descartes through the lookingglass- is it possible to believe what is contradictory

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Descartes through the LookingGlass: Is it Possibleto Believe What is Contradictory?

William F. Lawhead

Religious Studies / Volume 21 / Issue 02 / June 1985, pp 169 - 179DOI: 10.1017/S0034412500017170, Published online: 24 October 2008

Link to this article: http://journals.cambridge.org/abstract_S0034412500017170

How to cite this article:William F. Lawhead (1985). Descartes through the LookingGlass: Is it Possible toBelieve What is Contradictory?. Religious Studies, 21, pp 169-179 doi:10.1017/S0034412500017170

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Rel. Stud. 21, pp. 169-179

WILLIAM F. LAWHEADUniversity of Mississippi

DESCARTES THROUGH THELOOKING-GLASS: IS IT POSSIBLE TO

BELIEVE WHAT IS CONTRADICTORY?*

My text for this paper is taken from Lewis Carroll's Through the Looking-Glass.It is that well-known passage where Alice is having a frustrating conversationwith the White Queen.1 Alice responds to some of the Queen's absurdstatements by saying, 'One can't believe impossible things.' At which pointthe Queen snaps back: ' I daresay you haven't had much practice. When Iwas your age, I always did it for half-an-hour a day. Why, sometimes I'vebelieved as many as six impossible things before breakfast.'

What are we to make of this claim? Lewis Carroll, the story-teller logician,obviously intended this statement to be humorous because of its logicalabsurdity. But is it absurd? Is it perhaps possible that one can believe acontradiction? If so, could one ever have good reasons for such a belief? Whatsort of reasons would they be? If my purpose in this paper was merely toanalyze the white Queen's statement, this project might be philosophicallyfrivolous. However, there is a clear-cut case in the history of philosophy ofa noted philosopher who claimed to have believed in that which iscontradictory. Ironically, the philosopher I have in mind is not someone likeSoren Kierkegaard, but rather the first of the modern rationalists, ReneDescartes. As one commentator points out, 'There is a powerful and basicundercurrent of irrationalism in Descartes.'2 Another concludes that Des-cartes' position suggests that, in the final analysis, reality may be ' inherentlyabsurd'.3

For Descartes, our clearest conception of God is that He is perfect. Thisimplies that God has perfect or unlimited power. This is said to imply thatGod, unlike us, is not bound by or subject to any sort of logical necessitiesor eternal truths that are separate from Him. In fact, God has freely created

* An earlier version of this article was read at the Mid-South Philosophy Conference, Memphis StateUniversity, February 1982.

1 Lewis Carroll, Alice's Adventures in Wonderland and Through the Looking-Glass (New York: New American

Library, i960), p. 174.2 Leonard G. Miller, 'Descartes, mathematics, and God', Philosophical Review Uivi (October 1957), 464.

3 Harry Frankfurt, 'Descartes on the creation of the eternal truths', Philosophical Review LXXXVI

January 1977), 54.


17 WILLIAM F. LAWHEAD

those truths which we call 'eternal', i.e. those propositions which arenecessarily true for us and whose negations are self-contradictory and henceinconceivable, have been made to be this way by God. 'Necessary' truths arenecessary only for us. For God, they are merely one alternative that Hehappened to actualize, but He could have actualized completely opposite'necessary' truths. In other words, Descartes believed that what is logicallycontradictory is, in fact, possible. One respected Cartesian scholar claims thatthis doctrine is 'the pivot of the whole Cartesian system'.1 Whether this istrue or not, the issue has philosophical depth to it and we should avoid thetemptation to dismiss it prematurely.

My purpose here, then, is to explore the notion of believing a contradiction'in order to throw some light on some very perplexing passages in Descartes'correspondence and published writings. My procedure will be first to makethe notion of'believing a contradiction' as plausible as possible and thus givethe most charitable interpretation and reconstruction possible to Descartes'position. Then, I will argue that even with this charitable reconstruction,some insuperable difficulties still remain which undermine his position.

II

Before developing my argument, I will briefly review Descartes' position. Theearliest account we have of Descartes' doctrine is found in a letter toMersenne written in April 1630.2 From that time on, we find Descartesdoggedly reiterating his doctrine until the end of his life. A representativestatement of it may be found in a letter to Father Mesland written in 1644:

I turn to the difficulty of conceiving how it was free and indifferent for God to makeit not be true that the three angles of a triangle were equal to two right angles, orin general that contradictories could not be true together. It is easy to dispel thisdifficulty by considering that the power of God cannot have any limits, and thatour mind is finite and so created as to be able to conceive as possible things whichGod has wished to be in fact possible, but not to be able to conceive as possible thingswhich God could have made possible, but which He has in fact wished to makeimpossible. The first consideration shows us that God cannot have been determinedto make it true that contradictories cannot be true together, and therefore that Hecould have done the opposite. The second consideration shows us that even if thisbe true, we should not try to comprehend it since our nature is incapable of doingso.3

Throughout his discussions, Descartes lists examples of eternal truths whichwere created by God but whose contradictories could have been true. Some

1 A. Boyce Gibson, ' The eternal verities and the will of God in the philosophy of Descartes', Proceedings

of the Aristotelian Society xxx (1929-30), 46.2 See Descartes: Philosophical Letters, trans, and ed. Anthony Kenny (Oxford: Oxford University Press,

1970), p. 11.3 Kenny, pp. 150-1.


DESCARTES THROUGH THE LOOKING-GLASS I 7 I

of these are: (a) arithmetical truths (two times four equals eight),1 (b)geometrical truths (the three angles of a triangle are equal to two right angles,the radii of a circle are all equal),2'3 and (c) fundamental axioms (the wholeis equal to the sum of its parts).4 Descartes also gives examples of entitieswhich are inconceivable to us, but which could have been created by God'sinfinite power: (a) a mountain without a valley,5 (b) an aggregate of one andtwo which is not three,6 (c) a space which is completely void,7 (d) an extendedpiece of nothing,8 (e) a limited universe,9 and (/) atoms which are extendedand indivisible.10

in

Believing a contradiction is one example of believing what I do notcomprehend. Hence, to lead gently into the consideration of whether or notwe can believe a contradiction, it will be helpful to start with the broaderand less controversial question: 'Can I believe what I do not comprehend?'Of course, to answer this question affirmatively will not by itself answer ouroriginal question, for there are many things that I don't comprehend whichare not contradictions. It will, however, prepare the way for the more difficultquestion.

Our immediate answer to the preliminary question is likely to be: 'No!Of course you can't believe what you don't comprehend. Belief must alwaysbe preceded by understanding and your belief in the truth of a propositionmust always be exactly proportionate to your understanding of that prop-osition.' But this answer provokes its own questions. How much understandingmust we have of a proposition or of the key concepts within it before we areentitled to give assent to it? Doesn't fully understanding a proposition involve(in part) understanding what it entails and what it denies? Furthermore, tofully understand a proposition, must we not have some idea of whatassumptions it depends upon and what propositions are compatible with it?Must not the concepts it employs be totally lucid to us? To understand aproposition exhaustively might require that we unpack and analyse a verylarge or even unlimited number of connections, relationships, and concepts.Isn't one selling point of our Philosophy 101 courses the fact that most peoplehave a great many beliefs that they do not clearly understand and that theyneed to understand better? It would be absurd to say that becausephilosophers alone have fully analyzed and understood the concept of'mind'that they and only they are capable of believing that there are such things

1 Reply to Objections VI in The Philosophical Works of Descartes, trans. Elizabeth S. Haldane and

G. R. T . Ross (London: Cambr idge University Press, 1970), II, 2 :251 .2 Descartes, Reply to Objections VI, p. 248. 3 To Mersenne, 27 May 1930, Kenny, op. cit. p. 15.

4 To Mersenne, 17 May 1938, ibid., p. 55. 5 To Arnauld, 29 July 1648, ibid., p. 236.

6 To Arnauld, 29 July 1648, ibid., p. 236. 7 To Arnauld, 29 July 1648, ibid., p. 237.

8 To Arnauld, 29 July 1648, ibid., p. 237. * To Arnauld, 29 July 1648, ibid, p. 237.

10 To More, 5 February 1649, ibid., p. 241.



as minds. Perhaps there is a plausible, secular meaning that can be givento the Anselmian formula that ' I believe in order to understand.'1 It seems,then, that in order to responsibly believe that some proposition p is true, itis not required that I reach the unattainable goal of an exhaustive under-standing of/).

To be sure, I sometimes suspend belief about a matter until I am able togain a better understanding of it. If asked, for example, to state my definitiveopinion concerning some complicated economic theory, I am likely to pleadignorance. Thus, many of my beliefs about some issues are proportionate tomy understanding of those issues and the crucial concepts within them. Onthe other hand, it seems clear that our beliefs often do outrun ourunderstanding. Furthermore, I would argue that this in itself is not necessarilyimproper. To give assent to that which we do not fully understand need notviolate any reasonable 'ethic of belief, even when the belief does not involvea 'forced option' (to use William James' term).

If this last conclusion can be made plausible, then we will be well on theway to dealing with Descartes' thesis. With respect to God's creation of theeternal truths, Descartes claims that he knows this to be true even thoughhe cannot comprehend or conceive it.2 He then offers the following analogyas an illustration of this cognitive situation:

In the same way we can touch a mountain with our hands but we cannot put ourarms around it as we could put them around a tree or something else not too largefor them. To comprehend something is to embrace it in one's thought; to knowsomething it is sufficient to touch it with one's thought.3

Although we might want to carefully qualify this analogy, I wish to suggestthat even for some of the most mundane topics, we often have beliefs abouta matter even though we don't fully embrace it with our thought.

This conclusion is based on the fact that among the many propositions Ido not understand, some of them are propositions that others do understand.Furthermore, some of the propositions in this latter category are such thatI have good grounds for believing that others actually do understand them.Hilary Putnam refers to this situation as a 'division of linguistic labor'. Heclaims that:

Every linguistic community... possesses at least some terms whose associated' criteria' are known only to a subset of the speakers who acquire the terms, and whoseuse by the other speakers depends upon a structural cooperation between them andthe speakers in the relevant subsets.4

1 St Anselm, Proslogium, chap. 1.

2 To Mersenne, 27 May 1930, ibid., pp. 14-15.

3 To Mersenne, 27 May 1930, ibid., p. 15.

4 Hilary Putnam, 'Meaning and reference', Naming, Necessity, and Natural Kinds, ed. Stephen P.

Schwartz (Ithaca, N.Y.: Cornell University Press, 1977), p. 126.


DESCARTES THROUGH THE LOOKING-GLASS 173

Hence, there is a difference between:1i) my knowing that p has a meaning, and(2) my knowing what the meaning of/) is.It is possible for (i) to be the case without (2) being the case. In order

for (1) to be the case, it is enough that I have good evidence that some reliablepersons within the relevant linguistic community do know the meaning ofp. Furthermore, even though (2) may not be the case, it is still possible forthe following to be the case.

(3) My having adequate grounds for believing that p.This case is similar to the one just mentioned. If there are reliable persons

who do know and understand p. then my knowledge of this fact wouldconstitute sufficient grounds for (3). In addition to a division of linguisticlabour, we sometimes depend upon a 'division of epistemic labor'. Persons,whose knowledge we depend upon for the appropriate employment of a term,will be called the 'guarantors' of the meaning of that term.1

My position here can best be made more plausible by means of a fewexamples. Suppose that I do not really understand what an irrational numberis. Perhaps I am given a definition of the term but, because I ammathematically obtuse, the concept remains as opaque to me as before.Nevertheless, I do know several things to be true about irrational numbersbecause I have often heard competent mathematicians discussing them andI have seen them mentioned in mathematical textbooks. For example, I knowthat the square root of 2 is an irrational number. I know that irrationalnumbers can never be written in decimal notation with a finite number ofcharacters. I know that the early mathematician Eudoxus of Cnidus did somevery important work that was relevant to understanding irrational numbers.

Even though I cannot define 'irrational number' and do not comprehendwhat such entities are, this does not prevent me from having a number ofbeliefs about them. My beliefs are not based upon any 'knowledge byacquaintance' but are dependent upon the knowledge and understandingthat reliable mathematicians have. It would be wrong to point to this as anexample of the ad verecundiam fallacy. The fallacious appeal to authority occursonly when there are reasons to doubt the expertise of the authority or therelevance of that expertise to the issue in question. Many appeals to authorityare legitimate. Thus, I have some good reasons for my beliefs about irrationalnumbers even though I do not fully understand the concept myself. It maybe true that beliefs about things I barely understand usually do not play avery large role in my life. On the other hand, it may, for example, comfortmy romantic spirit to know that there are some things such as irrationalnumbers (whatever they are) which even mathematicians cannot pin down.

Allow me to present one more example. In observing the linguistic1 I have taken this term from Leon A. Immerman, 'Must we know what we say?', Religious Studies

xv (September 1979).



development of small children it is apparent, I believe, how little under-standing is required for there to be effective linguistic behavior. Once, Iobserved my three-year-old son becoming frustrated at his younger brotherbecause the latter was not doing his share to carry out my directive to pickup their toys. In a fit of rage, the older boy shouted, 'Andy, this is not anoptional experience in your life!' Naturally, he had heard me use this linein similar circumstances on other occasions. Even though he had littleknowledge of what 'optional experience' meant, he was able to use the termin an appropriate way. It is true that the function of his utterance wasprimarily expressive and directive. However, there was an element of beliefin it. There was his belief that what he said was a correct description of thesituation. As a matter of fact, he was right.

I do not think it will hurt my argument if I acknowledge that there maybe some psychological (and perhaps logical) limits to how little understandingI can have of a proposition and still meaningfully believe it. If a friend (whosegeneral knowledge I respect more than that of anyone else in the world)should state, for no apparent reason, that 'All gloxmox mib racklax,' I mayfind that this utterance does not inspire any sort of belief within me. In fact,I may not be sure that a declarative sentence has even been spoken. Withoutmore information about the context, the subject, or the purpose of this claim,there is not much there for me to grab hold of.

In the examples given previously, the subjects who did not understand keyterms in the propositions in question did at least have some sense of whatsorts of language-games employ these propositions and how these truth-claimswere interwoven with other propositions that they did understand and knowto be true. Furthermore, they were able to construct sentences containingthese problematic terms and use them in ways that were deemed appropriateby the relevent guarantors. The amount of understanding that is adequatefor giving minimal assent to a proposition lies somewhere between theunderstanding of God and that of an oyster. However, the line betweenunderstanding that is or is not an adequate prelude to belief is not a sharpone and is difficult to specify.

In this section I have argued that there may be situations in which ourbelief outruns our understanding. Of course, the happiest epistemiccircumstances are those in which the two accompany one another. But, asa matter of fact, there is rarely a perfect marriage between them. As theexample of the child illustrates, our linguistic and cognitive developmentinvolve a great deal of modeling behavior as we depend upon moreaccomplished or informed thinkers and speakers in order to know what itis wise for us to think and to say. As the mathematical example illustrates,this modelling still goes on in adult life. Just as everything cannot be proven,so everything cannot be understood by one individual (at least in practice).All our speech and thought develop and are carried on within a linguistic



and epistemic community with whom we continually interact. To deny thisis to embrace the mythical, Cartesian ideal of the Robinson Crusoe knowerwho is isolated and alone in his attempts to construct the edifice of knowledge.

IV

If I have managed to give some sense to the notion of' believing what I donot understand', then there is some hope that Descartes' belief in contra-dictions may be given some sense. It is obvious, however, that there are somemajor differences between these cases. Though I do not understand irrationalnumbers, I am confident that I could come to understand such things if Ihad some measure of mathematical aptitude and took the time and effortto penetrate the subject. However, Descartes' contradictory suppositions area quite different matter altogether. He believes, for example, that there isa possible world that God could create in which the following two propositionscould be true:

(4) X is a triangle.(5) The sum of X's interior angles are not equal to two right angles.Here, however, I sense that my problem in understanding this is not simply

due to my lack of knowledge. The sorts of possibilities that Descartesembraces seem to be incomprehensible and impenetrable in principle by thehuman mind. It is not only that we do not understand what Descartes asksus to believe, but that the whole of our understanding cries out that suchthings are impossible.

At this point, I need to suggest how Descartes might reply to the objectionthat he has simply thrown the laws of logic out the window and, hence, thatthere is no use reasoning with him and no use his trying to reason with us. Asone writer has said, ' If you buy contradictions you sell logic.n In Descartes'discussions, there seem to be two distinct kinds of contradictions. The firstkind of contradiction is what I will call a 'contradiction-1'. All cases ofcontradiction-1 are absolute impossibilities. This would include all prop-ositions that could not be true and all entities that could not exist in anypossible world. This is the strongest sense of' contradiction' and it is whatphilosophers usually mean when they use this term. Any cases of contradiction-1 would be contradictory not only for the human mind, but for the DivineMind as well. I do not believe that any reasonable interpretation of Descarteswould have him saying that 'everything is up for grabs.' If this were the case,the following two propositions could be true at the same time and in the samesense:

(6) God is omnipotent.(7) God is not omnipotent.

1 James Hall, Knowledge, Belief, and Transcendence (Boston: Houghton Mifflin Co., 1975), p. 84.



But Descartes' problematic thesis rests on the conviction that (6) is trueand (7) is false. He also believes that his conclusions concerning the eternaltruths logically follow from (6). In spite of what may seem to be the caseinitially, Descartes does not want to say that the Principle of Non-contradictionhas no validity whatsoever.1 Without the use of this principle, it would seemthat all reasoning as well as meaningful discourse and predication would bestultified. Anything could be meaningfully said of God and, therefore,nothing could be meaningfully asserted of Him. This clearly is not Descartes'position. Descartes often makes such statements as the following: 'For it isself-contradictory that the will of God should not have been from eternityindifferent to all that has come to pass or that ever will occur.. .'2

Descartes uses the term 'contradiction' in a second sense. This kind ofcontradiction I will call a 'contradiction-2'. A contradiction-2 is an epistemicimpossibility. Hence, it is relative to our knowledge and/or cognitiveapparatus. If the description of an entity or state of affairs is contradictory-2for us, then we cannot conceive how it ever could be actual and we havesevere problems comprehending it or making intelligible assertions about it.We cannot imagine how it could ever cohere with the rest of our knowledgeor our inescapable ways of thinking and speaking. An example of acontradiction-2 would be 'a circle with unequal radii' as well as the othercontradictory notions listed earlier. Descartes claims, then, that it would becontradictory-1 to suppose that there is anything that God's power could notenable Him to do, including the creation of entities in the contradiction-2category. The laws of logic, as we know them, are reliable when they areappropriately applied. Their scope, however, is not as wide as we would wishit to be.

Perhaps Descartes can receive some help from certain strategies incontemporary philosophy. I am referring to what has been called the' DuhemQuine thesis'. In Quine's famous attack upon empiricism, he arguesthat the distinction between analytic and synthetic statements is a matter ofdegree. Analytic statements is a matter of degree. Analytic statements aremerely those that are located at the core of our total system of beliefs. Theyare the ones within the system that we would be least likely to revise. Forthis reason, Quine argues that:Any statement can be held true come what may, if we make drastic enoughadjustments elsewhere in the system.... Conversely, by the same token, no statementis immune to revision. Revision even of the logical law of the excluded middle hasbeen proposed as a means of simplifying quantum mechanics.. ..3

In any large-scale quest for knowledge, we are faced with the decision of whatto take as our point of reference or what will constitute the unrevisable core

1 Cf. Harry Frankfurt's opposing opinion on this. Frankfurt, pp. 47-50.

2 Descartes, Reply to Objections VI, p. 248.

3 Willard Van Orman Quine, 'Two dogmas of empiricism', From a Logical Point of View (New York:

Harper & Row, 1963), p. 43.



in our conceptual scheme. Since our finite minds can never make everythingintelligible at the same time, we often face the decision of what we will taketo be paradigmatic and what will have to remain anomalous or else bereinterpreted. For example, some statement to the effect that ' Space and timeare relative' is a contradiction from the standpoint of Newtonian physics,but it is part of the central core of Einstein's physics. When he carried outhis revolution in physics, Einstein embraced ideas which initially seemed tobe paradoxical (or worse) to many of his contemporaries in order to makeother phenomena more intelligible.

Descartes seems to be operating in the same manner. His conviction is thatour conceptual scheme ultimately will have greater coherence if we makestatements about God's perfection more central and unrevisable within thetotal network of our beliefs, even though it means that we must sacrifice theabsolute necessity of truths that we had previously assumed to beunfalsifiable.

In spite of all of this, it still seems hard to make sense out of Descartes'claim that God could have created a world that seems contradictory to us.The difficulty is, of course, that we cannot conceive of that which we findto be inconceivable. To do so, we would have to obtain some sort of God-likeperspective. In fact, Descartes cautions us that it is vain to try to do this.'Again it is useless to inquire how God could from all eternity bring it aboutthat it should be untrue that twice four is eight, etc.; for I admit that thatcannot be understood by us.'1 But perhaps we can imagine that our presenthuman perspective is a God-like perspective from the standpoint of someother world. This is exactly what occurs in the delightful and now classicnineteenth-century fantasy, Flatland.2 In this story, we are presented with afictional world that consists only of two dimensions. The inhabitants of thisworld are conscious and intelligent lines, circles, triangles, squares, and allmanner of polygons. One of the squares existing in this plane is honouredwith the epiphany of a 'divine being' who has the form of a sphere.

To the Flatlander, the sphere first appears as a point and then as anexpanding circle as its three-dimensional reality passes through the plane ofFlatland. The sphere explains to the square that he comes from up aboveFlatland where there is another dimension of reality. To Flatlanders, ofcourse, all directions refer to directions within their plane. Hence, ' up ' means' northward'. The sphere explains, however, that to get to his world, you mustgo 'upward but not northward'. To the square, this directive is a baldcontradiction. What is being described is completely inconceivable to him.

The moral is obvious. The square is faced with a contradiction-2. But heis a victim of the limits of his experience, his conceptual system, his language,and the rigidity of his imagination. There are many more possibilities

1 Descartes, Reply to Objections VI, p. 251.

2 Edwin A. Abbott, Flatland: A Romance of Many Dimensions (New York: Harper & Row, 1963).


I78 WILLIAM F. LAWHEAD

conceivable to a three-dimensional being than to a Flatlander. Many of thesepossibilities would appear to be contradictory from a two-dimensionalperspective. From the standpoint of Descartes' position, we are like thesquare. There are possibilities for God that we cannot comprehend. It seemsfoolish to Descartes to allow the dimensions of our world and our minds tolimit God.

v

It is now time to summarize my reconstruction and defence of Descartes'position. I have suggested that the DuhemQuine thesis can be used to arguethat any statement can be believed and made into a paradigmatic propositionif we are willing to make the necessary readjustments in the rest of our beliefs.It is clear that for Descartes, the statement of his extreme view of God'somnipotence is such a statement. The revolution that has occurred in physicsand the fictional story of Flatland provide concrete pictures of how statementswhich describe impossibilities in one system could, nevertheless, be true whenseen from another perspective.

All that this accomplishes, however, is to give Descartes' position somemeasure of philosophical respectability. The real issue is whether or not ithas genuine cogency. In other words, are there good reasons for acceptingDescartes' view of omnipotence, even though the majority of philosophicaltheologians have rejected it? In spite of our attempts to stretch the limits ofthe human mind, the imagination still seems to be paralyzed when it triesto deal with the bizarre possible worlds that Descartes claims God canenvision.

Descartes could reply, once again, that complete understanding need notbe a prerequisite for belief. Allow me to restate the minimal conditions forbelief that I set out in section III. It was argued that:

(8) Some subject S has adequate grounds for believing p if:(a) someone (the guarantor) does understand and has adequate grounds

for believing p, and(b) S has adequate grounds for believing that (a).In spite of my best efforts to meet the challenge to Descartes' position, it

seems that he is checkmated at this point with no further moves available.Let us consider a concrete example to make clear where Descartes runs intoproblems. He claims that the following is true:

(9) There is a possible world in which articles with unequal radii exist.Now Descartes tries to convince us that though we cannot understand how

such contradictions could be possible, God can understand this. If this weretrue, then condition (8a) is met because God could serve as our guarantorof the sense and truth of these incomprehensible propositions. But how dowe know that this is true? In other words, do we know that (8b) is true?



To defend this point, Descartes could, perhaps claim that:(10) God has revealed to Descartes that (9) is true. However, he makes

no claims to have had a special revelation from God concerning thesecontradictions. Thus, he is not in the position of the Flatland square whocan discuss the third dimension with the sphere. Furthermore, if God hadgiven Descartes some unusual supernatural insight concerning thesecontradictions, this would make it a private truth for Descartes but not onethat would be universally available. Yet, he assumes that we will agree withthe reasonableness of his conclusions concerning the possibility ofcontradictions.

Apart from special revelation then, the only way that we might know thatGod conceives something to be possible is if we antecedently know it to bepossible. Hence, Descartes would have to show that:

(11) The world referred to in (9) can be conceived or imagined to bepossible by the human mind.

However, the whole problematic issue rests on the fact that (11) is not true.Therefore, Descartes has no way of knowing that what seems to be anabsurdity to us is not an absurdity to God as well.

In summary, I have tried to go as far as possible to sympathetically defendDescartes' position. In spite of all my best strategies, however, I am afraidthat this task is hopeless. Though I have conceded that we may give assentto what we do not understand, this still requires that there be a reliableguarantor for the sense and truth of what is not understood. Descartes hasnot provided this. Hence, he has no way of distinguishing a contradiction-2from a contradiction-1. Descartes is thus caught on the horns of a dilemma.If we stick only with what our reason tells us is possible, then we have toreject what, in principle, our reason cannot comprehend (anycontradiction-2). If this is the case, then the notion of God doing what iscontradictory is unacceptable. On the other hand, if we allow for thepossibility that contradictions could be true, then anything is possible, i.e.there is no such thing as a contradiction-1. If this is the case, then we cannotsay that it is impossible for God's omnipotence to be limited. The problemis that Descartes wants to maintain a distinction between genuine impossi-bilities and apparent impossibilities. However, with the materials he has towork with in his system, he has to give up one or the other.

When we feel ourselves overcome by philosophical ennui, we may beginto agree with Hamlet's reminder to Horatio: 'There are more things inheaven and earth.. .than are dreamt of in your philosophy.'1 However, ifthere are possibilities that transcend the philosophical imagination, this doesnot mean that they also transcend the laws of logic. At least, neitherDescartes, nor Hamlet, nor the White Queen have given us convincingreasons to believe that there are.

1 William Shakespeare, Hamlet, act i, sc. 5, lines 165 6.

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