Undecidability in Physics

 "... even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behaviour" 

https://www.nature.com/articles/nature16059

The past is clay - All yesterdays , a dream

El pasado es arcilla que el presente

labra a su antojo. Interminablemente.

Borges 

Todos los ayeres, un sueño

Los conjurados (1985)
 

On the authority of Science - Cohen

On the authority of Science:

"To be sure, the vast majority of people who are untrained can accept the results of science only on authority. But there is obviously an important difference between an establishment that is open and invites every one to come, study its methods, and suggest improvement, and one that regards the questioning of credentials as due to wickedness of heart..." 

Morris R. Cohen, Reason and Nature.

Social Entropy - Jefferson

The natural progress of things is for liberty to yield, and government to gain ground.

 

The "Man of System" & the "Man of Humanity and Benevolence"

A good citizen and the policy experts, as are called today, were a subject of analysis by Adam Smith (The Theory of Moral Sentiments, VI, II):

First, the good citizen:

The man whose public spirit is prompted altogether by humanity and benevolence, will respect the established powers and privileges even of individuals, and still more those of the great orders and societies, into which the state is divided. Though he should consider some of them as in some measure abusive, he will content himself with moderating, what he often cannot annihilate without great violence. When he cannot conquer the rooted prejudices of the people by reason and persuasion, he will not attempt to subdue them by force... He will accommodate, as well as he can, his public arrangements to the confirmed habits and prejudices of the people; and will remedy as well as he can, the inconveniencies which may flow from the want of those regulations which the people are averse to submit to. When he cannot establish the right, he will not disdain to ameliorate the wrong; but like Solon, when he cannot establish the best system of laws, he will endeavour to establish the best that the people can bear.

Policy experts, as are called today, were a subject of analysis by Adam Smith (The Theory of Moral Sentiments, VI, II):

The man of system, on the contrary, is apt to be very wise in his own conceit; and is often so enamoured with the supposed beauty of his own ideal plan of government, that he cannot suffer the smallest deviation from any part of it. He goes on to establish it completely and in all its parts, without any regard either to the great interests, or to the strong prejudices which may oppose it. He seems to imagine that he can arrange the different members of a great society with as much ease as the hand arranges the different pieces upon a chess-board. He does not consider that the pieces upon the chess-board have no other principle of motion besides that which the hand impresses upon them; but that, in the great chess-board of human society, every single piece has a principle of motion of its own, altogether different from that which the legislature might chuse to impress upon it. If those two principles coincide and act in the same direction, the game of human society will go on easily and harmoniously, and is very likely to be happy and successful. If they are opposite or different, the game will go on miserably, and the society must be at all times in the highest degree of disorder.

Some general, and even systematical, idea of the perfection of policy and law, may no doubt be necessary for directing the views of the statesman. But to insist upon establishing, and upon establishing all at once, and in spite of all opposition, every thing which that idea may seem to require, must often be the highest degree of arrogance. It is to erect his own judgment into the supreme standard of right and wrong. It is to fancy himself the only wise and worthy man in the commonwealth, and that his fellow-citizens should accommodate themselves to him and not he to them. It is upon this account, that of all political speculators, sovereign princes are by far the most dangerous. This arrogance is perfectly familiar to them. They entertain no doubt of the immense superiority of their own judgment. 

Moral Fabric of American Citizenry - James Madison

With regards the moral fabric of the citizenry, James Madison, 4th president of the republic, stated his view:

I go on this great republican principle, that the people will have virtue and intelligence to select men of virtue and wisdom. Is there no virtue among us? If there be not, we are in a wretched situation. No theoretical checks—no form of government can render us secure. To suppose that any form of government will secure liberty or happiness without any virtue in the people, is a chimerical idea. If there be sufficient virtue and intelligence in the community, it will be exercised in the selection of these men. So that we do not depend on their virtue, or put confidence in our rulers, but in the people who are to choose them.

Judicial Powers of the National Government, [20 June] 1788

References

https://founders.archives.gov/documents/Madison/01-11-02-0101

Differences between men's intellects?

Thesis 1: Men are equal in intellectual abilities (British Moral Philosophers)

Adam Smith (Wealth of Nations, book 1, Chap. 2)

The difference of natural talents in different men is, in reality, much less than we are aware of; and the very different genius which appears to distinguish men of different professions, 

when grown up to maturity, is not upon many occasions so much the cause as the effect of the division of labour. The difference between the most dissimilar characters, between a philosopher and a common street porter, for example, seems to arise not so much from nature as from habit, custom, and education. When they came into the world, and for the first six or eight years of their existence, they were, perhaps, very much alike, and neither their parents nor playfellows could perceive any remarkable difference. About that age, or soon after, they come to be employed in very different occupations. The difference of talents comes then to be taken notice of, and widens by degrees, till at last the vanity of the philosopher is willing to acknowledge scarce any resemblance... By nature a philosopher is not in genius and disposition half so different from a street porter, as a mastiff is from a greyhound, or a greyhound from a spaniel, or this last from a shepherd's dog.

David Hume (Of the Original Contract 1752)

...how nearly equal all men are in their bodily force, and even in their mental powers and faculties, till cultivated by education;

Thesis 2: Men are not equal in intellectual abilities (Enlightenment Philosophers)

John Locke (An Essay Concerning Human Understanding. book 4: chap 20, sec. 5)

affirm that there is a greater distance between some men and others in this respect than between some men and some beasts

Denis Diderot

He has not seen the insurmountable barrier that separates a man destined by nature for a given function, from a man who only brings to that function industry, interest and attention.

 

The Sages taught: One who eats in the marketplace is comparable to a dog, as he disrespects himself through his lack of embarrassment over eating in public. And some say he is even disqualified from bearing witness.

Talmud, Kiddushin 40b

Reference:

https://www.sefaria.org/Kiddushin.40b.8?lang=bi

Rousseau: Our minds have been corrupted in proportion as the arts and sciences have improved

 

Where there is no effect, it is idle to look for a cause: but here the effect is certain and the depravity actual; our minds have been corrupted in proportion as the arts and sciences have improved. Will it be said, that this is a misfortune peculiar to the present age? No, gentlemen, the evils resulting from our vain curiosity are as old as the world. The daily ebb and flow of the tides are not more regularly influenced by the moon, than the morals of a people by the progress of the arts and sciences. As their light has risen above our horizon, virtue has taken flight, and the same phenomenon has been constantly observed in all times and places... 

Take Greece, once peopled by heroes, who twice vanquished Asia. Letters, as yet in their infancy, had not corrupted the disposition of its inhabitants; but the progress of the sciences soon produced a dissoluteness of manners, and the imposition of the Macedonian yoke...

It was not till the days of Ennius and Terence that Rome, founded by a shepherd, and made illustrious by peasants, began to degenerate...

Reference:

Rousseau, J. The Social Contract and Discourses (1761): https://oll.libertyfund.org/titles/rousseau-the-social-contract-and-discourses/simple

Calculated Risk - Machiavelli

Né creda mai alcuno stato potere pigliare partiti sicuri, anzi pensi di avere a prenderli tutti dubbi; perché si trova questo nell’ordine delle cose, che mai non si cerca di fuggire un inconveniente che non si incorra in un altro. Tuttavia la prudenza consiste nel saper riconoscere le qualità degli inconvenienti, e nel pigliare il meno tristo per buono.

Different translations

Translation 1: Indeed, it had better recognize that it will always have to choose between risks, for that is the order of things. We never flee one peril without falling into another. Prudence lies in knowing how to distinguish between degrees of danger and in choosing the least danger as the best. (Donno transl.)

Translation 2: Never let any Government imagine that it can choose perfectly safe courses; rather let it expect to have to take very doubtful ones, because it is found in ordinary affairs that one never seeks to avoid one trouble without running into another; but prudence consists in knowing how to distinguish the character of troubles, and for choice to take the lesser evil.

Translation 3: No government should ever think that it can choose perfectly safe courses of action. Every government should expect to have to run risks, because in the ordinary course of events one never tries to avoid one trouble without running into another. Prudence consists in knowing how to weigh up troubles and choose the lesser ones.

Translation 4: In general, a ruler must never imagine that any decision he takes is safe; on the contrary he should reckon that any decision is potentially dangerous. It is in the nature of things that every time you try to avoid one danger you run into another. Good sense consists in being able to assess the dangers and choose the lesser of various evils.

The Prince, XXI

The past is a foreign country

The past is a foreign country; they do things differently there.” ― L.P. Hartley,

All Hands to the Pumps!

All Hands to the Pumps
Henry Scott Tuke
Around 1888

Operational concepts of Evidence

The philosopher P. Achinstein (Speculation, p. 16ff) developed a helpful concept of evidence. Four concepts are presented: potential, veridical, ES, and subjective.

(A) Some fact e is potential evidence that a hypothesis h holds, iff the probability of there being an explanatory connection between e and h, p(E(e,h)|e) > 1/2. (with e := true, e ⊬ h). 

* Notes to potential evidence

• the inequality probably means that p(E) ≠ 1/2, i.e. not indifferent or know-nothing situation,  because it'd be nice to have a 0% or 100%.
• The "explanatory connection" between e and h seems to be given by an additional list of assumptions (p. 194-195) which include correlations grounded in empirical data, etc.
• The "explanatory connection" E(e,h)|e explained in terms of a threshold probability of 50%, is maybe related to a statistical type of explanation (i.e. a la Wesley Salmon)?

Live according to Nature - Marcus Aurelius

The scholar Pierre Hadot answered that living according to nature in the Stoics, meant living according to 3 disciplines:

1. Discipline of action: living benevolently, so that all of mankind flourishes and achieves “happiness”.
2. Discipline of Assent: 
3. Discipline of Desire: self-control over irrational passions, “courage” and endurance in fear and suffering, and “self-discipline” (temperance).

References:

http://donaldrobertson.name/2013/02/20/introduction-to-stoicism-the-three-disciplines/

Johann Kaspar Sulzer: De conceptibus

Cap. I. De conceptibus et quomodo in species et genera ordinentur.
§l Quicquid in rerum natura sensibus nostris observatur, singulare est.

§2 Omne singulare ab alio singulari differt eo ipso, quod est aliud, et individuum vocatur.

§3 Omnia itaque in rerum natura sunt diversa, et licet sint innumerabilis, tamen semper unum non est alterum: unum individuum non est alterum individuum: Jacobus non est Johannes.

§4 Quamquam vero diversa sunt, in multis tamen convenire deprehendimus. In quibus conveniunt vel similia sunt, eo respectu ad eandem referuntur classem: in quibus non conveniunt, ad diversam classem referuntur.

§5 Quae ad eandem classem pertinent, idem nomen habent: diversa classis diversum nomen obtinet, et nomen unius classis alteri non convenit. v.g. Jacobus et Henricus, quia similes sunt, pertinent ad unam eandemque classem, cui virorum nomen est. Hinc uterque est vir. Anna vero et Maria, quia multum differunt a Jacobo et Henrico, diversam classem constituunt, quae nomine feminarum gaudet. Est ergo et Anna et Maria femina, sed vir non est femina nec femina vir.

§6 Ex collatione igitur rerum omnium plurimae classes rerum oriuntur, et semper diversae, quia classis una non est altera, §2, 3.

§7 Classes, quae ex similitudine individuorum promanant, erunt classes primi ordinis, et dicuntur species, vgr. mares, feminae.

§8 Classes primi ordinis, licet diversae, similitudinem quandam habent, quae similitudo exhibet classes secundi ordinis, seu classes specierum, et tales classes vocantur genera. Sic mares et feminae ex Jacobo, Henrico, Anna, Maria orti homines nominantur, hinc mares et feminae erunt species, homines vero genus.

§9 Classes, quae ex similitudine classium secundi ordinis oriuntur, tertii ordinis classes producunt, et generum superiorum nomine veniunt. Tale genus superius est, si homines et bruta conferuntur, et ex eo, quod utrinque vivunt et sentiunt, in unam classem ordinantur, quae classis animalium nomen habet, animal ergo erit genus superius.

§10 Ulterius sic procedendo classes quarti, quinti, cet. ordinis exhibentur, et sic superiora semper genera nobis sistuntur, donec tandem ad unam ultimam classem perveniamus, quae supremum genus dicitur, quod ens est [ ... ].

§13 Quod itaque genus nomen habet, et quidquid de genere dicitur, id nomen quoque habent omnia, quae sub hoc genere comprehenduntur ad individua usque, et de iis quoque absolute dicitur. Exemplum sit animal, quia homines, bruta, mares, feminae, cet. comprehendit, dicetur homo est animal, brutum, vir, femina, Jacobus, Maria, cet., est animal. Et si dicitur: animal sentit, etiam homo, brutum, vir, femina, Jacobus, Maria, sentit.

References:

See: Angelelli, I. (1974) LA JERARQUIA DE CLASES DE JOHANN CASPAR SULZER (1755). Cuadernos de Filosofia. Universidad de Buenos Aires. XIV, 21 , 1974

Philosophasters

A philosophaster is a “A shallow or pseudo-philosopher; a smatterer or pretender in philosophy”, according to the Oxford English Dictionary.

There's also a book by Robert Burton, of Melancholic fame, by the same name. The character names are funny, all of them charlatans in philosophy and theology:

Polypragmaticus, Pantomagus, Pedanus, Amphimacer, Theanus

Plato's "Grand Lie" - a.k.a. "Noble Lie"

Lie as a tool. Dangerous in the contents, and in the method of imposing it.

"The rulers then of the city may, if anybody, fitly lie on account of enemies or citizens for the benefit of the state; no others may have anything to do with it but for a layman to lie to rulers of that kind we shall affirm to be as great a sin, nay a greater, than it is for a patient not to tell physician or an athlete his trainer the truth about his bodily condition, or for a man to deceive the pilot about the ship and the sailors as to the real condition of himself or a fellow-sailor, and how they fare." (Republic 389b-c)
...

"...How then may we devise one of those needful falsehoods of which we lately spoke—just one Grand lie which may deceive the rulers, if that be possible, and at any rate the rest of the city? What sort of lie? he said. Nothing new, I replied; only an old Phoenician tale of what has often occurred before now in other places, (as the poets say, and have made the world believe,) though not in our time, and I do not know whether such an event could ever happen again, or could now even be made probable, if it did.

...I will speak ... the audacious fiction, which I propose to communicate gradually, first to the rulers, then to the soldiers, and lastly to the people. They are to be told that their youth was a dream, and the education and training which they received from us, an appearance only; in reality during all that time they were being formed and fed in the womb of the earth, where they themselves and their arms and appurtenances were manufactured; when they were completed, the earth, their mother, sent them up; and so, their country being their mother and also their nurse, they are bound to advise for her good, and to defend her against attacks, and her citizens they are to regard as children of the earth and their own brothers.

... Citizens, we shall say to them in our tale, you are brothers, yet God has framed you differently. Some of you have the power of command, and in the composition of these he has mingled gold, wherefore also they have the greatest honour; others he has made of silver, to be auxiliaries; others again who are to be husbandmen and craftsmen he has composed of brass and iron; and the species will generally be preserved in the children. But as all are of the same original stock, a golden parent will sometimes have a silver son, or a silver parent a golden son. And God proclaims as a first principle to the rulers, and above all else, that there is nothing which they should so anxiously guard, or of which they are to be such good guardians, as of the purity of the race. They should observe what elements mingle in their offspring; for if the son of a golden or silver parent has an admixture of brass and iron, then nature orders a transposition of ranks, and the eye of the ruler must not be pitiful towards the child because he has to descend in the scale and become a husbandman or artisan, just as there may be sons of artisans who having an admixture of gold or silver in them are raised to honour, and become guardians or auxiliaries. For an oracle says that when a man of brass or iron guards the State, it will be destroyed.

Such is the tale; is there any possibility of making our citizens believe in it? Not in the present generation, he replied; there is no way of accomplishing this; but their sons may be made to believe in the tale, and their sons' sons, and posterity after them. 
(Republic 414b ...)

Follow up...

The observation of intellectual Theodore Dalrymple offers a concrete instance of the application and consequences of this principle:

In my study of communist societies, I came to the conclusion that the purpose of communist propaganda was not to persuade or convince, nor to inform, but to humiliate; and therefore, the less it corresponded to reality the better. When people are forced to remain silent when they are being told the most obvious lies, or even worse when they are forced to repeat the lies themselves, they lose once and for all their sense of probity. To assent to obvious lies is to co-operate with evil, and in some small way to become evil oneself. One’s standing to resist anything is thus eroded, and even destroyed. A society of emasculated liars is easy to control. I think if you examine political correctness, it has the same effect and is intended to. 

(apparently in) Frontpage magazine (can't find exact reference)

Concept, Percept - Essence, Accident.

William Arthur Heidel (1868-1941), a philosopher son of a preacher, makes these interesting observations. His booklet "The necessary and the contingent in the Aristotelian system (1896)" is a very lucid treatment of concepts (and percepts).

• The Sophists then appeared, men of no system but surveying all, only to find a multitude of ineffectual predicates applied to the world.
• It is quite true, Aristotle admits, to say that chance is irrational; for reason deals only with what occurs always or at least for the most part, whereas chance lies in the reverse of these.
• Thus the contingent and the necessary, which possess a true meaning only within a limited scope defined by a particular end, are generalized and erected into absolute fact. But, really, absolute necessity is as unmeaning as absolute contingency. For both conceptions we shall do well to substitute that of less or greater completeness in the definition of fact.

He advances the idea that concepts are made with a end in view

• The concept, in other words, is to be gained by defining the particular: But just here we discover the bad influence of the Socratic induction, proceeding as it did by the elimination of the non-essential, without being fully conscious of the meaning of this exclusion...It was the nature of the particular, in fact, which constituted the concept.
• Viewed from a practical standpoint the exclusion of the non-essential from the concept is not only justified, but it even indicates a truth which ought to lead to the destruction of the theoretical category of "things" and so of the "given." When we are engaged in realizing an end which we have set up after a preliminary review or examination of our means, we find in our experience as presented in memory certain clusters of qualities which \ve commonly denote as things. These clusters are the net results, so to speak, of innumerable previous experiences, in which these "things" did service as ends in themselves or as means toward further ends. We cannot too gratefully acknowledge the serviceableness of this our minds' economy, by which our experience and, therefore, our whole fund of materials or means for future action is definitely organized so as to obviate the fatality of depending on more or less chance suggestions.
• The essential point, on the theoretical side, is to recognize that .. [he] readjust[s] these clusters of qualities, according as this or that content is peculiarly desirable for a particular end... 
• The previously discarded qualities, now again seen in the "things," are classed as "accidents" as opposed to the "essence." This once done, the arena is prepared for all the fruitless battles that have been fought over substance and attribute and inherence. ... I shall hope to show later on that this psychological fallacy is at the base of the distinction between the necessary and the contingent.
• ... the contingent and the necessary, which possess a true meaning only within a limited scope defined by a particular end, are generalized and erected into absolute fact. But, really, absolute necessity is as unmeaning as absolute contingency. For both conceptions we shall do well to substitute that of less or greater completeness in the definition of fact.

Collingwood's examples of Absolute Presuppositions

We do not acquire absolute presuppositions by arguing; on the contrary, unless we have them already arguing is impossible to us. Nor can we change them by arguing; unless they remained constant all our arguments would fall to pieces. We cannot confirm ourselves in them by ‘proving’ them; it is proof that depends on them, not they on proof (An Essay on Metaphysics 1998: 173).

What is the difference between presuppositions and assumptions? C. Ribeiro states:

Collingwood (1940) made a distinction between presuppositions and assumptions. Presuppositions are non-justified implicit implications. They differ from assumptions because the latter are stated openly, are explicit, not implicit. We assume by an act of free will: ‘To assume is to suppose by an act of free will. A person who ‘makes an assumption’ is making a supposition about which he is aware that he might if he chose make not that but another. (…)’ (Collingwood 1940: 27) Presuppositions, however, work in the darkness. But they establish logical connections with the statements formulated in our explicit thought. 

Hyrkannen () p. 255 observes:

• Presuppositions, especially absolute ones, could thus be defined as tacit assumptions, something humans take, more or less, for granted, or which are normally left unscrutinized, unreflected on, unquestioned, untested or unverified. We might call this dimension of thought the dimension of beliefs.

Louis O. Mink

• absolute presuppositions are ‘widely as well as deeply shared; they are ways in which men may think alike as well as be alike in what they think’
• What men have done can be understood only in terms of what they have thought. What they have thought can be understood only in terms of the questions and problems to which they sought answers. And what their questions and problems were can be understood only in terms of the conceptual systems in whose absence those questions and problems could not even arise and be formulated.

Some examples of AP:

• all events have a cause
• the principle of the continuity of nature in time and space, 
• the existence of God
• the principle that mathematics is applicable to the natural world and hence that natural science is essentially an applied mathematics
• all events happen according to law (EM, 150).
• nature is uniform (Mill's EM, 152)

References

• Ribeiro, C. (2015) http://www.philosophica.ugent.be/fulltexts/90-3.pdf
• Hyrkkänen, M. (2009) All History is, More or Less, Intellectual History: R. G. Collingwood's Contribution to the Theory and Methodology of Intellectual History, Intellectual History Review,19:2, 251 — 263
• Mink, L. Collingwood’s Dialectic of History, History & Theory, 7 (1968), 3–37 (25)

Adaequatio intellectus et rei

Adaequatio intellectus et rei: adequation of the intellect to things (correspondence). Or to paraphrase Hermann Lotze (Logica #130, p. 156), "thought follows reality". A frequent assumption (and fallacy) in science.

Schoolmen

The idea was expressed by William of Auvergne (1190-1249) as 

• adaequatio intellectus ad rem (adequation of the intellect to things). 

Other versions of the apothegm are:

• veritas est quod est, enuntiativus est natura veritatis et essentiae ejus (Isaac Israeli 823-932), 
• veritas est dispositio in re exteriore cum est ei aequalitas (Avicenna), 
• adequatio intellectus et rei (Aquinas following Israeli), 
• adequatio rei cum intellectu (Albertus Magnus).
• veritas transcendentalis significat entitatem rei, connotando cognitionem seu conceptum intellectus, cui talis entitas conformatur vel in quo talis res representatur (Suarez)
• Ordo et connexio idearum idem est ac ordo et connexio rerum (Spinoza)

Some wording of the schoolmen associated with this concept are:

• conformitas, correspondentia, convenientia, adaequatio, representatio.

Moderns

• Veritas auterm enunciationis seu iudicii nihil aliud est quam conformitas ore factae aut iudicii mente peracto cum ipsa enuntiata seu iudicata (Gassendi)
• ‘truth’, in the strict sense, refers to the conformity of a thought with its object (Descartes, Letter to Mersenne, 16.x.1639) 
• Idea vera debet convenire cum suo ideato (Spinoza)
• Let us be content with looking for truth in the correspondence between the propositions that are in the mind and the things they are about. (Leibniz New Essays, IV, v, 11)
• Leibniz wrote: "Dialogus de Connexione inter res et verba, et veritatis realitate" in 1677

20th Century

Ortega y Gasset in Historia como Sistema argues that:

• "the world of reality and the world of thought are each a cosmos corresponding one to the other, each compact and continuous, wherein nothing is abrupt, isolated or inaccessible  ...Western man believes, then, that the world possesses a rational structure, that is to say, that reality possesses an organization coincident with the organization of the human intellect, taking this, of course, in its purest form, that of mathematical reason.” - "En los últimos años del siglo XVI y ... primeros del XVII ... cree, pues, el hombre de Occidente que el mundo posee una estructura racional, es decir, que la realidad tiene una organización coincidente con la del intelecto humano, se entiende, con aquella forma del humano intelecto que es le más pura: con la razón matemática."

There's now the issue of whether the human intellect is really capable of grasping the infinite complexity of reality. John Duns Scoto phrases this as an objection:

Atqui impossibilis omnino est talis adaequatio et commesuratio inter potentiam finitam et et obiectum infinitum. Ergo, pariter impossibile est infinitum ab intellecto finiti comprehendi.

And White

...the finite mind is inadequate to grasp the infinite. SC108

And Cusanus

Quoniam ex se manifestum est infiniti ad finitum proportionem non esse (De Docta Ignorantia, Cap iii)

and Trithemius also echoes this argument, having resort to an interesting term "incircumscriptibilem":

Deum igitur nobis credere potius quae scire vel intelligere omnino necessarium fuit: propterea que penitus impossibile sit illam super divinam & incircumscriptibilem maiestatem comprehendi a nobis qui nihil intelligimus sine ministerio sensuum & discursu rationis. (Liber octo quaestionum ad Maximilianum Caesarem de fide et intellectu)

and Lactantius:

incogitabiles... inextricabiles...inaestimabilem potestatem. Dubitet vero aliquis, an quidquam difficile aut impossibile sit Deo, qui tanta tamque mirifica opera providentia excogitavit, virtute constituit, ratione perfecit; nunc autem spiritu sustentet, potestate moderetur, inexcogitabilis, ineffabilis, et nulli alii satis notus quam sibi? (Divinarum Inst., lib i)

But Arthur Eddington introduces a radically different account:

We have learnt that the exploration of the external world by the methods of physical science leads not to concrete reality, but to a world of symbols.

Along the same lines James Jeans suggests,

The essential fact is simply that all the pictures which science now draws of nature, and which alone seem capable of according with observational fact, are mathematical pictures...They are nothing more than pictures – fictions if you like, if by fiction you mean that science is not yet in contact with ultimate reality.”