§5 — Reciprocal or circular definition is abysmal – or groundless – and thus traditionally considered suspect, if not prima facie evidence of hopelessly defective reasoning. Unfounded circuitry is naturally disconcerting, when identified in the world, let alone in our thought processes. Under certain circumstances, however, characterized by cumulative bootstrapping, it can be an exceptional index of theoretical productivity. An especially remarkable example, from the perspective of this book, is provided by the intertwining of the questions ‘Is Bitcoin money?’ and ‘What is money?’ In holding these two questions open simultaneously – suspended within the abyss of what we do not know about either – the prospect is opened of learning something about both. What Bitcoin teaches, at a very early stage of apprehension, is that we do not yet have a confident answer to the question: What can money do?
§5.01 — An economical list of essential monetary functions is exhausted by just three indispensable entries. Money provides a medium of exchange, a store of value, and a unit of account. In other words, money facilitates commerce, preserves wealth, and sets a standard for economic calculation. According to a preliminary apprehension, it is a functional trinity of flow, stock, and metric. In support of these functions, money typically possesses a number of predictable qualities, most prominently the characteristics of scarcity, durability, verifiability, divisibility, portability (or communicability), and fungibility. Of these six qualities, the first three are essential to the preservation of monetary value, and the remaining three to commercial convenience. These aspects are reciprocally reinforcing, mutually establishing a standard unit of account (or of credit).
§5.02 — Attempts to establish a robust conceptualization of money’s functional trinity soon run into intricate difficulties. What appear to be merely formal differences, when captured at certain moments, and from limited perspectives, appear amid other circumstances as substantial distinctions, dense with historical contingency, and lacking even minimal ontological integrity. Consider, initially, the unit of account. As Braudel explains:
… these were imaginary units, used for reckoning, for estimating the relative value of coins, for fixing prices and wages and for keeping commercial accounts which could later be translated into any kind of currency, local or foreign, when the time came to move from the ledger to actual cash payment. … One would have to go back a very long way to find the coins corresponding to the money of account – but all such moneys had at some point in the past been real money.
§5.03 — No pure analysis of money, we can immediately see, is able to take us far on its own. A monetary regime is a synthesis – we might want to say an assemblage – consisting of heterogeneous elements mutually composing a functional whole. Insofar as a single monetary medium is able to integrate these elements, in a way that seems to facilitate a subsequent formal decomposition into neatly interlocking functions, a complex achievement has taken place, whose partial invisibility attests to its success – without detracting from its historical precariousness. It is only very late in the real process that a money system is able to appear as the near-perfect incarnation of a simple idea, internally differentiated by a logical structure.
§5.04 — The tension between money flow and stock – corresponding closely to that between commerce and wealth – is no more tractable to confident philosophical apprehension than the (partially abstract) unit of account. It, too, is a complex of ambivalences, wavering uncertainly between formal and substantial distinctions, and subject to dynamic swirls of cross-dependency. It is not only that each of these functions is also partially logical and / or semi-empirical, in itself. The inter-connections between them add further oscillations between logical disjunction and empirical difference. The functions of money as a means of payment (currency, flow) and a store of value (asset, stock), cannot be considered entirely in isolation, since the distinction involves both adjacency (real differences of media, in a relation of complex complementarity) and substitution (switchings between assets, guided by the intensity of ‘liquidity preference’). Money’s logical aspects and its multiple media cross-connect in theoretically inconvenient ways.
§5.05 — For example, the divisibility of money, a purely formal (arithmetical) relation from one regard, is incarnated in a substantial heterogeneity – between distinct metals – from another, and subject in this latter to variations in exchange rate across time. In the European economic tradition, gold ‘divides’ into silver on the basis of an ideal value relation of twelve to one. Yet, in actuality, this ideal was only occasionally, and – once again – precariously realized. The same distinction between monetized metals which played such a crucial analytical function within the monetary system (as an order of divisibility) simultaneously preserved its synthetic characteristics (as an exchange relation between different commodities). Historically, the difference between ideal and actual exchange values generated variations in ‘pressure’ comparable to meteorological conditions, as relative scarcities of gold or silver drove currency units across and beyond continents in storms lasting decades, or even centuries. Formal tokens of accountancy were at the same time the particles of substantial bullion flows. Mathematics mixed with metal, indissociably.
§5.1 — The functions of money will be under continuous examination throughout this chapter. What can money be reliably broken-down into? That is the question techno-frozen into every change machine. When grasped at a sufficient level of abstraction, the philosophical inquiry is not so very different. The logical pieces of money – its qualities – are therefore worth limning, tentatively, in advance. Since it is philosophically discomforting to rest a central analysis wholly upon consolidated empirical generalization (which is to say, upon tradition), the temptation is to search for a relevant principle. Can ‘the six qualities’ of money be convincingly rationalized, from a ramshackle list into a categorical structure, sub-divided in strict accordance with a conceptual principle? Since no unambiguous draft for such a schema is to be anticipated from historical evidence, it can only be supplied as a ‘regulative ideal’ or teleological model – to be excavated from the virtual, on the diagonal path of synthetic a priori construction.
§5.11 — Durability, at its most basic, is mere existence, or actual reality, insofar as this is conceived as occupation of time, or the possession of temporal characteristics in general (participation in duration). The monetary excellence of high comparative durability is an empirical feature, but one that is asymptotic to indefinite persistence, or non-locality in time – the limit of constant existence, at which it re-connects with the transcendental. Concrete currencies tend to closely approximate to this ideal. Precious metals, for instance, are indestructible (for all purposes of practical economic calculation). Ledger entries – while necessarily bound to physical incarnation – manifest an intrinsic idealization that approximates even more exactly to an absolute durability (identified with a substrate-independent institutional memory). Perishable goods disqualify themselves from serious consideration as monetary media (unless under very exceptional circumstances). For any store of value, extreme durability is a necessary, if not in itself a sufficient, condition.
§5.12 — Scarcity grounds economic value in general. Nothing that is freely available without the inconvenience of trade could conceivably have commercial worth. Abundance begins where economy ends, and Cornucopian thinking is not a type of economics, but rather its general denial. Scarcity finds its mathematico-philosophical outer limit in the concept of ‘finitude’ (since the division of infinity is economically incalculable), but this determination is too expansive to capture it well. Greater purchase is achieved by the notion of difficulty, especially as this is employed by the Bitcoin Protocol. The concept of scarcity is the complement of commercial trade-offs or industrial effort, and thus of economic activity. The scarcity of money presumes a solution to the DSP.
§5.121 — In combination, durability and scarcity provide the foundations of being and value, constituting an – as-yet generic – permanent asset, or (to reverse the order of determinations) an economic substance. At this elementary level of definition, it remains notably non-specific, encompassing such non-monetary assets as real estate, or stocks of imperishable commodities. To acquire a commercial function, as an essential step towards its operation as money, economic substance has to provide for convenient re-allocation. Money has not only to be valuable, but also distributable. (We will see a little later, and finally, that it has also to be credible.)
§5.13 — Divisibility enables money to match prices. The divisibility of the monetary medium sets the range of retail pricing options (and the subtlety of potential price competition). While money is only ideally continuous (or infinitely divisible), this condition is practically approximated by an acceptably fine granularity. The smallest unit of money in circulation corresponds to the point of commercial indifference, beyond which variation is considered irrelevant to economic decision making (as mere ‘rounding errors’). The trade-off between standardization of units and delicacy of quantitative differentiation sets an equilibrium point, to which the atoms of the currency approximate. In other words, coarseness is an imperfection relative to ideal money, tolerated for practical purposes. (The massive economic applicability of the calculus does not imply a significant appetite for monetary infinitesimals.) This feature of money acquires a new prominence in the era of digital-electronic micropayments. Already in the early decades of the computer era, it was anticipated that the friction afflicting minuscule monetary units would be electronically eliminable. Ted Nelson’s attention to the question is especially notable. Under these conditions, the zone of commercial indifference – where monetary quantities become ‘negligible’ – has the potential for transformation into a positive attractor. A massively expansive, monetarily hyper-sensitive agora opens distinctive commercial possibilities (extrapolated from those long developed within industrializing consumer capitalism). Minute margins become economically tolerable (in principle), due to the volumetric re-scaling of microscopic sums into significant quantities within Internet-globalized markets.
§5.14 — Communicability (techonomically supplanting ‘portability’) measures the degree to which money is transmissable. It is division, or distribution, apprehended not only as an arithmetical property, and a contractual consummation, but also as a physical transfer. Transmissibility is an implicit characteristic of the economic sign. To be in one place, rather than – any longer – in another place, is the irreducible material substrate of every notional re-allocation within double-entry book-keeping. A commercial transaction is always a process of reciprocal transference, requiring – on both sides – a real redistribution (of matter in space). Semiotic subtilization cannot fundamentally compromise this necessity. Even the mere revision of a ledger is never less than a physical event. Nevertheless, asymptotic dematerialization is a real feature of signs under conditions of techonomic escalation, exemplified by electronic information, and the satisfaction of commercial transference by a (micro-physical) revision of accounts.
§5.15 — Fungibility is a feature of the economic commodity in general, in the strong (and prevalent) sense of a tradable good undifferentiated by (significant) qualitative variation. By collapsing all dimensions of intrinsic comparison between instances of the same good onto a single quantitative axis, it optimizes the conditions for commercial computation and price competition. The extreme relevance of its application to money strengthens the case for confidently defining the latter as a general commodity (even if such a definition remains incomplete). Without fungibility of money, economic calculation would be drastically impaired – to such an extent that this characteristic is necessarily attributed to the abstract unit of account, as an ideal. This claim attains greater cogency if reversed: It is in order to fulfill the functional requirements of the unit of account that implemented concrete money systems acquire fungibility as an indispensable criterion for even minimal adequacy. Commercial quantities presuppose equivalences, or at least commensurabilities, even if between strictly ordinal-differential preference schedules (of the marginalist type), since they could not otherwise be arithmetically tractable. It is worth noting that weighing already assumes fungibility, and the correspondence of many monetary units to (forgotten) measures of weight is widely recognized. The elementary economic option involves a comparison, with some definite baseline of assumed fungibility providing a condition of calculability. Indeed, the basic concept – and practical institution – of price assumes fungibility. A system of ‘money’ whose instances were in any way better or worse, other than by being more or less, would be unable to compute settlements – even within modest transactions – without the introduction of complex supplementary information (about the monetary medium itself). Since, once again, perfect fungibility is a limit ideal, this problem is by no means entirely hypothetical. We might refer to qualitative interference in money systems as ‘Gresham noise’, especially as this applies to friction within their concrete processes of circulation, and thus to integral illiquidity. The entire techno-political problem of monetary standardization applies here. The practical idealization of money, within digital registers of pure quantities, retains implicit reference to a model of perfect fungibility, appropriate to the mathematical tool, or calculator.
§5.16 — Verifiability can be rigorously conceived as a practical extension of fungibility, or as an operational annex to it. It references some definite, practical checking procedure that qualifies money as credible. Dubious money cannot be confidently counted as any definite sum whatsoever. Across the vastly preponderant part of monetary history, the model verification procedure has been assaying. The assay underwrites monetary value determined as a quantity and purity of metal. In the age of paper money, verifiability refers primarily to protection against forgery, or counterfeiting. This characteristic binds money essentially to the production of trust. Money is able to redeem a promise, and thus validate it.
§5.17 — As an aside, at
this early stage in our discussion, it is notable that Bitcoin possesses all
six of these qualities, super-abundantly.
Its durability is – in principle –
absolute, although Bitcoin can in fact be lost or destroyed (see following
note); it is rigidly and quite exactly
scarce (to a fault, its critics
object); divisibility is also
unlimited in principle;
its communicability is extreme, based
on Internetworked digital electronics; its fungibility
is also absolute, given any set of realistic assumptions about user incentives;
and it is verified automatically in
its reproduction cycle. It would be difficult for Bitcoin’s status as money to
be more secure, insofar as ‘the six qualities’ are applied as a criterion.
 Such concerns, perfectly contextualized for our purposes here, are exemplified by the logical case for the Misesian Regression Theorem (as glossed by the Mises Wiki of the Ludwig von Mises Institute): “For many economists … a marginal utility explanation of money demand [would] simply be a circular argument: We need to explain why money has a certain exchange value on the market. It won’t do … to merely explain this by saying people have a marginal utility for money because of its purchasing power. After all, that’s what we’re trying to explain in the first place – why can people buy things with money …”
 The suggestion that Bitcoin is about more than money, while often intellectully productive, presumes a confident – if implicit – answer to a prior question concerning the nature and limits of money that is almost certainly unwarranted. In the same way that the world learnt, upon the innovation of Gödel coding (or transcendental arithmetic) that the set of Natural numbers included within itself the precise articulation of all possible formal systems – and indeed all possible configurations of (digitizable) information – precluding its subordination to any higher level of logical expression, so the innovation of reflexive (or self-validating) crypto-currency can be expected to demonstrate that the monetary sphere is no less semiotically comprehensive than comprehended, even potentially. Any consistent philosophy of money is compelled to be fully reflexive, since money is not rigorously determinable as a conceptually transcended object. In principle, money has no less to ‘say’ about philosophy than the inverse. Marxian materialism can be understood – if only partially – as a route to the articulation of this radical nonlinearity, or hierarchical disturbance, although it need not be allotted peculiar privileges in this respect.
The form of the question What can money do? is, of course, to be credited to Spinoza. As in its original instantiation, in the Ethics (“We do not know what a body can do”), the purpose of the question is to stall a premature transcendent resort. Any appeal – whether theoretical or practical – to look beyond money assumes the accomplishment of a preliminary determination that has simply not taken place.
 Additional monetary functions have been proposed, including that of a standard of deferred payment, and a measure of value, but these are formally derivable from the function of a unit of account under any reasonable extension of that concept.
 The inadequacy of this formulation will prove critical to the discussion that follows. In particular, the over-identification of means of payment with flow, and store of value with stock, obstructs diagonal exploration.
 From Fernand Braudel, Civilization & Capitalism 15th-18th Century, Volume I: The Structure of Everyday Life (p.465).
 From the dominant perspective of modernity, which is certainly invulnerable to casual dismissal, any assertion of natural categorical order in the absence of (at least implicit) explanatory mechanics is stereotypically scholastic. By merely describing order, even if in accordance with a superior formalization, a ‘neo-scholasticism’ assumes that which needs to be accounted for. Within the modern natural sciences, in contrast, categorization has been progressively subsumed into a framework of explanation. Whether in biology, chemistry, or particle physics, natural types emerge from genetic mechanisms and intrinsic compositional properties. A biological species is a cladistic unit, generated by an episode of separation (phyletic splitting), and characterized by identifiable gene frequencies. Linnaean classification thus acquires Darwinian explanatory justification. Chemical elements are produced by nuclear processes, and compositionally defined by sub-atomic structure. The particles of baryonic matter, comparably, have a cosmological genesis and compositional definition. The periodic table expresses physical principle, and not merely consistent order. Given these theoretical successes, it is understandable that classification is increasingly conceived by modern natural-scientific intelligence as a mere heuristic, with only provisional and dependent credibility. Order in the absence of theoretical explanation is no longer identified as a self-supporting structure, but as a problem, or research prompt. Patterns are to be derived. They are puzzles rather than conclusions. To think that any serious question is answered by a pattern approximates to a definition of scholasticism. A potentially deadly reflexivity lies latent in this conclusion (which recognizes ‘medievalism’ in thought without explaining it), but it is one that modernity has extreme tolerance to.
Kantian categories – as non-empirical forms – have some comparative security against the accusation of scholasticism. They withdraw inherent pattern from the empirical order of the natural world. Nevertheless, their apparent arbitrariness is a trigger for suspicion, and their ideality displaces natural-scientific skepticism, rather than dispelling it. (Supernatural foundations are intrinsically incredible to moderns, and even critically-disciplined categories can easily be taken for such.) Yet transcendental structures are not reducible without loss of information. Mechanism does not dissolve the machine. Categories are finally mathematical, with an order strongly analogous to that of the prime number series. Non-tautological apodicticity is the crucial (diagonal) trait. The cryptographic usage of the prime numbers is a demonstration of the transcendental (synthetic a priori) status of the series, and would be impossible otherwise. At the level of pure conceptuality, the number of the categories is an ineluctable consideration. Since causal mechanisms cannot be invoked as sufficient explanatory factors, without submitting to pre-critical error, the order of division demands a logical (or logico-mathematical) principle. The arcane meditations elicited can easily seem Baroque (or even ‘Byzantine’), in the fashion of all sufficiently-elaborate synthetic lock-picking exercises, since they lack any such preliminary principle. The principle comes only at the end. It is proposed here, then – perhaps inevitably – that the six-fold categorical structure of ideal money is founded trans-empirically. History can illustrate, but not explain it.
The order of monetary qualities has necessarily to assume a structure determined by the three semiotic dimensions (of signification, indication, and allocation) doubled by the binary partition of the monetary function between stock and flow. The topological pattern of this double circuit, without transcendent disjunction, is decidedly Möbian. The six essential qualities of money would thus fall into three dyads, according to its suitability for accumulation and exchange under each of its three basic semiotic aspects. In other words, money requires a triple semiotic instantiation as index, sign, and token, all amphibiously adapted to the twin functional requirements of storage, and circulation. Its six qualities exceed factuality. They fall out of a (transcendental) diagram, automatically, as a complex synthetic a priori proposition. What they exhibit is something like a numerical hyper-object, and more specifically a Möbian (or continuously double-sided) triad. If time is money, then three twinned-phases are assumed. The outcome, optimally, exhibits the exoteric finality proper to a transcendental deduction.
 ‘Exceptional circumstances’ in this case includes simple antiquity. A ‘shekel’, notably, was originally a weight of barley.
 Within an urban, highly-commercialized context, the comparatively unusual case, in which the commodity is adjusted quantitatively, in conformity with an inflexible monetary unit, is seen in the phenomenon of the ‘dollar store’. The situation appears remarkable because it involves heterogeneous items, whose accommodation to monetary chunking demands the solution to a puzzle (and perhaps also an abnormal variation in ‘mark-up’ levels). The far more usual case is exemplified by small market transactions of fungible commodities (which can be measured by weighing). It is at the edge of the money economy, where formal currency units, due to their comparative scarcity, enjoy an unusual privilege – and even a numinous exoticism – that such trades become especially typical.
 Ted Nelson’s ideas were so far ahead of the available technology that they struggled for practical relevance. This untimeliness earned him the honorific title “the Babbage of the web” from The Economist magazine. The word ‘micropayment’ is among his many coinages. http://www.economist.com/node/442985
 Capital teleology inclines to the substitution of market-scale for unit-margins, under the pressure of competition. ‘Globalization’ is nothing else. Already in the mid-19th century, Manchester mill-owners notoriously dreamed of “adding an inch to every Chinaman’s shirt-tail”.
 Monetary communicability requires successful delivery. For instance, it involves the problem of secure transportation. In the case of all physical monetary media, therefore, the question of communication involves certain gross security considerations. Physical portability of precious materials is intrinsically complicated by the threat of criminal interdiction. In consequence, the communicability of gold cannot be held down to a narrowly economic issue, since it is afflicted by political risk. Nor can the interdiction of gold delivery cannot be dismissed as a merely hypothetical or improbable threat. More generally, a commodity cannot be traded without first tacitly admitting to its possession. FDR’s Executive Order 6102 (1933) criminalized gold ‘hoarding’ within the United States. The very physicality that supported gold’s monetary virtues was thus immediately exposed as a political vulnerability. Without crypto-security, hard money exists only under contingent conditions of state tolerance. Reciprocally, full-fiat currency is initiated by a police action. On both sides, there is extreme sensitivity to the discretion of the state.
 Fungibility has been built into the technical definition of the commodity, as the meaning of this word – in its professional economic usage – has narrowed since the 19th century. Within this domain, ‘commoditization’ has been stripped of its philosophical thickness and generality, until it refers only to the loss of product differentiation from any tradable good, and thus to the reign of naked price competition. A commodity in this sense has no intrinsic peculiarities that bind it to a specific producer (though extrinsic differentiation – by spatio-temporal location – still applies). Goods serving as production inputs, especially – but not exclusively – raw materials, are the exemplary case. A slippage in the direction of money thus occurs when sources of supply cease to be differentiated by product quality. Fungibility and quantification are closely-related concepts. Due to their affinity with exceptionally frictionless, highly-liquid markets, commodities (in the narrow, contemporary sense) make attractive speculative assets, and thus operate as (broad) money. The conceptual transition between the narrow sense of the commodity and the broad sense of money is mediated by precious metals. Gold, silver, and platinum, no less than iron, ethene, or consistent grades of petroleum, are defined as commodities by their physical (chemical) properties, grounded practically in standardized extraction and refining techniques. They converge upon product qualities. Fungibility includes an indifference to genesis. It is therefore linked to a definite commercial amnesia. Such anti-memory links it conceptually to the untraceable, as this applies to the hyper-fungible monetary medium of cash. The thing about ‘dirty money is that you don’t know where it’s been. (Literal dirt, however, is Gresham noise.)
 Monetary homogeneity – which is to say, the quality of qualitative neutralization – has been a consistent provocation for romantic criticism, not least by influential strands of the Marxist tradition, whose convergence with Nietzschean criticism of modernity has been typically pursued through this theme. To quantify is to level, and flatten. It submits the world to the form of the equation, and subsequently to practical reconfiguration as interchangeable units. The aesthetic denunciation of commoditization has typically made of this a central objection.
 Any qualitative variation in the nature of currency units interferes with their economic signal, by cross-cutting price calculation with extraneous considerations. As Thomas Gresham noted, the incentive to dispose of ‘bad’ money can become a pseudo-commercial motive in itself. It thus distracts from the primary information-processing function of the price system. Historically-evidenced money systems are those in which the problem of Gresham noise has been effectively contained. If this had not been the case, we might be disinclined to call the commercial media in question money at all. It can easily be noticed that any such ‘currency’ – if afflicted by intrinsic heterogeneities beyond a very limited point – begins to acquire the features of a barter good, with all of the economic coordination and computation problems that follow. Gresham noise is also applicable – by analogy – to foreign exchange markets, where comparison between monies is most formally advanced. The concept is not fully preserved in this case, however, because the heterogeneities submitted to Forex market evaluation do not attest to a deficit of fungibility within any given currency, but rather the opposite. The very notion of a consistent exchange rate assumes the quasi-perfect fungibility of each currency, as a condition of its presence on the market. Trading into and between crypto-currencies can, in this respect, be similarly conceptually handled.
 See: ‘Bitcoin as a Store of Value, Unit of Account, and Medium of Exchange’ (Daniel Krawisz, 2015/01/12).
 In respect to its ultimate quantity, and thus scarcity, perfect exactitude has to be denied to Bitcoin on the deflationary side, because Bitcoin destruction reduces the final stock (below 21,000,000) in a way that is not always easily accountable. Coins can be accidentally lost, without any prospect of recovery, simply through the forgetting of private key. They can also be deliberately destroyed, through consignment to the crypto-currency analog of a black hole. While some of these bitcoin death addresses are known, they need not be, although their behavior on the public ledger will be indicative.
 For practical purposes, the divisibility of BTC was set initially to only eight decimal places (a 100-millionth of a bitcoin), a unit named a ‘Satoshi’.
 Although every bitcoin is singularly identifiable, there is no plausibly conceivable economic incentive that would lead a user to prefer – even infinitesimally – any particular bitcoin over any other. The currency is entirely devoid of commercially-relevant inhomogeneities, except under condition of a hard fork in the system.