Faith, paradox and the argumentum

Abstract. The pseudonymous author of this article argues that neither Kierkegaard nor Climacus in the Concluding Unscientific Postscript are claiming that Christian beliefs are nonsense or contradictory, but that it is contrary to universal epistemic norms to believe these beliefs or even to believe they can be believed. In an appendix for which the rest of the article is a preparation the author gives an interpretation of the pseudonymity and form‑content contradiction and of how Kierkegaard in a sense agrees with all the assertions made in the Postscript. If Kierkegaard is right, this article could only have been written pseudonymously.

Editor’s foreword

Analogously to Kierkegaard’s relation to his pseudonyms, the legal and literary responsibility for talk is mine, but that is all. I am going to read you a pamphlet by a Johannes Post-Climacum which I have edited. The pamphlet has a “main part” and an “appendix”.

The purpose of my whole production is to examine what Kierkegaard was doing rather than whether he was in fact right. But if he was right (in fact, in persona propria I think he was not), the unusual form of this production is quite essential to it. – Editor

Faith, paradox, reason, and the argumentum spiritus sancti in Climacus and Kierkegaard

Johannes Post‑Climacum

edited by Alexander R. Pruss

April 26, 2001

1 Introduction

I would like to thank my editor’s for his kindness in reading my pamphlet at the meeting of the Soren Kierkegaard Society, though it is beyond me to know why he would be interested in the work of a poor humorist such as I am.

Both Johannes Climacus and Soren Kierkegaard have written on faith, paradox and reason. While Soren Kierkegaard is the creator of the persona of Johannes Climacus, Kierkegaard insists that none of the remarks of the pseudonymous authors whom he has created should be attributed back to Kierkegaard. As a rough guide, Climacus represents a non‑Christian (or perhaps pre‑Christian) attitude and Kierkegaard a fuller Christian approach. Some justification for this approach will be suggested in my Appendix.

The most hair‑raising claim that Johannes Climacus makes in theConcluding Unscientific Postscript to Philosophical Fragments is that not only is probabilifying evidence (“approximation”) for Christianity not helpful in attaining to Christian faith, but on the contrary the less evidence there is, the better, and the crowning evidence for Christianity is its maximal absurdity. This notorious claim, not surprisingly, has led some interpreters to accuse him of misologism and/or to conclude that the primary purpose of the Postscript is merely to innoculate one against the error of using a speculative philosophical approach in subjective domains. After all, how can we measure the degree of absurdity of statements?[1] If the central doctrines of Christianity are an absurdity, isn’t their conjunction with the claim that cows fly a greater absurdity?

2 The paradox and nonsense

2.1 The Trisector

The central notion of Religiousness B is the paradox which is to be believed.[2] Climacus says: “an individual in faith relinquishes the understanding and believes against the understanding”.[3] The paradoxicality of the paradox, according to Climacus, is not in any way diminished by the believer’s gaining understanding.[4] In fact, we will see it increases.

To throw the notion of a paradox into relief, let me introduce the Trisector.[5] The Trisector has heard that mathematicians say it is impossible to trisect an angle with compass and straightedge.[6] Nonetheless, the Trisector writes: “I have done what two and a half millenia of mathematicians have failed to do.” He notifies his local newspaper, which dutifully prints a story about the local mathematical genius who has solved the great riddle of geometry. Eventually, the Trisector writes up his construction, publishes it himself, and sends it out to Mathematics Departments at various Universities.

By means of trigonometry, a Mathematician checks that while the construction is wrong, nonetheless it is a close approximation.[7] She writes the Trisector, telling him about his error and about there being a mathematical proof of the impossibility of a construction of the type he claims to have. The Trisector is unconvinced and supposes there is a mathematical conspiracy to silence him.

It seems the Trisector believes against logic. He is convinced that an angle can be trisected, even though mathematical logic rigorously proves this is impossible. Thus, at first sight, the Trisector seems to be in a position not too different from that of the person that Climacus describes as believing “against the understanding”. How does Climacus’ believer differ from my Trisector?

2.2 Dialectics and understanding

Climacus emphasizes a need for dialectics and for use of the understanding.

[A Christian] may very well have understanding (indeed, he must have it in order to believe against the understanding.)[8]

The one purpose to which the understanding in the paradoxical‑religious sphere may be applied is to show that the “absolute paradox ... cannot be understood.”[9] Here, Climacus is speaking specifically of what he calls the “wise”, and not just the “simple”, believer.

In fact, objective and disinterested reason does have a position in examining the paradox, not only for Climacus, but even for Kierkegaard himself, who wrote:

Speculation can present the problems, can recognize that every individual problem is a problem for faith, is compounded and characterized in such a way that it is a problem for faith—and then can submit: Will you believe or not?

Furthermore, speculation can supervise and check faith [...] to see that there is no rattle‑brained mixing with faith of categories which are not objects of faith but, for example, of speculation.[10]

The task is not to understand Christianity but to comprehend that one cannot comprehend. This is the holy cause of faith, and reflection is therefore sanctified by being used in this way.[11]

Climacus says that the believer (at least, I suppose, the “wise”, but perhaps not the “simple”) can himself advance the objections against the paradox which he believes, and that this is what distinguishes “nonsense” from the “incomprehensible”.[12] It is in this that we see the difference between Climacus’ believer and the Trisector. The Trisector was given objections against his views by the Mathematician. But presumably, he did not understand the objections, or at least see their logical force. Arguably, if he did, then he could not hold that his proofs are correct. Climacus’ believer (assuming such a person exists), on the other hand, understands the objections, is able to state them clearly, and yet believes. This understanding of the objections means that he understands that the paradox is a paradox. This understanding distinguishes the “wise” believer from the Trisector.

2.3 Nonsense and logical contradiction

In talking of paradox, is Climacus and/or Kierkegaard claiming that Christian beliefs are nonsense or logically contradictory? Climacus does after all talk of belief against the understanding.[13]

However, Kierkegaard himself says that what he expresses

by saying that Christianity consists of paradox, philosophy in mediation, Leibniz expresses by distinguishing between what is above reason and what is against reason. Faith is above reason.[14]

Thus, Kierkegaard appears to be equating his notion of a paradox with what in Leibnizian terminology is “above reason”, and so one perhaps should not equate Kierkegaardian “against the understanding” with the Leibnizian “against reason”, the latter of which does simply mean “contradictory” or “nonsense”.

De minimis, Climacus and Kierkegaard hold that the Christian who is really accepting faith is not doing so because of having evidence making the faith sufficiently probable. If one accepts the normative epistemological view that one should not accept propositions without probable evidence, then such an acceptance of faith is contrary to universal[15] epistemic norms, and as such can be described as “against the understanding”. In fact, such a going against epistemic norms reminds one of the teleological suspension of the ethical that Johannes de Silentio describes in Fear and Trembling, and Climacus’ insistence on understanding that the paradox is against the understanding is analogous to de Silentio’s emphasis on how before Abraham’s sacrifice of Isaac it was necessary that Abraham should deeply love Isaac and on how he would have to act in fear and trembling. Unlike the psychopath and the Trisector, Abraham and the Climacean believer know they are transgressing objective norms.

Yet the structure of Climacus’ argument suggests he takes Christianity, and specifically the Incarnation, to be contradictory. He talks of an event believed to be historical and yet which Climacus alleges “consists of that which can become historical only against its nature, consequently by virtue of the absurd.”[16] Is this not a self-contradictory belief? Yet, Kierkegaard speaking in persona propria plainly asserted in his unpublished writings that the Incarnation is not self‑contradictory.[17]

Rather, I would suggest that what is essential for Climacus and Kierkegaard in the alleged “contradiction” is that it is a contrary to reason for us existing finite beings, i.e., that there is a subjective problem. The problem being subjective means that the problem is one not in the propositions as they are in themselves but in our believing of them.

Let me suggest a start of an account of what “against the understanding” could mean, though I do not claim that precisely this is what Climacus meant. Let T₀ consist of the doctrines of the Christian faith, let T be T₀ together with any epistemically certain philosophical propositions that Climacus and Kierkegaard might admit, and let C(T) be the assertion that T is logically consistent. Thus, I would suggest that what Climacus and Kierkegaard are saying is in part that acceptance of the proposition C(T) is against the understanding, in the sense of “against the understanding” as contrary to universal epistemic norms, that is, there not being sufficient evidence for us existing finite beings to believe the proposition that T is logically consistent. Moreover, at least the “wise” are aware of this.

Climacus’ claim about the Incarnation is then that as far as we know the nature of God, it is against universal epistemic norms to accept that the event is logically compatible with the Being’s nature. This reading has the advantage that it is compatible with Kierkegaard’s approval of Leibniz’s distinction between faith beyond reason and faith against reason, and that it does not force us to attribute direct misologism to Climacus, and explains why Christian apologists like Thomas Aquinas who only defended Christian doctrines against the charge of incoherence are not a target for Climacus or Kierkegaard.

3 Coming to believe, believing, and the argumentum spiritus sancti

3.1 Climacus

But one can also give a stronger reading of the subjective contradiction in the acceptance of Christian doctrines, of course for Climacus only conditionally on the assumption that there exists a person having faith in the sense of Religiousness B.

Let T₁ be the conjunction of the doctrines T₀ of Christianity with the claim C(T) that they are consistent with reason.[18] Inductively define T_n+1 be the proposition that it is possible for T_n to be believed by an existing human being who is fully aware of all paradoxicalities involved in T_n. Then, the strengthened reading of the paradox would be that T_n is against the understanding for all n, where I always understand “p is against the understanding” as meaning that it is against universal epistemic norms to accept p as true (i.e., no existing human being can have sufficient evidence to conclude that p). Thus, in particular, on this reading of Climacus, by T₂ not only is it against the understanding to accept that the Christian doctrine is consistent, but in fact it is against the understanding to accept that someone can believe the doctrine while understanding its paradoxicality (i.e., it is against the understanding to accept T₁). The slightly stronger reading is well in line with Climacus only being able to suppose there is such a thing as a Christian.

3.2 Kierkegaard

As opposed to Climacus, Kierkegaard was a Christian, and he holds that once the faith is present, “the faith itself is the testimony, faith is the justification” [19]; he calls this the “inward proof, argumentum spiritus sancti.” [20]Admittedly, these utterances made in persona prioria were written four years after the Postscript, but I will argue it is in logical continuity with Climacus. Kierkegaard assures us that for faith, the absurdity of the faith is not absurd.[21] Soe concludes that for Kierkegaard “the thought content of Christianity is not nonsense but is clear and understandable within the sphere of faith.” [22] I do not see justification in Kierkegaard for supposing a claim of such strength, but if we replace “clear and understandable” by the weaker “not absurd”, then the conclusion appears reasonable.

For Kierkegaard, there is an essential difference between the viewpoint of a believer and of an unbeliever. For Climacus, it is contrary to the understanding for a human being to come to believe that the thought‑content T₀ of Christianity is true, and perhaps even more strongly, one can add, to make an act of assent to the possibility of an existing human being making an act of assent in T₀, or even in its consistency, while understanding the paradoxical nature of T₀. However, I now claim that according to Kierkegaard, once a human being has faith, then this human being can justifiedly continue to believe T₀. Thus the difficulty is with coming to believe, and not so much with continuing to believe (although I will have to say something more about this in the conclusions of this pamphlet). Between the two one must place the famous Lessing‑Climacus‑Kierkegaard leap.

What is Kierkegaard’s argumentum spiritus sancti? One could suppose that it may be some kind of religious or mystical experience. However, this reading would seem to make the argumentum into something immediate, while Kierkegaard says:

“the testimony of the Spirit” is really present and is decisively present only when all the spontaneous, immediate testimonies have been nullified.[23]

Instead of positing a religious experience, I would like to propose that Kierkegaard’s argumentum may in fact be an argument, or may be made into an argument, which I will reconstruct as follows: Kierkegaard believes the central doctrines T₀ of Christianity. These doctrines are maximally paradoxical. Kierkegaard when coming to believe these doctrines was aware of their maximal paradoxicality. Moreover, Kierkegaard now knows that he believes these propositions. But this shows that a miracle has occurred somewhere. For if the doctrines are maximally paradoxical in the sense I explicated, then it is contrary to our human reason not only to believe the doctrines but to believe that anyone believes them. Yet Kierkegaard not only believes that someone—namely, he himself—believes these doctrines, but he knows it, since presumably he knows what he believes. Therefore, Kierkegaard knows that a miracle has occurred—the miracle of believing a maximally paradoxical proposition. And the existence of this miracle is then itself testimony. And perhaps just as only God can effect a teleological suspension of the ethical, so, too, only God can effect this kind of a miracle.

According to Kierkegaard, the argumentum spiritus sancti is present as a testimony “deep within” the believer when “everything is going against” the believer.[24] The idea that for Kierkegaard it is present when things are against the believer supports the claim that Kierkegaard may have been thinking of something along the lines of my above argument. For it is precisely when “everything is going against” the believer that the miracle of belief is most clear: it is then clearest that such a maximally paradoxical doctrine could only be believed through a miracle. Kierkegaard explicitly says: “[T]here is another existing which follows faith. But the first must never be forgotten—otherwise Christianity is completely displaced.”[25] It is not surprising that Kierkegaard should think that if one has faith, then one has a witness to its truth; after all, if faith is venturing “out into water 70,000 fathoms deep”[26], then doing this, if it be possible, may be argued to be miraculous. Moreover, in his journals, Kierkegaard says: “If you do not have faith, then at least believe that you will indeed come to have faith—and then you do have faith.”[27] For indeed to believe that you will have faith, assuming you know what faith is, is to already believe something paradoxical on the above account of the maximal paradoxicality of faith.

4 Conclusions

Admittedly, this argumentum is a most curious argument. It will be of no help whatsoever to a non-believer. For according to Climacus the non-believer does not know that anybody believes the central doctrines of Christianity. Nor will it be of any help to the believer who loses faith. For then just as no one but Kierkegaard and God can know that Kierkegaard believes, so neither can the believer know that she believed in the past. Thus, the argument is only for those who have faith, and so it justifies but does not remove existential pathos. This then is the paradox of the argumentum spiritus sancti. Faith itself justifies itself, but yet this justification does not reduce the paradoxicality of the faith. For once one rests on the justification as on argument, the faith ceases to be itself paradoxical—but then the argument disappears, for it only applies if the faith is in a paradox. Kierkegaard will say this is an irreducible paradox and that nothing more can be said about it—but that a Christian is to exist in it.

Appendix: Interpretation of the Postscript

In the above, we have reasoned rather objectively and very seriously about subjective matters, basing ourselves on the utterances of Messrs. Climacus and Kierkegaard. Moreover, we have disregarded the Appendix to the Postscript where Climacus revokes all he wrote while noting that to write and revoke is different from not writing at all.

There are three ways of justifying the above serious investigation of arguments.

a. Swallowing the bait

First of all, one could simply say that the arguments that Climacus brings up are intrinsically interesting, and that for philosophical investigation it is the intrinsic interest of the arguments that matters, and the question of whether Climacus intends the arguments in earnest or in jest, or whether they were typed by a randomly typing monkey, is irrelevant. This attitude is, of course, quite contrary to that of Climacus and Kierkegaard. Insofar as the Postscript appears, at least in some sense, to be a satire of speculative philosophy, such considerations could simply imply that one has swallowed the bait—one would be no better than the German reviewer of the Fragments.[28] But of course, for the satire to be a good satire, the arguments have to be good ones, and thus worthy of examination.

b. Objective reasoning about subjectivity

Climacus is objectively reasoning about subjectivity. This constitutes an intrinsic form‑content contradiction in Climacus’ work. Climacus himself realizes the contradiction, and withdraws his work. [29] At the same time, he is careful to note that “to write a book and to revoke it is not the same as refraining from writing it” [30]. We, the readers, may take this as meaning that having gone through his book and having seen the form‑content contradiction work its way out, we will be innoculated against committing the same kind of contradiction ourselves. Moreover, Climacus, as a humorist [31], will have had a good laugh over how we were taken in by the work and how the punchline—his appendix—punctured our pretensions of being able to objectively reason about subjectivity.

My enterprise of having seriously examined the arguments of the humorist then appears to be an intrinsically humorous and self‑defeating one. Yet, while healthy laughter at the ways of the assistant professor was quite possibly the reason why Mr. Johannes Climacus, humorist, wrote the Postscript, perhaps there is a deeper reason as to why Mr. Soren Kierkegaard, M.Theol., consented not only to edit it, but also to publish it at his own expense.

Kierkegaard wrote about the Postscript:

To be a Christian involves a double danger.

First, all the intense internal suffering involved in becoming a Christian, this losing human reason and being crucified on the paradox.—This is the issue Concluding Postscript presents as ideally as possible. [32]

It certainly thus sounds as if we are to make more use of the Postscript than just to see the failure of speculation.

In seeking for deeper reasons for the Postscript, it is essential to recall that Kierkegaard himself is not against objective considerations of one’s subjectivity.

The majority of men are truncated I’s; what was structured by nature as the possibility of being sharpened to an I is quickly truncated to a third person.

It is something altogether different to relate objectively to one’s own subjectivity.

Take Socrates! … [I]n danger he himself relates objectively to his own person; in the moment he himself is condemned to death he talks about his sentence as if he were an entirely separate third party. He is subjectivity raised to the second power; his relationship is one of objectivity just like that of a true poet in relation to his poetic production; with this objectivity he relates to his own subjectivity.[33]

Objective reasoning about one’s subjectivity is something that Kierkegaard places a high value on. [34]

However, an important qualification is to be noted: on one’s own subjectivity. Given one’s subjectivity, one can reason objectively about it. Climacus, on the other hand, by his own admission appears not to be a Christian; as such, his reasoning is not about his subjectivity, but about Christian subjectivity in general. Yet, since Climacus is neither a Christian nor has he ever been decisively face‑to‑face with Christianity[35], he has no grasp of the meaning of what he is reasoning about. He is reasoning about abstract subjectivity, unlike Socrates who reasons about his own concrete subjectivity, and abstract subjectivity is no subjectivity at all. Through his argumentation, he can perhaps be said to be trying to gradually climb to Christianity without a leap[36]—a description making his surname quite appropriate as Mulhall notes. [37]

What is wrong with Climacus’ work is not so much the argumentation or the use of an argumentative form, but the fact that the arguments are not about anything existent, because the author has not grasped the existence that the arguments are talking about. The problem is not with the argument but with the argumenter. His words appear to concern existing persons, and yet because he has not grasped them, they become purely abstract arguments like the arguments of mathematics would be if we accepted a logicist view that mathematics is merely the study of logical implications. However, this does not rule out the possibility of the arguments being formally correct. Insofar as Climacus has not grasped the meaning of subjectivity and inwardness[38], his arguments are merely formal without essential[39] content, much like the propositions of logicist mathematics, and one falls for the joke whose punchline is the Postscript’s Appendix if one ascribes essential content to it.

Kierkegaard is not Climacus. Kierkegaard was evidently a person deeply concerned about Christianity. He was a Christian. As such, his approach to Christianity was such that I could from a Kierkegaardian standpoint suspect him of being inward and existentially subjective. But just as Climacus could not actually be sure that Lessing was such as Climacus thought him to have been, neither can I, from a Kierkegaardian standpoint, be truly certain that Kierkegaard was a Christian. Henceforth, I assume he was. Then, Kierkegaard could objectively reason about his own subjectivity, his own inwardness and his own God‑relationship. In fact, he would probably consider it his duty to reason in that way, as I noted before. The merely formal arguments that Climacus has produced (or at least some of them) could then be applied as an analysis of Kierkegaard’s subjectivity, Kierkegaard’s inwardness and Kierkegaard’s God‑relationship. For Kierkegaard, these formal arguments would then have content, since Kierkegaard has, I assume, really grasped the concepts about which these arguments proceed.

So why then does not Kierkegaard sign the book entirely himself, and simply qualify all the statements that seem to be talking of abstract subjectivity (and thus causing the form‑content chasm) by making them talk of his subjectivity? It is not a mere matter of modesty: If Kierkegaard signed the work himself and made it talk of Kierkegaard’s subjectivity, then the work would no longer be a forceful exhibit of the form‑content contradiction. The reader would no longer learn to avoid abstract objective talk about subjectivity in general, would not learn that “subjectivity in general is an oxymoron”, in the way that the reductio ad absurdum produced by Climacus teaches her.

But even more importantly, if Kierkegaard himself signed the book (having rewritten it of course to talk about his subjectivity), then the ideal reader could no longer relate it to her subjectivity. It would be essentially a book about Kierkegaard’s subjectivity. A reader might try to overcome this by saying that Kierkegaard’s subjectivity is a special case of the subjectivity of all human beings, and therefore what Kierkegaard writes is applicable to all human subjectivity (this is an argument by induction from one instance!), and therefore since she is a human being, it applies to her subjectivity. But of course this argument would be the exact opposite of how subjective truths are to be grasped, since they are not to be grasped through the syllogism that one is a member of some objective class. Thus, if Kierkegaard wrote the book about Kierkegaard’s subjectivity, it would be free of subjective content for the reader—and objective content would probably also elude her, since even if Kierkegaard can objectively reason about his subjectivity since he (I have assumed) grasps the requisite concepts of it and succeeds in referring to it, she cannot objectively reason about his subjectivity, since even if she grasps her subjectivity, she cannot grasp Kierkegaard’s subjectivity.[40]

Thus the Postscript has two levels of indirection. First, Climacus gives his arguments in a direct fashion. Then, Climacus has a good laugh over the reader who was taken in and revokes his arguments, since they do after all violate the form‑content congruence that should be present in such communications. Through this, the ideal reader should learn that she cannot objectively reason about subjective‑issues‑in‑general. The sting has been planted. And perhaps this is how far it gets with some readers. But it can actually go one step further in two different ways. Firstly, it could be that the reader will take the text as having content vis‑à‑vis Kierkegaard’s subjectivity and inwardness; this, as I have argued several paragraphs above, will not be very helpful to her—absolute passion cannot be grasped by third parties.[41]

But on the other hand, perhaps the reader has some grasp of her subjectivity and inwardness on her own, and perhaps she is a Christian. Then, the reader can apply the text to her subjectivity and inwardness, and it will have content for her. In this case, we will have had the structure of a double negation. First, Climacus negates the work through the revocation—in Hegelian terminology, this is not an abstract negation but a determinate one, since the work leaves a sting. Secondly, the reader herself may negate the revocation by seeing that while Climacus had no business talking objectively of subjectivity and inwardness in general, she has every right to reason in her own mind about her subjectivity and inwardness—and the formally correct arguments (if they are formally correct—which was an issue for the first part of this pamphlet[42]) take on content from her existence.

Thus, the reader sees herself in the mirror of the text.[43] If the reader is a speculative thinker, then she sees a caricature of a speculative thinker trying ridiculously to use speculative methods in a subjective realm—such a reader will see only one negation, one revocation; assuming the Kierkegaard’s works have been functioning as they should, this might be what has happened to more than commentator. But if the reader is someone who has decisively met with Christianity, then she may in fact see that not only is the book revoked by Climacus, but there is another level of indirection, that involved in Kierkegaard’s involvement with the book—and hence there is overall a double negation (which, as every Hegelian and each intuitionist will say, is of course not the same as a direct assertion). This mirror‑like function recalls the epigraph on Stages on Life’s Way:

Such works are mirrors: when an ape looks in, no apostle can look out.

But I, Johannes Post‑Climacum, cannot utter a single word about the reader’s subjectivity or her inwardness or her infinite interestedness. Were I, Johannes Post‑Climacum, to have decisively met with Christianity, I could reason objectively about my subjectivity or my inwardness or my infinite interest, but as it stands this sentence—and the whole paper including the present Appendix and the present withdrawal—is empty of content and hereby withdrawn.

Editor’s afterword

Thus far Mr. Post‑Climacum’s pamphlet. He wrote well, and I would be inclined to say that, from the Kierkegaardian viewpoint, everything (excepting the concluding paragraph above) he wrote would have been defensible—assuming that he had decisively met with Christianity. Though if he had met with Christianity, then according to Magister Kierkagaard, he would not be able to write as he did. Beyond Mr. Climacus is only Religiousness A and Religiousness B.[44] It is obvious that Religiousness B has not been reached by Mr. Post‑Climacum. Suppose Mr. Post‑Climacum has reached Religiousness A. Then surely he would not consider himself as being in any way superior to Mr. Climacus, and so the name Post‑Climacum would appear presumptuous, unless of course Mr. Post‑Climacum intends his name in a merely temporal way, which would seem reasonable, but of course as a third party I cannot be sure.

Were someone to ask whether I can apply the text to myself in any way, and as to whether this present sentence makes sense, this would not be a question that, if Kierkegaard is right, could be answered objectively to third parties, and indeed if Kierkegaard is right, I must revoke this sentence as soon as you have understood it—if not sooner.

– Editor

[5]The Trisector will be quite close to some real existing human beings portrayed by Dudley [U. Dudley, A Budget of Trisections, New York: Springer Verlag, 1987], and hence is not really a fictional construction, although I do not know if all the features described fall within any single person. Angle trisectors are some of the most common members of the species. Other members of the species are such characters as circle squarers, but these seem to be more rare these days.

[6]Indeed, it is an established mathematical theorem that it is impossible to give a finite procedure whereby with compass and straightedge an arbitrary angle is trisected. In fact, it is impossible to trisect a 60^Υ angle.

[7]A non‑fictional example of such a Mathematician would be U. Dudley. Note that it is possible to produce procedures which come arbitrarily close to trisecting angles, but they will never be exact.

[10]Soren Kierkegaard, Entry 3315 (1850), in: Journals and Papers, edited and translated by H. V. Hong and E. H. Hong, Bloomington: Indiana University Press, 1967. Further references to the Journals and Papers will be flagged “JP” and the entry number and date will be given.

[15]The universality of such norms is not essential to the argument, but Climacus would probably hold that epistemic norms in the objective sphere, i.e., as concerning the understanding, are universal.

[18]Note that T₁ may well be equivalent to T₀, since if T₀ is true, then it may be argued to be necessarily compatible with all epistemically certain propositions, so that C(T) would follow.

[26]This phrase is one of Kierkegaard’s favorites and is oft repeated; see, e.g., JP 1142 (1851).

[34]It is worth noting that Kierkegaard, contrary to some readings, also places a real value on objective matters such as doctrine. For instance in JP 4544 (1848) we read that “in the initial period of Christianity ... it was certainly doctrine that gave occasion for conflict more than anything else,” but that “[i]n Christendom doctrine is really taken for granted”. Thus it appears that the main reason why Kierkegaard does not focus much on the specifics of doctrine is that this is no longer an occasion for serious conflict in Christendom (except, he notes in the same passage, in the case of a “sectarian movement”); what matters for Kierkegaard in his era is “interiorizing the doctrine” (Ibid.).

[35]For Kierkegaard, it might be possible to come face‑to‑face with Christianity, grasp its content in a subjective way, and yet be able to either say Fiat or Non fiat to its demands. However, Climacus has not come face‑to‑face with Christianity; he has neither decisively said Fiat nor Non fiat, and he does not know what it would be like to have said Fiat.

[37]Ibid. To strengthen this point, note that the names of Kierkegaard’s pseudonymous authors were chosen by the authors themselves, as Kierkegaard notes in his First and Last Explanation [in: CUP, p. [626]].

[38]And for Kierkegaard it is a contradiction to “grasp the meaning of subjectivity and inwardness.” As existing subject, one can only grasp the meaning of one’s subjectivity and one’s inwardness.

[39]Perhaps some content may be ascribed to them, but not the essential content which is subjective.

[40]Indeed, the very phrase “Kierkegaard’s subjectivity” would be one that she cannot grasp the content of.

[42]And the main body of my pamphlet, less this Appendix, is in part concerned with the question of this formal correctness.

[43]When my reading of the Postscript was explained by my editor to Nick Hill, the latter reminded the editor about Kierkegaard’s trope of the mirror. It is to this kind reminder, for which both I and my editor are grateful, that I owe the present paragraph.