course not!” However, the point of many of these questions is not the answers themselves, but the way in which we are to understand what the questions mean. By now it should come as no surprise that God’s knowledge must be his essence. But there are some stunning conclusions that follow from this fact: God’s knowledge is creative; God knows all future contingents. Omniscience is larger than it might seem at first.

The Thread of the Argument

A1: It would seem natural to think that God has knowledge in a pre-eminent way, given what we know about God so far. However, since our very concept of knowledge is derived from what we know about creatures, we must remember that when we talk about the knowledge of God we're talking analogously. So, we must think about how God’s knowledge differs in character from our knowledge. According to Aquinas, we have knowledge of a thing when we have some sort of grasp of the form of the thing in our mind. However, the form of the thing that we have in our mind does not inform matter. (Otherwise, knowing something would involve that thing being physically present in our minds!) So, in a certain sense, our capacity to know depends on being free from matter. From this, Aquinas deduces that the freer from matter that a being is, the better the being can know. Since God is immaterial in the highest degree, he has knowledge in the highest degree. Now Aquinas can deal with the objections that are based on the assumption that God’s knowledge is just like our knowledge. To do this, we can think about what a creature’s knowledge consists in, and then eliminate any imperfections. So for example, God's knowledge is a pure actuality; God knows all things “all in one go”; God's knowledge does not come to be, it always is.

A2: To ask whether God understands himself may seem very odd indeed; but Aquinas’s task is to work through the consequences of our analogical understanding of “how God works”. Here Aquinas quotes Aristotle to the effect that when we sense something or when we understand something, the senses and the intellect move from potentiality to actuality with respect to what is sensed or understood respectively. For example, when we understand something our intellect is “informed” by an “intelligible species” (the immaterial form corresponding to the object itself that the mind grasps), moving from potentiality to the actuality of understanding that object. Since God is pure actuality, it immediately follows that He possesses all intelligible species within His intellect (as He cannot be in potentiality to any of them). Since there are no accidental forms in God, it also follows that all of these intelligible species are actually God’s very intellect. So, we can say, in a sense, that God’s intellect encompasses everything that there is. The answer to the second objection points out that although human knowledge involves a potentiality moving to actuality (through learning, for example), God’s intellect is not like this. The reply to the third objection introduces the important notion of the “passive intellect”. Aquinas considered the intellect to be divided into two parts: the “agent intellect” that organises and assimilates the information received from the senses (so it is the “active” part of the intellect) and the “passive intellect” that receives and keeps the intelligible species offered to it by the agent intellect.

A3: Similarly, God has comprehensive knowledge of Himself, in that He knows everything there is to know in the most perfect way possible. This follows from God’s pure actuality. The purpose of this article appears to be to deal with particular objections drawn from the created world that suggest that “comprehending” involves circumscription of a number of things (facts, for example). Since Aquinas believes that there are no actual infinities in the created world (Ia Q7 a4), application of this idea to God would seem to imply that His intellect must be finite in some way. Aquinas deals with these objections (especially in the reply to objection 2) by coming very close the modern notion of one-to-one correspondence in that “God is finite to Himself” is taken as meaning that there is some proportion between God and His intellect! (See the background document on infinity).

A4: We often think of understanding as being an activity, so if we apply that sort of thinking to God it would be difficult to see how His understanding could be His substance. (How could an activity be a substance?) On the contrary, Aquinas insists that understanding is not an activity that proceeds from an agent but rather is a perfection, an actuality, within the agent. Again, as God is pure actuality and within God there are no accidents, God’s understanding must be identical with His substance.

A5: God understand Himself, and clearly He must know things external to Himself, but in what sense? Again, it is tempting to push the analogy between human knowing and divine knowing too far. We might point to the fact that learning adds something to us and contributes to our perfection; if the same happened with God, this would lead to us to conclude that God was added to or perfected by things external to Himself, which is clearly nonsense. Aquinas rejects this parallel, pointing out that as He is the first efficient cause of everything He must know everything in causing it. (Indeed, as His act of being is the same as His act of knowing, article 8 can assert that His act of knowing is itself creative.) Aquinas continues with an important distinction: we can know things through themselves in that we can grasp a thing’s intelligible species through our direct sensation of them; or we can know things indirectly through inference from the parts to a whole or from a reflection in a mirror or through a thing’s effects. When we apply this to God, we realize that God understands Himself through Himself; but also, he sees other things through Himself as well and not in themselves, because His essence already contains those other things in likeness.

A6: The distance between God and created beings is extreme; and God has an awful lot of things to know. Does this mean that He knows things other than Himself only in a general sort of way (“here’s the form of a cow, let’s instantiate two hundred million of them”) or does he know every particular created thing specifically in the sense of what makes one individual different from another? (“This one’s got brown spots, this one’s black and white …”) Scripture is very particular in emphasising that God does know individuals intimately, so the length of Aquinas’s argument here may seem surprising. The reason for this length is that Aquinas is concerned to refute a number of mistaken ideas about God’s knowledge. At the heart of Aquinas’s position is the observation that a generalized sort of knowledge is an imperfect sort of knowledge; we cannot deny perfection in God, therefore God’s knowledge is specific. So we are to believe that things are to be found in God not only as regards what they have in common but also in regards as to what makes them different from one another. Later, in article 11 Aquinas will take this argument further and will show that God knows individuals as specific individuals.

A7: Our knowledge is discursive; that is, we know a lot of things but at any specific instant we can only consider one thing at a time. Similarly, when we think about a particular thing, our thought considers one aspect of that thing at a time. The same is not true of God. He sees everything in one act, with no temporal or logical succession; He sees everything in His substance.

A8: St. Augustine said that “God does not know all creatures because they exist; they exist because He knows them”. In this article, Aquinas will hand on this teaching that God’s knowledge is causal, with the image of God as the artist producing the work of art. Since His intellect is the same as His act of knowing, His knowing is causative. Now, knowledge of the work of art to be produced involves the intelligible species of that thing existing in the intellect. But an intelligible species existing in the intellect doesn’t necessarily cause the existence of that thing; an act of the will is required as well to bring it to be. So it is with God; His knowledge is the cause of the being of things in conjunction with His will.

A9: God knows everything that exists, but what about things that don’t exist? In what sense can they be known anyway? Aquinas affirms that “God knows all things that are in any way whatever”, but then has to explain how we can talk about the non-existence of things. If we think about unicorns then we can say that they do not exist as concrete particulars in the world, but they still have some sort of existence in our minds or we could not even talk about them. Aquinas’s solution follows this line of thought. God knows everything that exists and everything that can potentially exist. These things all exist in His intellect; they come to be by the single act of His will. However, a distinction is made between different sorts of non-existence: we can consider things that currently don’t exist but which have existed in the past or will exist in the future. God is in eternity with His “present” gaze directed to the whole of time so He can “see” these sorts of (currently for us) non-existing things in their proper time. God knows these sorts of things through what is called “knowledge of vision”. But He can also know those things that currently don’t exist, never have existed, and never will exist! These things only ever exist in potentiality, but it is a potentiality that God knows through His “knowledge of simple understanding”.

A10: Does God know evils? Since He knows everything, surely He must know evils as part of everything. But God’s knowledge is creative, so does God therefore create evil? Evil is a privation of the good and therefore in potentiality to its corresponding good; but God is pure actuality, how can a potentiality be part of His substance via His knowledge? Aquinas turns these tricky questions around by asserting that perfect knowledge involves knowing the balance between potentiality and actuality in things and in knowing its being as far as it is in being. Therefore God must know evils through knowing the degree to which things are. So God’s causative knowledge does not cause the evil of a thing but causes the goodness of the thing insofar as it is good. Similarly, possessing knowledge of a potentiality is not the same as having a potentiality in the intellect; rather it reflects complete knowledge of the thing known.

A11: Aquinas has already dealt (in article 6) with God’s specific knowledge of things. Now he takes the argument one step further; He knows each individual thing as an individual. Again, this may seem a curious question, but Aquinas is concerned to refute incorrect understandings of knowledge. The objections to this article focus on the proposition that since God is totally free of matter and since matter is the principle of individuation of any thing, God cannot know things inasmuch as they are individuated by matter. God is, so to speak, far removed from the realm of the individual and His knowledge is confined to the universal. Aquinas points out that certain attempts to get over these objections by suggesting that God knows individuals through universal causes don’t work. He answers that since our knowledge of individuals is part of our perfection and all perfections of creatures exist in God, God must know individuals too. Building on the answer to article 8, Aquinas argues that since God’s knowledge is causal, His knowledge must extend to all the factors that make individuals individual, or else He couldn’t cause them.

A12: Aquinas now asks whether God can know infinities. This might be rather tricky as we’ve already seen that he takes the view that although we can conceive of unlimited things, actual completed infinities do not exist. How then can God know them? Since God knows not only that which is but also that which is not, and the latter is infinite, He must know infinities. We might think that Aquinas may retreat to the assertion that God knows infinities through his “knowledge of simple understanding” that we met in article 9; but he doesn’t. Aquinas actually asserts that God knows infinities through His “knowledge of vision”, i.e. as laid out before Him as he surveys all of created time from the vantage point of eternity. This is because God knows the infinite number of actual and potential thoughts that all rational creatures have. The reason that God knows these infinities is that God knows every aspect of every individual (as we have seen in article 11) and that knowledge is creative (for all that is or can be). In the answers to the first two objections, Aquinas suggests that although we have to go through unlimited potential infinities part by part, not able to know them as an infinite whole, God can grasp their whole infinity in one go. However, his answer to the third objection suggests that even God cannot “quantify” an infinite set. I suspect that if Aquinas had a modern understanding of infinite sets, he would alter his answer to this objection and allow God to quantify infinite sets in His act of knowing.

A13: A future contingent event is an event in our future that is neither necessarily true nor necessarily false. Does God know future contingents? It might seem that He does not because God causes all things that He knows and it’s hard to see how His causative knowledge can be anything other than necessary. Similarly, if God knows everything that is in one act of knowing that traverses all of our time, how could it be that everything that is going to be could be anything other than determined (and therefore not contingent)? These questions are among the most intractable in philosophical theology (and apply to any religion in which there is a sufficiently “powerful” God). Aquinas’s answer is disarmingly simple: God knows all things; some things are future contingent (our acts of free will, for example); therefore God knows future contingents. He elaborates his basic answer by observing that we can consider future events contingent in different ways: these basically correspond to God’s way of seeing them as immediately present to Him; and to our way of seeing them as contingent through causes not determined to a particular outcome. Aquinas’s point of view appears to boil down to saying that the kind of knowledge that God has is sufficiently different to our knowledge that it is consistent to say that God can know something as determined whilst it can be contingent to our knowledge.

A14: A “proposition” as far as Aquinas is concerned is a sentence affirming or denying a predicate of a subject. Propositions are abstract in the sense that they are independent of the language in which they are expressed. Does God’s knowledge include propositional knowledge? It might be argued that constructing propositions to express facts is something special to the way that humans think. We think of a subject and of the predicates associated with it and construct propositions to express these relationships; a very linear and methodical way of thinking. Surely God’s knowledge is above this rather plodding way of doing things? However, since God knows everything about every individual, He must know the propositions that each individual forms. However, God’s knowledge of these propositions is not like ours; He knows everything in one act of knowing and does not have to plod through the process of putting propositions together. He knows these things through the essence of their truth or falsehood, abstracted from their means of expression.

A15: In the created world things proceed with the flow of time, changing this way and that. God knows all of these changes, so it would seem that His knowledge must therefore change. Not so, God is unchangeable (Ia 9.1) and His substance is His knowledge (article 4), so His knowledge is unchanging. The answers to the objections follow the same pattern as given in Q9 where Aquinas considered the relations between creatures existing in time with God existing in eternity; relations can change whilst one of the parties within the relation remains unchanged.

A16: In his commentary on Aristotle’s Metaphysics, Aquinas wrote that “the end of theoretical knowledge is truth, whereas that of practical knowledge is action”. He inherits the idea that knowledge can be divided into these categories of theoretical and practical and he asks here which category God’s knowledge falls into. As he has already shown that God’s knowledge is causative, we might think that His knowledge is therefore practical. Conversely, Aristotle claimed that theoretical knowledge is more excellent than practical knowledge; therefore God’s knowledge must be theoretical. Aquinas argues that God’s knowledge of Himself must be theoretical as there is no sense in which He (who is pure actuality) can be produced any further. But His knowledge of everything created is both practical and theoretical as He knows all things both from the point of view of what they are in themselves and form the point of view of bringing them to be.

Handy Concepts

  • The “agent intellect” organises and assimilates the information received from the senses (so it is the “active” part of the intellect) and the “passive intellect” receives and keeps the intelligible species offered to it by the agent intellect.
  • “Intelligible species” are the immaterial forms of things that our intellect grasps in order to understand them.
  • The “knowledge of approbation” is God’s knowledge of things considered as their cause.
  • God’s “knowledge of vision” applies to things that although they do not exist now, either have existed or will exist in the future. God’s “knowledge of simple understanding” applies to things that do not exist, never have existed and never will exist.
  • A future contingent event is an event in our future that is neither necessarily true nor necessarily false.
  • A “proposition” is a sentence affirming or denying a predicate of a subject.


  • We pointed out that article 11 raises problems in philosophical theology that are very difficult. For example, actions that are the result of our free will are future contingent (before the actions are placed). If God has knowledge of vision of such events how can they really be considered as free choices (as opposed to determined)? In particular, how can our free choice to turn to the Lord (or not) truly be considered free?
  • In article 12, it appears that Aquinas’s concept of infinity makes him reach conclusions that he might reconsider in the light of modern knowledge of the infinite.

Sunday, 23 May 2010


I thought that it might be useful to gather together a few remarks about how infinity is considered in modern mathematics.

Underlying the mathematical treatment of infinity, there are a couple of fundamental observations about the nature of number.

The first is that of “1 to 1 correspondence”. When we say that there are three things sitting on the table, there is some notion that we can count them; I may even count them on my fingers. This is an example of putting the objects on the table into 1 to 1 correspondence with three of my fingers. Similarly, there is a very fundamental notion that any three objects may be put into 1 to 1 correspondence with any other three objects.

The second fundamental observation concerns the idea of “succession”. We think of the number three as being the number after the number after one. Indeed, as we count, we count off the numbers in succession: after any whole number is its successor.

Corresponding to these two fundamental notions, we get the idea of “cardinal number” and “ordinal number” respectively. Informally, a cardinal number measures how big a particular set is (in the sense of measuring how many elements there are in the set by putting its elements into 1 to 1 correspondence with a set of known size), and an ordinal number measures a set by putting its elements in order and counting them off in succession.

You’ll have noticed that when you count things on your fingers, you often use both concepts at the same time! You put the elements of the set of things into 1 to 1 correspondence with your fingers and you also order the set of things using the implied order on your set of fingers. However, notice that in putting objects in 1 to 1 correspondence with your fingers, there’s no need to use your fingers in any particular order (so the notion of cardinality and ordinality are at least notionally distinct). Notwithstanding this, there is a deep relationship between ordinal and cardinal numbers and this relationship remains true for non finite sets, but I’ll have to leave discussion of this fact to the textbooks.

Once we’ve got these ideas of cardinal numbers and ordinal numbers fixed, we can now start thinking about sets that are bigger than everyday finite sets. For example, consider the set that has all the natural numbers as its members: A={0,1,2,3,...}. Clearly this set is bigger than any finite set, but how big is it? Are there any sets bigger than any finite set but smaller than this set A?

To make sense of these questions, I’ll have to introduce a little bit of terminology. Let f: A --> B represent a correspondence (like the 1 to 1 correspondences we’ve been talking about above). So f takes an element a of the set A and pairs it with an element b of the set B (which we write f(a)=b). We say that f is a “surjection” when every element of B is paired with an element of A. We say that f is an “injection” when any element of B that is paired with an element of A is paired with a unique element of A. A 1 to 1 correspondence (also called a “bijection”) is then both a surjection (every element is paired) and an injection (but uniquely).

With these ideas defined I can now say that two sets are the “same size” if there is a bijection between them. I can also say that set B is “bigger” than set A if there is an injection from A to B, but no injection from B to A. Intuitively speaking, there are more elements in the set B than there are in the set A. You start off pairing the elements of set A with elements of set B, but you run out of elements from set A before you finish the elements of set B.

Having made sense of the notion of “bigger” and “smaller”, back to our set A={0,1,2,3,...}. In answer to our two questions, it can be shown that there is no non-finite set smaller than it and hence it is the smallest non-finite set. We will assign a symbol to its size: aleph-zero, the smallest “transfinite cardinal number”.

We’ve only got one of them so far, but we can already start to think what it means to do arithmetic on transfinite numbers. If we think about finite sets, we observe that if we have two sets of distinct objects then the number of elements in the two sets put together (in their “union”) is equal to the sum of the number of elements in each of the sets taken separately. So, if we have four things on the table and three things on the chair we have seven things altogether. We can write this as card(A) + card(B) = card(A union B). We can now simply take this as the definition of cardinal addition.

So, for example, what is 3 + aleph-zero? To answer this question, we take a set with three elements in it, such as {potato, chair, pen} and form the union of it with a set with aleph-zero elements in it, such as A={0, 1, 2, ...}, to form {potato, chair, pen, 0, 1, 2, ...} = C. I hope that it is clear to you that this set C can be put into 1 to 1 correspondence with A. Hence it is the same size as A, therefore 3 + aleph-zero = aleph-zero.

We’ve claimed that there are no transfinite cardinals smaller than aleph-zero; are there any bigger? Yes, in fact there are infinitely many larger transfinite cardinals. The easiest way of generating some of them is through the process of exponentiation. For finite sets, it can be shown that the set of all subsets of a set with n elements in it has size 2 tot he power n. So, we extend this to a definition: if a set X has cardinality k, we define 2 to the power k to be the cardinal of the set of all subsets of X. Now, for finite sets, it’s clear that 2 to the power k is bigger than k. This remains true for any set.

(Proof: suppose g:A-->set of all subsets of A, is a bijection. Form the set B={x in A such that x is not contained in g(x)}. Now clearly B is a subset of A, so there must be an element y of A such that g(y) = B. Now think about whether y is an element of B: if it is, it isn’t; if it isn’t, it is! Contradiction, so such a bijection cannot exist).

So, 2 raised to the power of aleph-zero is bigger than aleph-zero. We’ll call it aleph-one. 2 raised to the power aleph-one is bigger than aleph-one. We’ll call it aleph-two. And so on! In fact, aleph-one is the cardinality of the continuum (that is, the set of all real numbers, or equivalently of the set of all points on a geometrical line).

(Optional mind blowing fact: we can ask whether there are any cardinal numbers bigger than aleph-zero but smaller than aleph-one (this is the “continuum hypothesis”). In fact, whether there is or is not such a cardinal number cannot be proved from the normal axioms of set theory! One can define two different types of set theory: one in which you assume there is such a cardinal as an axiom and one where you assume the opposite.)

You can also define transfinite ordinal numbers, but I thought you would have probably had enough by now!

Now, much of this theory of the infinite was worked out during the latter part of the 19th century but it’s surprising to learn how close the medievals came to working out this theory before the Black Death and the Renaissance put an end to this sort of intellectual inquiry. So Saint Thomas would not have had our understanding of the infinite, but we must not underestimate how close to our understanding his generation came. He knew perfectly well, for example, the difference between a potential infinity (something in principle unlimited) and a completed infinity (such as the geometrical line). However, he did not conceive of the enumeration of an infinite set – so in Q7a4 he says that one must be able to enumerate a multitude and since infinity is not a number, you can’t have an infinite multitude. Now, although current physics does suggest that the universe is finite in extent, it is not beyond our comprehension to think of an infinite-in-all-directions steady-state universe with stars dotted about evenly. In such possible world, there would have to be infinitely many stars.

Does the failure of Aquinas’s argument make any difference to theology? I’m not sure that it does. He seems to be concerned in Q7 to “safeguard” the infinity of the infinite realm of God against any possible intrusion from the mundane created world and put yet more distance between God and creation. Does it matter if he hasn’t in this regard? Hasn’t he done enough already in showing the extent of God’s transcendence?

Perhaps one concern that Aquinas may have had was that if creation could be infinite-in-all-directions, how could God be “outside” creation? Where would there be for him to “fit”? Of course, one of the things that Aquinas was not aware of, that we are, is the idea of the “intrinsic geometry” of the universe (i.e. being a four-dimensional space time manifold); that the universe, even if infinite, can be conceived of as an object and that “placing” God as transcending space and time need not be problematical. Still, I’m not too sure of the likelihood of Aquinas having this concern. He certainly saw no problem with putting God “outside” of time; putting him outside of space too would surely come naturally. He was well beyond panentheism centuries before anyone had thought of it!

Monday, 3 May 2010

Open Thread on Metaphysics

We thought it would be a good idea to have a thread devoted to any questions folk have about the metaphysics that we've met in Aquinas.

Fire away in the responses!

In Our Time on Aquinas

From Melvyn Bragg's series we have a programme on Thomas Aquinas that may interest you!

H/T to Simon K.

Question 13 - Talking About God

Why this Question Matters.

In the previous question Aquinas has argued that we can know God, in various different sorts of ways. He now turns to the question of how we can talk about God. That God is talked about is undeniably true, for example in Scripture. However, how can we know that our talk about God is not simply nonsense? If it is not nonsense, in what way are the things we say about God true, especially given the radical difference between us and God? In this question, Aquinas will introduce the very important idea of analogical predication. That is, in talking about God the words that we use are not used in the same way as we use them when we talk about created things, nor are they used in a completely different way; our talk about God uses words in analogy to the way we use them when talking about created things.

The Thread of the Argument

A1. The words that we have to describe things and the way that they are put together in language would appear to derive primarily from our perceptions of created reality. Does it make any sense to try and apply words to such a transcendental thing as God? The objections of this article focus in on the different functions that words have in language and argue that such functions make no sense when one attempts to apply them to God. In particular, each in turn of abstract and concrete nouns, verbs, participles and pronouns, as they are ordinarily used in language cannot be used to describe God.

Aquinas, following Aristotle, points out that we use words to designate thoughts and that these thoughts designate things; therefore words refer to things that are known. In the previous questions he has already shown that we can know God to a certain extent, therefore we can use words to describe this limited understanding of God. However, we cannot use words to express the divine essence as it is in itself.

In the reply to the objections, Aquinas returns to the fact that we know God through his creatures. We use concrete nouns to refer to concrete things that are composites of matter and form and we use abstract nouns to refer to forms. When we use nouns to talk about God we use them in a way an analogous to this. In a similar way, Aquinas goes through the other parts of speech indicating the senses in which they are used of God.

A2. Having shown that it makes some sense to use words in describing God, Aquinas now turns to the question of whether we can talk about God's substance, i.e. what He is in himself. Aquinas immediately asserts that there is no problem in describing what God is not, or in describing the relationship of creatures to God. What he wants to know is what it means when we say things like “God is good” or that “God is wise”. He is keen to deny interpretations of such phrases that dilute their strength. So he will not accept that such positive attributions are actually to be interpreted as negative statements; nor will he accept that they indicate relationships to creatures. In particular, he will not accept that saying things like “God is good” is equivalent to saying that God is the cause of goodness in other things; the latter is true, but it does not capture the meaning of the original assertion.

Aquinas's solution is that such statements do talk about God's substance but that they do it in an inadequate way. As before, he claims that we know God through His creatures and that creatures resemble Him in the way that effects resemble their causes. However, as this resemblance is imperfect the words we use of God can form true assertions, but ones that don’t capture the fullness of God’s substance. So when we say “God is good” we are really asserting that goodness exists in God in a higher way than it exists in us. We describe goodness as it is known to exist in us as caused by God and apply it as a true but inadequate representation of how it exists in that cause.

A3. We can talk about God using words; we can say things that are true about Him, but our use of language to talk about God will always be imperfect. In this and the next few articles Aquinas enquires in more detail into how language functions when we talk about God. In this article Aquinas is concerned with whether we are always stuck in the realm of the metaphorical when we talk about God, or whether we can we say things of him literally.

Aquinas’s position is subtle. When we say that “God is good” we are speaking the literal truth about God. However, our notion of the good is derived from the good we see in creatures, and the goodness of God far exceeds that. So when we describe God as good, the word “good” that we're using in the sentence does not adequately point at the goodness of God himself. It is as if the sentence itself is literally true but the words in the sentence are mere shadows of what they really should be. In fact, words like “good” are most appropriately associated with God and only secondarily associated with creatures; we only have a limited understanding of what such words mean.

A4. The next article deals with a question that is really quite subtle and awkward for anyone who wishes to claim that we can talk about God. God is entirely simple and therefore anything truly predicated of him is identical with his essence: God's goodness is his essence; God's strength is his essence; and so on. Therefore it would seem that anything we truly say of him is a synonym for anything else we say of him.

The objections attempt to head off any reply that might simply suggest that we describe him from different points of view. To illustrate this, consider looking at a physical object like a vase from different points of view. When we look at one side of the vase we see something different from when we look at another side of it. We may build up a mental picture of the object based on these different points of view, but the different points of view themselves are of genuinely different aspects of the object. If God is entirely simple then our so-called different points of view of Him are not different at all as far as He is concerned. We’re simply using different words to describe exactly the same thing. Frankly, this is a waste of breath.

Aquinas will have none of this: we know God through creatures, and we know God's perfections as they are divided up in many and various ways in the perfections of creatures. We describe God through those perfections which are each imperfect realizations of God’s perfections, imperfect each in their own way. Those different perfections are not described by synonyms even though they derive from a perfectly simple being. The different points of view are not useless because they each represent the single reality in a different imperfect but complementary way. If we take the example of the vase, it is as though we were viewing it every time from the same place, but with different colours of light and with different resolution. We would see the same thing but imperfectly each time; the complementary imperfections would lead to complementary true and non-synonymous descriptions of what we saw.

A5. We use a term univocally when the term has a single meaning; we use it equivocally when it has different meanings according to context. So we can use a word like “bark” univocally when we speak of this dog barking and then that dog barking. We can use it equivocally when we first talk about the bark of a dog and then about the bark of a tree. We have seen that our use of words is derived from our knowledge of creatures. So when we use these same words to talk about God are we using them univocally or equivocally? In other words, do words have the same meanings when talking about God and about creatures or do they rather have completely different meanings?

If we were talking equivocally about God it would seem that there would be no resemblance between God and his creatures, which would contradict the fact that we know God through his creatures. So it would therefore seem that we must be talking about God univocally. However, we simply do not use words in the same way about God as we use them about creatures, as we have seen above, so we must be talking about God equivocally. These two lines of reasoning contradict each other.

Aquinas's answer is to observe that the use of words is not exhausted by the univocal and the equivocal. We also frequently use words in an analogical way; for example, when we describe a diet as healthy. By this we do not mean that a certain plate of food can run a mile in under six minutes and has an appropriate blood pressure; we mean that it is a plate of food conducive the health of the one who eats it. The analogical use of the word is derived from some primary use; there is certain order or relationship between them. When we use words about God and about creatures Aquinas claims that we use them in such an analogical way. That is, the words that we use to describe creatures are used to describe God in a way that mirrors the imperfect resemblance between creatures and God.

In the reply to the first objection, Aquinas extends the ideas of the univocal, the equivocal and the analogical to the case of causes, extending what he said in Ia.q6.a1. In general, a univocal cause is one that transmits its nature to its effects. So, for example, parents transmit human nature to their children. On the other hand, a non-univocal cause is different in nature from its effects; the sun is the cause of life on earth but we are not balls of fusing hydrogen. However, when we consider God as universal cause of all creatures, we should not think of Him as being a wholly equivocal cause, as we do resemble Him in some ways. It makes more sense to think of Him as an analogical cause, in that His creatures do resemble him, albeit imperfectly.

A6. In the third article, Aquinas suggested that as far as the words used to describe perfections are concerned, they are used primarily of God and only secondarily of creatures. In this article Aquinas goes further and discusses which classes of words are primarily used of creatures (and secondarily of God) and which are primarily used of God (and secondarily of creatures).

Aquinas starts by elaborating on what he said about the analogical use of language in the previous article. In order to understand the analogical use of a word in describing something, firstly you have to understand how the word is used of the central thing to which it refers. All analogical usage of a word flows from the ordering it has to some central meaning; the primary application of the word is to this central thing. So, for example, to understand the analogical use of the word “healthy” when applied to urine or to diet, one has first to understand how these usages relate to the health of an animal. Then one realizes that “healthy urine” refers to something diagnostic of good health and that a “healthy diet” is something that promotes good health.

Turning back to the issue under study in this article, Aquinas can now argue that when we speak metaphorically of God, the words used apply primarily to creatures and secondarily to God. On the other hand, when we talk literally but analogically about God, the words used apply primarily to God and secondarily to creatures. The central meanings of these analogical terms refer to God, as He is the eminent exemplar of all these properties.

A7. God does not exist in time; his existence is eternal. So what sense can we make of statements involving God and temporal succession? For example, when we say that “God is Lord of all” we might infer that there must be things for God to be Lord of. These things are things created by God that had to come into existence at some point in time. Some of them may go out of existence at some other point in time. What this statement appears to set up is some kind of relation between God and His creatures that changes over time. This might begin to make us nervous, because it appears to be attributing change in something to do with God; we might prefer to say that “God is Lord of all” actually applies from eternity and does not imply temporal succession.

So, in order to answer this question, Aquinas has to start off with a technical discussion of what appears to be a completely different subject; he considers the notion of a relation. He has to do this because temporal statements about God are really about the relations between God and things that exist in time. Aquinas is returning to unfinished business from Ia.q10.

We are well acquainted with relations in real life: “I am the father of my son”; “that chair is to the left of the table”; “those two animals are both cats”. Each of these sentences indicates a relationship between things. Aquinas, being a good Aristotelian, is committed to the idea that some relations at least can be considered to involve real existence. He goes through three possibilities. In the first case, some relations need not reflect any reality in the things that are related. For example, all the pieces of furniture in the left half of this room are related by that fact, but this does not reflect anything in the pieces of furniture themselves but merely how I've arranged them. In the second case, some relations exist because of a reality in all the objects that are related. I am the father of my son, and this relation exists because of realities that are true of my son and of me. Finally, it is possible for a relation to exist because of something real in one object alone. We can talk about the right-hand side of a column, for example, because it is on the right-hand side of me. But if I were to turn around, what had formerly been the right-hand side of the column would now be the left-hand side. Nothing has changed in the column; the change has been in me. Similarly, if I am thinking about my mug of coffee, this expresses a fact about me but nothing about the mug of coffee.

At the end of this discussion about relations, Aquinas reaches the punch line: since God is altogether outside the order of creatures, being related to God is a reality in creatures but being related to creatures is not a reality in God. This is because a real relation that God has with a creature would have to be an accident in God; but we know there are no accidents in God because he is entirely simple.

Finally Aquinas applies this discussion to the original question about time. We can talk about relationships that God has with creatures that involve change and temporal sequence; but not because there is any change in Him but because there is change in the creatures. This means that such of talk about God is consistent with God being unchangeable, which was discussed in Ia.q9.

The objections and the replies to these objections go through a series of examples illustrating how we are to understand this notion of temporal relation in respect to God. For example, “God is Lord” can quite reasonably be understood as a temporal statement as long as the relations with creatures described above are understood correctly. It is also quite reasonable to understand it as eternally true in that it describes something about what God is essentially in order that He could be Lord of creatures.

A8. Aquinas asks whether the word “God” is the name of a nature. The objections suggest that etymologically the word is derived from meanings that point to activity, so that the word “God” must itself name an activity rather than a nature. Also, since we don't know what God's nature is we can't really name it.

Aquinas's answer is that language is more complicated than the objections would allow. He takes the simple example of a rock, pointing out that the word “rock” signifies what the rock is rather than what the rock does, after having claimed that we derive the word “rock” (in Latin) from what it does. Similarly, he admits that we don't know what God's nature is but he denies that we can't use a word to point to it. We understand the nature of things by abstracting from their properties and from their effects; our language would surely be impoverished if we were not able to name the abstraction even if it was partial and contingent.

A9. Should we reserve the name “God” for God alone? Aquinas makes a number of distinctions in the way that we use names. For example, he makes a distinction between the proper and the metaphorical use of a name. “He is a lion”, for example, could mean that he is in fact a large fierce feline animal, or it could refer to the fact that someone is brave.

A further distinction is between names that can apply to many individuals (there are many lions, for example) and those that are not (for example, a proper name like Achilles). Proper names like Achilles can only be used of other individuals in a metaphorical way as when we want to indicate that some of the attributes of the individual apply to someone else. For names that can apply to many individuals, even when we know of only one example of something, we can abstract its form and hypothesize other exemplars of the form. Aquinas suggests the example of the sun for such an individual, which is rather nice because we do now know of other examples of stars!

Aquinas argues that the word “God” is an example of a name that can only properly apply to one individual. “God” signifies the divine nature, and there's only one of them. However, this does not stop us using the word “God” metaphorically in certain contexts.

A10. Having discussed the proper and the metaphorical use of the name “God”, it should come as no surprise that Aquinas now turns to its univocal and analogical uses. When one person who has a correct understanding of the term “God” is arguing with another who has a faulty understanding are their usages of the word “God” univocal? Similarly, if we use the word “God” to refer to things that in some way share in divinity as well as for the divine nature itself, are we speaking univocally?

Aquinas answers that, in these cases, the word “God” is being used analogically. In the first case the one with a faulty understanding of God is using the word “God” analogically with respect to the true meaning of the term. For the second example, those things that have some share in the divine nature are referred to as “God” analogically. We have to recall, from the sixth article, that the analogical use of terms is founded upon the relation of the analogical use to the central use. In this case, the central use of the term refers to the divine substance; therefore all uses of the term that do not refer to the divine substance are analogical uses.

Notice in this article that there are three objections and yet five replies to the objections! Aquinas uses the last two replies to the objections to continue the discussion started in the sed contra.

A11. The Tetragrammaton, which is often translated He who is, is used as a name for God in Exodus. Is it the most appropriate name for Him? Aquinas argues that it is and gives three reasons for considering it as such.

Firstly, the name doesn't point to any particular thing but simply to existence itself. If we recall that Aquinas has already established God to be self-subsistence existence in Ia.q3.a4, then we see that such a name is the most appropriate for God. The second argument observes that this is about as general a name as a name can be and therefore restricts its subject in as minimal a way as possible. As we cannot, in this life, grasp what God is in Himself then a name like this is the most appropriate for God. Finally, the name points to being in the present; this gives us a hint of His eternity.

A12. The final article in this question returns to the theme of how we can say things about God when the terms we use in our propositions derive their meaning from created reality which is so different from Him. In particular, we may be happy in formulating what God is not, but how can we make affirmative propositions about Him?

For example, in a sentence that involves a subject and predicate we tend to understand the predicate in terms of a form, and the subject in terms of the thing that has the form. In a sentence like “God is such-and-such”, the subject is purely simple and the attribution of the form “such and such” to God would seem to contradict that simplicity as it appears to attribute composition to God. (He is this and He is that and He is the other appears to make Him a composite of this, that and the other.)

On the other hand, there are affirmative statements of the faith such as “God is three persons in one substance” that must be taken both as being meaningful and as true.

Aquinas acknowledges the difficulty but insists that such sentences can be considered true in the sense that they allow us to consider God through a number of different concepts. Even though God is simple, and therefore any true statement about His substance must refer to the same thing, the subject/predicate structure of an affirmative proposition allows us to think about God in a particular way. It is as if teasing the subject and predicate apart in the proposition allows us to represent different ways of thinking about God; whilst having the subject and predicate together in an affirmative proposition represents His unity.

If we take a series of affirmative propositions as meaning that there is a composition in God, then we would be falling into error. But we must differentiate between thinking that “He is this and He is that and He is the other” as a composition and “we can think of Him as this and we can think of Him as that and we can think of Him as the other”.

Summary & Handy Concepts

  • Words designate thoughts and thoughts designate things. So, insofar as we can have some understanding of God, we can express our thoughts about Him in words. These words do not point directly at the substance of God, though.
  • When we do talk about God literally (as in “God is good”) we do so in an imperfect way and the words we use are used in analogy of God’s perfection with respect to the terms we use.
  • We describe God’s perfections using words derived from the perfections of creatures. These terms each give us an imperfect but complementary view of God’s perfections and therefore they are not all synonymous.
  • Terms can be used univocally, equivocally or analogically. When we are not talking metaphorically about God, we predicate terms analogically of Him.
  • Causation can be thought of in terms of the univocal, the equivocal and the analogical causes. We should think of God’s causation as analogical as, although He does not cause what is like Him, some things He causes bear a resemblance to Him.
  • The fifth article refers to the fallacy of equivocation. Here is an example of such a fallacy: “all pigs are kept in pens, pens are something to write with, and therefore all pigs are kept in something to write with”.
  • When we speak metaphorically of God the terms used apply primarily to creatures and only secondarily to God. On the other hand, when we speak analogically of God the terms used apply primarily to God and secondarily to creatures.
  • We can make temporal statements about God that make sense as long as we remember that these define relations in creatures but not in God.
  • The notion of relation discussed in the seventh article will be very important when we come to consider God as Trinity later in the summa.
  • The name “God” names a nature that truly applies only to God alone; the name “He who is” is the most appropriate for God.
  • Faulty uses of the term “God” use it in analogy to the correct usage.
  • Although they are imperfect, we can make affirmative statements about God.

Revised 11/04/12