Solid Ground

Liquid                       -                    Solid
Undefined                -                    Defined
Chaos                        -                   Logos
Unsure                     -                     Sure
Change                     -                    Permanence
Unknown                 -                    Known
Plurality                   -                    Unity
Decentrate                -                    Concentrate
Complex                  -                    Simple
Impure                      -                    Pure
Heterogenous           -                    Homogenous
Immanent                 -                    Transcendent
Imperfect                  -                    Perfect
Earth                        -                    Heavens
Matter                       -                    Pattern
Mother                      -                    Father
Man                          -                    God

Ultimately, God is useful because He gives a seal of approval. In a world in which nothing is certain - in which all footholds, under enough pressure, crack and crumble into smaller pieces - He provides certainty; a bedrock.

Everything is incomplete and so everything can be broken apart. Even the most solid-seeming of entities has a weakness, an opening. God, however, is complete, and so He provides a full stop to the regress.

This is why many irreligious people can be said to display religious behaviours. Inasmuch as the scientists at CERN are looking for a bedrock, they are, metaphorically speaking, looking for God. They are looking for something to serve the same purpose: to provide certainty, an end to the regress.

In some sense, then, any search for certainty is a search for God. If we accept that nothing can ever be truly certain - that everything is incomplete - then all certainty is a form of faith: an expedient conviction.

Oh, if only it were possible to find understanding," Joseph exclaimed.

"If only there were a dogma to believe in. Everything is contradictory, everything tangential; there are no certainties anywhere.

Everything can be interpreted one way and then again interpreted in the opposite sense. The whole of world history can be explained as development and progress and can also be seen as nothing but decadence and meaninglessness.

Isn't there any truth? Is there no real and valid doctrine?"

The master had never heard him speak so fervently. He walked on in silence for a little, then said: "There is truth, my boy. But the doctrine you desire, absolute, perfect dogma that alone provides wisdom, does not exist.

Nor should you long for a perfect doctrine, my friend. Rather, you should long for the perfection of yourself. The diety is within you, not in ideas and books. Truth is lived, not taught. Be prepared for conflicts, Joseph Knecht - I can see that they already have begun.

[Herman Hesse]
The Glass Bead Game

[...] I lived like a blind man in the position in which I had been put, without considering what it was, because in that position I had been born and had grown up and it was therefore natural for me [...]

And it must always necessarily seem to us that the others are mistaken, thinking that a given form, a given act is not this and is not thus.

But inevitably, a little later, if we shift one degree, we realize we were also mistaken, and it isn't this and it isn't thus; so in the end we are obliged to recognize that it will never be this or thus in any stable, sure way; but first one way, then another, and at a certain point all will seem to us mistaken, or all true, which amounts to the same thing; because a reality wasn't assigned to us and doesn't exist, and we have to make it ourselves, if we want it to be [...]

What sort of reality can the majority of men manage to establish in themselves? Wretched, unsteady, uncertain.

And oppressors, of course, take advantage! Or rather, they deceive themselves that they can take advantage, making others undergo or accept the meaning and value they assign themselves, to the others, to things, so all will see and feel, think and speak in their way.

But everything that can be imagined about us is really possible, even if it isn't true for us. The others don't care whether or not it's true for us. It's true for them. So true that the others, if you don't cling fast to the the reality you have given yourself, can actually lead you to grant that even truer than the reality you have given yourself is the one they give you.

[Luigi Pirandello]
One, No One & One Hundred Thousand, p.59, 62, 85, 86, 135

You see, that’s why I think that people have affairs.

Well, I mean, you know, in the theater, if you get good reviews, you feel for a moment that you’ve got your hands on something. You know what I mean? I mean it’s a good feeling.

But then that feeling goes quite quickly. And once again you don’t know quite what you should do next. What’ll happen? Well, have an affair and up to a certain point you can really feel that you’re on firm ground.

You know, there’s a sexual conquest to be made, there are different questions: does she enjoy the ears being nibbled, how intensely can you talk about Schopenhauer in some elegant French restaurant.  

Whatever nonsense it is. It’s all, I think, to give you the semblance that there’s firm earth.

Well, have a real relationship with a person that goes on for years, that’s completely unpredictable. Then you’ve cut off all your ties to the land and you’re sailing into the unknown, into uncharted seas.

I mean, you know, people hold on to these images: father, mother, husband, wife, again for the same reason: ’cause they seem to provide some firm ground. But there’s no wife there. What does that mean, a wife? A husband? A son? A baby holds your hands and then suddenly there’s this huge man lifting you off the ground, and then he’s gone. Where’s that son?

Dialogue from 'My Dinner With Andre' (film)

Here we have the empiricist's case, as it is still put by some of my positivist friends.

I shall try to show that this case is as little valid as Bacon's; that the answer to the question of the sources of knowledge goes against the empiricist; and, finally, that this whole question of ultimate sources - sources to which one may appeal, as one might to a higher court or a higher authority - must be rejected as based upon a mistake.

First I want to show that if you actually went on questioning The Times and its correspondents about the sources of their knowledge, you would in fact never arrive at all those observations by eyewitnesses in the existence of which the empiricist believes.

You would find, rather, that with every single step you take, the need for further steps increases in snowball-like fashion. 

Take as an example [...] the assertion 'The Prime Minister has decided to return to London several days ahead of schedule'. Now assume for a moment that somebody doubts this assertion, or feels the need to investigate its truth. What shall he do? If he has a friend in the Prime Minister's office, the simplest and most direct way would be to ring him up; and if this friend corroborates the message, then that is that.

In other words, the investigator will, if possible, try to check, or to examine, the asserted fact itself, rather than trace the source of the information. But according to the empiricist theory, the assertion 'I have read it in The Times' is merely a first step in a justification procedure consisting in tracing the ultimate source. What is the next step?

There are at least two next steps. One would be to reflect that 'I have read it in The Times' is also an assertion, and that we might ask 'What is the source of your knowledge that you read it in The Times and not, say, in a paper looking very similar to The Times?' The other is to ask The Times for the sources of its knowledge.

The answer to the first question may be 'But we have only The Times on order and we always get it in the morning', which gives rise to a host of further questions about sources which we shall not pursue.

The second question may elicit from the editor of The Times the answer: 'We had a telephone call from the Prime Minister's office.' Now according to the empiricist procedure, we should at this stage ask next: 'Who is the gentleman who received the telephone call?' and then get his observation report; but we should also have to ask that gentleman: 'What is the source of your knowledge that the voice you heard came from an official in the Prime Minister's office?', and so on.

There is a simple reason why this tedious sequence of questions never comes to a satisfactory conclusion. It is this. Every witness must always make ample use, in his report, of his knowledge of persons, places, things, linguistic usages, social conventions, and so on. He cannot rely merely upon his eyes or ears, especially if his report is to be of use in justifying any assertion worth justifying.

But this fact must of course always raise new questions as to the sources of those elements of his knowledge which are not immediately observational.

This is why the programme of tracing back all knowledge to its ultimate source in observation is logically impossible to carry through: it leads to an infinite regress.

(The doctrine that truth is manifest cuts off the regress. This is interesting because it may help to explain the attractiveness of that doctrine.)

[Karl Popper]
'The Problem of Induction'

For [scientists] and for philosophers [...] induction has presented an unsolved problem at the very foundations of human knowledge, and until such time as it might be solved the whole of science, however intrinsically consistent and extrinsically useful, must be conceded to be somehow floating in mid air, unfixed to terra firma.

[...] induction, Popper is saying, is a dispensable concept, a myth. It does not exist. There is no such thing.

[Bryan Magee]
Popper, p. 22, 31

In 1931 Kurt Godel created a stir in the World of Mathematics and Logic when he revealed that it was impossible to embrace mathematics within a single system of logic.

He accomplished this by proving, first, that any consistent system —that includes the arithmetic of whole numbers— is incomplete. In other words, there are true statements or concepts within the system that cannot be deduced from the postulates that make up the system.

[...] Godel's Proof indirectly shows that in order to determine the consistency of any new system we must construct or uncover another system beyond it.

Over and over this cycle must be repeated to determine the consistency of more and more elaborate systems. 

[John R. Boyd]
'Destruction and Creation'

The primary Buddhist dictum is that life is suffering. 

What does that mean? It means that because you’re finite and you’re surrounded by something that’s absolute, in a sense you’re in a battle you can never win because there’s always more of what it is that you’re trying to contend with than there is with you. 

And worse than that, and it’s for this reason that tyrannies can’t last, is that the thing that you’re contending with isn’t even static. It keeps changing. 

So that what worked for you yesterday won’t necessarily work for you tomorrow.

[Jordan B. Peterson]
'Reality and the Sacred

In quantum mechanics, the uncertainty principle, also known as Heisenberg's uncertainty principle, is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.

'Uncertainty principle'

[Quantum mechanics] allows us to describe what everything in the universe is made of, how it interacts, and how it all fits together. But it comes at a huge price.

At its most fundamental level we have to accept that nature is ruled by chance and probability. 

Heisenberg’s uncertainty principle dictates that there are certain limits on the sorts of questions we can ask the atomic world; and most crucially, while we now know so much more about what an atom is and how it behaves, we have to give up any possibility of imagining what it looks like.

[Jim Al-Khalili]
Atom, The Clash of the Titans (documentary)

I find it ludicrous to present the uncertainty principle as having anything to do with uncertainty. Why? First, this uncertainty is Gaussian. On average, it will disappear - recall that no one person's weight will significantly change the total weight of a thousand people.

We may always remain uncertain about the future positions of small particles, but these uncertainties are very small and very numerous, and they average out [...] Most other types of randomness do not average out!

If there is one thing on this planet that is not so uncertain, it is the behaviour of a collection of subatomic particles! Why? Because [...] when you look at an object, composed of a collection of particles, the fluctuations of the particles tend to balance out.

[Nassim Nicholas Taleb]
The Black Swan, p. 287


The uncertainty principle concerns the boundaries of Middle World, of the realm of the known. It shows us that those boundaries are fuzzy, not distinct.

Whilst the exact position of an object's particulars may be unknown, the existence of the object itself is not thrown into question. Its boundaries are blurry, but only from a certain perspective - zoom out a little and they appear distinct enough.

There is no outside-text.

[Jacques Derrida]

Rorty draws a further distinction between "strong" and "weak" textualists that serves to distinguish Derrida from most of his American progeny in literary criticism, as well as from hermeneuticists like Gadamer.

The weak textualist still claims to have deciphered the secret of the text, to have broken its code, to have gotten at what it really says in a way missed by previous interpreters. The strong textualist makes a claim that is similar - the claim to have gotten more out of the text than the author or the intended audience could possibly have found there. But unlike the weak textualist, the strong textualist does not believe there really is a secret code, or that the notion of getting the text "right" makes any sense at all.

This is because the idea of the right interpretation is the idea of an interpretation that could bring interpretation to an end. But there can be no such final interpretation.

Interpretation always involves further interpretation, reinterpretation, and so on in a process that is strictly, and in principle, incompleteable. From the strong textualist perspective, the very idea that there could be anything like the right, final, definitive interpretation is a self-deception. They believe that interpretation is creation and not discovery, the violent imposition of a "grid" on the text to use Foucault's expression.

[Rick Roderick]
'Reading Derrida Politically (Contra Rorty)', PRAXIS International (PRAXIS International), issue: 4 / 1986, p. 443

[...] it is a major precept of modern structural linguistics that meaning is not a relation of identity between signifier and signified but a product of the differences, the signifying contrasts and relationships that exist at every level of language.

 [...] language is always and everywhere a system of differential signs [...] meaning subsists in various structures of relationship and not in some ideal correspondence between sound and sense [...]

To think logocentrically is to dream of a 'transcendental signified', of a meaning outside and beyond the differential play of language that would finally put a stop to this unnerving predicament. 

Deconstruction defines its own project by contrast as a perpetual reminder that meaning is always the 'sign of a sign'; that thought cannot escape this logic of endless supplementarity [...]

[Christopher Norris]
Derrida, p. 85-6

Because human experience is linguistically prestructured, yet the various structures of language possess no demonstrable connection with an independent reality, the human mind can never claim access to any reality other than that determined by its local form of life. 

Language is a “cage" (Wittgenstein). Moreover, linguistic meaning itself can be shown to be fundamentally unstable, because the contexts that determine meaning are never fixed, and beneath the surface of every apparently coherent text can be found a plurality of incompatible meanings. 

No interpretation of a text can claim decisive authority because that which is being interpreted inevitably contains hidden contradictions that undermine its coherence. 

Hence all meaning is ultimately undecidable, and there is no "true" meaning. No underlying primal reality can be said to provide the foundation for human attempts to represent truth. Texts refer only to other texts, in an infinite regress, with no secure basis in something external to language. One can never escape from "the play of signifiers." The multiplicity of incommensurable human truths exposes and defeats the conventional assumption that the mind can progress ever forward to a nearer grasp of reality. 

[Richard Tarnas]
The Passion of the Western Mind, p. 399

Every genuine scientific theory then, in Popper’s view, is prohibitive, in the sense that it forbids, by implication, particular events or occurrences. As such it can be tested and falsified, but never logically verified.

Thus Popper stresses that it should not be inferred from the fact that a theory has withstood the most rigorous testing, for however long a period of time, that it has been verified;

rather we should recognise that such a theory has received a high measure of corroboration, and may be provisionally retained as the best available theory until it is finally falsified (if indeed it is ever falsified), and/or is superseded by a better theory.

'Karl Popper'

Drawing on the insights of Hume and Kant, Popper noted that science can never produce knowledge that is certain, nor even probable. 

Man observes the universe as a stranger, making imaginative guesses about its structure and workings. He cannot approach the world without such bold conjectures in the background, for every observed fact presupposes an interpretive focus. 

In science, these conjectures must be continually and systematically tested; yet however many tests are successfully passed, any theory can never be viewed as more than an imperfectly corroborated conjecture. At any time, a new test could falsify it. No scientific truth is immune to such a possibility. 

Even the basic facts are relative, always potentially subject to a radical reinterpretation in a new framework. Man can never claim to know the real essences of things. Before the virtual infinitude of the world's phenomena, human ignorance itself is infinite. 

The wisest strategy is to learn from one's inevitable mistakes.

[Richard Tarnas]
The Passion of the Western Mind, p. 360

The form or presentation of logic, [Hegel] says, has three sides or moments. These sides are not parts of logic, but, rather, moments of “every logical concept”, as well as “of everything true in general”.

The first moment—the moment of the understanding—is the moment of fixity, in which concepts or forms have a seemingly stable definition or determination.

The second moment—the “dialectical” or “negatively rational” moment—is the moment of instability.

In this moment, a one-sidedness or restrictedness in the determination from the moment of understanding comes to the fore, and the determination that was fixed in the first moment passes into its opposite. There is something particular about the determination in the moment of understanding—a specific weakness, or some specific aspect that was ignored in its one-sidedness or restrictedness—that leads it to fall apart in the dialectical moment.

Hegel describes this process as a process of “self-sublation” [...] The moment of understanding sublates itself because its own character or nature—its one-sidedness or restrictedness—destabilizes its definition and leads it to pass into its opposite.

The third moment—the “speculative” or “positively rational” moment—grasps the unity of the opposition between the first two determinations, or is the positive result of the dissolution or transition of those determinations.

'Hegel's Dialectics'

At stake was nothing less than the progression of Western culture into its next stage of maturity. The first stage of this maturation, in Rorty's eyes, was overcoming the pre-Enlightenment religious outlook, which required humans to appeal to something nonhuman and divine for moral guidance and truth when in fact they should have been seeking moral guidance among themselves.

Many thinkers acknowledge the freedom that this aspect of the Enlightenment has brought.

But Rorty regrets that few of them see a parallel between overcoming the dubious religious idea of a nonhuman divine Other and overcoming the dubious scientific idea of conforming our inquiry to the way the world really is.

Such metaphysical pretensions, Rorty believes, are the traces of unprofitable ways of talking about the world, and if philosophers can persuade people to stop talking as though our worldview describes things as they really are, they can make a substantive contribution to the de-divinizing of the world.

Rather than assuming that our inquiry can cease when it hits the hard bedrock of truth, Rorty wants people to realize that the goals of inquiry continually evolve and are best met by an enduring commitment to experimentation, novelty, poetic creativity, and pluralism.

[James Ryerson]
'The Quest for Uncertainty: Richard Rorty's pragmatic pilgrimage'

Conceiving the possibility that alternative sciences could exist allows us to look back at Western science and ask how much of it is inevitable and objective, and how much is culturally conditioned and determined.

To take one example, the desire for an ultimate level to matter, and the need for a final solution that will provide closure to scientific questioning, does appear to be the manifestation of a persistent trait in Western civilization.

This is not necessarily shared by other cultures that may be more willing to accept an infinity of qualitatively different levels and explanations that are forever open.

Western novels are generally created around a logical scheme of development with a beginning, middle, and end. But many Arabic stories have no end and very little development. Classical Western music involves the alternation of tension and resolution and moves forward toward a coda in which everything is to be resolved and ended in a formal way.

By contrast, Islamic music moves in a more inward way, not having any particular goal or ending, but rather opening into an infinity of variations between the various notes.

The need for all-embracing explanations, fundamental levels, and definite endings may therefore not be so much a characteristic of "science" itself but of a particular cultural mindset within the West.

[F. David Peat]
From Certainty to Uncertainty, p. 209-10

[...] any coastline is - in a sense - infinitely long. In another sense, the answer depends on the length of your ruler.

Consider one plausible method of measuring. A surveyor takes a set of dividers, opens them to a length of one yard, and walks them along the coastline. The resulting number of yards is just an approximation of the true length, because the dividers skip over twists and turns smaller than one yard, but the surveyor writes the number down anyway.

Then he sets the dividers to a smaller length—say, one foot—and repeats the process. He arrives at a somewhat greater length, because the dividers will capture more of the detail and it will take more than three one-foot steps to cover the distance previously covered by a one-yard step. He writes this new number down, sets the dividers at four inches, and starts again.

This mental experiment, using imaginary dividers, is a way of quantifying the effect of observing an object from different distances, at different scales.

An observer trying to estimate the length of England’s coastline from a satellite will make a smaller guess than an observer trying to walk its coves and beaches, who will make a smaller guess in turn than a snail negotiating every pebble.

Common sense suggests that, although these estimates will continue to get larger, they will approach some particular final value, the true length of the coastline. The measurements should converge, in other words. And in fact, if a coastline were some Euclidean shape, such as a circle, this method of summing finer and finer straight-line distances would indeed converge.

But Mandelbrot found that as the scale of measurement becomes smaller, the measured length of a coastline rises without limit, bays and peninsulas revealing ever-smaller subbays and subpeninsulas—at least down to atomic scales, where the process does finally come to an end. Perhaps.

[James Gleick]
Chaos, p. 95-6

Experience is forever in motion, ramifying and unpredictable.

In order for us to know anything at all, that thing must have enduring properties. If all things flow, and one can never step into the same river twice [...] one will always be taken unawares by experience, since nothing being ever repeated, nothing can ever be known.

We have to find a way of fixing it as it flies, stepping back from the immediacy of experience, stepping outside the flow. 

Hence the brain has to attend to the world in two completely different ways, and in so doing to bring two different worlds into being.

In the one, we experience - the live, complex, embodied, world of individual, always unique beings, forever in flux, a net of interdependencies, forming and re-forming wholes, a world with which we are deeply connected.

In the other we 'experience' our experience in a special way: a 're-presented' version of it, containing now static, separable, bounded, but essentially fragmented entities, grouped into classes, on which predictions can be based.

This kind of attention isolates, fixes and makes each thing explicit by bringing it under the spotlight of attention. In doing so it renders things inert, mechanical, lifeless. But it also enables us for the first time to know, and consequently to learn and to make things. This gives us power.

[Iain McGilchrist]
The Master and his Emissary, p. 30-1

[...] there are no lasting, final units, no atoms, no monads: here too the 'being' of things has been inserted by us (for practical, useful, perspectival reasons) [...]

[Friedrich Nietzsche]
Writings from the Late Notebooks, p. 212

How much one needs a faith in order to flourish, how much that is "firm" and that one does not wish to be shaken because one clings to it, that is the measure of the degree of one's strength (or, to put the point more clearly, of one's weakness) [...]

Conversely, one could conceive of such a pleasure and power of self-determination, such a freedom of the will that the spirit would take leave of all faith and every wish for certainty, being practised on maintaining itself on insubstantial ropes and possibilities and dancing even near abysses. Such a spirit would be the free spirit par excellence.

[Friedrich Nietzsche]
The Gay Science, 347; cf. A, 54
On the Genealogy of Morals, III, 24

If we look at the history of opinions, we see that the empiricist tendency has largely prevailed in science, while in philosophy the absolutist tendency has had everything its own way.

The characteristic sort of happiness, indeed, which philosophies yield has mainly consisted in the conviction felt by each successive school or system that by it bottom-certitude had been attained. 

"Other philosophies are collections of opinions, mostly false; my philosophy gives standing-ground forever,"-who does not recognize in this the key-note of every system worthy of the name? A system, to be a system at all, must come as a closed system, reversible in this or that detail, perchance, but in its essential features never!

But now, since we are all such absolutists by instinct, what in our quality of students of philosophy ought we to do about the fact? Shall we espouse and indorse it? Or shall we treat it as a weakness of our nature from which we must free ourselves, if we can?

Objective evidence and certitude are doubtless very fine ideals to play with, but where on this moonlit and dream-visited planet are they found? I am, therefore, myself a complete empiricist so far as my theory of human knowledge goes.

I live, to be sure, by the practical faith that we must go on experiencing and thinking over our experience, for only thus can our opinions grow more true; but to hold any one of them--I absolutely do not care which--as if it never could be reinterpretable or corrigible, I believe to be a tremendously mistaken attitude, and I think that the whole history of philosophy will bear me out. 

Apart from abstract propositions of comparison (such as two and two are the same as four), propositions which tell us nothing by themselves about concrete reality, we find no proposition ever regarded by any one as evidently certain that has not either been called a falsehood, or at least had its truth sincerely questioned by some one else.

The 'absolutely' true, meaning what no farther experience will ever alter, is that ideal vanishing-point towards which we imagine that all our temporary truths will some day converge. It runs on all fours with the perfectly wise man, and with the absolutely complete experience; and, if these ideals are ever realized, they will all be realized together.

Meanwhile we have to live to-day by what truth we can get to-day, and be ready to-morrow to call it falsehood. Ptolemaic astronomy, euclidean space, aristotelian logic, scholastic metaphysics, were expedient for centuries, but human experience has boiled over those limits, and we now call these things only relatively true, or true within those borders of experience. 'Absolutely' they are false; for we know that those limits were casual, and might have been transcended by past theorists just as they are by present thinkers.

[William James]
'Pragmatism's Conception of Truth' and 'The Will to Believe', Pragmatism and Other Writings, p. 98, 205-7

The import of the difference between pragmatism and rationalism is now in sight throughout its whole extent. The essential contrast is that for rationalism reality is ready-made and complete from all eternity, while for pragmatism it is still in the making, and awaits part of its complexion from the future. On the one side the universe is absolutely secure, on the other it is still pursuing its adventures.

On the pragmatist side we have only one edition of the universe, unfinished, growing in all sorts of places, especially in the places where thinking beings are at work.

On the rationalist side we have a universe in many editions, one real one, the infinite folio, or edition de luxe, eternally complete; and then the various finite editions, full of false readings, distorted and mutilated each in its own way.

And first let me say that it is impossible not to see a temperamental difference at work in the choice of sides. The rationalist mind, radically taken, is of a doctrinaire and authoritative complexion: the phrase 'must be' is ever on its lips. The belly-band of its universe must be tight. A radical pragmatist on the other hand is a happy-go-lucky anarchistic sort of creature. If he had to live in a tub like Diogenes he wouldn't mind at all if the hoops were loose and the staves let in the sun.

For pluralistic pragmatism, truth grows up inside of all the finite experiences. They lean on each other, but the whole of them, if such a whole there be, leans on nothing. All 'homes' are in finite experience; finite experience as such is homeless. Nothing outside of the flux secures the issue of it. It can hope salvation only from its own intrinsic promises and potencies.

What then would tighten this loose universe, according to the professors?

Something to support the finite many, to tie it to, to unify and anchor it. Something unexposed to accident, something eternal and unalterable. The mutable in experience must be founded on immutability.

Behind our de facto world, our world in act, there must be a de jure duplicate fixed and previous, with all that can happen here already there in posse, every drop of blood, every smallest appointed and provided, stamped and branded, without chance of variation.

The negatives that haunt our ideals here below must be themselves negated in the absolutely Real. This alone makes the universe solid. This is the resting deep. We live upon the stormy surface; but with this our anchor holds, for it grapples rocky bottom.

This is Wordsworth's "central peace subsisting at the heart of endless agitation." This is Vivekananda's mystical One of which I read to you. This is Reality with the big R, reality that makes the timeless claim, reality to which defeat can't happen. This is what the men of principles, and in general all the men whom I called tender-minded in my first lecture, think themselves obliged to postulate.

You see how differently people take things. The world we live in exists diffused and distributed, in the form of an indefinitely numerous lot of eaches, coherent in all sorts of ways and degrees; and the tough-minded are perfectly willing to keep them at that valuation. They can stand that kind of world, their temper being well adapted to its insecurity.

Not so the tender-minded party. They must back the world we find ourselves born into by "another and a better" world in which the eaches form an All and the All a One that logically presupposes, co-implicates, and secures each each without exception.

Abstractly, or taken like the word winter, as a memorandum of past experience that orients us towards the future, the notion of the absolute world is indispensable. Concretely taken, it is also indispensable, at least to certain minds, for it determines them religiously, being often a thing to change their lives by, and by changing their lives, to change whatever in the outer order depends on them.

[William James]
'Pragmatism and Humanism', Pragmatism and Other Writings, p. 113-17

Nietzsche […] thinks that the fact that science rests on the “faith” that “nothing is needed more than truth, and in relation to it everything else has only second-rate value” shows that science rests on unquestioned presuppositions that make it continuous with the dogmatic tradition it opposes and fights.

“One assumes that it is harmful, dangerous, calamitous to be deceived.” But this, he continues, is groundless. On many occasions it is much more advantageous to be deceived about the facts than to know the truth about them. Therefore, the unconditional faith “that truth is more important than any other thing, including every other conviction… could never have come into being if both truth and untruth proved to be useful, which is the case.”

The unconditional will to truth springs from an effort on our part to deny nature in general, and our nature, to which deception and error are essential, in particular.

“[…] Christian morality itself, the concept of truthfulness that was understood even more rigorously, the father confessor’s refinement of the Christian conscience, translated and sublimated into a scientific conscience, into intellectual cleanliness at any price.”

Science is itself the descendent of the Christian emphasis on truthfulness, and the discipline of “two thousand years of truthfulness… finally forbids itself the lie involved in belief in God.”

“A depreciation of the ascetic ideal unavoidably involves a depreciation of science,” because both depend essentially on the unconditional faith that “truth is inestimable and cannot be criticised.”

[Alexander Nehamas]
Nietzsche: Life as Literature, p. 130-3

[…] elegant maths has this property: it is perfectly right, not 99 percent so. This property appeals to mechanistic maids who do not want to deal with ambiguities. 

Unfortunately you have to cheat somewhere to make the world fit perfect mathematics; and you have to fudge your assumptions somewhere.

We have seen […] that professional “pure” mathematicians, however, are as honest as they come. So where matters get confusing is when someone […] tries to be mathematical and airtight rather than focus on fitness to reality.

[…] those who started the game of “formal thinking,” by manufacturing phone premises in oder to generate “rigorous” theories […] wrecked the ideas of John Maynard Keynes, which they tried to formalise (Keynes was interested in uncertainty, and complained about the mind-closing certainties induced by models).

[…] participants in the formal thinking venture were […] in a delusional state under the effect of mathematics - what Dieudonn√© called “the music of reason,” and what I call Locke’s madness.

All of them can be safely accused of having invented an imaginary world, one that lent itself to their mathematics.

[Nassim Nicholas Taleb]
The Black Swan, p. 283

In Hume's view, two kinds of propositions are possible, one based purely on sensation and the other purely on the intellect. 

A proposition based on sensation concerns obvious matters of concrete fact (e.g., “it is a sunny day"), which are always contingent (they could have been different, though in fact they were not). By contrast, a proposition based purely on intellect concerns relations between concepts (e.g., "all squares have four equal sides"), and these are always necessary—that is, their denial leads to self-contradiction. 

But the truths of pure reason, such as those of mathematics, are necessary only because they exist in a self-contained system with no mandatory reference to the external world. 

They are true only by logical definition, by making explicit what is implicit in their own terms, and these can claim no necessary relation to the nature of things. Hence the only truths of which pure reason is capable are tautological. 

Reason alone cannot assert a truth about the ultimate nature of things.

[Richard Tarnas]
The Passion of the Western Mind, p. 338

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