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In which the curmudgeonly old sod puts the world to rights.
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Newsletter cribnotes

Modernism, formalism versus pragmatism

  • Vertex versus edge
  • Text versus meaning
  • Algorithm versus heuristic
  • Formal versus informal
  • Tool versus application
  • Innate versus emergent
  • Obvious versus subtle
  • God versus Darwin
  • Simple versus complex
  • Quantitative versus qualitative
  • Calculated versus interpreted
  • Static versus dynamic
  • Stocks versus flows
  • Structure versus interaction
  • Nouns versus verbs
  • Trees versus wood
  • Permanent versus ephemeral

“I should explain that in the Soviet scientific community in those days, mechanistic determinism held sway over all other approaches. Researchers believed that the natural world was governed by the iron law of cause and effect. This mentality was a product of the political environment.”

— Cixin Liu, Ball Lightning

A running theme in the JC is the distinction between top-down and bottom-up of organisation models.

The financial services world is currently in the swoon of a passionate love affair with data, technology and the algorithm. Thought leaders perceive an inevitable, short, path to a singularity where everything can be planned, everything calculated, everything provisioned, and reliance on on irrational, costly, inconstant, error-prone meatsacks will finally be indefensible. This time is different; a we have before us a future of technological unemployment and unlimited leisure. The challenge is going to be figuring out what to do with all our spare time.

As you will know by now the JC is a crusty old refusenik, and while that is in great part a function of self-interest — he is an irrational, costly, inconstant, error-prone meatsack — there are broader metaphysical considerations at play.

Before we mortgage our futures to the machine, it is worth nutting through the digital prophecies to see if they hold water.

Every story needs a narrative — if that isn’t to beg the question — and this one starts with a fundamental, philosophical divide: between one on hand determinism: the view that the causal principle holds, all outcomes can and where possible should be calculated from first principles, the principle challenge is outright data processing capacity; and on the other pragmatism: the view that, whether that’s true or not, it’s too hard, to constraining, and it’s better to live with uncertainty and figure things out as we go.

Determinism begets modernism and aspires to centralisation: processing power is aggregated, optimised and the main function of management is orderly administration and maintenance of a machine which will, by operation of logic, dispense optimal outcomes.

Pragmatism begets systems thinking and aspires to decentralisation: the world is a fundamentally unpredictable thing, best dealt with experienced experts, and the main function of management is to empower and equip experts and optimise their ability to communicate.

Algorithms versus heuristics.

Perfection versus good enough.

Modernism

The top-down models are “modernist”. They view organisations as complicated machines, ultimately directed and controlled by a homunculus sitting at the bridge in a kind of Cartesian theatre. Formal design is important, and follows (centrally determined) function; the better regimented the parts of your contraption and the more efficient it is, the better it will navigate the crises and opportunities presented by the environment in which it operates — the market. Modernism regards the market — for all practical purposes — as an infinitely complicated mathematical problem: hard, but ultimately calculable. Modellable. So when the model turns out not to work, the answer is to develop it.

“In 1988 a first international regulation was crafted to regulate the capital a bank needs so that it is unlikely to default, known as the Basel Accord (Basel I). This agreement was 30 pages long and the calculations could be done with paper and pen. It was revised in 2004 to something more magnificent, Basel II. With a great deal of added detail and new complex risk models, Basel II was 347 pages long. A few years after the creation of this masterpiece tailored to make the world safe, the financial crisis of 2008 broke out. The reaction was to weave an even more complex regulation, Basel III, which came to 616 pages. Whereas Basel I was translated into 18 pages of primary legislation in the United States, Basel III required more than 1,000 pages. I have asked central bank regulators: who understands the consequences of Basel III? The unanimous answer was “probably not a soul”.”

Gerd Gigerenzer, Risk Savvy: How To Make Good Decisions

These shortcomings in engineering and technology mean we cannot — yet — fully solve that problem. But we should prioritise the algorithm, and deploy humans in its service. We still need humans to make sure the machine operates as best it can, but the further humans in the organisation get from that central executive function, and the better the algorithm gets, the more humans resemble a maintenance crew: their task is simply to ensure the orderly functioning of the plant. As technology advances, human agency can be progressively decommissioned.

The modernist narrative focusses on what it can see, which is necessarily limited to the formal inputs and outputs of its own model. There are at least two consequences of this. Firstly, the modernist narrative cannot see informal, but often vital, interactions between components of the system that its model does not consider material. These are the random acts of kindness, the jobs the staff do that are not in the service catalogue, that explain the difference between excellent performance and work-to-rule.

Secondly, modernism is a negative sum game: its baseline is immediate, costless performance of the program. Positive variance from this baseline is not possible: the goal is to lose as little energy as possible. As with a Newtonian equation, real-world performance never meets theoretical conditions: friction and imperfection means an inevitable loss of energy and increase in entropy.

In Newton’s theory, acceleration equals mass times force. In the practical world, acceleration is inevitably less than mass x force. We know that friction, gravity, heat, entropic energy loss means in the real world, observed A will never be quite amount to M*F. Engineering and environmental control move real A closer to theoretical A, but it is practically impossible for real A to equal theoretical A, and theoretically impossible to exceed it. Engineering is there for a negative sum game: no amount of engineering, efficiency or insight can on yield an acceleration equal to or greater than M*A.

The modernist disposition holds that the same is true in an organisation.

Human operators create a great deal more entropy than machines. If the only measurement is flawless performance of an algorithm, humans must be worse at it then machines. There is no credit given to insight, diagnosis, creation of alternative models or narratives comma because in the the modernist framework, there is no such thing as a valid alternative model. Economics is a kind of applied physics. There is no room for alternative facts.

Business, and government, suffers from a kind of physics envy. It wants the world to be the kind of place where the input and the change are proportionate: everything is numerically expressible and the amount you spend on something is proportionate to the scale of your success.

Rory Sutherland

If it is true that bettering an algorithm is impossible then it stands to reason: meatware is expensive and inconstant: the largest risk to the organisation is human error, thus the strategic direction of an organisation’s development is to eliminate where possible the need for human intervention. Where that is not possible, human activity should be constrained by rigid guidelines and policies to reduce the probability of mishap, and monitored and audited to record and correct those errors that do happen top prevent them happening again. To the modernist, malfunction and human error are overarching business risks.

This worldview is one that appeals to many people in business management. Others might find it it rather desolate. But desolation is no argument against it if it is correct.

Pragmatism

When a man throws a ball high in the air and catches it again, he behaves as if he had solved a set of differential equations in predicting the trajectory of the ball. He may neither know nor care what a differential equation is, but this does not affect his skill with the ball. At some subconscious level, something functionally equivalent to the mathematical calculations is going on.

Richard Dawkins[1]

When you get too close to your material, sometimes you can’t see an absurdity even if it pinches you on the nose. Not only does a person catching a cricket ball not solve differential equations, or anything like it (let alone functionally equivalent), but she can’t. She would need the inputs for every differential equation in play. Just to determine a trajectory is: Y = H + X * tan(α) - G * X² / 2 * V₀² * cos²(α).

Bear in mind you don’t know the velocity, angle, vector, or starting coordinates of the projectile, all of which you would need just to perform that differential equation

Bottom-up models are, for want of a better world, “pragmatic”. They see the organisation as a constantly changing organism operating with incomplete, ambiguous information in an environment that is also constantly in flux. To survive, firms must respond dynamically and imaginatively to unpredictable, non-linear interactions in the environment which is constantly shape-shifting into new configurations in unexpected, and unexpectable, ways. For a pragmatist, practical control must be exercised at the points where the organisation interacts with its environment. A firm should have talented, empowered, well-equipped people — subject matter experts — to handle those interactions. Those in the central management function have a holistic view of the environment and can provide aspiration and tools to the subject matter experts, but real decision making is done by those experts at the edges, not the the management function in the middle.

Intellectually, the battle ought to have been won by the pragmatists long since (systems theory, complexity theory, even, for all its obsession with algorithms, evolutionary theory line up with pragmatism), but modernism keeps devising new ways of getting itself back in the game, and over the last twenty years has been winning. What with the giant strides of the information revolution, the forthcoming singularity, technological unemployment, the abolition of boom and bust in 2005, and the effective management and distribution of financial risks through sophisticated financial derivatives (amirite?), it is easy to be lulled into a sense of security.

Getting down amongst the elephants and turtles is not to everyone’s taste, but if you do it helps to see the planet on top of it more clearly. Here’s a distinction to draw: between things and interactions between things. Nouns versus verbs.

The illusion of permanence and the Ship of Theseus

We see that even many of the markers we treat as formal, fixed and permanent are really temporary: the Dread Pirate Roberts effect: the personnel comprising a corporation change over time. Likewise institutions: corporations merge, change business models, change locations, move into different markets. IBM of 2021 is very different from the IBM of 1971.

But the individuals may be fleeting and transitory; the residue they leave behind is not: The corporation’s devotion to the formal means that successive individuals become progressively constrained by their predecessors actions and decisions — even if, in the mean time the dynamic considerations that led to the decision no longer prevail. A rule that has been there for a long time, but that no-one knows the provenance of, acquires a kind of mystical quality. I think this is the inverse of the “Lindy effect”.

The illusion of significance

Because we can see the formal structures easily we tend to imbue them with significance, and assume the static connections between the formal structures are what matters. For example the org chart: this places every person in a firm in a logical, hierarchical relationship to everyone else, and can be neatly and easily controlled, that’s not to say many organisation charts become positively Byzantine.

There is much management theory around the relationship of “spans” and “layers”[2] optimal organisation charts no more than 5 layers of management; no more than 5 direct reports and so on. This, from People Puzzles, is pretty funny:

How many is too many?
Around five direct reports seems to be the optimum number, according to Mark and Alison, although there are some scenarios where up to nine can work.
When it comes to the senior team in a company, however, too many people reporting directly to the owner manager can really hold the business back. Alison recalls working with someone who had 13 people reporting directly to her. “She had to do 13 appraisals at the end of every year!” she says. “It simply wasn’t an effective use of her time.”

Witness the formalist disposition, when the most significant thing you can do is carry out a formal process. The ethos is this: look after the form and the substance will look after itself full stop take care of the pennies and the pounds look after themselves. But this is the reverse colon this is to look after the pounds and assume the pennies will take care of themselves.

In any case you can’t encode mandatory small teams and a flat structure. There is a mathematical relationship between them: the smaller the average team, the more management layers there must be.

And besides, this is to miss the map for the territory. An organisation chart is a static map of the firm configured in the abstract, in theory, before it does anything. This is how the machine functions when it is idling. Org charts are the plan you have before you get punched in the mouth. Formal reporting lines are often the most sclerotic, rusty and resented interaction channels in the organisation. Communications up and down them — usually reluctant, strained, for the sake of it — are at best responsive to commercial imperatives, and derivative of them: the firm’s business is done only when the gears are engaged, and that means its personnel communicate with those who are not in their immediate hierarchy. The business unit is a cog: what matters is the effect a cog has when it is engaged.

But as the complicatedness of our organisations has grown we have developed more and more internal engines which engage not with the outside world but with each other in in heat generating, vibrating, noise emitting, wasteful energy consumption. Of course one needs compliance but when NZ compliance needs its own chief operating officers and and its own internal audit it drift away from optimal efficiency. I know of one internal audit department that has its own internal auditor. Who audits that function? We approach an infinite regression. But the buck must stop somewhere.

You can understand the wish to focus on reporting lines — formal organistional structure — because it can be easily seen. It is is legible. It is measurable. Auditable. But it misses the organisation’s real arterial network: lateral communications that cross the organisation’s internal and external boundaries: these are the communications that employees must make — between internal specialists in different departments and with the firm’s clients and external suppliers — to get their job done and move the organisation along. Note: it is in these interactions, themselves that things happen: it is here that tensions manifest themselves, problems emerge and opportunities arise, and that these things are resolved. It is not the drill, but the hole in the wall.

These are informal interactions. They are not well documented, and from above, not well understood. They are hard to see. They are not legible. Yep everyone who has worked in a large organisation knows that there are a small number of key people, usually not in significant formal roles, who who get things done. They know histories, they have networks, they understand procedures and and, more importantly, workarounds. These are the ad hoc mechanics that keep the the superstructure on the road.

They are hard to see precisely because they do not derive their significance from their formality, but from their function. From the frequency of interaction and the comprehensiveness of connection. These people are the super spreaders. They are the informal hubs of a multiple hub-and-spoke network. They earn their authority not from their formal position, nor their formal grading, but their informal reputation, earned daily, interaction by interaction.

A map of interactions is not a top-down, God’s-eye view. It disregards the artificial cascade of formal authority, in favour of informal credibility. It reveals the organisation as a point-to-point multi-nodal network, is a far richer organisation than that revealed by the org chart. This is how the firm actually works, and and inevitably the formal organisation will frustrate it.

Yet no firm I know of even considers it. Yet, with data analytics, it would not even be hard to do: Log the firm’s communication records for data to see where those communications go: what is the informal structure of the firm? Who are the nodes?

Typically, vertical, staff-to-manager communications don’t have those qualities. Reporting lines are more an interaction constraint rather than an indicator of productivity. They impede the firm from interacting freely.

The modernist theory is that the firm is a unitary machine that must be centrally managed and controlled from the top; therefore the more organisational structure the better.

The “agilist” advocates removing layers, disestablishing silos, and decluttering the organisational structure.

The agile theory is that risks and opportunities both arise unexpectedly, come from places unanticipated by the formal management structure, and therefore the optimal organising principle is to allow talented people at the the coalface the maximum flexibility to react to those risks and opportunities. Thus, the imperative is to have the best people, with the best equipment, in the best place to react skilfully. Those people aren’t middle managers, the optimal equipment isn’t the one that leaves the best audit trail, and that place is not the board room, much less the steering committee or the operating committee. It is out there in the jungle. the fewest number of formal impediments to their creative use by those people.

For a modernist, this is inevitably a scary prospect. The modernist view is that as long as the structure is correct the quality of the people in any of the positions on the organisational structure is immaterial as they have predefined roles to perform.

So to understand a business one needs not understand its formal structure, but its informal structure: not the roles but the people who fill them: who are the key people whom others go to to help get things done; to break through logjams, to ensure the management is on side? These lines will not show up in any organisational structure. They are not what James C. Scott would describe as legible. They are hard to see: they are the beaten tracks through the jungle: the neural pathways that light up when the machine is thinking. They show up in email traffic, phone records, swipecode data.

Turtles

Talking Politics with Adam Curtis

The idea that the truth is in the patterns in the days that human cannot even see.

Money as an abstract token of value that has no intrinsic value

Advertising generates economic production, rather than economic production generating advertising.

Authenticity

The importance of authenticity. Why is it not the same when it isn't David gilmour playing that guitar solo?

The importance of effort. We should not underestimate how we we value the effort required to produce intellectual property. Many years ago go robotics engineers designed a contraction that could play the flight of the bumblebee on classical guitar. Undoubtedly the machine was extremely complex, the programming highly ingenious and it executed the police flawlessly at tempo, undoubtedly more perfectly then the finest classical guitarist could. But would you pay money to sit in a concert hall and watch a robot playing classical guitar? Once the technical problem has been solved and can be inexpensively replicated the value of the performance tends to 0. Even though we can can program robots to flawlessly play, at no cost, we will still pay good money to watch a human virtuoso doing the same thing less well than the machine.

The segues into a conversation about the meaning of value. The same way that meaning does not exist in the words on a page, value does not exist in in the technical performance of a skill, but lies somewhere between the performer and and it's audience. Similarly, science is not simply demarcation of the correct answers to questions, but is demarcation of the correct questions requiring answers. This is a dynamic. It is complex in the technical sense, the ground rules are approximate and shift without warning based on the attitudes of the conversants.

Leaving aside all the overpowering psychological reasons not to value an AI version of Pink Floyd, there is the bluntly practical one. They can only ever be a flawless moment it can recombine existing elements into a new you form. But it cannot create genuinely new you output because it is not the artist. Whatever the machine comes up with it will not be what nirvana's next album was going to be. Of course, we cannot know that, but consider an AI algorithm directed at The Beatles first four albums. Is there any chance it could have devised music resembling that on revolver or rubber soul let alone tough White album or sergeant pepper's? An AI analysing Pablo honey and The bends will not produce amnesiac or kid A.

Allegory, fairy stories and the hubris of taking things literally

We have been been warning ourselves since the dawn of civilization about the folly of using magic to take shortcuts. If we take Arthur C. Clarke at his word that any sufficiently advanced technology is indistinguishable from magic then are we forgetting our oldest lessons?

===

“People of every age seem to be in a sort of post-truth scenario here, where I get to pick my own facts. There are a lot of facts out of there, I get to pick the ones that I like, and I can go with those, and nobody can really tell me that those aren’t the facts because it’s my truth. Those are my facts, and don’t tell me they’re not.”

— Robert Prentice[3]

All the lies I told to you:
Some of them came true.

— Chris Isaak, Move Along

Things and propositions about things

Most conspiracy theories contain a grain of truth. There has to be something for the credulous to glom onto. Critical theory’s grain of truth, ironically, is “there is no such thing as a grain of truth”. Well, not quite — “it is true that there is no truth” refutes itself, after all — but rather, that the very idea of “objective truth” makes no sense on its own terms. It is incoherent. There can be no objective truth, the same way there can’t be a square triangle.

“Things” are properties of the universe. They have (we presume) temporal continuity,[4] whether we see them or not, and whether we talk about them or not.[5] “Truths” are propositions about things. Propositions put things into a relationship with each other: “the cat sat on the mat”. “Gordon is a moron”.

“Propositions” are properties not of the universe, but of language. They are prisoners of the language they are articulated in. They cannot exist outside it. Beyond it, they are only marks on a page.

“گربه روی تشک نشست”[6]

See?

Thus, “things” aren’t true or false: only “propositions about things” are.

Analytic and synthetic and propositions

Bear with me for a brief technical interlude. This won’t take long. There are two kinds of propositions: analytic ones, and synthetic ones. Analytic propositions are logically true as a function of the language they are expressed in. Synthetic propositions tell us about the world beyond the language. Think of analytical propositions as mathematical statements, and synthetic propositions as scientific statements.

A square is a regular polygon having four sides of equal length that are joined at right angles.

This is analytically “true” because, in the language of Euclidean geometry, a polygon that does not meet those criteria is not a square.

This is an absolute truth, but it is not “objective”. It does not transcend the logical axioms of the language in which it is expressed.

The “truth” of a synthetic proposition, if it has one, derives from how the proposition relates to the world beyond the logical axioms of the language in which it is expressed.

The cat is sitting on the dog’s mat.

It is, of course, trivially true that mathematical truths are true. When we talk about there being objective truth, we mean there are synthetic — scientific —propositions

A truth cannot “transcend” the language it is expressed in, because that language gives the proposition meaning. It doesn’t make sense for the truth to transcend it's medium.[7] There is the further difficulty that “language” itself is an indeterminate, incomplete, unbounded thing; no two individuals share exactly the same vocabulary, let alone the same cultural experiences to map to that vocabulary, let alone the same metaphorical schemes. It is what James P. Carse would describe as “dramatic” and not “theatrical”.[8] This makes the business of acquiring and communicating in a language — where meaning does not reside in the textual marks, but in the indeterminate cultural milieu in which the communication occurred — all the more mysterious. That we call it “communication”; that we infer from that a lossless transmission of information from one mind, is a deep well of mortal frustration.

This is its debt to post-modernism, and it is a proposition that contemporary rationalists find hard to accept, whether hailing from the right — see Douglas Murray’s The Madness of Crowds for an articulate example — or the left — see Helen Pluckrose’s patient and detailed examination in Cynical Theories.

The problem, all seem to agree, is this post-modern rejection of truth. And it isn’t by any means limited to the critical theorists: it lives in Kellyanne Conway’s “alternative facts”, in Elon Musk’s Twitter feed, and the generally relaxed attitude to rigorous fact-checking of the populist right.

At the same time we lament the death of “authenticity” — is it the same thing as truth? Is it what we mean by “truth”? — and with it, the terminal defection of logic from the mechanical operation of the world.

We think: what have we done? Have we syllogised truth away altogether? Have we passed a point of no return? Some kind of event horizon between truth and post truth; an invisible force-field from the outside in a collection of received veracities, which once you permeate it, once you cross its threshold all reality dissolves and it is suddenly the only visible truth that remains, in a twisting kaleidoscope of unfathomable nonsense — truth is no longer possible?

Nowhere is this more evident than the blockchain, and its two most startling, and contradictory creations: bitcoin on one hand: the utter rejection of any underlying reality: bitcoin unashamedly represents “value” as a totally abstracted essence; a theoretical quality, disconnected from our ugly Platonic cave, floating free of any messy, ugly corporeal, earthly extension that might taint it with mortal frailty; the non-fungible token on the other, a means vouchsafed by that very same essential abstraction from the earthen shores, of achieving unimpeachable authenticity. A non-fungible token cannot be replicated, it can’t be cloned, copied or imitated: it is immutably, eternally, digitally unique

The irony deepens, for defenders of the enlightenment bring critical theory to book for its ignorance of obvious truths, while critical theory itself has bootstrapped itself into assembling a new set of of objective truths, which happened to be different to the conventional enlightenment ones.

The deep problem that critical theory has, all agree (from Christopher Hitchens, Richard Dawkins, Helen Pluckrose, Douglas Murray and recently Matthew Syed) is that something things — physical sciences are a favourite example — just are true. No amount of identifying with an alternative theory of gravity will stop you from hitting the ground if you throw yourself out of a window.

On the other hand Jacob Howland made the interesting assertion recently that so completely has critical theory escape its postmodern origins, that it has become captured by, of all people the high modernists who inhabit an intellectual world that seeks to solve all problems by top-down taxonomies and computation.

An illiberal alliance of technological corporatism and progressivism is rapidly turning universities into a “talent pipeline” for the digital age. When fully constructed, this pipeline will deliver a large and steady flow of human capital, packaged in certifiable skill sets and monetised in social-impact or “pay-for-success” bonds. But the strongly particular or eccentric shapes of mind, character, and taste that make human beings, as John Stuart Mill says, “a noble and beautiful object of contemplation” would clog the talent pipeline.

Critical theory has escaped its usual confines in the liberal arts faculties of universities and is now inhabiting the management and human resource departments of corporations, and who are using their rationalist framework to advance what is a fairly radical political agenda. Critical theory is not an alternative narrative by which we can puncture the arrogant assumptions of the capitalist class: it has displaced them altogether and is making its own arrogant assumptions in their place.

That’s not altogether a bad thing — although the practical effects of the updated dogma seem more pronounced the further from the executive suite you go — but it seems to me to substitute one set of bad ideas with another.

The idea of transcendent truth — a truth that holds regardless of language, culture or power structure in which it is articulated — is not false (that would be a paradox right?) So much as incoherent. It is incoherent because, as Richard Rorty pointed out, truth is a property of a sentence about the world, not the world itself. Truth depends on language.

And languages are intrinsically ambiguous. This is the tragedy and the triumph of the human condition.

The statement there is no truth is not an article of postmodern faith, by the way: you can trace it back as far as David Hume, Adam Smith, Charles Darwin Friedrich Nietzsche, Karl Popper, Thomas Kuhn and Richard Rorty. I know, I know: all old, dead, white, men. And Nancy Cartwright.

If you accept the proposition that truth is a function of a sentence and therefore the language of that sentence, for there to be a transcendent truth the language in which it was uttered would necessarily need to be complete, comprehensive, and itself true. The nearest linguistic structures that we have to to complete languages are those of mathematics. Yet we know that mathematics is a necessarily incomplete language: from that we know that any natural language is necessarily incomplete; and in the case of science we know with certainty that science is not what a complete and comprehensive statement of the laws of the physical universe.

We haven’t solved the universe yet. There are large fundamental unknowns; dark matter; dark energy; the incommensurability of quantum mechanics and and special relativity. Even if the concept of transcendent truth were coherent we would have nothing like enough information to access it. In the same way that the fielder does not have enough physical information to calculate the trajectory of a cricket ball, and therefore pragmatically approximates it, so we do not have anything like enough information to confidently predict the scientific performance of the universe and therefore we pragmatically approximate it.

Pragmatic approximations, being provisional, contingent, and subject to revision at any time are are more tolerant, plural and liberal than concrete scientific calculations.

The lack of a a coherent concept of transcendent truth is a a roadmap to tolerance, pluralism, and liberalism. It obliges us to treat as contingent anything we know, to expect things to change and to be prepared for new and more effective ways of looking at the world. All it requires is that we substitute a certainty about how we view the world and ash that we see it as true with a pragmatism about how we view the world, seeing it as effective.===


Power structures are all around us

  1. The Selfish Gene, 2nd Ed., 95 — see it on Dawkins’ website.
  2. Let me google that for you.
  3. Robert Prentice, quoted in Gabrielle Bluestone’s Hype
  4. Though even temporal continuity is a function of language: computer code has no tense, and therefore no temporal continuity.
  5. David Hume’s causal scepticism put paid, centuries ago, to the idea that we can be sure about this.
  6. Translated from Persian into English: “the cat sat on the mat.”
  7. This is not even to take the point that, thanks to the indeterminacy of closed logical sets, no statement in a natural language can possibly have a unique, exclusive meaning.
  8. In his Finite and Infinite Games.