Does A=A?
Posted: June 2, 2012 | Author: Nate Shannon | Filed under: Article | Tags: Apologetics, Logic, Metaphysics, Rationality, Truth, Vern Poythress | Leave a comment »Is A=A, the “law of identity,” true?*
The law of identity, written as ‘A=A’, is among the most basic principles of logic and reason. But is it true? We assume that it is. Philosophers and logicians do too, and they will say that it is ‘necessarily’ true. They’ll say “it must be true” or “it cannot be false” or “it is true in all possible worlds.”
So is A=A “necessarily true”, or true in all possible worlds? That depends on what a possible world is. Often, possible worlds are defined implicitly or explicitly as complete, logically coherent states of affairs. In that case, A=A is true in every possible world just as there are dogs in every possible world in which there are dogs. It’s true simply by stipulation, that is, because we say so. That’s not much help.
Suppose we rephrase the question, “is it necessarily true?” and ask the more prosaic, “is it true?” Is it true that A=A? This way we’ll be able to approach more broadly and more cautiously the question of the truth of A=A. (I will avoid referring to it as the “law” of identity, since it’s status as law is under question here.)
A Literal Take on A=A
Let’s consider two ways A=A could be taken. First, a “literal” way. A=A means, quite literally, the self-identity of the first letter of the Latin alphabet, as represented, the capital ‘A’—as in, “the letter A is the same as the letter A.”
This literal or simplistic read has some advantages, e.g., that’s what it looks like it’s saying. Disadvantages are that, first, it might not be strictly true. The Latin letter A, even in this upper case form, is an abstraction; it’s the type whose tokens are, written or spoken, here or there, now or then, innumerable and distinct. So two more options emerge.
To say A=A might be to say that all instantiations are of the same type, or that the type is self-identical. That might sound good, but then there is the problem of identifying the type. Or it might mean that this instantiation of A is identical to this one over here, this second one; and it will be obviously false in that case, if we take it to mean that one instantiation of A, one token of the type, is identical to the other.
A second disadvantage is that no one takes it in this literal way. And a third: the literal way of taking it means that the proposition it represents (as opposed to the sentence) is specifically and exclusively about a single letter from the Latin alphabet (whether type or token), which is a fixed and concrete referent (or at least it has an exclusive distribution). So the second disadvantage probably explains the first: no one interested in the so-called ‘law of identity’ wants to focus his energy on a fixed and concrete referent for A.
The Formal Take on A=A
A second way to read A=A is to take A not as representing itself, but as a nameless stand-in, a variable, a contentless placeholder, and this is how it’s usually taken. Of course “A” is not a nameless, contentless something, as we’ve seen: it’s a particular letter from a particular Western alphabet. But we’ll pretend to ignore that, because we’re only interested in its function, not its identity; we’re interested in form rather than content.
Well, is it true? Fortunately for us, A=A makes a very simple claim, so it shouldn’t be too difficult to discover whether it’s true or false. All it says is that A is the same as, identical to, and for all practical purposes interchangeable with A. Simple enough.
We’ll self-consciously stick with our second approach to A=A, foregoing the concrete identity of the letter A and thinking instead exclusively in terms of its function as a variable or placeholder. In that case, instead of asking “is A the same as A,” we should ask, “does A stand-in for the same thing that A stands-in for?” or “does A always represent the same thing?” In other words, we need to know whether there is equivocation. If there is equivocation, A=A is false; if there is not, A=A is true.
Is there equivocation in A=A? Sticking strictly to our second, formal read of A=A, we are forbidden from answering that question. In order to say whether there is equivocation, we’d have to know the referent, the meaning, the content; but we have determined that we don’t know that, or that there isn’t a particular referent, because we’re taking things strictly formally. If there isn’t a referent, or if we can’t say whether there is or what it is, what of our question?
Assuming Truth
To some degree, notice, we’ve already called into question the sufficiency of formal validity for validity simpliciter. In other words, pure form may contain internal limitations that raise doubts about formal validity.
But the point is, we can’t say whether A=A is true, without, that is, some knowledge—or some assumption, at least—about what A refers to. Philosophers generally agree that A=A is true. In fact, they very often say things like “it is necessarily true,” and “it cannot be false.” Thus the rubric of the “law” of identity. Is there an assumption here? I think there is.
The assumption is that in both instances, A refers to the same thing. Assuming that, A=A is true, at least once. But the assumption is more than that; if A referred to the same thing in two instances, it might not be necessarily true. It would have to be true in all instances. And how many instances of A are there? Innumerable, limitless instances. And the claim that A=A is necessarily true and is never false is inseparable from the claim that A always—in innumerable, limitless instances—refers to the same thing. Of course, of all those instances—innumerable as they are—we know of only an infinitesimally small percentage. Strictly speaking, according to a purely formal read of A=A, we don’t know of any, but even if we cheat a little, our acquaintance with the referents of A is immeasurably small compared to the total number, which is immeasurably great. The epistemic right was have to speak about the truth of A=A is perpetually more presumptuous than we care to admit, and the philosopher’s claim that A=A is always true is, we can now see, not only purely stipulative but quite plainly a claim to infinite, unlimited knowledge.
And the claim that A=A “cannot be false”, that it must be true, is even more audacious. It’s difficult to see any grounds for a legislative decree of that kind. Why on earth, by what standard, must A always refer to the same thing? What then of the “necessity” of the so-called “law” of identity?
So it would seem that the law of identity is a claim which, logically speaking, we can live neither with nor without.
*I am very much indebted to Vern Poythress’ work on logic, including his 1995 article in the Westminster Theological Journal, “Reforming Ontology and Logic in Light of the Trinity,” and his forthcoming book on logic (Crossway, 2013), particularly Part I.C. The Problem of Classification.
Review of Brian Davies, Thomas Aquinas on God and Evil
Posted: May 30, 2012 | Author: Nate Shannon | Filed under: Book Review | Tags: Problem of Evil, Thomas Aquinas | Leave a comment »
Brian Davies, Thomas Aquinas on God and Evil. OUP, 2011.
This is a tremendous little text. It is eminently readable and substantive, clear and efficient but not superficial. Although the problem of evil is not the first topic for which we would think to turn to Aquinas, this friendly volume would be an excellent read for anyone—philosopher, theologian, the fabled interested lay reader—looking for a inviting primer on the towering doctor of the Roman church.
Davies’ purpose is simple: to reconstruct Aquinas’ views on God and evil. Since Aquinas, Davies explains, “never offers a stand-alone discussion of what contemporary philosophers have come to call the problem of evil,” and, on an initial read at least, it appears that “what now passes as the problem of evil goes unmentioned in Aquinas’ writings,” Davies must “engage in such bringing together so that you [the reader] can see what Aquinas actually does think with respect to the topic of God and evil” (6). Lucky for the reader, Davies, an expert on Thomas, offers masterful if introductory expositions of a handful of relevant Thomistic teachings including “what he takes the world to be, what he takes God to be, how he thinks of God’s relation to the world, how he approaches the notion of divine providence, and how he thinks of God’s goodness (both in itself an in relation to us)” (6-7). Additionally, “this piecing together needs also, and crucially, to take account of things that Aquinas says with an eye on what he takes to be Christian revelation” (7).
And that is largely the sum of what happens in the text. Davies’ treatment is, needless to say, only introductory, and it is purely expository. He makes no effort to defend Aquinas’ views—qualifying phrases like “so Aquinas thinks” are ubiquitous—and he makes no effort to engage in the interpretive disputes that keep Thomas scholars busy. One might be tempted to attribute Davies’ elusion of the important questions raised in secondary literature or Davies’ reluctance to take an evaluative stance to any of a number of less charitable takes on the author’s effort here: the text is superficial or the author ignores interpretations at odds with his own or is entirely ignorant of them or the work just isn’t at the scholarly level—but none of these is true of this volume, that I can see. Thomas Aquinas on God and Evil aims to be a careful and accurate report of Aquinas’ views on the problem of evil—or whatever his views would have been, had he addressed the problem in its modern permutation—that clarifies all the relevant Thomistic teachings for the reader completely new to Thomas. Only a real master of the subject matter could achieve something like that, in less than 150 pages and in graceful, winsome prose to boot. In my view, the text achieves its goal and makes it look easy.
I have elected not to provide a summary here of Aquinas’ views on evil for a couple of reasons, the main one being that I don’t think it’s necessary to do so in a review of a book of this kind. To respond to the views explored in it would be to respond to Aquinas, but Aquinas didn’t write this book. Had Davies pieced together Aquinas’ views on evil in order to defend a modified Thomist answer to the problem, for example, or to engage in a study of the internal consistency of Thomas’ thought or to provide an alternative to another secondary source, a review might be expected to offer both summary and some critical interaction. I might also be more inclined to engage the content of the text more directly if I knew Thomas and Thomas scholarship well enough to spot distinctive interpretive decisions on Davies’ part, but I do not; and thus, once again, the beauty of this little text: it is a most welcoming introduction to the thought of Aquinas. I will add one personal thought, however: as a Reformed reader, I was struck, as I often am when reading Thomas or reading about Thomas, by this: the analytical genius and ingenuity of Thomas’ bold and freely speculative theological style.
Anderson and Welty’s Ambiguous Necessity
Posted: May 24, 2012 | Author: Nate Shannon | Filed under: Response/rejoinder | Tags: Apologetics, Greg Welty, James Anderson, Metaphysics, Philosophia Christi, Presuppositionalism, Transcendental Argument for the Existence of God | 2 Comments »In their argument for the existence of God from the laws of logic,* James Anderson and Greg Welty (AW) claim that the laws of logic exist necessarily. Their claim is that the laws of logic possess de re necessity, the type of necessity—metaphysical necessity—predicated of objects. How do they get there? They don’t, in my view, and their oversight is a smooth ambiguity between de re and de dicto necessity.
In sum, the relevant portion of their argument proceeds thus: they say that the laws of logic are necessarily true. Then they say that the laws of logic are propositions, and that propositions exist; that is, propositions are not merely nominal (existing in name only) but have real existence, they are actual things. If a proposition is necessarily true, and propositions are things, a necessarily true proposition is a necessary thing, a thing that exists necessarily. In this argument, the propositional property of being necessarily true is replaced by de re necessity, necessarily existing; but these are not the same thing at all, and even though this is an essential step in their argument, AW make no argument specifically for the de re necessity of the laws of logic. Indeed I think evading that responsibility was prudent; such an argument would face considerable difficulties.
So a proposition that is necessarily true is not the same thing as a proposition that exists necessarily, not at all. AW confuse the two. De dicto and de re necessity are slyly swapped one for the other, and AW’s argument slips quite smoothly, they suppose, from the realm of contingent being to the realm of necessary being; but the transition is spurious. We can see this in a couple of ways.
One way to see this is simply by drawing a clear distinction between propositions and their objects—what propositions are ‘about’—and understanding how exactly the two are related. We’ll see that propositions are distinct but inseparable from their objects, and that the modality they attribute, necessity in this case, is distinct from the modality or the necessity they possess.
Is the law of identity (A=A) necessarily true? I think there are important theological issues to consider before affirming, in the strongest sense, that it is; but for now, suppose that it is. What would make the proposition ‘necessarily, A=A’ true? It would have to be the case that necessarily, A=A. A’s being necessarily identical to A is the necessary condition of the law of identity’s being necessarily true; and since the latter is essentially dependent upon the former, the proposition on the state of affairs, clearly they are distinct. The important difference between the two is that the law of identity has de dicto necessity, while A’s being identical to A has de re necessity.
A proposition is essentially ‘about’ something, as AW note; propositions are essentially intentional. (This quality of intentionality or ‘aboutness’ serves AW as the link between propositions and personal minds.) So a proposition is essentially parasitic on the thing it is about, on that thing or state of affairs obtaining, being true, being actual, or whatever. The law of identity is the attribution of de re necessity to the state of affairs A=A, but the attribution itself—the law, the proposition—can have only de dicto necessity.
AW affirm that propositions exist, in an attempt to make them more like the sorts of objects that can have de re necessity; but this is irrelevant: real existence does not change the fact that the modality of propositions, just like the truth value of propositions, and even the essence itself of a proposition, is derivative and dependent upon a state of affairs distinct from any proposition ‘about’ that state of affairs. Affirming the real existence of propositions does not change in any way the intentional—i.e., derivative—nature of propositions; neither can it change the sort of necessity that a proposition might have.
Now a second way. AW also confuse de re and de dicto necessity by failing to distinguish between a proposition’s being true at a possible world and a proposition’s being true in a possible world. To be true in a possible world, a proposition must exist in that world; to be true of or at a possible world, the proposition must only describe that world. A proposition can be true of a possible world without existing in it. AW blur this distinction: “. . . the law of noncontradiction is true not only in the actual world but also in every possible world” (325). The first clause ascribes de dicto necessity to the law of noncontradiction; but to say, in the second clause, that the LNC is true in every possible world rather than at, is to affirm that it exists every possible world; and this is to affirm both de dicto and de re necessity without distinguishing the two. The next sentence reads: “There is no possible world in which that logical law is false (or fails to be true in any other way)” (325-6). Here again, de dicto and de re are confounded. If there is no possible world in which the law of noncontradiction is false, it does not follow necessarily that the LNC is true in all possible worlds. For to not be false the law does not have to exist; it might not exist at all and still be ‘not false’. But to not fail to be true, it must exist. A proposition’s not being false does not imply that proposition’s necessarily existing. They follow this a short time later by saying, “we would simply invite you to reflect on whether you really can conceive of a possible world in which contradictions abound” (326). The challenge has no bite, since the nonexistence of the LNC does not imply a world of contradiction. The best way to think that it does is to confuse de re and de dicto categories and to think that true in all possible worlds is the same as true of all possible worlds. To be true in a possible world, a proposition must exist in that world; to be true of a possible world, the proposition must only describe that world, but might not exist in it.
And now a third way. What about the possible world at which God chooses not to create, and he alone exists? De dicto necessity, maybe; de re, no.
To be charitable, we might grant strong de dicto necessity of some propositions. To see how, take the most difficult case, conditional propositions—most difficult because they appear to make no metaphysical investment. Take the proposition If all men are mortal, and Socrates is a man, then Socrates is mortal. Is this proposition necessary de dicto, de re, or both? It appears to be true that, at all possible worlds, even worlds in which neither men nor Socrates exist, if all men were mortal, and Socrates was a man, he would be mortal too. At, I think, even the possible world which consists of only God, the possible world in which God chooses not to create, this proposition would be necessarily true—at that world, that is, of it. For certainly God could bring it about that both components of the antecedent obtained, and if he did, then the consequent obtains as well.
The proposition does not have de re necessity, however; it does not exist necessarily, because it does not exist in the possible state of affairs which is only God: God necessarily thinks only himself. That is, according to the doctrine of divine simplicity, God’s mind and thoughts are identical to his being; the only necessarily existing thing, because God did not have to create, is God himself; thus God does not necessarily think anything other than himself. No thought content can be imputed to God, lest we imply the thought content to be on a metaphysical par with God himself. The proposition in question, the LNC, is of course not a part of the essential being of : it is not God. So we might grant qualified de dicto necessity of a proposition: the proposition is true in every world in which it exists; but we are not obligated to grant de re necessity to a necessarily true proposition. Neither obligated, nor, indeed, even encouraged—there appears to be no reason to do so.
AW do so nonetheless. They say propositions are real entities (they exist); the proposition A=A, or whatever law of logic, is necessarily true; therefore, A=A exists necessarily. But this simply doesn’t follow. The modality of any proposition, specifically the modality of it’s truth value, is de dicto only, and derivative of the modality of the objects the proposition is ‘about’. De dicto necessity is distinct from de re necessity, and propositions are things essentially de dicto; with one exception only: God’s speaking has de re necessity; his word is truth (Jn 17:17) and necessarily accomplishes its purposes (Isa 55:11).
This ambiguity is worked fairly tightly into the argument AW offer. They say that propositions exist necessarily and that propositions are essentially thoughts (because essentially intentional). They conclude that there must be, therefore, a necessarily existing mind (one or more). Interestingly, there is no reason that AW have opted to emphasize the ‘necessity’ of propositions at the expense of the essential intentionality of propositions rather than the other way around, except, perhaps, that it is the better of the two options for their argument. By de-emphasizing intentionality, a wedge labeled ‘necessity’ is driven between the laws of logic and the things they are necessarily ‘about’. By thus popping them loose from the tangible world, this procedure gives the wildly false impression that the laws of logic must exist, world or no world. This is what I meant when I said above that AW hope by this maneuver to step from the realm of contingent being to the realm of necessary being, but it can’t be done. Had the balance been maintained between necessity and intentionality, or between the form and content, of propositions—of, in this case, the laws of logic—a truer estimation of the nature of propositions would have remained in view. It also would have been clear that no propositions exist necessarily, save those essential to the only necessarily existing thing: the eternal, triune, simple, a se God.
*James N. Anderson and Greg Welty, “Lord of Noncontradiction: An Argument for God from Logic,” Philosophia Christi 13 no. 2 (2011). I’ve written a more complete response to this article here.
What’s in a name? Image Nominal Realism
Posted: May 19, 2012 | Author: Nate Shannon | Filed under: Article | Tags: Apologetics, Metaphysics | Leave a comment »Intro
In this post I will introduce what can only be the initial stages of what I shall call image nominal realism, a form of realism (of universals or classifications) based on the doctrine of creation and particular features of Genesis chapters 1-2, esp. 2:19-20. I cannot provide a full account of this proposal here, of course, nor would anyone want me to, much less a careful defense of it. However, what I hope is the distinctive attraction of image nominal realism, that it seeks—maybe even finds—a biblical path between the horns of nominalism and realism, should be clear enough.
Before getting to the proposal itself, I want to say that there will be points at which the question may be raised whether the Bible speaks truly or literally rather than metaphorically about God. I will, for example, point to the mention in Gen 2:19 of God bringing the animals to Adam, “to see what he [the man] would call them,” as the text says. So the obvious question is how we should understand this ascription of a particular rational strategy on the part of God to find out what Adam would do (suggesting that God does not know). I will simply take the Scripture as speaking ‘truly’ insofar as, whatever the passage means, neither the omniscience of God (of even future contingents) nor the sovereignty and providence of God (even over future contingents, including the determinations of the human will) nor the genuineness of Adam’s freely naming the animals are impugned. In other words, I am aware of the purported difficulties anthropomorphisms such as God’s waiting to see what Adam will do present. Since they appear to present no difficulty for Scripture itself, whatever it says here must be a priori consistent with what is says everywhere else—namely, that God is omniscient and sovereign and that man is responsible for his always religiously and ethically significant choices. Anyway, this is standard Reformed stuff.
Regarding image nominal realism, this line of thought occurred to me in conjunction with a paper written by a friend, Paul Maxwell. In that paper, Paul speaks of the prophetic nature of language in Gen 2:19 and distinguishes between the archetypal prophetic—creative ex nihilo—language of God and the ectypal prophetic language of Adam in giving names to things. In Adam’s naming the animals in Gen 2:19, he is exercising, even fulfilling (in part) image- or vice-regency in the garden of God. This is clear from the larger context of the imago Dei language (Gen 1:26-7), from the broader testimony of Scripture to the vice-regal role of man (of which Adam and Christ are the two paragon figures), and from the immediate context: Gen 2:18 says that the whole scene unfolds for the purpose of finding a helper ‘fit’ for Adam or ‘corresponding’ to him. That relationship may be viewed, I suppose, as a reflection of the original eimi/eikon or archetype/ectype relationship between God and man: man as imago Dei, the helper as the image of Adam (Gen 2:23—“bone of my bones and flesh of my flesh”—certainly conveys this kind of relation). That’s mouthful. All that is to say that Maxwell brought careful attention to the characterization of Adam’s naming as ectypcal and patterned after the archetypcal or original creative speech of God. Here I will look first at the archetypal/ectypal relation, focusing on the image status of Adam’s naming the animals. Then I will move on to say something about the ontology of those names.
Exegesis of Adam as Image-king in Naming
There a number of broad biblical theological considerations relevant to understanding the first man’s unique role as image-king, not least of which is the corporate-covenantal structure of biblical eschatology (and then of soteriology). For now, we may focus simply on the two verses that tell the story of Adam’s naming the animals.
In Gen 2:19 we are reminded that “out of the ground the LORD God formed every beast of the field and every bird of the heavens.” Why this abrupt reminder of the events of the previous chapter? Notice that without it, the passage would move from God’s deciding to find a helper fit for Adam, to Adam’s cataloging each section of the parade of lower beasts that marches before him. The indication would be that Adam’s naming the animals was incidental to his looking for a helper. But add the reminder: “out of the ground the LORD God formed every beast of the field and every bird of the heavens,” and it becomes the obvious theme of the passage that Adam is naming God’s creatures; what God brought into being from nothing by the power of his word, Adam names, categorizes, and, in a sense, subjects to his own image-dominion by the derivative power and authority of his own speech. However we might put it, what strikes the reader of this passage is Adam’s creaturely imitation of the creative speech of God.
God’s self-conscious bestowal of image-regency is clear from at least the following two points. First, God “brought them to the man to see what he would call them,” and “whatever the man called them, that was their name” (2:19). However we parse the details, clearly the idea here is that God delegates to Adam the naming—categorizing, classifying—of the animals.
Remember of course that God had created not only individual animals but kinds as well. This is clear enough from the text. The animals (individuals) are created and multiply according to their kinds. And now Adam sits on his tiny, spatio-temporally limited image throne and obediently, re-creatively re-constitutes the animals and their kinds, according to his own level of (derivative) knowledge and (derivative) being.
Secondly, Adam’s unique status as image-regent is also evident in the fact that among all the creatures of the earth, a helper fit for him was not found. Adam finds himself unique among creatures. God then creates a helper for Adam, but not by mere fiat: he creates her ‘from’ or ‘out of’ Adam. Eve is Adam’s ectype. The Creator/creature distinction—the original archetype/ectype distinction—cannot be reproduced; but on the created level, Adam’s helper is his image. This is indeed a profound mystery (Eph 5:32), but surely one thing clear from this passage is Adam’s unique identity as the image-regent in the garden of God.
The Ontology of Adam’s Naming
So far we have seen a distinction between God’s original being and action and creaturely being and action in terms of dominion over creation and in terms of creative speech. To draw attention to aspects of this distinction is simply to articulate the Creator/creature distinction in terms of the specifics of Gen 2:18-20 and Adam’s activity in terms of his identity as imago Dei. And we can be even more specific still; we can accordingly fill out the ontology of creaturely kinds as well.
As mentioned, God created both things and kinds. The things that swim and swarm and creep and crawl and fly are of kinds (kinds per se do none of these things), according to which they multiply. As a prelude to Adam’s presiding over the parade of animals, we are reminded of God’s sovereign and free creation of these things and their kinds. This reminder conspicuously sets the stage for Adam’s naming as derivative, created, image-naming. Adam’s naming the animals is image-naming; it is re-interpretive, re-creative, and subordinate to divine creative speech.
Adam’s naming does however bear a quality of newness and originality, as the text appears to acknowledge: “. . . whatever the man called every living creature, that was its name. The man gave names to all livestock and to the birds of the heavens and to every beast of the field” (2:19-20).
Amplifying this quality of newness in Adam’s naming activity is the significance of naming, esp. as seen in the Old Testament. Places as well as persons are given names which capture their significance. They are called what they are and what they mean for the person naming them, often in explicit religious self-consciousness. Just after our passage, the woman will be called ‘isha‘ because she is taken from ‘ish,’ (2:23) and then later “Eve, because she was the mother of all living” (3:20). Soon “she conceived and bore Cain, saying ‘I have gotten a man with the help of the LORD,’” (4:1) where ‘Cain’ is associated with the Hebrew word for ‘gotten,’ and then “she bore a son and called his name Seth, for she said, ‘God has appointed for me another offspring instead of Abel . . ,’” (4:25) where ‘Seth’ is associated with ‘he appointed.’ And so on. Readers of the OT are familiar with this.
Think now of Adam’s naming the animals. Naturally the names given to the animals had to be somewhat less dear to Adam than the names of Adam’s own sons; nonetheless we may assume that Adam called the animals according to their nature as he understood it. Perhaps, as Eve had conceived of the names of Cain and Seth in terms of the witness they bore to God’s activity, Adam also named the animals according to God’s activity relative to them, original creation. I cannot conjecture what kind of names those would have been; perhaps one animal exemplified the gentleness of God, another God’s attention to every detail of creation, another his majesty or his beauty; but we can surmise that Adam’s naming of the animals (1) is an original and sovereign bestowal of identity, and (2) was likely carried out in acute awareness of God’s sovereign activity in creating the animals, and, perhaps, (3) was an exercise of pious and obedient acknowledgment of the ethically loaded image-role Adam bore, as communicated to him by so many features of his environment.
Specifically now, Adam’s names or categories are twice created: they are (1) irreducibly of the created order and thus in a fundamental way brought into being by the free creative speech of God, and (2) they are brought into being by the free creative activity of man. To put it another way, there is archetype/ectype ambiguity in terms of the “creativity” of Adam’s speech. God’s creating activity is unique; it is ex nihilo. Man does not create in this sense. But it would appear that he does more than simply manipulate pre-existent stuff: “. . . whatever the man called every living creature, that was its name.” So Adam is creative, and the names he gives are original. But he is not creative in the sense that he creates something utterly (ex nihilo) original, as only God can do. We should understand Adam’s activity as neither the same (univocal) nor utterly distinct (equivocal) from God’s activity, but like it in some ways, on a creaturely level, and unlike it in others (analogical); Adam is imago Dei.
So Adam creates kinds; but he can, strictly speaking, only re-create. So we ask, what is the relationship between God’s original things and kinds and Adam’s derivative things and kinds? Adam’s cognitive states are never identical to God’s. Even when Adam has true beliefs or thinks truly about things—meaning that his grasp of some thing or attitude toward it is consistent with God’s—his cognitive content is never identical to God’s. His knowledge may be be true, as far as it goes, but it is always creaturely (finite, derivative, and subject to error [non-sinful error at this point]). The same, then, should be said for Adam’s names: they are derivative, finite, subject to error and change. They may be no less magnificent than other creations of man—works of art or feats of engineering—no less insightful, no less utilitarian; but being no more than man himself, and being essentially of the created order, they are mere image-names.
Finally, worth noting is the coincidence of three things or events: the animals themselves, Adam’s utterance of the given classifications or names, and Adam’s cognitive content. I am inclined to think of this coincidence as an original moment or unity to which we may refer when questions of ontology arise: in answer to the question, ‘what is a proposition?’, we would be able to deny that a proposition is essentially divorced from either utterance or employment in reason (actuality) or individual entities, while affirming that it is something real.
So what is a name or a universal? It is an image-designation, re-interpretive of the divinely created original, that is distinct but essentially inseparable from utterance, instantiation, and cognitive content. Since a name is distinguishable from those original factors, we may speak of it in distinction from them; since it is essentially inseparable from them, we are ultimately untroubled by worries about abstract ontology. Yes, a name is abstract, but not essentially.
In sum, the two essential components of image nominal realism are the image status of Adam’s naming, including both metaphysical and ethical dimensions, and the original coincidence of the various elements of naming: the entity itself, the utterance, and the cognitive content.
Response to Anderson and Welty, “Lord of Noncontradiction”
Posted: May 10, 2012 | Author: Nate Shannon | Filed under: Article, Response/rejoinder | Tags: Apologetics, Greg Welty, James Anderson, Metaphysics, Philosophia Christi, Presuppositionalism, Transcendental Argument for the Existence of God | 1 Comment »In a recent article in Philosophia Christi, entitled “The Lord of Noncontradiction,” authors James N. Anderson and Greg Welty argue that “the very idea of logical laws presupposes the existence of God” (338). They claim, in sum, “one can logically argue against God only if God exists” (337).
I appreciate what AW do in this article, and I think their argument has a number of strengths. I endorse wholeheartedly their conclusion, with the caveat that “God” refer only to the triune Christian God (AW use the term more loosely in this article.). And I agree, for example, that for the consistency and reliability of the laws of logic, to account for the necessity of the laws of logic, in other words, those laws must be understood as consistent with the nature of a necessary being. And that’s just where I would part ways with AW: the laws of logic are consistent with the being of God—God is the standard and original of self-consistency, not the other way around; and unfortunately AW’s argument does things the other way around. AW’s argument maps the necessity of the laws of logic onto the nature of the necessary being. The result is a vague and spurious theism. The exact misstep, in my view, is AW’s incorporation of a univocal notion of necessity, and by implication, of being. Their argument reads an awful lot like a cosmological argument that affirms the abstract necessity of sufficient causality, for example. If there is an effective transcendental argument here, it is this: a univocal notion of being destroys true theism.
A fully Christian presuppositional approach would affirm triune theism and the essential distinction between the necessary being of the triune God, and the created, contingent being of everything else. Affirming the C/c distinction from the outset helps us see (1) the illegitimacy of a univocal notion of being, and thus (2) the need for self-consciously analogical notions of necessity and being. There is the necessity of the triune God, and there is created necessity, just as there is the necessary being of the triune God, and the contingent being of the created order. We affirm that the laws of logic are like God and revelatory of his nature—indeed, if God were not self-consistent, we could not know him; but the laws of logic themselves are not God. They are features of the created order intelligible in light of the a se, triune being of God; but they are only created analogues of the divine nature.
In this response, I will (I) summarize AW’s argument, (II) point to some of difficulties if faces, and then (III) briefly discuss Christian theistic analogical reason and the laws of logic.
I. Anderson and Welty’s Argument
They write,
In summary, the argument runs as follows. The laws of logic are necessary truths about truths; they are necessarily true propositions. Propositions are real entities, but cannot be physical entities; they are essentially thoughts. So the laws of logic are necessarily true thoughts. Since they are true in every possible world, they must exist in every possible world. But if there are necessarily existent thoughts, there must be a necessarily existent mind; and if there is a necessarily existent mind, there must be a necessarily existent person. A necessarily existent person must be spiritual in nature, because no physical entity exists necessarily. Thus, if there are laws of logic, there must also be a necessarily existent, personal, spiritual being. The laws of logic imply the existence of God (336-7).
And they add this footnote: “But not necessarily a unipersonal God; the conclusion of the argument is entirely compatible with Trinitarianism. Strictly speaking, the argument shows that there must be at least one necessarily existent person; it does not show that there must be one and only one necessarily existent person” (337 n.33).
Notice that logical necessity implies a univocal notion of possibility: there is only one kind of possibility, and that is logical possibility. When AW say, “the laws of logic are necessary truths about truths,” and that “they are necessarily true propositions,” they mean that the laws of logic could not have been false. So they say, “We cannot imagine a possible world in which the law of noncontradiction is false” (326). And,
we would simply invite you to reflect on whether you really can conceive of a possible world in which contradictions abound. What would that look like? . . . In any case, the very idea of a possible world in which the law of noncontradiction is false is arguably incoherent, because our notions of possibility and noncontradiction are bound up with one another. The criterion of logical consistency—conformity to the law of noncontradiction—is surely the first criterion we apply when determining whether a world is possible or impossible. The notion of noncontradiction lies at the core of our understanding of possibility (326).
The authors appeal to imagination: “we cannot imagine,” and “we . . . invite you to imagine.” I am not convinced that this appeal is necessary for their argument, but it is indicative of the metaphysical ceiling of a univocal notion of necessity. Nonetheless, notice that logical necessity implies a univocal notion of possibility; nothing that violates the laws of logic is possible, and only what is logical is possible. So far so good; univocity appears to have caused us no problems up to this point.
AW then argue that the laws of logic are necessarily true thoughts; they are true in every possible world, and they are thought in every possible world. If thought requires mind, there must be a mind in every possible world, at least one mind (perhaps as many as one mind per necessarily true proposition) at least as necessary as the laws of logic. And a mind, by definition, is personal. Nor up to this point has univocity caused any explicit problems, but I suspect this is a weaker point in the argument. One may be a realist regarding the laws of logic without committing to their being thoughts, the thoughts of one or more self-conscious minds.
The more critical reader might object when AW claim that propositions are thoughts. And it is tough to see the connection there. AW argue this point saying that the laws of logic exhibit intentionality, which is a distinctive feature of the mental (333-5), but I am not sure that this feature is consistent with the notion of necessity we are working with.
The laws of logic are what logicians call “statement forms,” they are forms without content. The law of noncontradiction says that it is never the case that both p and not p, or that it cannot be said of a thing that it both is and is not (in the same way at the same time). Symbolic logic might show it like this: ~(p • ~p). Now that is strictly formal; it has no content. It is a “statement form.” When we insert an actual proposition for p, we get an actual statement: “It is false that the Yankees play baseball and it is not the case that the Yankees play baseball.” For the laws of logic to be necessary, they must be without content, they must be formal; and by virtue of being formal, they are necessary, or true in all possible worlds.
So the laws of logic possess self-contained or self-reflexive directness, as long as they are necessary. The moment they are ‘about’ something other than themselves, they are no longer strictly necessary. So either the laws of logic are necessary or they have the sort of intentionality which is the ‘aboutness’ characteristic of the mental, but not both.
For example, God exists a se, which means that he is self-defined in his being and knowledge. That specifically means that he depends on nothing outside of himself for his being or knowledge, and thus that God is incomprehensible. The Reformed have traditionally said that the only object of God’s necessary knowledge is his own being, so the self-reflexive ‘aboutness’ of God’s knowledge is a function of the aseity of his being. (God’s self-reflexive being and knowledge are not purely formal, without content; he being and knowledge are triune and personal: Father, Son, and Spirit, self-reflexive being and knowledge.)
As AW affirm: there is no possible world in which the laws of logic are not true. This is because the possible is the logical. The only things strictly necessary in that case are the laws of logic; they need nothing else in order to exist. So is there a possible world in which only the laws of logic exist, and nothing else?
A mind, by definition they say, is personal. But necessity is the key attribute of this mind: it is necessary and therefore nonphysical, and it is necessary and therefore eternal. So because of necessity, this mind, or minds, is personal, nonphysical, and eternal—and that is, as Aquinas might say, what we call God. Here I think we have a problem, and the problem is more obvious if sufficient doubt can be raised about the connection AW draw between realism concerning the laws of logic and the existence of personal mind(s). Aside from that, the problem begins to emerge when we attempt to clarity the relation of logic to the mind(s), which we will do shortly. Here is how AW put it:
AW recognize that their argument requires that God eternally think the laws of logic. They say, “the laws of logic couldn’t be our thoughts—or the thoughts of any other contingent being for that matter—for as we have seen, the laws of logic exist necessarily if they exist at all . . . they can only be the thoughts of a necessarily existent mind” (336). And since the laws of logic are necessarily existent, God must essentially and eternally think them: “the laws of logic should be understood . . . as divine thoughts about the essential relations between divine thoughts. The laws of logic are nothing other than what God thinks about his thoughts qua thoughts” (337).
The univocity of AW’s notion of necessity has entailed a univocal notion of possibility—only that which is logically possible is possible. In other words, there is no possible world in which the laws of logic do not obtain. As we have seen, this notion in itself might present a problem for an essential step in their argument: necessity and intentionality are difficult to reconcile. Furthermore, the univocal notion of necessity is constitutive of the mind AW have discovered: necessity implies nonphysicality and eternity. And more importantly, it must be the case that this mind, in all possible worlds—that is, essentially—thinks the laws of logic. AW say that the laws of logic are God’s thoughts about his own thoughts. I think this notion is also problematic.
II. A Few Questions
A univocal notion of necessity, and consequently of possibility, is essential to AW’s argument for the existence of God. I have tried to indicate specifically some of the ways in which such a notion functions in their argument. I would now like to raise a few more questions about this proposal, questions which I believe raise the issue of the viability of an argument for the existence of God that presupposes a univocal notion of necessity.
I have two specifically theological concerns. The first is as follows. AW say that “the argument shows that there must be at least one necessarily existent person,” but not that “there must be one and only one necessarily existent person.” The argument, they point out, “is entirely compatible with Trinitarianism” (337 n.33).
To find in the end that the conclusion is ‘not incompatible with the truth’ is a bit of a let down. Any notion at all of one or more necessary or transcendent mind(s) enjoys the full support of this argument. So the conclusion does not do much to commend AW’s approach to presuppositional or transcendental arguments, and indeed falls well short of a presuppositional argument for Christian truth, which is supposed to presuppose Christian truth. AW say, “one can logically argue against God only if God exists” (337). To avoid ambiguity, it should read “one can logically argue against X only if X is true, where X is Deism, any form of monotheism or any form of polytheism—as many necessary minds as you like—theistic pluralism, pantheism, absolute idealism, and maybe even a theory of religious self-projection.” AW note that “naturalists eager to evade the force of a theistic argument will hardly find a comfortable refuge in Absolute idealism” (336 n.32). But an absolute idealist sure might. And AW are too modest: the naturalist might be eager to evade the force of their argument, but he might not be able; if their argument persuades him, he may well become an absolute idealist.
I think rather that the deflated conclusion is indicative of a specific presupposition, univocal necessity, and by implication, univocal being. To show how, we might ask how would we go on to argue that this mind is triune and a se, rather than singular or plural or just our own (see 336 n.31) or that logic itself is independently eternal or whatever else. Is triunity presupposed by the laws of logic (univocally conceived), or would we have to introduce revelation? And if we turn to revelation at that point, why bother with the argument from logic? Or, do the laws of logic imply the self-revelation of God? Do they presuppose the voluntary condescension of the eternal, a se, triune, personal God? Do the laws of logic even allow for such a God or for divine condescension? If they do not, it would seem that presupposing a univocal notion of necessity has stranded our theologizing in the created order. But anyway, the conclusion of AW’s argument is so vague that if commending Christian truth is our goal, clearly the hard work—actually all of the work—is still ahead of us.
This leads to my second theological concern. AW say that the laws of logic are “what God thinks about his thoughts qua thoughts” (337). When they say “thoughts qua thoughts,” they mean to indicate the purely formal nature of the laws of logic.
What does it mean that God has purely formal thoughts about his thoughts as thoughts? I find this confusing in the following way. If God has second order thoughts about his first order thoughts, which is what this appears to mean, does he then have third order thoughts, thoughts about his thoughts about his thoughts? God would be a philosopher of logic in that case, thinking abstractly, and maybe even nonlogically (if they are truly third order thoughts rather than still only first order thoughts) about the nature of the law of identity, the law of noncontradiction, the law of the excluded middle, whatever else. This is incoherent. There are no nonlogical thoughts, AW might say. So only first and second order thoughts—thoughts and thoughts about those thoughts—are possible. So how can God have third order thoughts, and then maybe fourth, and so on? Clearly he cannot.
What about this alternative: God does not think about his thoughts, but he is in some sense aware of the logical consistency of his own thoughts. If we charge AW with ambiguity in their use of the term “thought,” we can take this route. Indeed, this approach sounds better, and avoids the weird regress of thoughts about thoughts about thoughts. God is conscious of his intellectual self-consistency.
However this is not what AW claim. They claim that God has second order thoughts which are themselves the purely formal laws of logic, which have as their content God’s first order thoughts. But then those thoughts are not purely formal; they have content other than themselves. Their content is God’s first order thoughts, which are thoughts with content. More precisely, first order thoughts are their content. God’s thoughts must be their own content, unless we affirm that God thinks essentially about something outside of himself, which could be only one of two things: nothing or creation. If God essentially thinks nothing and then thinks the laws of logic about those thoughts, God is only logic, logic is God. If God thinks essentially about something created, he must have created himself, or God and the world exist correlatively and are both eternal. For this reason, I suppose, AW say that God’s second order thoughts are about God’s first order thoughts as thoughts. But God’s first order thoughts are never just thoughts; only the second order are. The only alternative remaining is this: abstract self-reflection is a feature of the first order as well, so that there are, essential to God, thoughts about thoughts that God then thinks about. We would then have three tiers of divine thoughts again, and the third is redundant. One final question: what are God’s thoughts, anyway? What are those thoughts about? What is the stuff that God extracts from his thoughts in order to think about them as thoughts? And why are we supposing that God has those first order thoughts anyway? Maybe he does not.
All that aside, AW claim that God has thoughts, but then he also has thoughts somewhat like this: “self-consistency.” Strange, I think. But what if God does not think about his self-consistency, for just a moment? What if he does not objectify his self-consistency and think about it, and instead he merely has self-consistent thoughts? What if he has no second order thoughts and instead just thinks himself, but not about himself? Would the laws of logic exist at that moment?
If we may distinguish between transitive and intransitive self-consistent thoughts, which the laws of logic claim to do anyway, we would be able to posit a possible world in which God is not thinking the laws of logic explicitly, while he could still both exist and think in perfect self-consistency. I think that we may make this distinction, and so posit such a world; and at that possible world, God is necessary but the laws of logic are not necessary in the same way as the being of God is, but only as abstract and analogical (creaturely) theological reflection. They are necessarily true because the self-consistent being of God exists necessarily, but they are not necessarily thought, and they cannot be true when they are not thought, as AW affirm.
It is not only possible to affirm intransitive divine thoughts about anything essential to God, in light of the doctrine of divine simplicity, it is an orthodox imperative to do so. To say that God thinks objectively about the laws of logic is to say that the laws of logic are objective relative to God’s being, and exist outside him. This violates simplicity, which denies distinctions between God’s thought and God’s being. This is clearly not what AW are arguing, so, again, we must affirm that the laws of logic are a kind of intransitive, essential self-awareness in God. And now the problem.
According to the doctrine of divine simplicity, God’s thoughts are one with his being. Indeed AW think this much is true of any mind: “. . . thoughts belong essentially to the minds that produce them” (336 n.31). So if we think thoughts that are essential to God’s being—exactly those thoughts that God thinks about his own thoughts—are we not participating in the divine essence? If we affirm simplicity, in other words, we either flirt with pantheism or we must deny that our thoughts are ever identical to God’s; we must deny univocity of thought; or, hoping to maintain simplicity and the C/c distinction, we may say that the laws of logic are abstract objects existing independently of both God and man. In that case, perhaps God knows the laws of logic in all possible worlds because he is omniscient in all possible worlds and the laws of logic exist in all possible worlds, not because he essentially thinks the laws of logic. If that were the case, logic, existing a se and governing God’s thoughts and actions from without, would be as much God as God is, perhaps more so. Even more troubling is this question: would we be able to affirm in this case that God’s being is essentially coherent and self-consistent, and that, therefore, divine revelation is also coherent and self-consistent? Or might not God be in at least one possible world illogical or inconsistent, even in his very essence?
Divine simplicity hardly lacks sustained critique in the literature today, nor abstract objects able defenders, nor the self-consistency of revelation committed advocates. So what is the problem with these alternatives? Their significant disadvantage is that they both (1) are plainly heterodox, and (2) enjoy the full support of AW’s argument. AW’s argument—univocal reason, specifically—is not consistent with orthodox trinitarianism, as they claim, but sharply opposed to it. Their argument proves a God neither biblical nor confessionally orthodox, nor, to be sure, worthy of the name.
Finally, I disagree that the laws of logic are true in all possible worlds, or that the laws of logic are necessarily true in the univocal sense. It is possible that God choose not to create. Odd to say, but there is a possible world in which there is no (spatio-temporal) world and the only state of affairs is the Triune God. At that world, there would be only God. What would the laws of logic look like in case there was only the eternal, a se, triune God? In essence, what is the relation of logic to being of God?
III. Christian Theistic Analogical Reason and the Laws of Logic
Let us back up for a moment. AW’s argument recognizes the basic features of the laws of logic—they pinpoint the unique characteristics of the universal laws of thought, that these laws are universal and necessary, that they are abstract, but that they are also personal. They recognize that there is an analogy between the human mind and human reason and the laws of thought, but they also recognize that the laws of thought transcend human reason. And there can be no doubt that the laws of logic exhibit these ‘divine’ attributes and a kind of godliness.
AW then conclude that the laws of logic show us, in effect, an unknown god(s), although a good deal is known about this god: that who or whatever it is or they are, all of its or their actions and thoughts are consistent with the laws of logic, that this (or these) god(s) is/are eternal and necessarily existent, and him/her/it/theirself the determiner of true and false, right and wrong, possible and impossible.
Paul responds to a similar generic piety when he speaks at the Areopagus by proclaiming the one true God. He declares that by raising Christ from the dead, God made it clear that he would no longer tolerate this kind of ignorance. And when Paul writes to the Christians in Rome, he may have the Greek piety in mind: he says that godliness is plainly revealed in what has been made and that particular divine attributes, even the very nature of God, are evident in creation. He also says in that first chapter of Romans that unbelievers take these created things to be their gods, worshiping the creature rather than the creator. Aspects of the created order are taken to be gods, which means that the derivative, contingent, analogical, created essence of their nature is denied, and they are taken as ultimate in and of themselves.
John 1 demonstrates a similar tactic to Paul’s. John writes a direct response to the Greek idea that an impersonal, independently existent logos provides the rational and intelligible coherence of history and experience. (Of course idolatrous Greek lore was awash with personalism as well.) John does exactly what Paul did in Athens. He proclaims that Christ is the true logos.
John 1 alludes to Genesis 1 in which God’s speech is the original rational speech, bringing order out of chaos. He names and distinguishes things and kinds, and he infuses the world with reason and coherence by placing animals in contexts suitable to their natures, and so on. John says that the Word is the eternal logic and reason of God. And indeed, the Word is God, existing in eternity along side the Father.
So, what is the relation of logic to the being of God? Succinctly, the being of God, in its necessary self-consistency, is the archetype, and the necessity and self-consistency of logic is ectypal. The a se, triune, personal God is the self-consistent original, and the Word of God is the wisdom, the reason, and the speech of God the Father. God’s thoughts and deeds are self-consistent with his whole being because the Word is God (John 1:1); so it is the triune being of God which is a se and original, rather than univocal self-consistency itself.
Univocal reasoning is not Christian presuppositional reasoning. Self-consciously Christian reasoning presupposes the a se, triune, personal God, and the contingency of everything else, including the laws of logic. There are two kinds of being: God and everything else. God is the only necessary thing; nothing but God exists necessarily. Rather than thinking univocally about necessity or possibility, Christian presuppositionalism thinks analogically: The self-existent triune God is the archetype, the eimi, and the creation is the ectype, the eikon, or image. Presupposing the triune God as archetype original means that we interpret creation in light of God rather than God in light of creation.
Logical necessity points to the self-consistency of the world, and we must understand the existence self-consistency of the world as derivative and dependent. It is image existence and image self-consistency. Specifically, the laws of logic are abstract but created; they are necessary but contingent upon the free decision to create, and they reveal the creator only analogically. About the realism/nominalism debate, Vern Poythress writes, “Realism maintained that universals had a ‘real’ existence, whereas nominalism contended that universals were simply humanly convenient names . . . The dichotomy is in fact a false one. . . Both presuppose each other and neither is more fundamental than the other” (197). Therefore the purported abstractness of the laws of logic is deceptive: “Thus philosophers,” those Poythress calls “rationalist,” “think that they can manipulate their categories without reference to an associational aspect or an instantiational aspect. The categories are supposedly association-free and instance-free.” And, he says, “Thus, within Aristotle’s system, syllogisms can operate only with unitarian ontology” (204). “But,” Poythress responds, “philosophers are in fact human beings. Hence, they have themselves learned language from associations and instances” (198). And he says, “Philosophical reflection is idealized. Philosophers project their reflection out toward an ideal that is association-free and instance-free” (199). In other words, there are no pure abstractions available to the finite mind; there are only abstractions from created things. Not even God thinks pure abstractions; he thinks himself, and God is not an abstraction. (If God is not a purely formal abstraction, would AW allow God to exist necessarily?)
Poythress decries the ultimately ethical nature of the philosopher’s handling of abstract categories: This “particular type of idealization . . . is intrinsically and irreducibly idolatrous. According to this approach, the ideal category is a self-identical classification, but with no instantiational or associational aspect” (199).
Poythress, in sum, argues that the laws of logic, speciously abstracted from essential relations and instantiations—univocally conceived, in other words, presuppose and exalt a unitarian ontology which denies trinitarianism. The laws of logic must be understood as true only the basis of, and intelligible only in light of, trinitarian theism and a trinitarian doctrine of creation that maintains the C/c distinction:
These practical derivations ‘work’ because they are analogical instantiations of the archetypcal divine modus ponens and other aspects of divine self-consistency. Modus ponens is intrinsically an analogical concept. So is the law of the excluded middle and other laws of logic, because all such laws are intelligible only through analogical relations to a divine, Trinitarian archetype (210).
If God had not created the world, triune, personal, divine self-consistency would exist, but created analogues—the laws of logic as we know them—would not.
It does us no good to map finite self-consistency onto our theology proper; rather, we presuppose image self-consistency as finite but reflective of the self-contained triune creator. The laws of logic are true but not ultimate; like the world they describe, they might not have been. The eimi/eikon distinction is the proper starting point for Christian presuppositional reasoning.
Sources
James N. Anderson and Greg Welty, “The Lord of Noncontradiction: An Argument for God from Logic,” Philosophia Christi 13, No. 2 (2011): 321-38.
Vern Poythress, “Reforming Ontology and Logic in Light of the Trinity: An Application of Van Til’s Idea of Analogy,” Westminster Theological Journal 57 no.1 (1995): 187-219.
