1.3.3 On the Infinite Intelligible
In arguing against general skepticism, Descartes placed great emphasis on the idea of the infinite, since, he argued, the idea of the infinite is not an idea that our finite minds can manufacture. This led other philosophers to consider the nature of this idea of the infinite. The most important of the positions put forward is that of Malebranche. Suppose, says Malebranche, someone falls to the earth from heaven, with no prior experience of the earth. He begins to walk in a straight line along one of the earth’s great circles; let us also suppose that no mountains or oceans impede him. If he is wise, he will not assume even after many days that the surface of the earth is infinite. We know that he is right, for if he walks long enough, he will eventually return to his starting point because the earth is finite. While, in the course of walking, he recognized that his journey would be an indefinitely long one, he is able to distinguish its being an indefinitely long one from its being infinite. The idea of extension, however, is different; this idea is inexhaustible, and, says Malebranche, this is because the mind "sees it as actually infinite, because it knows very well it will never exhaust it” (JS 15). Geometry is concerned with infinites (infinite lines, infinite divisibility, and so forth). We do not, however, have to test its claims against the finite things we sense; we seem to perceive the infinite. And we need to be able to do so in order to distinguish it from that which is merely a large indefinite finite. Likewise, we recognize that the square root of two is a number requiring infinite precision. As Malebranche says (LO 614), "The mind sees clearly that this proportion is such that only God could comprehend it, and that it cannot be expressed exactly, because to do so, a fraction both of whose terms were infinite would be required."**
What is said of infinity here applies as well to what is related to it. All universal ideas imply the infinite, because to be universal is to be such as to represent infinite possible instances (JS 27); for the same reason, recognizing that an idea is universal and not particular requires recognizing that the former applies to infinite possible particulars. If your idea of a circle were merely a confused assemblage of particular circles, for instance, it would not be applicable to all circles, but only to the indefinite group delineated by the assemblage; the finite explanans would not be adequate to the infinite explanandum. Likewise, what is said of infinity applies to necessity, because what is necessary must pertain to infinite possibilities; therefore necessity cannot be recognized without the idea of the infinite. Similar things may be said of the capacity of ideas to be true for all possible times, or from infinite possible perspectives.
From this, Malebranche concludes that ideas must in fact be perceived in a being that is other than ourselves, one that is infinite, necessary, eternal, and so forth; this is divine Reason. We recognize that the infinites that only God could comprehend them. And we recognize further that our own minds are not infinite; we are finite. Therefore we can only consult the idea of the infinite in inexhaustible Reason. "No creature is infinite; infinite Reason, therefore, is not a creature" (LO 614). As John Norris summarizes the position (Reason and Religion, p. 198), "For 'tis plain that we perceive Infinites, though we do not comprehend it, and that our mind has a very Distinct Idea of God, which it could not have but by its union with God. Since 'tis absurd to suppose that the Idea of God should be from anything that is Created."
Orestes Brownson reasons in a way similar way, based on Vincenzo Gioberti's development and adaptation of Malebranchean arguments. In the simplified form he gives the argument in his novel, Charles Elwood, when we look into reason, we find the ideas of the finite and the infinite. The idea of the infinite cannot be derived from another idea; our experience is finite, but "from no imaginable number of finites can I deduce the infinite" (p. 210). It is only on the basis of the idea of the infinite that we can recognize anything specifically as finite. "As my first experience is of finite things, the conception of the infinite must precede experience, and must therefore be a transcendental idea", which is to say, "a conception of the pure reason prior to all experience." Reason, then, requires that there be some infinite; but it cannot be our own minds, and it cannot be anything natural, in the sense of being the kind of thing we experience through the senses. Therefore it must be supernatural. "The conception of unity, of perfection, would lead me to the same result." However, he also considers the matter in a somewhat different way in his article, "The Existence of God". Even an atheist must concede that something is intelligible. "But as what is not cannot act, so what is not cannot be intelligible." What is intelligible must then be found in some real being; it could not be in a merely possible being, since possibility is a power of the real, and it could not be a merely abstract being, because what is abstract can only be apprehended in the apprehension of the real. What is intelligible, then, must be real. This intelligible, however, must either be a necessary real being or a contingent real being. If we say that the intelligible is necessary real being, we say that it is God. If it is contingent, however, there must be a necessary and eternal real being, since the contingent depends on the necessary in such a way as to be unintelligible without it. So anything being intelligible implies that God exists. "The conclusion here is evident, but if we analyze it we shall find that it is not that God is, but that what is really apprehended in every act of intelligence as the intelligible, without which the act were impossible, is God."
These views seem to come near to something right, yet not quite to attain it. Therefore, guided by what is reasonable in such views, we may argue the matter from the beginning, as follows.
(1) Our intellect by understanding reaches toward the infinite. As St. Thomas says (ST 1.86.2), never does our intellect understand so many things, that it cannot understand more. We can recognize this more specifically in a number of ways.
(1.1) First, as was noted by Descartes, 'finite' and 'infinite' are correlatives; because of this, to recognize correctly that something finite requires recognizing that it is not infinite. We do, however, correctly recognize some things as finite, and therefore our understanding must in some way and in some sense extend to the infinite. Moreover, we can, as Malebranche says distinguish the infinite from the mere indefinite that we obtain when build up from finite things.
(1.2) Second, we see that our intellect must have some direction to the infinite from considering mathematics. The examples of thought reaching to infinity in mathematics are numerous. For instance, given any finite quantity, our intellect can think of a greater one. As St. Thomas says (SCG 1.43), Our intellect extends to the infinite in understanding; and a sign of this is that, given any finite quantity, our intellect can think of a greater one. And as St. Augustine says of numbers (Civ Dei 12.18), For it is very certain that they are infinite; since, no matter of what number you suppose an end to be made, this number can be, I will not say, increased by the addition of one more, but however great it be, and however vast be the multitude of which it is the rational and scientific expression, it can still be not only doubled, but even multiplied. Moreover, each number is so defined by its own properties, that no two numbers are equal. They are therefore both unequal and different from one another; and while they are simply finite, collectively they are infinite. Obviously our thought must be able in some way to reach the infinite to consider the infinite collectively. Likewise, by the Pythagorean theorem, we can identify numbers, like the square root of two, that are infinitely precise, and we can recognize that a geometrical line admits of infinite distinct constructions of points.
We may see this again from an argument based on a thought by Dedekind ("What are numbers and what are they good for?"). We know we have possible objects of thought that are picked out determinately by what can be thought about them, like mathematical objects. These objects can in turn be associated in the mind, i.e., thought-together in a determinate way. This Dedekind calls a 'system'. The system just is the determinate thinking-together of the objects that are its elements; thus each system is itself a possible object of thought. When every element of one system is an element of another system, the first is at least a part of the second; and it is a proper part when this is true but the systems are not the same. Finally, we can relate the elements of one system to another; Dedekind calls this a 'transformation', with the other system being called the 'transform'. The transformation between two systems that are related by a one-to-one between their elements is similar, and a system is infinite if it is similar to at least one of its proper parts. From this Dedekind draws his argument that all of the determinate possible objects of one's thought are infinite. If we consider the system S that includes all such determinate possible objects of my thought, then if 's' is an element of S, 's can be an object of my thought' is also an element of S, by definition of S. It is also related to s by a transformation; so if we consider the system S' that is the transform of S in this way, we find that it is both a proper part of S and similar to it, because S certainly includes things that are not indicators of something else being an object of thought, and S and S' are able to be put into one-to-one-correspondence. In other words, for every object of thought s, one can have the further object of thought 's is an object of thought'; we can do this one-to-one correspondence with everything about which we can think, but if we take all the explicit 'is an object of thought' thoughts, they will be a proper part of the totality of objects of thought, because there will be some objects of thought (like myself) that are not thoughts involving the explicit form 'is an object of thought'. So the whole of what can be thought is infinite.
A very great many others could be included. All of these mathematical infinites are potential infinites rather than actual infinites, but they are truly infinite, not indefinite finites. Some confusion reigns on this matter due to confusion about the terms 'potential infinite' and 'actual infinite' which can be used in somewhat different way. Many gravely err in taking 'potential infinite' to mean what is not infinite at all, like an indefinite finite. This is contrary to the point. In the sense meant here, there are infinite potential points in a plane; actual points require a construction making them points, as in the crossing of two actual lines. There are infinite potential numbers; actual numbers require a construction of counting, proportion, set construction, or the like to make them actual numbers. An actual infinite in this sense requires infinite constructions actually done. We have done no such thing, nor do we know that anything has done it. Nonetheless, these potential infinites are truly infinite, and thus that we are able to recognize and reason with them shows that we are able to extend our minds to the infinite in understanding.
(1.3) Third, we recognize that our intellect must have some orientation to the infinite when we consider the requirements of logic, as Malebranche recognized, for logic requires an understanding of universality, necessity, and the like. Or, in the words of Aquinas (ST 1.76.5 ad4), The intellectual soul, as comprehending universals, has a power that is open to infinite things, and again (ST 1.86.2 ad4), it can know the universal, which is abstracted from individual matter, and which consequently is not limited to one individual, but, considered in itself, extends to an infinite number of individuals.
A related argument can be adapted from Kant and modified. In disjunctive syllogisms or eliminative reasoning, as well as in induction in the scholastic sense, we take a sphere of possibilities and divide it into particular possibilities, which may or may not overlap but need at least to be conceptualized distinctly to have a division. We may then eliminate possibilities, or show that something is true for all of the possibilities. This division is often expressed in a disjunctive judgment, like 'Either p or q', but the division can have as many possibilities as might be relevant; indeed, in some fields, it might sometimes have more possibilities than we can individually count. But there are infinite possibilities consistent with each other, and thus our minds extend to the infinite in understanding.
(1.4) Further, adapting an argument from Josiah Royce, we recognize that our intellect must in some way extend to the infinite when we consider the nature of error, which we can hardly doubt occurs. As Royce notes in The Religious Aspect of Philosophy, an error is not identifiable as an error simply on its own, but only by being put in a proper context. To err is to miss the target, one might say; it is impossible to err without contextualizing the error in relation to a target. In other words, something is an error only insofar as it is related to what it opposes; the error is a fragment of a larger whole, and can only be called an error in relation to that larger whole. This is true for all possible error, of which there are infinitely many different kinds. For instance, one might err in mathematics about the number one, about the number two, and so forth. Thus the intelligible whole in the context of which all possible errors can be recognized must be infinite. As Royce, who is an idealist, prefers to put it (RAP, p. 393), "Either then there is no error, or else judgments are true or false only in reference to a higher inclusive thought, which they presuppose, and which must, in the last analysis, be assumed as Infinite and all-inclusive."
(1.5) Further, we recognize that our intellect must in some way extend to the infinite when we consider human practices of explanation. Infinity has always arisen in our attempt to explain the world. Perhaps the earliest clear recognition of infinity that we can definitely identify, in fact, arose in the efforts to explain the world causally. Ancient philosophers attributed to the fundamental features of the universe some kind of infinity, because infinite things derive from them. And, of course, it follows from this that the kind of infinity they attributed to the first principle was that which was appropriate to the kind of cause they were considering.
Those who explained things materially, for instance, attributed a material infinity to their first principles, like some kind of infinite body or extension, or something capable of taking endlessly many different forms. The infinity of matter lay in its being potential for different forms, but it receives a termination, and thus finitude, in receiving its form. Likewise, the infinity of form consists in its being common to many different material embodiments, but when it receives its matter, it is found in this one, and thus also receives finitude. However, these are not wholly symmetrical, because matter is completed by the form making it finite, and therefore there is something incomplete or imperfect to the infinity of matter, whereas this is not true of formal infinity, which is not completed by matter but contracted by it, and thus there is a completeness to formal infinity that exceeds material infinity, as indeed we see in comparing mathematics to physics. But infinity in either matter or form implies infinity for ends, as well.
(1.6) The notion of the infinite is implicit in our understanding of being, which is implicit in our understanding of everything else. Being is capable of infinitely different modes. Therefore we think of finite being not as being as such, but as limited in its being by something. The same may be said for intelligibility itself, since being is the first intelligible our intellect attains.
We may take it, then, that our intellect has a capability reaching to the infinite in some way; that is to say, the intellect tends toward the infinite in such a way that we can understand something of the infinite.
(2) This capability of the intellect requires that there be some infinite intelligible. That is, this ordering of the intellect to the infinite would be in vain unless there were an infinite intelligible to serve as an end for it.
There must, for instance, be something to distinguish such an ordering from an ordering to the mere indefinite. We see this in considering empiricist attempts to account for our recognition of the infinities in our understanding. Thus, in Berkeley's early notebooks, he toys with the idea that the Pythagorean theorem might actually not be true but merely useful as a kind of recipe; and Hume in his account of equality in the Treatise argues that geometry is a loose rather than an accurate field, based on the tendency of our mind to continue a while in the same track. The reason for these oddities is that empiricism as they understood it has no ability to distinguish the indefinite from the infinite, because if you attempt to explain the infinite entirely from the finite, the latter provides no resources for telling the difference between the infinitely large or small and the indefinitely so. Either the capability of the intellect to reach to the infinite in some way is due wholly to finite things or at least also to something infinite. But it seems clear that it cannot be explained as due wholly to finite things.
When we consider the matter carefully, it is clear that inquiry is structured by the tendency to this infinite intelligible. The intellect in inquiry obviously is directed toward understanding the intelligible object of its inquiry, which is selected out of all intelligible objects that might be investigated. No inquiry, however, considers only its intelligible object. In order to understand anything, this object must be related to other things in an intelligible way. For instance, an effect must be intelligibly related to an intelligible cause. More than that, appropriate inquiry requires relating the object to the inquirer, and, if the inquirer uses any means, the means, in some intelligible way; we see this in the methodological and critical aspects of inquiry. For instance, if we are studying Mars by telescope, full inquiry will perhaps consider whether features we are seeing are due to optical illusions or errors in the equipment or even psychological expectations or sociological pressure; we will perhaps need to consider whether we are reasoning or calculating correctly, and whether our theories of the way light travels are correct. In addition, we may have to consider contaminating influence from the environment. Even if we do not consider these things specifically, they are relevant and possible, and inquiry will at least indirectly involve situating or contextualizing the object of inquiry within this broader context. And some of the feature of this intelligible 'situation' are, for reasons already noted, infinite, which we see in considering the mathematics, the logic, and the relation of what is studied to being. Nor could we say this is just some fiction in the mind, since otherwise all inquiry would merely be the vain searching of our own fictions.
We see this as well if we consider error again. Nothing is an error unless it is defective with respect to some truth that makes it intelligible as an error. Thus every possible error implies a greater intelligibility within which it has its nature as error, and within which it is properly related to the intelligible truths with respect to which it is defective. There are, however, infinitely many possible errors. For instance, one error would be to conclude that 1 + 1 = 1, another that 1 + 1 = 3, another that 1 + 1 = 4, and so forth infinitely, all of which must be intelligibly linked to the single truth, 1 + 1 = 2, in order to be errors at all; and so it goes for every truth and every combination of truth. To recognize this, however, requires that there be some intelligibility that actually relates all these properly and in an intelligibly unified way, to which we more closely conform when we correct our errors.
(3) Thus there must actually be some infinite intelligible. What is intelligible is so because of its actuality, not its potentiality, and insofar as it is actual; thus the infinite intelligible, intelligibly unifying what can be known in our inquiry into what is, must be an intelligibly actuality. We can see this with error, as well; as Royce says (RAP 429-430), "The conditions of possible error must be actual." Therefore Aquinas says (SCG 1.43), There must be some infinite intelligible thing that must be the maximum of things.
It is necessary to clear up certain errors that have been made on these points by considering the alternatives available. There are only three ways to think of this infinite intelligible, since our intellect is a power specified by various objects according to various ends. Either it must formally be our intellectual power itself (or some intrinsic feature of it), or it must be a form specifying the intellect as its objective cause, or it must be the final cause of our intellect.
(A) The first possibility, that it must be formally either our intellectual power itself or some intrinsic feature of it, is impossible, although it has a certain superficial plausibility. It is true that the intellect must be such as to tend to the infinite in a recognizable way. It is also true that this requires that the intellect have a power that is in some way infinite. As St. Thomas says (ST 1.86.2 ad4), As our intellect is infinite in power, so does it know the infinite, for its power is indeed infinite inasmuch as it is not terminated by corporeal matter. But, first, this is what is to be explained, not the explanation of it. And second, our intellect does not understand the infinite either actually or habitually, but potentially and by indirect reflection on the potential. Infinity is something open to us insofar as we can consider successively one thing after another, and recognize our own operation in doing so in an abstract way. When we recognize the infinity of the natural numbers, we recognize not each natural number individually and all together, but understand what a natural number is and what succession of numbers is, and therefore that a successor to any natural number can always be identified. But this is not to know something about the mind, but to know something about numbers and numerable things. And we see a sign of this in that our understanding seems to depend on sensory processing; we can know beyond what we sense and imagine, but only by abstraction, so that we know them in a general way and in their universal principles.
(B) We can recognize on similar grounds that the infinite intelligible cannot be a form or immediate object of our intellect, in the way that Malebranche, for instance, suggests. Infinity is potentially in our mind, not actually or habitually, through considering successively one thing after another, and therefore known only in a potential and confused manner. But the infinite intelligible cannot be merely potential and confused in order to structure our inquiry.
This leaves only (C). We can thus conclude to it.
(4) This infinite intelligible must be the final cause of our intellect. We recognize the infinite intelligible as that to which our intellect tends in understanding, that is as the final cause of our intellect. This is reasonable even on general grounds. All intellectual progress, philosophical, scientific, or in any other way connected with understanding, is impossible except with respect to some end that is such that it distinguishes progress from regress, stagnation, or mere difference. Without an end, there is no way to tell how something stands with regard to worse or better, less perfect or more perfect, erroneous or right. This end, as the end of intellectual progress, must be intelligible, and given the nature of the intellect, it must not be subject to any intelligible limitations.
In this way, much sense may be made of the more plausible philosophical views of the rationalists, the transcendentalists, and the idealists, for often their primary error consists simply in treating what must be regarded as an end for the intellect as if it were a formal object or else an intrinsic feature of the intellect itself. When this is corrected, they will often be found to converge on something more tenable than their own position.
The infinite intelligible must be be a superordinate end for nature in the manner we have previously noted. First, because intelligibility is most properly associated with the final cause. Second, the orientation of the intellect to it is itself a natural order to an end, not selected by the intellect itself, and thus must be due to some intelligence other than itself setting its end in the manner of an end. As Royce puts it (RAP p. 427), "Our thought needs the Infinite Thought in order that it may get, through this Infinite judge, even the privilege of being so much as even in error." Third, for our intelligible ends to have any relation to the natural world, so that we can know the latter, our intellect and the natural world must be united by some end to which they are both subordinate. Thus it is because both intellect and nature tend toward the infinite intelligible as an end that the intellect can understand what is natural; for we cannot recognize as nature what is not intelligible, and all limited intelligibles are subordinate to that intelligible which is without limit.
Such an infinite intelligible, superordinate end for inquiry and thus superordinate end for natural things, must be divine. Things are intelligible to the extent that they are unvarying, unified, and not limited, and thus the infinite intelligible must be immutable, simple, and eternal. It must also be that than which no greater can be thought, because nothing can be thought that is greater than an infinite intelligible unifying all intelligibility. Thus all our understanding and knowledge in a way implies the divine; as St. Thomas says (DV 2.2 ad1), All knowers implicitly know God in whatever is known, and as Pierre Rousselot says (L'Intellectualisme p. 40), "Intelligence is the faculty of being in general only as it is the faculty of infinite being." Because of this, sense may often be made of a priori or 'ontological' arguments for God's existence; that is, while they seem to be concerned with an object of intellect, they are often better regarded as a posteriori arguments, moving from the tendency of the intellect to its final cause. Other things than God are known because of God, but because God is the final cause of our intellect and its activity, not because God is the first object of our intellect. As object, the divine exceeds our grasp; as St. Bonaventure says (Sent 188.8.131.52), Divine light is inaccessible to the powers of every created nature on account of its preeminence. However, the divine is the destiny of all intellects.
From this we find that God is infinite and in what way in which infinity can be attributed to the divine. It is clear that God is not infinite in terms of either discrete or continuous quantity; He must rather be an infinite of intelligibility, which is an even more fundamental form of infinity, as St. Thomas says (SCG 1.43): There must be some infinite intelligible thing that must be the maximum of things. Everything other than God is relatively infinite rather than simply infinite, because everything other than the divine will fall short of the infinite of intelligibility in some way. A material infinite is limited by its form, and has its infinity in its unlimited potential for form. A formal infinite is more properly called 'infinite'; but forms are limited by their matter, and only have their infinity to the extent that they exceed material limitations. Even if you had a form that had no material limitations at all, it would be limited by the contraction of its nature to a particular determinate kind of intelligibility. However, the infinite intelligible is not so contracted, being in some way inclusive of all other intelligibility. Thus its infinity might be called an absolute formal infinity; but we could perhaps more accurately call it a final infinity, that is the infinity appropriate to the very possibility of final causality as such, and thus to the very possibility of all causality.
These matters are related to sublimity. The sublime, properly speaking, is that which by its greatness exceeds all comparison. It is generally experienced as that which overwhelms but in a way such as to exalt. Human beings have many experiences of sublimity; we find sublimity in the vastness of view from a mountaintop, in the seemingly endless heaven of seemingly infinite stars, in the dynamic glory of the storm, in the epic sweep of great literature about great deeds, in luminous truth, in mysterious beauty, in moral law. Now, it is clear that in some of these experiences, what is directly experienced is not literally in excess of all comparison; for instance, we do not actually see infinity in the heaven or in the number of its stars. Because of this, Kant has argued that the infinity that we experience in sublime experiences is actually our own, the sublimity of a reason that can consider mathematical infinity and moral unconditionality. We can see now, however, that this is nearly true (for instance, it is true that things to do with reason are often sublime), but that the same error noted above has interfered with an adequate account, because Kant has made a formal feature of reason what is in fact a final end to which it tends, the infinite intelligible. From this we can see that God is most sublime; as the Psalmist says (Ps 144:3), Great is the Lord and greatly to be praised; of his greatness there is no end. We can also better understand an aspect of the divine sublimity, namely, that it is both luminous and mysterious. It is luminous because the divine, being the infinite intelligible superordinate to all other intelligibles, But it is also mysterious, because its infinity exceeds the power of our intellect formally to capture. As St. Thomas says (ST 1.12.1), But what is supremely knowable in itself, may not be knowable to a particular intellect, on account of the excess of the intelligible object above the intellect; as, for example, the sun, which is supremely visible, cannot be seen by the bat by reason of its excess of light.
1.3.4 On the Love of Wisdom
Philosophy in the most proper sense is love of wisdom. As such it is contrasted with many things, but most often with sophistry, which, as St. Clement of Alexandria says (Strom 1.8), makes false opinions like true by means of words, whether for the purpose of persuading or for the purpose of victory in wrangling and toying with people, which are then treated as the purpose of reasoning. But philosophy differs from this in that it is concerned wisdom, and, indeed, not merely apparent wisdom, as might occur if one simply persuaded others to regard oneself as wise or if one seemed wise by vanquishing them in dispute, but true wisdom. As Plato argues in the Gorgias, the philosopher takes the distinction between real and apparent seriously, recognizing that they can come apart: real versus apparent knowledge, reasoning that is really good versus reasoning that is only apparently good, and ultimately, real wisdom as opposed to apparent wisdom. Thus Clement describing the opposition of philosophers to sophistry, continues, For Plato openly called sophistry an evil art. And Aristotle, following him, demonstrates it to be a dishonest art, which abstracts in a specious manner the whole business of wisdom, and professes a wisdom which it has not studied. The philosopher recognizes that the only victory that matters in reasoning is to become more wise, and the only persuasion that matters if being persuaded to a wiser position or view; to one who truly loves wisdom it is intolerable that the goal of wisdom be subordinated to the manipulation or domination of others or to cleverness in the use of a method for such ends. Likewise, the philosopher is wary of pretending to the name or appearance of wisdom; Pythagoras, indeed, coined the term so that men might their true place as being always in need of pursuing wisdom. For to one who loves wisdom, finding a humility in love, it seems impudent to call oneself wise based on the rudiments we usually have; as St. Paul says, Knowledge puffs up while love builds up. For this reason also Plato regularly puns on the similarity between the erotic, that is the arts of love, and the erotetic, the arts of questioning and inquiring.
Philosophy, then, is a pursuit and a devotion, a love that inquires. As St. Clement says (Strom 2.9), The philosopher loves and likes the truth, being now considered as a friend, on account of his love, from his being a true servant. Such a person may well say (Pr 8:11), Wisdom is more precious than precious stones and nothing desirable can compare with her. Such philosophy begins in wondering. As Plato has Socrates say to Theaetetus (Theatetus 155d), "For this feeling of wonder shows that you are a philosopher, since wonder is the only beginning of philosophy, and he who said that Iris", that is, the messenger of heaven, "was the child of Thaumas", which Plato interprets as thauma, wonder, "made a good genealogy." Aristotle agrees, saying (Met 1.3 982b), "It is through wonder that men now begin and originally began to philosophize; wondering in the first place at obvious perplexities, and then by gradual progression raising questions about the greater matters too, e.g. about the changes of the moon and of the sun, about the stars and about the origin of the universe." Clement of Alexandria, too, insists on this, saying (Strom 2.9), The beginning of knowledge is wondering at objects, as Plato says is in his Theætetus; and Matthew exhorting in the Traditions, says, Wonder at what is before you; laying this down first as the foundation of further knowledge. So also in the Gospel to the Hebrews it is written, He that wonders shall reign, and he that has reigned shall rest. If we wish to understand philosophy, then, we would do well to pay attention to wondering, a natural activity closely bound to our existence as persons.
Wondering seems to have two essential preconditions: ignorance and the desire to know and understand. In a sense, all human beings are ignorant before they are not, but it is the mark of the philosopher to be aware of this. Socrates did not rest with his ignorance, but sought to inquire with others, to determine what they knew and did not know, and in the same way Confucius says, "Yu, shall I tell you what knowledge is? When you know a thing to hold that you know it, and when you do not know it to allow that you do not know it: this is knowledge." That is to say, it is essential to human knowing actually to sort out what we know from what we do not know. In saying this, we learn what we do not know, and it is this that makes it possible for us to know more. Thus we find Plato's Socrates, considering himself most ignorant, coming to the conclusion that the Oracle at Delphi, in saying that he was wisest of the Greeks, really intended to highlight the limitations of human knowledge, using Socrates as the model, and concludes that its meaning was (Ap 23b), "This one of you, O human beings, is wisest, who, like Socrates, recognizes that he is in truth of no account with respect to wisdom." Likewise, it is said in the Analects (Ana 13), "A superior man, in regard to what he does not know, shows a cautious reserve." This aware ignorance is not terminal, but is of such a kind as to dispose to more careful inquiry and closer pursuit of truth. Thus it is also said (Ana 9), "The Teacher said, Am I indeed possessed of knowledge? I am not knowing. But if a mean person, who appears quite empty-like, ask anything of me, I set it forth from one end to the other," that is, faced with a question to which he did not know the answer, he investigated it thoroughly in order to discover what he had not known.
Such a philosophical ignorance can only be non-terminal if it is properly joined with the desire to know and the love of learning that comes from it. Aristotle famously tells us (Met 1.1), "All men desire by nature to know." That is to say, all human beings have an intrinsic tendency to knowing that is part of their human nature, even where it is impeded by other factors in some way. It is this desire to know that, in unimpeded, form, gives us the love of learning that does not shirk the occasionally hard road of coming to know, as when Confucius says (Ana 1), "Is it not pleasant to learn with constant perseverance and application?" The combination of aware ignorance and the desire to know leads to wondering; this wondering is not itself a desire but an intellectual reflection considering possibilities that grows out of it.
While wondering has ignorance and the desire to know as its preconditions, it is constituted by the intellectual apprehension of what we may call the mirandum, the wonderful or thing of wonder, and in philosophy this particularly is expressed by the articulation of this into the aporia, the set of puzzles about it, about which we may wonder. The aporetic is literally that in which there is no pre-established path for knowing. All wondering is a wondering at or about something; we have the mirandum as our object and out of this we begin to identify what it is in the object that makes us wonder, namely, something that makes us think that there is a gap between what is and what seems. For instance, things may seem a certain way if we look at common opinions of clever men, but we may have an experience of them that does not fit with this seeming; this makes us wonder what is the cause of such a divergence, and we begin to articulate this by determining how the experience does not fit the common opinion. Or we may have come to accept something by familiarity, such as the shining of the sun in the sky, but then something happens, like a solar eclipse, and we wonder what makes the difference between what happened and what we would normally assume. Thus the immediate object of wondering is the mirandum articulated into aporia, and, more remotely, the causes that are relevant to it.
We wonder because we are ignorant, but it is also true that we may say that in wondering we are no longer merely ignorant, for to wonder is to begin to think through something. This wondering may or may not find its term in science or knowledge, but it raises us out of mere ignorance whether it does or not, and in doing so it in a way disposes us better to know. As some have noted, because of this philosophy has a kind of affinity with poetry; thus Aristotle says (Met 1.3 982b), "The philosopher is to some extent a lover of myth, for myths are composed of wonders", and Confucius says (Ana 8), "It is by the Odes that the mind is aroused." Poetry, like philosophy, appeals to the human desire to know the things we do not know; it shows us wonders, that we may wonder. Philosophy goes beyond this; in philosophy we wonder that we may no longer be ignorant. But the two should not necessarily be opposed. As Aquinas notes, the rudiments of philosophical knowledge were often found in poets. Likewise, metaphors are wonders in speech by which we may come better to understand real things, and may of course be useful as such for both the poet and the philosopher. Further, one wondering so as to know may find an appropriate vehicle in poems, like Dante, or in novels, like Austen, and not merely in syllogisms and other analytic instruments. In all these ways we are lifted above mere ignorance by wondering.
Wondering by its nature has an end to which it tends. The immediate end of wondering is coherence or intelligibility in things, which we possess in knowing and understanding. To wonder is to examine the puzzling for what is intelligible. This immediate end of wondering serves as a means to the end of philosophy, which, since philosophy is love of wisdom, is wisdom. This, of course, makes sense in that all knowing and understanding are commonly recognized to be means to wisdom.
From this we can see more clearly that philosophy is natural to human beings insofar as we are human, and this is true of us both individually and insofar as we form communities and societies. Individually, as Bonaventure says (QDMT 1.1), a desire for wisdom has been implanted in the minds of men, for the Philosopher says, 'All men by nature desire to know.' This desire for wisdom manifests itself in many ways, but in all ways we find it a pursuit suitable for a human person. From this we can recognize that to philosophize, that is to say, to act in love of wisdom, is a natural human function, and is the most complete expression of our desire to know. This is confirmed by the impossibility of human beings doing without it. As St. Clement says (Strom 6.18), But if we are not to philosophize, what then?...The consequence, even in that case, is that we must philosophize. For if someone says that the wise course is not to philosophize, then we must act out of love for wisdom to follow this advice; if someone says that philosophizing is pointless, we must philosophize in order to determine this; if someone says that philosophy is in itself absurd, we must reason philosophically in order to understand what philosophy is so as to see its absurdity. Therefore philosophical desire for wisdom is natural to the individual human being. A human being who never wondered, who never asked why things are as they are, or why things should be as they should be, or who never attempted to reason to an answer, would necessarily be stunted as a human being.
Philosophy also a natural tendency of our nature insofar as we are social. We see this even in elementary ways, if you get people together to muse or argue about things that they regard as important. We see it in the crucial importance of advice and example to our own rational lives. And we see it in teaching itself, for in a sense, teaching is not the giving of knowledge from one to the other, but a more experienced student studying with a less experienced student. The Romantic philosophers spoke of symphilosophie, complementary minds philosophizing communally, a group of friends coming together to philosophize with each other, in something that goes beyond mere sympathy in opinion and sentiment, in such a way that through discussion and argument the result is the result of them all. As discussion among close friends attests, we are at our best, intellectually, in such joint pursuit of wisdom, because the wisdom philosophy seeks is that to which the social aspects of our intellectual nature also tend.
Without insisting on it, we can perhaps see all of this summarized in the unified progression given in Analects 1.1, which says, "The Teacher said, To study and find a use for one's study, is this not a pleasure? To have friends come from afar, is this not a source of enjoyment? To be unrecognized and unacknowledged but to be without resentment, is this not to be a noble man?" These are best seen as not three distinct questions but as describing the same thing in three ways. First, to learn and continually return to what is learned is consistently a pleasure, a sign that the philosophical pursuit is a fulfillment of our nature. Second, this study is done with friends from afar, whether literally from elsewhere or figuratively from other intellectual positions; this coming together with others is a source of joy, a sign that the philosophical pursuit fulfills us not merely individually but insofar as we are social beings. And third, this philosophical pursuit is not, like the pursuit of sophists and orators, a pursuit of benefit or profit; the noble person can endure being unacknowledged, unhonored, because what the noble person is worth far more than such honors. In this we find a full account of philosophy in the true sense, one that recognizes it as an activity of fulfilling our human potential.
That the pursuit of wisdom is rooted in human nature is recognized by the wisdom literature of many cultures; thus, for instance, sacred scripture says in the person of Wisdom (Pr 8:4), To you, O people, I cry out, and my call is to sons of men. All human beings then may be said to have a vocation to wisdom, which is fulfilled in philosophy. Given this, we may say with St. Thomas (SCG 1.2) Among all human studies, the study of wisdom is the most complete, the most sublime, the most useful, and the most joyful, for it is the fulfilment of the major aspirations that constitute human life as human. Likewise, we may agree with St. John Paul II, saying (Fides et ratio, Intr. 3), Born and nurtured when the human being first asked questions about the reason for things and their purpose, philosophy shows in different modes and forms that the desire for truth is part of human nature itself.
Wisdom is commonly said to be that knowledge or understanding that sets all things in order, and that is more wise that sets more in order. That is, they are called wise who order and judge, and we say people are wise with respect to a certain kind or genus of thing when, knowing the fundamental principles and causes of that genus, they act in light of this knowledge. Thus an excellent mechanic is wise about machines and a great engineer is wise about designs; in both cases this happens why they know their field intimately. The one who best knows a field, however, is the one who best understands the principles and causes on which it depends. Likewise, prudence is a kind of practical wisdom, since the prudent person, understanding the true ends of life, directs human actions to good ends, and thus best able to discern the right and viable way. Different kinds of wisdom, however, may be greater or less as wisdom, for some are concerned with more fundamental principles, and thus the wisdom associated with them is more architectonic. The name of wisdom, therefore, is most properly given to the most architectonic wisdom; and this is the wisdom to which consideration of what is truly universal belongs. As Aristotle says (Met 1.1), "All men suppose that what is called wisdom has reference to first causes and principles." This will particularly concern final causes; as St. Thomas says (SCG 1.1), The end is the standard of governing and ordering for all things ordered to an end.
From all that has been said, we can see that the ordering of the philosophical being to wisdom as a destiny is a natural ordering to an end. Thus wisdom is final cause of our nature; as Bonaventure says (QDMT 1.1), there is no love for what is completely unknown, and Clement says (Strom 2.9), It is impossible for an ignorant man, while he remains ignorant, to philosophize not having apprehended the idea of wisdom; since philosophy is an effort to grasp what truly is, and the studies that conduce thereto. Philosophy is an activity expressive of our intellectual natures in their flourishing, and thus must have a real final cause. The order of philosophy to wisdom would be in vain were there no wisdom that is universally architectonic; and in this sense we can understand Bonaventure's comment (QDMT 1.1), some knowledge of this highest wisdom must be implanted in the human mind.
This is, as we have noted for the infinite intelligible, not as formal cause but as final cause. Indeed, the universally architectonic wisdom must be the infinite intelligible, because the wisdom sought by philosophy is that which sets all things in its intelligible order. Thus the end to which our intellectual nature, in both its theoretical and its practical work, as seen in its purest form in philosophical love of wisdom, is the infinite intelligible, that is, infinite being, as something with which to be intellectual united and which to contemplate. If this intelligible end did not exist, intellectual nature would be in vain, which is absurd. But it must also be the superordinate end of nature, for this architectonic wisdom is a final cause not selected by us for our intellects but is the natural end for all possible intellects, without which they could not exist; it must therefore select the ends of natural things.
Universally architectonic wisdom must therefore be divine. It must be immutable, for what orders all is not ordered by what it orders; it must be simple, because what is composite is set in order by something else; it must be eternal, because it can have no beginning, nor end, nor proper measure according to change. And we see signs of this in philosophy itself, for, as Bonaventure says (QDMT 1.1), the most desirable wisdom is eternal, and as the Horoi, or Platonic Definitions says, philosophy is desire for "knowledge of what always is." Since it orders all, universally architectonic wisdom must also be that than which no greater can be thought, because, as ordering all, there is no higher standard of ordering against which it could be measured, nor is anything thinkable greater than that which fulfills all intellectual pursuit and inclination. Thus we may say, as we find written in Sirach (1:8), There is one who is wise, greatly to be feared, sitting on his throne. Likewise, St. Clement of Alexandria says (Strom 2.9), the Divine alone is to be regarded as naturally wise. Therefore also wisdom, which has taught the truth, is the power of God; and in it the perfection of knowledge is embraced. In this light, and particularly insofar as the universally architectonic wisdom must be the universally superordinate end, we can often make sense of even very elementary design arguments for God's existence, which, although often incomplete and merely suggestive, are concerned with the wisdom-ish character of the natural world, and argue thence to architectonic wisdom setting all things in order on the basis of this appearance suggestive of wise ordering.
In the first book of the Confessions, St. Augustine notes that our hearts are restless until they rest in God, but, alas, even from the beginning we often seem to go wrong, hating learning, or, if learning, doing it only for vain benefits, or, if learning for its own sake, without regard for what is best to learn. Nonetheless, in all learning done out of love of truth and wisdom, however imperfect, we do find some goodness from God. We see then the sublimity and humility of human wisdom, so far as we attain it in our limited ways at various stages of our existence, for it is derived from that wisdom than which can be thought no greater, an echo of it, something as if it were divine, and yet we grasp it only in part, and only in the pursuit, not by nature but only by love of it, so that the wisest human person is in a sense more accurately called a philosopher, a lover of wisdom, than a wise person, and certainly in comparison with the universally architectonic wisdom. For this reason, in human beings it is better to love wisdom than to know wise things; as Aquinas says (ST 2-1.66.6 ad1), knowledge is is perfected by the known being in the knower, whereas love is perfected by the lover being drawn to the beloved. The wisdom to which we may be drawn by love is greater than any wisdom we may have come to possess. And it is in this loving pursuit of wisdom that we are at our best.
Thus our holy predecessors made clear that our wisdom, such as we may have it, depends on respect for divine things. We find this in sacred scripture, which emphasizes it vehemently and repeatedly. Thus we read in Proverbs (1:7), The fear of the Lord is the beginning of knowledge, but fools despise wisdom and instruction, and (9:10), The fear of the Lord is the beginning of wisdom, and the knowledge of the Holy One is understanding. We find in the book of Job (28:28), And he said to man, Behold the fear of the Lord, that is wisdom, and to turn away from evil is understanding. Likewise, the Psalmist says (111:10), linking both fear of the Lord and the beginning of wisdom to observance of Torah, The fear of the Lord is the beginning of wisdom; all who follow his precepts gain rich understanding. And in Sirach, who emphasizes this idea of the Torah as wisdom given to us, we find this emphasized even more strongly. The first verse (1:1) tells us, All wisdom comes from the Lord, and is with him forever, and as noted above, we are told (1:8), There is one who is wise, and greatly to be feared, sitting on his throne. Then we have four statements of the relation between fear of the Lord and wisdom. First (1:14), To fear the Lord is the beginning of wisdom; she was created with the faithful in the womb. Second (1:16), To fear the Lord is wisdom's full measure; she satisfies men with her fruits. Third (1:18), The fear of the Lord is the crown of wisdom, making peace and perfect health to flourish. Fourth (1:20), To fear the Lord is the root of wisdom, and her branches are long life, which in some manuscripts is connected in the next verse with the fact that to fear the Lord drives away sins. And later in his summary, he says (1:27), The fear of the Lord is wisdom and instruction, and he connects it with humility, not exalting oneself. In any case, we do find that where people wholly lose sight of the ultimate divine nature of wisdom, the sense of philosophy as love of wisdom begins to fade and the reasoning of men becomes puffed up with sophistry and wrangling, whereas even merely maintaining respect and humility before it preserves the possibility of true love of wisdom.
In pursuing this wisdom, we are imperfect, however, and, our perspectives and our grasp on wisdom being limited, human philosophies, however beautiful and brilliant, cannot be identified with wisdom in itself. They are, rather, at best cloudy mirrors. And at worst, people led by vanity and self-importance seize this or that aspect of wisdom, this or that intelligible truth, and without regard for all the others attempt to turn everything into it. Nonetheless, from all cases in which there is any of love's tendency to wisdom at all, much can be learned. As St. Clement of Alexandria says (Strom 1.13), just as the Bacchantes tore asunder the limbs of Pentheus, so the sects both of barbarian and Hellenic philosophy have done with truth, and each vaunts as the whole truth the portion which has fallen to its lot. But all, in my opinion, are illuminated by the dawn of Light. Let all, therefore, both Greeks and barbarians, who have aspired after the truth — both those who possess not a little, and those who have any portion — produce whatever they have of the word of truth. And where true lovers of wisdom, however the state of their knowledge and however far apart their starting-points, come together as friends from afar, much more can be gleaned, and we find, by coming together, a greater unity which our partial recognitions only approximate in limited ways, because we discover, on the basis of a mutual love of wisdom arising from a common human nature, that our partial recognitions are in some complementary. As John Paul II says (Fides et ratio, Intr.3), It is an innate property of human reason to ask why things are as they are, even though the answers which gradually emerge are set within a horizon which reveals how the different human cultures are complementary. But all these philosophical aspects, in varying ways and to varying degrees, with varying clarity and varying success, tend toward the divine wisdom; as Clement also says (Strom 6.17), The philosophers, therefore, who, trained to their own peculiar power of perception by the spirit of perception, when they investigate, not a part of philosophy, but philosophy absolutely, testify to the truth in a truth-loving and humble spirit; if in the case of good things said by those even who are of different sentiments they advance to understanding, through the divine administration, and the ineffable Goodness, which always, as far as possible, leads the nature of existences to that which is better. Taking it in this sense, we can agree with the comment by Friedrich Schlegel (Athenaeum Fragments 344), "Philosophy is a mutual search for omniscience."
When we consider the causality of the world, then, we find that there is a necessity for the final cause, and in particular for a universally superordinate cause that makes determinate the causality of natural things. When we consider the natural tendency of the intellect, which is to the intelligible, we find that there is a necessity for an infinite intelligible as that which is the end for the intellect. When we consider the love of wisdom as a preeminent natural expression of the intellectual nature, we find that there is a necessity for a universally architectonic wisdom. Each of these is related to the previous as more specific to the more general; thus we have seen that an ultimate end, infinitely intelligible, so as to be all-governing wisdom must actually be, based on natural causation, intellectual disposition, and philosophy itself.
Therefore from actuality and potentiality, from communication and participation, and from finality and tendency, we have more than adequate reason to hold that there is something divine. However, for the completion of this demonstration, there are a few additional things that need to be considered, namely, the relationship of these arguments to each other, possible objections to their conclusion, what can be known from these arguments, and how we can speak of the divine on the basis of these. To these we will turn.
* Nicolas Malebranche, Dialogues on Metaphysics and on Religion, Jolley & Scott, trs. Cambridge University Press (Cambridge: 1997).
** Nicolas Malebranche, The Search after Truth, Lennon & Olscamp, trs. Cambridge University Press (Cambridge: 1997).