The Enigma of Reason by Hugo Mercier
My rating: 5 of 5 stars

The First Rule of Rationality: There are No Rules of Rationality

Reason is one of those terms, like time or God, which seems obvious until it’s taken seriously. It then dissipates into a semantic haze with no solid meaning whatsoever. No one can find it outside the language which postulates and defines it. Reason, that is, is a purely linguistic phenomenon. And even within language its content is elusive.

Think about it. Reason cannot be logical deduction because deduction requires premises that are postulated without reference to logic. Reason cannot be induction from empirical data because there is no limit to the amount of opposing data which might be supplied.

Scientific method, however that is conceived, can’t be reason. What is deemed acceptable by scientists, however they are identified historically, is subject to continuously changing criteria of evidence and technique.

Philosophy can’t be reason since it always starts with a presumption of what is important in life. Or for that matter after life. And the choice of what is important for many philosophers seems arbitrary if not downright unreasonable.

Yet despite our inability to define what we mean by reason, we tend to treat it as a kind of species-specific superpower. Isn’t reason what distinguishes us from brute animals? Doesn’t reason allow us to transcend the limitations of physical force in resolving our conflicts? Isn’t it reason which allows us to achieve such heights of achievement as space travel and the internet?

There are good reasons to answer all these questions negatively. And in an admirably self-referential way, this is exactly what the authors do: “Reason, we will argue, is a mechanism for intuitive inferences about one kind of representations, namely, reasons.” Reason is about giving and comparing the worth of reasons, often in a most unreasonable manner.

Reason is an interactive process which cannot be reduced to a method or a formula: “We produce reasons in order to justify our thoughts and actions to others and to produce arguments to convince others to think and act as we suggest. We also use reason to evaluate not so much our own thought as the reasons others produce to justify themselves or to convince us.” Anyone who doubts this proposition has never been married, or certainly not been married for long.

In other words, reason is the way human beings communicate. Reason is uniquely human to the extent that human language is unique. Reason is an inherent element of language not something that is applied to language. Reason is how language is employed - to influence others.

The implications of this insight are profoundly important. Reason is not scientific, or rational, or objective; it is political; it is meant to justify and convince. Those who try to fix the meaning of reason are merely employing reason unreasonably for their own ends.

Reason is the profound strength and the equally profound flaw of language. It is the strength of an immeasurably strong linguistic technology that allows complex communal efforts; and it is the flaw of that technology that we are unable to escape from it. Language becomes an imperative which must be used.

Argument is superior to violence, we say. But only for the winners of the argument. Every political system, which is of course defined in language, has a means of keeping the losers of arguments from violence - the potential for even greater violence. Language’s claim to superiority is therefore fatuous. As the authors say, the purpose of reason is always the same - to justify and convince. And failing that, to compel.

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Where Mathematics Come From: How the Embodied Mind Brings Mathematics into Being 
by 

George Lakoff, 

 

Rafael Núñez

 

BlackOxford's review 

Jul 27, 2020  ·  edit

liked it

bookshelves: epistemology-language, mathematics 

Linguistic Overreach?

Get ready; here’s the headline news: MATHEMATICS IS A HUMAN CONSTRUCTION JUST LIKE LANGUAGE. In fact mathematics is a language and employs the same parts of the human brain and nervous system as any other language. It’s arguably the most precise language we have. But there is no truth to the rumour, first formulated by Plato, that the central elements of mathematics - numbers - have any existence beyond our use of them.

That’s it, ladies and gentlemen. We can rest easy in our beds. Mathematics, it appears, has the same metaphorical structure as any other language. If some alien civilisation has mathematical knowledge, it will resemble ours only to the extent that their bodies and physical environment resemble our own. Sci-fi writers as well as philosophers have got it wrong. Mathematics is in our bodies.

Well, that’s not right either. Mathematics is not in our heads. Like all language, it exists among us when we communicate with each other. We condition each other to recognise and respond to mathematical language. So it only seems to be external to us entirely. But technically speaking, mathematics is more like the Christian God than the pagan god of Plato - it is in us, among us and beyond us, all at the same time.

To some extent this conclusion is passé. Linguists have known about the realities of language for some time. The proposition that mathematics is just a kind of language is hardly revolutionary. So the authors feel compelled to venture out on some thin ice: “To make our discussion of classical mathematics tractable while still showing its depth and richness, we have limited ourselves to one profound and central question: What does Euler's classic equation*... mean?”

This is a very silly question it seems to me. The equation means exactly what it says, no more, no less. Each of its terms is ultimately defined circularly by the other terms, just as in any language. Like the meaning of a Beethoven Symphony or a novel by Jane Austen, its meaning is entirely contained in its expression, or rather in the various interpretations of its expression, which are simply more expressions. To suggest otherwise would be to re-introduce Plato’s religious vision of a realm of eternal forms. Mathematics may be generated by human physiology and its needs but this does not imply that mathematics - including ideas like infinity, imaginary numbers, negative numbers, irrational numbers, etc. - have any definite meaning perceptible to our bodies. 

The elements of Euler’s equation may indeed be, as the authors claim, metaphors. But as such the interpretive problem merely has been moved from mathematics to natural language. This is not an advance. It gets us no closer to its meaning other than how it is used by mathematicians. So their discussion of the equation seems seriously off the mark. On the other hand, perhaps it’s just my interpretation that is deficient!

* Euler’s Equation is certainly a profound and profoundly disturbing statement. It summarises the relationship among some of the most important, and on the face of it incommensurable, kinds of mathematical entities. See here for further discussion: https://www.goodreads.com/review/show...

 

Version Control by Dexter Palmer
My rating: 2 of 5 stars

Ennui

Millennial musings about life, love and the point of the universe. Lots of characters, lots of issues. Endless soul searching, tech referencing, white-girl conversing, couples coupling and uncoupling while a vaguely threatening new political order operates in the background.

At several points I thought I grasped a possible central theme emerging from the set-piece conversations. The presumptuousness of scientific method, the adverse social effects of infotech, the perennial haplessness of the young, the relevance (or lack of it) of philosophical inquiry (particularly about time travel) and modern practises of grief popped up as candidates, only to see them diluted in the rising sea of topics, concerns, arguments, and existential angst.

Do people really talk like this? “But most people don’t want to—don’t laugh—most people don’t want to change the world, right? They might, you know, go out and vote or something, but for the most part they’re happy to live in the world like it is. And there’s nothing wrong with that. But stupid me—I have ideals.” Not in my generation. It’s all so cute, so twee, so self-centred.

Ultimately I think I found the key in my own experience of reading the book: boredom. These are boring lives engaged in a boring society with only the most boring responses to events. Cheap science, cheap politics and cheap theology drown out the possibility for empathy in the background of human tragedy. Yet another story, therefore, that makes me glad to be past it.

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The Melancholy of Resistance 
by 

László Krasznahorkai, 

 

George Szirtes (Translator)

 

BlackOxford's review 

Jul 12, 2020  ·  edit

it was amazing

bookshelves: hungarian, criticism, culture 

The Normality Of Chaos

Paragraph-length sentences; chapter-like paragraphs, book-length chapters; and a very different kind of stream of consciousness constituted not by random events but by the intentions which are interrupted or thwarted by these events. The events are only noticed because that is precisely what they do. They disrupt routine, inhibit political ambition, prevent family union, prevent family dissolution, and frustrate announced national purpose.

This is the central theme of Melancholy, suffering. Everyone suffers the consequences of their desires. The universality of suffering depicted is worthy of Emil Cioran or Thomas Ligotti. Everyone is their own worst enemy, being driven mad by the desire for the world, particularly other people, to be other than it is. The nexus of these divergent desires is disaster, seemingly inescapable suffering. Inexplicably, the more they suffer, the more they commit to their desires.

In the midst of this suffering arrives a whale, billed by its circus attendants as The Biggest Whale In The World. The whale - or its carcass - is accompanied by “signs and omens,” the inexplicable events that are so disconcerting and threaten the disintegration of each individual world of desire. The whale also suffers, more acutely than any other creature since it is caged in a steel aquarium into which its ‘followers’ have consigned it. The whale suffers, in other words, for the desires of others.

Whether the whale refers to the Buddha or to Christ - perhaps to both - or to other suffering gods of myth and legend is open to interpretation. What is relevant to the story is that it is a symbol of the train-wreck of not human nature but rather human civilisation as the diversity of ambitions, goals, ideals, and aspirations intersect. The remedy for this condition is not to be found even in religion, worship of the whale, since such devotion merely adds to the sum total of diverse desires... as well as the death of the whale.

In the end, some desires are furthered, others are not. But this is temporary. There is no equilibrium of desire, just arbitrary points from which to expose its persistence. Resistance is not just futile, it also adds to the problem. Hence the associated feeling of anxious sadness.

Postscript: Melancholy might be considered as a worked-out literary example of the Impossibility Theorem formulated by the economist Kenneth Arrow in 1950. According to this theorem, any situation requiring group consensus among people with even slightly different utility functions (that is, desires) will result in a further situation which all can temporarily accept but which none want. See here for further elucidation: https://www.goodreads.com/review/show...

Lost Knowledge of the Imagination by Gary Lachman
My rating: 1 of 5 stars

Unimaginative Nonsense

Nonsense. The contention that a language of science has replaced a language of myth to the detriment of the world is nonsense.

Lachman blames the pre-Socratic Greeks for starting the rot in language. Measurement and the language of mathematics are particularly vile. They empty out the existential reality of everything and leave us with sterile husks of mere scientific concepts. According to him the results are disastrous: “Anomie, apathy, alienation, a sense of existential ‘So what?’ accompanied the success of our now seemingly unstoppable aim of quantifying all of existence and our experience of it.”

Lachman gropes continuously for examples to demonstrate how evil his idea of scientific terminology is. He says, for example, “The spirit of geometry works sequentially, reasoning its way step-by-step, following its rules, whereas the intuitive minds sees everything all at once. It arrives at its goal in one glance, not by a process of deduction.” Step by step reasoning - bad; intuitive understanding of wholes - good. Perhaps he could benefit by reading Ian Hacking’s exposition about how important both intuition and the process of deduction are in mathematics: https://www.goodreads.com/review/show...

That Lachman attempts to make science conform with his idea of social evil is apparent. What he would like us all to do about this evil is less clear. He wants more ‘imagination’ but is convinced that we no longer know what imagination is. He defines it as “our ability to grasp reality;” and claims have lost knowledge of this critical skill through the pernicious intrusion of unimaginative science into every aspect of our lives.

The obvious question that has to be posed to Lachman is ‘How could you possibly know this?’ If the connection between our language and our words is flawed, the error is inexpressible in the language we have. Many have claimed linguistic superiority as a matter of divine revelation as a solution to this epistemological problem - Hebrew for Jews, Latin for Christians, Arabic for Muslims. Lachman is very big on Owen Barfield’s so-called Anthroposophy, a sort of poetic systems theory of the world, which was influential with C.S. Lewis and the other members of the Oxford Inklings.

So Lachman likes poets, especially religious poets, the more mystical the better: Goethe, Hamann, Jung, Cassirer. So do I. And I have some sympathy with Lachman’s rather spiritual view that language, scientific or not, does not capture reality. But to claim that poetic or religious language somehow does and in some way demonstrates superior imaginative skill is not just bogus but stupid. Lachman is well read; but he is also a closet religious fundamentalist who believes that he and his pals have an inside track on which language has the right connections with those things that are not-language.

As I said: Nonsense. And not very imaginative nonsense given that its all been said before.

Postscript: See here for Lachman’s language suggestions: https://share.icloud.com/photos/0wqof...

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Why Is There Philosophy of Mathematics At All? by Ian Hacking
My rating: 4 of 5 stars

Mathematical Epistemology

This is a rambling compendium of mathematical wisdom and opinion by a leading philosopher of science. Given its subject matter and the issues it addresses it might appear irrelevant to everyday concerns, particularly politics. If so, appearances are decidedly deceiving. The central theme of the book - the nature of scientific proof - is arguably the most important issue confronting democracies around the world. Controversies about Covid-19 and Donald Trump make the point conclusively.

Epistemology, the study of how we put our experiences into language, that is to say, how we prove what we think we know when we make claims about reality, has been a hot philosophical topic for several centuries. The bad news is that the epistemological project is dead in the water and has been for some time. The connections between language and that which is not-language are too unreliable, too unstable to tell with any certainty what language is false, misleading, incomplete, or biased. There are no agreed upon rules, methods, or algorithms by which any statement whatsoever can be fact-checked, verified, or proven to be absolutely true or false.

The reason for our ultimate inability to distinguish between fact and fiction is not because we have lost contact with something we casually call reality, but because as soon as we bring our experiences of reality into language, those experiences, and the reality to which these experiences are a response, become distorted in ways that are impossible to correct. Language, whatever else it might be, is not reality. But we have nothing but language in which to express reality. Without language, we would not even be able to discuss reality; we would also not have the epistemological problem.

This inadequacy applies even to the most precise and well-studied language we have at our disposal - mathematics. Unlike any other language, mathematics is minutely and invariably defined. Its vocabulary (numbers) is infinite but every element is always related to every other element in a precise way. The way in which these elements are related to each other (their grammar or rules of use) can be stated axiomatically. And the results produced by mathematicians (proofs) remain valid from era to era, culture to culture, and even according to most mathematicians, from galaxy to galaxy.

Mathematics is as close as we are ever likely to get to the perfect language. The reason for this is that it is a language which refers only to itself. It makes no pretence to describing a reality beyond itself. The mathematical world is entirely self-contained. Its potentially infinite expressiveness has been obviously useful but because its expressions are equally obviously only about itself not about the reality which transcends all language. Furthermore, it contains elements that could not exist in any reality outside of the mathematical language in which they are expressed (dimensionless points, negative numbers, etc.). Mathematics is its own reality.

So mathematics shouldn’t have an epistemological problem. Its language doesn’t have to be correlated with anything except itself. Yet despite its apparent linguistic perfection, mathematics has a dirty little secret. What constitutes mathematical proof is not at all a settled matter. Even mathematics suffers the epistemological impasse, although in a somewhat different way than other languages. Non-mathematical languages confront the apparent problem of connecting language with that which is not-language. Mathematics shows that the problem exists in connecting language with itself.

Hacking identifies two dominant schools of thought about mathematical proof - the Cartesian and the Leibnizian. Both are commonly held within the community of mathematicians, often simultaneously by the same people. But, as Hacking explains these are rather different conceptions, not only of proof but also of what constitutes truth.

Cartesian proof involves comprehending a whole, seeing the beginning middle and end of an argument comprehensively in an appreciation of a mathematical problem. The essential element of a Cartesian proof is intuition, that instinctive sense that things fit together in a certain way. It involves an aesthetic of overall rightness, not in the details but in the overall trajectory and elegance of a mathematical argument.

Leibnizian proof is a step by step mechanical process of inference that moves methodically (tediously perhaps from a Cartesian perspective) from minute inference to minute inference. The aesthetic of this sort of proof is one of rigour rather than elegance. It is literally the way that modern digital machines work - in a plodding, uncreative, unimaginative process of logical progression.

According to Hacking, most mathematicians think of themselves as Cartesianists, yet present themselves professionally as Leibnizian. Few, in fact, would deny the importance of both methods and are probably unaware of their methodological transpositions as they go about their work because “What counts is the lived experience of the entire mathematical activity of bringing a proof into existence...”

In other words the two aesthetics sit side by side in mathematics without conflict because the community of mathematicians recognises their joint value and doesn’t attempt to prioritise or differentially value them. In fact, I don’t think it would be offensive to Hacking or his colleagues to say that this acceptance of the two aesthetics is a reasonable definition of the community of mathematicians itself. There is no formal agreement among them because their doesn’t need to be. This is just how the community works.

That the relative importance of these two aesthetics has varied over time, and among important mathematicians is a central part of Hacking’s argument. But this is just a more or less polite way of saying that there are no fixed, permanent, or eternally valid criteria of proof in mathematics. What counts as proof is a matter of the mores of the current community. This is not to say that historical proofs are often rejected (although they may be from time to time); but that the way in which new proofs are generated and approved within the community is.

This process of changing criteria of proof is a subtle one, mainly because it takes place not through the use of established mathematical language but in the creation of variants and dialects which are engaged in, at least for a time, independently. The relative emphasis of elegance and mechanical rigour (or other aesthetic criteria for that matter) may shift substantially yet remain unnoticed by the users of the ‘received’ language. Historically this was the case with geometry and algebra for example; and more recently between geometry and number theory.

There are currently several hundred recognised sub-fields of mathematics, many with their own specialised language and communal methods of proof. The so-called Langlands Project is an effort to effectively translate among these mathematical dialects. As more and more mathematical languages are generated - by the Project itself as well as the course of mathematical research - it is clear that such an attempt at ‘unification’ has what amounts to an infinite horizon. This means that its goal will never be reached.

In short, even in mathematics, the closure of the ‘epistemological gap’ by the identification of a definitive method of proof is really not something on which to bet the farm. Hacking quotes Ludwig Wittgenstein approvingly on the matter: “I should like to say: mathematics is a MOTLEY of techniques of proof - and upon this is based its manifold applicability and its importance.”

In other words mathematical language is powerful just to the extent it is basically uncertain. It might be instructive to remember this when we employ the rather less precise language of everyday life. Politics rules, OK?

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