Risto

What is Facebook, and what are its implications for the authenticity of Dasein? Here, Facebook itself replies, declaring; "Facebook helps you connect and share with the people in your life," in pursuit of its "mission ... to give people the power to ... make the world more open and connected." (Hereafter, Facebook is referenced as FB.) Thus FB describes its relation to Dasein using the characteristics: "helps"; "connect"; "share"; "open"; and "power." Structurally speaking therefore, FB believes it "helps" facilitate "open" relationships between people, and positions itself as "the power" that "helps" "connect" "life" on "the world."

With respect to physical extent, FB's claims are accurate, as its digital community involves over 800 million users, and those users span the entire planet. However, these details are not ontologically illuminating, and we observe that FB's response to our question is decidedly ontical, and offers little more than a categorical enumeration. Furthermore, additional investigation of the FB web site reveals no deeper answer, but yields only an expanded feature list. Therefore, the self-descriptions of FB do not open a path towards the answer we seek.

Hence, we reformulate: ontologically speaking, what is the nature of the relation between FB and Dasein? Formulated thus, we see that to uncover the relationship of FB to Dasein, we must investigate existentially; and, comporting ourselves towards investigation in the mode of phenomenological inquiry, we will here apply the concepts and approaches of Martin Heidegger's existential analytic, as outlined in his philosophical opus Being and Time. Using Heidegger's existential analytic, we shall develop a phenomenological perspective on FB, and apply this towards acquiring an appreciation for the potential implications of FB with regards to the authenticity of its users.

In existential terms, FB is computer software, and is therefore equipment. As equipment, FB has equipmental Being, and is ready-to-hand in its everydayness, as something in-order-to, be it something-in-order-to process images, or something-in-order-to communicate with friends. These examples of FB's in-order-to are specific, and here the question arises: what is FB's everyday in-order-to in its generality?

FB has been designed to represent people, social structures, and social interactions, digitally. Within the equipment that is FB, people and interactions are based on user profiles and their relationships. Because FB has equipmental Being, an individual FB user profile ontically determines that user's FB-based equipmental Being, and permits that user to participate in FB activities, including: posting personal data, such as age and address; joining FB groups; posting FB pictures; and, sending FB messages. In this way, the particular equipment whose being is FB takes the notion of an individual Dasein, then expands on that notion to include the concept of inter-Dasein relations, and builds up a digital system of inter-Dasein structures, intended to mirror the social structures that attend Dasein's Being-in-the-world.

In its attempt to mirror the social structures attending Being-in-the-world, it is inarguable that FB has succeeded remarkably in presenting users with a comprehensive digital representation of Being and their own being, and offers remarkably diverse digital forms of social connections, by recreating a world-like experience of the "they," and FB thus has its being as an impressive imitation of social relations in-the-world. However, though FB presents a convincing technological approximation of those aspects it reproduces, what are the limits of this approximation?

What defines FB is its existence: its being is existentiell. Existentially, Dasein has its Being as Being-in-the-world, while FB has its Being as equipment in-the-world. Thus, we immediately perceive that FB can never recreate Being-in-the-world, because the Being of FB is grounded within and limited by its existentiell facticity. FB enables the individual Dasein to study its characteristics ontically and identify the apparently discrete elements of its Being, and then prioritize those elements in-order-to recombine them categorically in the form of an FB profile. But it can never be the case that an FB profile corresponds fully to Dasein's Being-in-the-world. This is because ontology is always prior to the ontical, and "Subjecting the manifold to tabulation does not ensure any actual understanding of what lies there before us as thus set in order." Irrespective of the depth and scope of factical features given digital expression on FB; "We shall not get a genuine knowledge of essences simply by the syncretic activity of universal comparison and classification." This is because Dasein exists outside of and beyond FB, and it is precisely Dasein's existence and the totality of existential Being-in-the-world that FB cuts out, and that FB can never capture because it is digital and equipmental. Quite simply, FB aspires to worldhood but is ontical, and the worldhood-of-the-world is realized only ontologically. Existentially then, we appreciate that when FB "helps you connect and share with the people in your life," the connections it offers are restricted by its Being, which is existentiell.

Thus, we exhibit FB in its generality, and answer the first half of our opening question: phenomenologically, what is Facebook? FB is equipment taken up for-the-sake-of socializing, and its users are involved with the "they" not in the Being of existence, but via the Being of equipment. Through its software, FB permits Dasein to interact only with the digital "they" existentielly, and never existentially.

Appreciating the existentiell nature of FB and FB profiles, we may now address the remainder of our opening question: what are FB's implications for the authenticity of Dasein?

To answer this, we begin with Dasein. Per Heidegger; "The 'essence' of Dasein lies in its existence" -- which is existential. Further to this, we know the 'essence' of FB lies in its existence, which is existentiell and never existential. Accordingly, the existence of FB's characteristics is existentiell, and all of its software features have equipmental Being, and never existential Being. Therefore, an FB user's profile and its FB-relationships with the-FB-"they" have equipmental Being. However, the equipmental Being of FB and FB user profiles is markedly different from the equipmental Being of, for example, a hammer, and this must be addressed.

In existentiell terms, a direct comparison makes the point: a hammer is taken up for-the-sake-of something that precedes our picking it up, for example hammering a nail in-the-world. In contrast, FB is taken up in-the-world for-the-sake-of taking up social interactions within FB's digital FB-world (which presents its own engaging digital representation of people, social structures, and social interactions). In phenomenological terms, the study of a hammer brings out its relationship to Dasein with regards to existential and existentiell structures and elements in-the-world, while the study of FB brings out its relationship to Dasein with regards to existential and existentiell structures and elements in-the-world, as well as existentiell structures and elements in the digital FB-world. So while Dasein comports itself towards a hammer in terms of Dasein's Being and the hammer's equipmental Being, what we must ask is: does Dasein comport itself towards FB in the same way as Dasein comports itself towards a hammer? Does Dasein comport itself to FB primarily in terms of Dasein's Being and FB's equipmental Being?

To answer this, we must examine Dasein's interactions with FB. An individual Dasein takes up FB in its ready-to-handness, creates an FB profile using some subset of their personal characteristics as perceived and prioritized by that Dasein in-the-world, and creates for itself an FB-Dasein in an FB-world. As noted, the FB-world is a software reconstruction of aspects of the worldhood-of-the-world, taken up by hundreds of millions of users around the-world, and these hundreds of millions of users each generate an FB-Dasein to interact with other FB-Dasein via the relations and elements of the FB-world, where that FB-world possesses an ever-increasing number of FB-Dasein and FB-based relations (friends, pictures, notes, conversations, forum messages, et al), and this results in the perpetual occurrence of FB-social-events, amidst the-FB-"they", and propels the evolution of the FB-society. Thusly, the being of FB is endowed with an absorbing FB-social totality; for, even though FB is digital and therefore finite, its finite characteristics appear infinite from the perspective of the individual user, because no single user could ever explore or exhaust all available FB-relations, regardless of the time available. In this way, the-FB-world is an interminable system for the individual Dasein, a fact that obtains regardless of the manner in which FB's factical features are reduced (whether in terms of statistics, or any other ontical quantification). Just as the full totality of experiences and ideation of Being-in-the-world are inaccessible to Dasein, the full FB-totality of FB-experiences and FB-elements are inaccessible to FB-Dasein in-the-FB-world, and Dasein in-the-world.

Therefore, the general nature of Dasein's interaction with FB is such that Dasein takes up FB as the "they" does, immerses itself concernfully inside the seemingly infinite FB-totality, and occupies its FB-Dasein as the-FB-"they" does, in-order-to upload the pictures Dasein feels it is important to upload, post comments and join groups important to Dasein's FB-"they"-self, and judge FB-society as the-FB-"they" does. By such activities, the-FB-"they"-self as the-FB-"they" sustains "itself factically in the averageness of that which belongs to it, of that which it regards as valid and that which it does not, and of that to which it grants success and that to which it denies it," and success has been granted to FB by the "they" and FB-"they", for FB involves over 800 million users, who collectively "spend more than 700 billion minutes per month" in-the-FB-world.

The relevance of this to Dasein proceeds as follows: (i) in its everydayness, Dasein is falling among the "they"; (ii) fallen in the publicness of the "they", the "they"-self of Dasein is consumed by the shared equipment of a common, public world; (iii) today, FB is among the most widely shared public equipment; (iv) hundreds of millions of Dasein spend billions of minutes per month sustaining FB-life and FB-society, and have augmented social-life-in-the-world with social-life-in-the-FB-world; and therefore, (v) the "they" clearly (pre)supposes FB-life is part of "leading and sustaining a full and genuine 'life'," and this brings Dasein's falling "they"-self to unreflectively suppose FB-life is indispensable in its own 'life.'

With this we observe how the being of FB differs from the being of a hammer: in phenomenological terms, Dasein does not comport itself to FB simply in terms of Dasein's Being and FB's equipmental Being. Rather, because "everyday Dasein draws its pre-ontological way of interpreting its Being" from "the kind of Being which belongs to the 'they'," and because FB users possess an FB-Dasein with FB-social-relations amongst the-FB-"they" in a highly developed FB-life that millions of Dasein attend to and aggrandize on a daily and even hourly basis, Dasein may easily -- and, this is the point: often does -- become involved with FB not in a mode of awareness that discerns its equipmental Being, but in terms it has confused with the structures and experiences of Being-in-the-world. Even though FB-Dasein and FB-life have existentiell Being(-in-the-world) and never existential Being(-in-the-world), Dasein today comports itself towards FB as an actual replacement for at least some aspects of social interaction in-the-world, by considering FB an indispensable feature of 'life' -- a conclusion further supported by the fact that the "they" and Dasein's "they"-self currently suppose FB-life is a component of a "full and genuine 'life'," even though prior to 2004 a "full and genuine 'life' " was to be had without FB, because FB did not exist. What are the implications of this for authenticity?

As outlined earlier, Dasein exists outside of and beyond FB, and it is existence that FB cuts out, and that FB can never capture because it is digital and equipmental. However, regardless of the fact that FB can never replace social interaction in-the-world (and can therefore never be a necessary part of 'life'), Dasein today acts as though it can, and is. Accordingly, the impact of FB on Dasein's authenticity is explicated by questioning the most basic FB activity: what happens when Dasein creates and maintains an FB user profile?

In filling out its FB profile, Dasein undertakes a semi-reflective process of concernful selection, and the direction this selection takes is guided by the details FB permits the user to enter, and by the standards of the "they"-self and the-FB-"they"-self in fallenness. This selection adheres to the manner in which the "they" selects, and in this "the real dictatorship of the 'they' is unfolded," for on every FB page and in the representation and presentation of every FB element, the selections of the-FB-"they" intrude visually and structurally. The "they" qua the-FB-"they" select those factical realities that present "them" and FB-"them" in the best possible light. "Everyone is the other, and no one is himself"; and the-FB-"they" uploads pictures in which they and their privileged companions are at their most appealing, and others are not; the-FB-"they" join groups that are exclusive, and embellish what is fashionable; and the-FB-"they" works to post more popular and not more meaningful content than others. Here, all FB-Dasein are involved, and reflect each other, and thus the concernful selection of FB-Dasein amounts to an eternal struggle to "one up" the-FB-other -- an impossibility, because every FB-Dasein is the-FB-other.

Falsity arises as Dasein works to present FB-Dasein in the best of all possible ways, for it selectively and willfully excludes all factical realities that do not contribute to FB-Dasein's superiority in-the-FB-world. This results in an inaccurate and fanciful (digital) representation of Dasein's Being-in-the-world, based on the delusive toiling of Dasein in-the-world, as it works to shore up its own falsity. This falsity inflicts the preclusion of authentic being, because "the being of Dasein is care," where care is a unity of falling, facticity, and existence -- hence the falsity of FB-Dasein negates Dasein's facticity, while at the same time the equipmental Being of FB cuts out existence, and only falling remains. Having concernfully selected only those facts of existence that bring Dasein a malicious and unsustainable contentment, Dasein is delivered unto "a tranquility, for which everything is 'in the best of order' and all doors are open"; and this "Falling ... which tempts itself, is at the same time tranquillizing." By this tranquillizing all moods that diminish contentment are suppressed, and because "Understanding always has its mood," the tranquillizing contentment that arises from selectively constructing an FB-Dasein radically reduces the range of possible understanding to the range of what is understood in contentment. Anxiety, guilt, and conscience are buried and become unrecognizable, and the entire project of Being-in-the-world is obstructed by the comfortable FB-relationships of a comfortable FB-Dasein, whose Dasein in-the-world is narrowed in to comfortable thoughts.

Ultimately, FB is therefore manifest as a technological system that offers a simulacra of worldness in its being, and by this simulacra Dasein's ownmost being is selectively differentiated in to a digitalized FB-being, by way of a process that promotes inauthentic structures and datum, thus inducing users to accept inauthenticity as an axiomatic starting point for self-reflection, and resulting in the equipmentalization of Dasein, and the reduction of opportunities for authenticity to arise in-the-world.

However, though FB encourages inauthenticity and discourages probity, the situation is not irresolvable, for; "inauthenticity is based on the possibility of authenticity" -- and here we observe a route away from FB's tranquillizing fallenness. FB can never reproduce the worldness-of-the-world, and by taking it apart and seeing what it is not, Dasein can move from engaging FB as ready-to-hand to engaging it as present-at-hand, thus opening Dasein to "a clearing-away of concealments and obscurities, as a breaking up of the disguises with which Dasein bars its own way." In a word: care remains possible, and it always remains possible for an FB user to recomport themselves to FB in a manner that befits its equipmentality.

As violins wax maudlin, viewers of the BBC documentary Dangerous Knowledge are introduced to "a small group of ... brilliant minds," who in the nineteenth- and twentieth-centuries; "unraveled our old, cozy certainties about math and the universe." These brilliant minds we are told, unraveled certainties that were so unassailable and beguiling that; "once they had looked at these problems, they could not look away, and pursued the questions to the brink of insanity, and then over it to madness and suicide." Here, and through the rest of documentary, the presenter suggests a direct, and even mono-causal relation between deep mathematics and deep disturbances of mind, as apparently revealed by the life and works of four brilliant thinkers, including the mathematician and philosopher Kurt Gödel (1906 - 1978).

Gödel, it is true, exhibited paranoia, and the idea that mathematics induced his mind to madness is certainly a romantic one, suggesting the image of a tragically brilliant Narcissus, who observed the reflection of logical structures so beautiful he could not turn away, and was thereby psychically diminished. Quite apart from romanticism however, this begs the question: is this so? Can mathematics push a mind "to the brink of insanity, and then over it"? Is mathematics dangerous knowledge?

The query seems an odd one, however, the BBC presenter himself is fully solemn when making his claims, and in making such claims he is not alone. Many observers ponder the connection between deep mathematics and psychology, and, taking Gödel's work as inspiration, one biographer has suggestively entitled her book Incompleteness: The Proof and Paradox of Kurt Gödel, therein invoking Gödel's famous incompleteness theorem in connection to madness, stating;

"Gödel's theorems are darkly mirrored in the predicament of psychopathology: Just as no proof of the consistency of a formal system can be accomplished within the system itself, so, too, no validation of our rationality -- of our very sanity -- can be accomplished using our rationality itself. How can a person, operating within a system of beliefs, including beliefs about beliefs, get outside that system to determine whether it is rational? If your entire system becomes infected with madness, including the very rules by which you reason, then how can you ever reason your way out of your madness?"

Here the suggestion is not that mathematics is necessarily dangerous, but that the mathematical results of Gödel's incompleteness theorem might in some way help us unpack the predicament of "a person, operating within a system of beliefs" whose "entire system becomes infected with madness." Again, we must ask: is this so?

Quite apart from claims proposing some mathematics of madness, the question of how incompleteness bears on the mind merits consideration, and, keeping one eye on the connection between math and human states of mind, we will here examine the basic implications of Gödel's incompleteness theorem for the mind. Because we are concerned with the significance of the incompleteness theorem as it relates to what humans may know as regards the mind, we will first expound the claims and conclusions of the theorem, then discuss the implications that do (and do not) follow from the theorem, and follow this with observations on what we may reasonably believe the theorem tells us about human thought and the mind.

Here we begin with an exegetic account of the content and significance of the theorem, including a limited discussion of the mathematical details.

Collectively, the term "incompleteness theorem" refers to two individual theorems that pertain to formal mathematical systems with an arithmetical segment, where such a system is determined by its language, axioms, and rules of inference. With respect to the characteristics of such systems, the first incompleteness theorem speaks to the provability of arithmetic sentences within a specific system, and concerns the mathematical notions of consistency and completeness. Mathematically speaking, if a formal system is consistent, then it contains no contradictions; if the sentence A is provable in the system S using the axioms, language, and rules of S, then not-A is not provable within S. Conversely, if a formal system is inconsistent, then logical contradictions are provable by S, and for some sentence A, the sentences A and not-A are both provable within S. Or, as one commentator has it: "anything follows from a contradiction." Separately, if a formal system is complete, then that system permits the construction of proofs for all logical consequences following from the system's axioms and rules, and all consequences are decidable.

Taking these definitions and descriptions, we now state Gödel's first incompleteness theorem:

If the formal system S exhibits arithmetic and is consistent, then S is necessarily incomplete, and there exists an arithmetical sentence A in S that is undecidable in S; when S is consistent it is not also complete, and when S is complete it is not also consistent

(Note that this formulation is not categorical, but is composed to help us later locate connections between incompleteness and the mind. As noted, here we will focus on the content and significance of incompleteness, and not its technical aspects.)

The inability to decide the specific arithmetic sentence A pertains specifically to system S, while the characteristic "there exists an arithmetical sentence A in S that is undecidable in S" is applicable to formal mathematical systems exhibiting arithmetic. In connection to exhibiting arithmetic, the first theorem is apposite to any system that includes what Torkel Franzén has dubbed a "certain amount of arithmetic," meaning a formal system that includes sufficient arithmetical language, rules, and axioms to apply the first incompleteness theorem for that system. The phrase "certain amount of arithmetic" is somewhat esoteric, though necessarily so, as Franzén explains;

"if a property of natural numbers, such as being the sum of two primes, can be checked by a mechanical computation, then if a number n has that property, there is an elementary mathematical proof that n has the property. The 'certain amount of arithmetic' that a formal system S needs to encompass for the proof of the first incompleteness theorem to apply to S is precisely the arithmetic needed to substantiate this claim."

So, if the formal system S exhibits this certain amount of arithmetic, then by the first theorem we know S is incomplete with regard to its certain amount of arithmetic. Because the first theorem appertains to provability, it is notable that the certain amount of arithmetic does not need to be extensive or complicated, and the conclusion of the first theorem bears alike on systems that are elementary and on systems that are highly abstract.

Moving from completeness to consistency, the second incompleteness theorem speaks to the provability of the consistency of formal mathematical systems possessing a certain amount of arithmetic, and states:

If the formal system S exhibits arithmetic and is consistent, its consistency is not provable within S; it is not possible to prove Con_S (the consistency of S) using the axioms, language, and rules of S

Like the first theorem, the second theorem describes a characteristic of formal mathematical systems that express arithmetic, and also like the first theorem, its references are not absolute, but relative to some specific system S. The statement "if the formal system S exhibits arithmetic and is consistent, its consistency is not provable within S" explicates the inability of proving Con_S using system S in reference only to system S, and has no specific implications for other systems. It may be the case that Con_S can be proved in another system, but the second theorem presents no insight regarding such prospects.

We thus observe that the title of the incompleteness theorem arises from its proof that the arithmetic segment of a formal system is incomplete and cannot provide decidability for all statements, and that the consistency of arithmetic cannot be shown arithmetically. These remarkable results were arrived at arithmetically, and this fact is central to understanding the generation and consequences of the theorem, which apply to formal systems in a general way.

In order to develop his proofs arithmetically and generally, Gödel contrived a method to enable a formal system to make statements such as Con_S, which is a statement in S about S. This he achieved by the development of new mathematical innovations, Gödel sentences and the arithmetization of syntax, and by applying the basic logical implication that for the Gödel sentence G within the system S, if S is consistent then G is true. The Gödel sentence G is an arithmetical construct that can be calculated for arithmetical proofs and sentences, and because formal systems make statements about their own arithmetical constructs, Gödel sentences therefore permit formal systems to make statements about their own proofs and sentences. Accordingly, because Gödel sentences and the arithmetization of syntax are arithmetical, the incompleteness theorem applies generally to formal mathematical systems that possess the requisite arithmetic (Franzén's "certain amount of arithmetic"), whether a system does or does not include other mathematical or non-mathematical objects.

With respect to the consequences and implications of incompleteness, the theorem's conclusions are specifically about arithmetic, and the theorem does not explicitly state or conclude anything about a system's non-arithmetical or non-mathematical objects. This means the incompleteness theorem has no direct applicability outside of mathematics. Nevertheless, like all systems we develop, mathematically or otherwise, the theorem itself is a product of the human mind and must have some implications for the mind, if indirectly, and must have some implications for statements that are not strictly arithmetical or mathematical. What might some of those implications be, and how are they to be uncovered?

Reflecting on the content and conclusions of the incompleteness theorem as outlined above, we see the theorem suggests a number of questions and areas of inquiry, with respect to its implications for knowledge of the mind. In particular, if the mathematical systems we conceive cannot be both consistent and complete, or prove their own consistency, and no single system can provide decidability for all arithmetic, then what does it mean for humans to speak and think of the truthfulness of a mathematical proof? In this connection, what are the consequences of incompleteness for the mathematical frameworks that the mind is able to formalize, and what does incompleteness mean for human attempts to represent arithmetical knowledge using formal systems, and related attempts to convert formal systems in to machine-based representations of those systems? Does incompleteness imply the mathematical abilities of the mind exceed the abilities of (humanly built) systems and machines?

To develop a fundamental understanding of these issues, and uncover the relationship between incompleteness and its implications for human knowledge of the mind, we will discuss these questions individually, while also considering their interrelationships.

Beginning with the question of how humans should regard mathematical knowledge, it is instructive to express this question as a skeptical inquiry regarding the nature and outcomes of mathematics: are proofs generated using humanly defined mathematical systems to be taken as objectively and universally truthful, irrespective of humans, human thought, and intellectual structures? This is a popular and perennial question, not originally or specifically motivated by the incompleteness theorem, but the consequences of the incompleteness theorem do have a bearing on any answer.

The incompleteness theorem formalized that we can develop a consistent theory that proves the theory itself is not consistent, and that the consistency of a system is no guarantee the system will not prove false sentences. This was shown to be a general problem, and what this means is that it is right for skepticism to arise regarding the results of mathematical claims developed using even consistent systems. Thus, one of the most basic consequences of the incompleteness theorem for human knowledge of the mind is that we are rightly skeptical about the probity of knowledge arising within that particular subset of our knowledge that is encapsulated and expressed in the formal mathematical systems we conceive and work with.

Accepting this as inescapable, how should humans comport themselves towards formal mathematical proofs, and what does it mean for an arithmetical statement to be true? This line of inquiry also existed long before the advent of the incompleteness theorem, and while the incompleteness theorem by no means solves the question, it does strengthen our understanding that the soundness of an arithmetical proof imputes to that proof not the objective property that it is universally true irrespective of all qualifications, but rather, what we know is that the proof was generated in a logically conclusive manner using the language, axioms, and rules of inference of those systems that prove it. In this way, the incompleteness theorem assists in rounding out our notion of arithmetic truth, by showing us that particular proofs and theorems will always have truth and falsity relative to their systems, and not have truthfulness in an absolute, universal sense. This helps us better distinguish formal systemic truth from the notion of truthfulness for an arithmetical sentence, which is not relative (because in a non-relative way, uttering the "words 'the twin prime conjecture is true' is simply another way of saying exactly what the twin prime conjecture says. It is a mathematical statement, not a statement about ... any relation between language and a mathematical reality").

In contrast to the indirect observation that the incompleteness theorem "rounds out" our notion of arithmetic truth, one of the most important direct consequences of the incompleteness theorem pertains to David Hilbert's famous Program (which was a source of inspiration for the theorem's development). Where Hilbert sought to bring about the development of a concrete, consistent, formal system whose axioms, language, and rules determined the set of all arithmetical problems, Gödel's theorem proved that for any consistent formal system, there exists an undecidable sentence in the system. Therefore, regardless of the size or complexity of a system, no system can prove all statements concretely, and Hilbert's mathematical program as originally conceived is unattainable, because no single construction can expose and treat of all arithmetic. Thus, in addition to skepticism regarding the universal probity of mathematical statements conceived by the mind, the implication for the mind here is that it can never generate a formal definition that encompasses all human arithmetical knowledge.

Because we are unable to construct a single system that encompasses all human arithmetical knowledge, we therefore know our mathematical potential goes beyond our ability to formalize mathematics. To see this what this means, let us begin with the goal of maintaining systemic consistency, and consider the system S, to which we add the statement C; "S is consistent." S+C remains consistent. Now add C1; "S+C is consistent." S+C+C1 remains consistent; and so forth. Here we can continually construct simple systemic extensions with no end, by repeatedly adding to a consistent system the axiomatic statement that the existing system is consistent, thus yielding new systems that are consistent and determine more than prior systems. Proportionate to this demonstration, the implication of the incompleteness theorem for our knowledge of the mind is that its arithmetical knowledge is inexhaustible.

Inexhaustibility leads to questions about the limits of mathematical machines and computers, and has prompted some to claim that a direct consequence of incompleteness is that because our mathematical potential is inexhaustible and goes beyond our ability to formalize mathematics, we therefore know the human mind's arithmetical processing powers will always exceed those of computers, regardless of technological advancement. But does this follow from incompleteness? We know it possible to formalize our systems and represent them via computers and computer-based operations, and we also know we cannot fully capture our arithmetical abilities in a single system; but does this mean the human mind's arithmetical abilities exceed our computers?

If we consider Gödel sentences, then one fact we are certain of regarding these sentences is the formal implication that if a system S is consistent then its statements about its Gödel sentences are true. However, incompleteness does not tell us whether or not S is consistent. For this reason, the consequence of incompleteness for machine-based representations of human mathematical abilities is the familiar one: humans are unable to build a single computer-based representation of a formal system that solves every arithmetical problem, because we cannot define such a system. Thus, incompleteness does have implications for attempts at constructing machine-based representations of the human mind, but those implications do not include, or support the claim that the arithmetical ability of the human mind exceeds the arithmetical ability of humanly defined mathematical systems (be those systems computer-based or not). We cannot conclude from incompleteness that the mind's arithmetical processing powers will eternally exceed those of computers, regardless of technological developments.

Accepting the conclusions of the incompleteness theorem and reflecting on the discussion above, we can reasonably accept the following consequences of incompleteness for human knowledge of the mind: humans are right to approach their proofs and mathematical knowledge with some measure of skepticism, owing to the property of systemic relativity; our minds can not construct a formal definition that encompasses all humanly accessible arithmetical knowledge; the mind's arithmetical knowledge is inexhaustible; and, we are given no reason to believe the mind's arithmetical ability will permanently exceed the abilities of humanly defined systems, including computers. With this list of implications in hand, we discover while looking back to the opening comments of this paper the existence of a striking lack in the basic connections between incompleteness and the mind: madness.

Insofar as it is a product of the human mind, Gödel's incompleteness theorem is exceptional, and precisely because of this, when examining its content and implications the student of incompleteness must be careful, because the direct implications of the theorem are mathematical and metamathematical, and though the theorem's indirect implications do extend beyond their specific mathematical content, its non-mathematical implications are by no means simple to explicate. Notably, the truth of this is well supported by the existence of the book Gödel's Theorem: An Incomplete Guide to Its Use and Abuse, wherein the author's primary purpose is to disabuse readers of many inspiring, but patently incorrect interpretations of the incompleteness theorem inside and outside of mathematics, noting that much of the confusion regarding incompleteness stems from the fact that it is a commentary on systems.

Reflecting on systems and the conceptual development of mathematics, it appears we find in our history something of a human drive to systematize. In our written records, we observe repeated attempts to develop exact and exhaustive systems: from Euclid's Elements to Aristotle's Categories and Frege's Foundations of Arithmetic; from the Christian Bible to Bacon's Novum Organon and Hegel's Phenomenology of Spirit; and beyond. In these works the drive to systematize is manifest metaphysically, analytically, algebraically, and arithmetically; and, though it is true these works and their systems are products of the mind and must reflect the mind in some fashion, and though we also recognize with certainty that mathematics can be used to predict empirical phenomena, we also recognize that formally speaking, students of the philosophy of mathematics must be careful not to conflate mathematical concepts and conclusions with metaphysical precepts and suppositions. The content and methods of mathematics differs substantively from the content and methods of, for example, the physical and social sciences.

Gödel himself commented on the exigencies of human ideas, expression, and understanding, and noted; "The more I think about language, the more it amazes me that people ever understand each other at all."

Towards the end of understanding, and being careful not to misrepresent the basic implications of Gödel's incompleteness theorems for knowledge of the mind, we have accepted the systemic relativity of mathematical truth, the inability of total arithmetical formalization, mathematical inexhaustibility, and the fact that incompleteness does not mean the mind's arithmetical abilities will continue to exceed those of computers. Expressly, what we do not accept is any suggestion, however oblique, that the content of the incompleteness theorem somehow drove Kurt Gödel mad, or that the content of the theorem might be used to explain madness.

While incompleteness does have implications for human knowledge of the mind, we must respond to all claims that systematize the mathematics of madness with an elementary inquiry: if powerful mathematical insight induces madness, why is there not an endless profusion of insane math students? If the content of the incompleteness theorem drove Kurt Gödel mad, then surely others who have worked with the theorem -- or with the theories of Cantor, Boltzmann, and Turing -- should have been driven to madness as well. Here we find ourselves far removed from the realm of mathematical thought, and, as a consequence of our analysis above, we understand that any discussion of madness is far removed from discussion of Gödel's incompleteness theorem.

In a recent article, Jim Sleeper rightly and righteously reminds his fellow Americans that while Obama is off doing his I-see-it-fit-to-preside-politically-over-millions thing; "it's up to the rest of us to find our civic-republican selves and start building a better politics with others who are doing that, too." This is the final sentence in Sleeper's article, and this is an interesting fact to note, because it's not the end of his argumentative direction. Sleeper is certainly on the right track to expounding a basic tenet of civic living, but he never reaches the necessary conclusion, which is: politics is up to all of us, at all times, regardless of existing political structures and conditions; and, what's more: it always has been.

The clues to understanding why Sleeper never reaches this conclusion lie in the rest of his article, and in particular the following statement, with which he leads in to his final sentence; "Obama has failed to find his inner Lincoln. But someone else will." So, per Sleeper, politics is (1) up to those of us who are not Presidents and politicians, and (2) up to those of us who are Presidents and politicians. This may appear to make sense, as it can easily be interpreted to say little more than politics is up to all of us. That however is not what has been said. What has been said is (1) there exists a natural separation between politicians and "the rest of us," and (2) political Lincoln-types occur, and in between the occurence of Lincoln-types "it's up to the rest of us to find our civic-republican selves and start building a better politics."

We have to ask: which is it? Either politics is up to "the rest of us" -- that is, all of us (at all times, regardless of existing political structures and conditions) -- or else "the rest of us" must sit back and not interfere in politics, because that's the only definite way to ensure those politicians with inner Lincolns are given the necessary social, political, and economic latitude to find their "inner Lincoln."

This idea, Sleeper's "inner Lincoln," might appeal to some, but what does it mean, exactly? Do we all have an inner Lincoln? Only some of us? If only some of us, how do we know which ones? How do those with an inner Lincoln find it? Some may be tempted to let Sleeper off the hook for waxing romantic about inner Lincolns, by pointing out it was nothing more than a rhetorical device; an allusion meant to highlight what some feel the incumbent could have done while in power, but manifestly did not do. That response however would also be waxing romantic, and worse, would answer nothing. If the discussion at hand is important, then it's important to be exact, and what I asked was: what is Sleeper saying, exactly?

To state "Obama has failed to find his inner Lincoln," and "someone else will," and "in the meantime it's up to the rest of us to find our civic-republican selves" is to presume that at some stage, under some sociopolitical conditions it's both feasible and acceptable for "the rest of us" not to develop "our civic-republican selves," and merely watch as Lincoln-types go about ruling civic life -- for "the rest of us."

Either civic life is up to all of us, and we all share in the costs and rewards, or civic life is up to elites who are permitted to develop themselves and society as they see fit regardless of the desires of non-elites, and thus elites determine the distribution of costs and rewards. These notions are mutually exclusive, and this is not a matter of degree, because these two conditions can not exist together except by way of paradox-condoning apologetics; if political elites exist, be they Lincoln-types or not, then those elites make civic decisions that by definition discount the input of non-elites, and hence the civic life of non-elites is not under their own control. So what is it other than paradox-condoning apologetics to pronounce; "Obama has failed to find his inner Lincoln. But someone else will, and in the meantime it's up to the rest of us to find our civic-republican selves and start building a better politics with others who are doing that, too"? Let's not overlook the fact that what Sleeper has done is to choose one elite as an exemplar, and then recommend to another elite that he model himself after Sleeper's chosen exemplar elite, an act which in itself is contradictory.

Considering these contradictions, it's interesting to note that Sleeper opens his article with a statement about reasonability in politics, claiming; "Hannah Arendt characterized politics as a realm of 'speech-acts,' in which words are close enough to deeds so that the words aren't evasive or empty and the deeds aren't mindless or brutal." Now, this is my first exposure to the writings of Jim Sleeper, and I have to be sure to make it known I have no idea where he stands on the questions of Neo-Liberal power politics. However, the issue here is what Sleeper has said in this article, and with Sleeper's reference to Arendt in hand, I must also note that Sleeper himself makes at least one claim within this article that is both mindless and brutal.

Near the beginning of his article (at the beginning of his fifth paragraph), Sleeper states; "I credit Obama with elevating racial politics." Is this reduction not mindless and brutal, in its discounting of the generations of civil and social activism undertaken by the nameless masses throughout American history? Did Obama elevate racial politics? Of course not. Obama the individual did not single-handedly direct "the rest of us" towards an elevated racial politics. If anything, Obama tapped into the popular currents and undercurrents of his era and prior eras, and has perhaps been able to work with countless others in a socially progressive direction on some issues, including racial politics. Even the previous sentence as I've composed it does not, and indeed can not do justice to the tens of millions of people who have worked for, died for, and supported civil rights; but the previous sentence, as I've composed it, is a far more just characterization of reality than the absurd Great Man reduction; "I credit Obama with elevating racial politics," which does mindless brutality to all those not included in the statement.

Sleeper does go on to discuss Martin Luther King and his followers, but again, Sleeper seems to apportion an inordinate share of credit to King, by excluding adequate mention of King's supporters, without whom King could have done nothing, a fact that King himself well understood and referred to constantly. Was King a unique individual? Yes. Did King elevate racial politics? Not without the rest of us he didn't.

Connecting this to Lincoln-types and Lincoln: did Lincoln elevate racial politics with all other Americans in absentia? Of course not. Just like Obama, he tapped into the popular currents and undercurrents of his era and prior eras, and was able to work with countless others in a socially progressive direction on some issues, including racial politics. The question is: did Obama and Lincoln regulate, or even control the politics of their era? Did they come to govern because their political philosophies and abilities were independently superior to popular and widely possessed political philosophies and abilities? Or, might Obama and Lincoln have attached themselves to the popular currents and undercurrents of their era in order to obtain popular support for themselves towards the end of obtaining personal political power, thus disclosing the fact that the elevation of racial politics occurred primarily not because of Lincoln-types, but because of sociopolitical trends that had power regardless of Lincoln-types?

Obama and Lincoln (and King) may stand out as political actors, but that is categorically because they were a part of something that was already happening without them.

"Every human being at every stage of history or pre-history is born into a society and from his earliest years is moulded by that society. The language which he speaks is not an individual inheritance, but a social acquisition from the group in which he grows up. Both language and environment help to determine the character of his thought; his earliest ideas come to him from others. As has been well said, the individual apart from society would be both speechless and mindless."

Similarly; every human being at every stage of history or pre-history is born into a society and from their earliest years their achievements are both framed and permitted by that society. The heights a person attains are not of individual creation, but rest atop social and historical acquisitions from the groups to which that person has been exposed. Both language and environment help to determine the reach, depth, and originality of a person's thought; which is to say, a preponderance of our ideas originate outside of us. The individual attempting to advance civic culture while working apart from society itself would be both hopeless and fruitless.

Keeping society, the individual, and civic culture in mind, let's think about the basic premise of Sleeper's claim; "I credit Obama with elevating racial politics." Have racial politics actually been elevated by Obama since his entrance in to the White House? If so, then how, and for who? If we're serious about discussing racial politics, then at the very least we have to discuss (1) the incarceration of minorities, and (2) income inequality.

Looking first at the incarceration of minorities, is it not the case that the racially centred observations of Angela Davis' book Are Prisons Obsolete? are just as true today as they were in 2003, after almost three years of Obama in government? Davis observes -- not argues, observes -- that during her "career as an antiprison activist" she has "seen the population of U.S. prisons increase with such rapidity that many people in black, Latino, and Native American communities now have a far greater chance of going to prison than of getting a decent education." Has that situation been elevated since Obama entered the White House? No. Quite to the contrary.

So, if racial politics have been elevated, how and for who have they been elevated? Here again, we require exactness. Looking at the matter economically, one might say racial politics have been elevated for the upper and middle classes. But what about other economic groups? In the matter of income inequalities, we discover that Obama is the president of a government whose economic, and therefore social policies harm precisely those groups that already had "a far greater chance of going to prison than of getting a decent education." Still today, even after Obama's supposed elevation of racial politics, "A new study of U.S. census data reveals that wealth gaps between whites and minorities in the United States have grown to their widest levels since the U.S. government began tracking them a quarter-century ago."

Considering the points outlined above, who cares if a person that made $60,000 a year can now make $70,000, or worse $75,000? (Yes "worse," for all those who make less, regardless of ethnicity or background.) Perhaps Obama's "speech" has punctuated racial politics more than the previous president's, but on balance have the results of Obama's "speech-acts" contributed to eradicating the wealth gap or fixing the distorted relationship between black, Latino, and Native American communities and the prison-industrial complex? Clearly the answer is no. Is it then responsible to "credit Obama with elevating racial politics"? No, it is not responsible, and to intone otherwise is mindless and brutal.

Tying this back to my opening statement that Sleeper never reaches the necessary conclusion, that politics is up to all of us, then how should we take Jim Sleeper's Lincoln-types/the-rest-of-us dichotomy? It seems Sleeper would have "the rest of us" support and sustain elites as they attempt to find their "inner Lincoln," so that those elites can then guide us through a society in which even the most glaring contradictions are glossed over via paradoxical apologetics that credit an elite who "has failed to find his inner Lincoln" "with elevating racial politics" amidst raging race based political problems that have patently not been elevated by said elite. Is there any way to define such a society as one "in which words are close enough to deeds so that the words aren't evasive or empty and the deeds aren't mindless or brutal"?

This I leave you to decide for yourself, because politics is up to all of us, at all times, regardless of existing political structures and conditions; and, what's more: it always has been.

"... but the Krell forgot one thing: monsters, John. Monsters from the id."

-- Lt. "Doc" Ostrow

"I realize today that nothing in the world is more distasteful to a man than to take the path that leads to himself."

-- Herman Hesse qua Emil Sinclair

One: I respect your human rights, but not your ideas. None may respect your ideas, none, and even less your actions; most especially your choices. Although, such an important distinction has but little chance of penetrating the psycho-material anxiety defended by the monsters of your id.

Some jest to retrieve perspective. Some jest because they loath reality.

After all, but before nothing, One felt it acceptably necessary to descend; "I guess he wasn't one of her superstars." Having no intimation of the dangers such as a One's, believing there is little or nothing to learn from those "lower" -- nothing whatsoever. But the "ultimate criterion of the value of a functional whole is the degree of its internal harmony or integratedness," not the ludicrous id of some erratic emptor. Not for the nonce, none "lower" than McLuhan professed it is those below who keep those above afloat, and not the distaste of some Morbian id.

Morbius, like you, has it all figured out, except himself.

If the object of your well-developed system is to reduce arbitrariness, then the object is also to reduce unfoundedness to its furthest conceptual vanishing point. Yet any and every individual, being individual, cannot help being arbitrary. So how that Great theories be something other than a partial trajectory of arbitrariness? Greatness being claimed to arise from One, only because the One arbitrarily assigns to themselves the efforts and accomplishments of countless others. This of course we shall call Absurdity.

Is not the damnation of such a One their mutually assured intellective destruction? Petty pedagogues, sleeping scholars; fagged faculty, barren benches. The middle class being the class of the middle, living in "balanced" insanity. You are-to-be as your temporality is deployed. If One deploys One's time for catechizing distaste -- "I guess he wasn't one of her superstars" -- then in what direction has One developed their's and One's being?

Catechizing distaste. Of all the axioms to organize One's being around, One chooses distaste. Thus the secrets of life become banal devices for combination into fragrant honours. Fatal honours from the id. But you are grand and do not have a spinet, because it is not long surrounded by the same walls and upholstery!

But no: your learned lack of non-Absurd creativity does not constitute my politics. A "new reality Is better than ... a fantasy of defeat." If it is mostly brightness that is embellished, must One be surprised to discover it is mostly brightness that has developed?

The test could hardly be simpler: was it promulgated top down or bottom up? This discloses whose interests it represents. How then, hideous Jinn, may any who enter from below, as most must, possibly escape your disgust?

Fate behold the arts
of ordinary men
whom Charybdis betakes
and wastes by every whim.

Sartor abdicaret, Sartor Resartus, in fear of One who held themselves never contingent; One who applies all creativity towards abusing others as badly, if as subtly as possible; predictability and determination not being the same as not being malicious.

Being malicious; "superstars." An alcazar framework that normalizes and ensures the punishment of everything "unsuper."

We do only those things we deem necessary. Could such suppuration make One feel necessary? It was untrue. What Thoreau called the smoke of opinion, what Wilde observed as its all too palpable violence, and what Ostrow dubbed Monsters from the id.

If it is important to understand, then flowing from this is an obligation -- an obligation mind you -- to respectfully demand proof. Being-open to being-challenging and being-challenged. The importance that no belief-claim stand protected from inquiry.

Discard thy distaste, for here is a noble metaphysic on which to pin your physics: treat others not as though protecting a forbidden planet, and escape the curse of Hesse.

"Being-with is an existential constituent of Being-in-the-world. Dasein-with has proved to be a kind of Being which entities encountered within-the-world have as their own. So far as Dasein is at all, it has Being-with-one-another as its kind of Being. This cannot be conceived as a summative result of the occurrence of several 'subjects'. Even to come across a number of 'subjects' [einer Anzahl von "Subjekten"] becomes possible only if the Others who are concerned proximally in their Dasein-with are treated merely as 'numerals' ["Nummer"]. Such a number of 'subjects' gets discovered only by a definite Being-with-and-towards-one-another. This 'inconsiderate' Being-with 'reckons' ["rechnet"] with the Others without seriously 'counting on them' ["auf sie zählt"], or without even wanting to 'have anything to do' with them."