About The Shootings

With acknowledgement to the Chuck Gallery.

By Thomas Scarborough

About the tragic shootings in the USA, a few things are clear. Firstly, they have been possible because the weapons were accessible. Secondly, they have happened, by and large, in educational institutions. Thirdly, the shooters have targeted institutions, not individuals.

I have had the privilege of studying theology in the USA. I have studied, too, in other parts of the world. Yet what I experienced in the USA seemed unlike anything else. There was a rising feeling within me of being violated. Thankfully I never had any thoughts of harming anyone—yet the thought crossed my mind: could there be any relation to the massacres?

Beyond that sense of violation, in many cases, students may struggle to know what they are experiencing. In my own case, the situation was unusually transparent. It was not difficult to connect my feelings with the ideology which aroused them.

In theology, there has been a growing tide in the USA, which has its origins in the philosophy of Europe in the mid 20th century—more exactly, in the philosophy of Ludwig Wittgenstein. The theologian R.L. Sturch describes it like this, in the New Dictionary of Theology: ‘In terms derived from Wittgenstein, religion may be seen as a ‘form of life’ or ‘language-game’. Debate within the ‘form of life’ is legitimate, but about the form itself there can be none; either it is adopted or it is not.’ Without so much as entering into theological niceties, we may note some strong language: a form of life ‘is adopted, or it is not’, while debate is ‘legitimate’ only within a given life form. 

Take an instance of such theology, which calls itself a Theology of Communal Practice. Theologians Nancey Murphy and Brad Kallenburg state, ‘What has to be accepted, the given, is—so one could say—forms of life ... The viability of a historical community depends on the ongoing felicity of its communications. Thus, for the society to be viable, most of this communication has to be ‘true’ most of the time.’ Again, without so much as doing any theological analysis, we may simply note the strong language: forms of life ‘have to be accepted’, they are ‘given’, and they ‘have to be true’.

While this hardly serves to prove a point, such ‘compulsive’ thinking is all-pervasive in theological seminaries in the USA—while it is its application that creates the stress.

How should one guarantee ‘felicity of communications’? How should one preserve ‘legitimate' debate? How should one press ‘acceptance’? It need not be through open confrontation—in fact it may more often than not be through the violence of silence. ‘Illegitimate’ debate is greeted with silent stares—or it is channeled, rerouted, deflected. It stacks reading lists, it sustains and manages felicitous communications, it promotes methodological exercises which skirt around the content. In short, it defeats the student. This is the violation.

Is this felt in other educational institutions in the USA? While I do not have direct experience of it, the answer is yes. The psychologist Peter Gray, in Psychology Today, surveyed the ‘seven sins’ of US education. One of the items on his list was ‘Inhibition of critical thinking.’ There is a ‘powerful force’, he wrote, ‘against honest debate’. Yet the force is not merely theoretical. There are students who feel it. Forensic psychologist Stephen Diamond puts the violence down to this: ‘We are prone to feeling hurt’—and in some cases, pathologically.

Seung Hui Cho was a killer who issued a manifesto. On page one, he wrote, ‘Ask yourself what you did to me.’ His entire manifesto, while on the one hand an inscrutable rant, on the other hand reveals a sense of being violated. ‘For every action, there is an equal and opposite reaction,’ he wrote. Is this the reaction to the ‘powerful force against honest debate’?

A brief post such as this cannot hope to answer this question—yet it is surely a question which needs to be asked, and answered. As much as one needs to control access to weapons, one may equally need to overhaul the educational system—and its philosophy.

Huston Smith, a popular writer on religion, considered, ‘Our humanness flourishes to the extent that we steep ourselves in [ultimate] questions—ponder them, circle them, obsess over them, and in the end allow the obsession to consume us.’ There is little humanness in excluding or marginalising issues—in speaking the language of the ‘given’, the ‘legitimate’, and so on—whether it be in seminaries or elsewhere. One needs the marketplace of ideas—together with the freedom, transparency, bravery, and skill that its negotiation requires.

Fermi's Paradox . . . But What If?

Posted by Keith Tidman

Seven decades ago, the physicist-of-atomic-bomb-fame, Enrico Fermi, pondered with his lunchtime companions at Los Alamos whether other intelligent life forms populate planets around the Milky Way, and if so, why we have no evidence of them? He purportedly asked, “Where are they?”, meaning, of course, the alien beings. Because if other complex, intelligent, technology-clever life forms have even a fraction of humankind’s proclivity toward curiosity and, let’s say, colonization, then why is there no evidence of them having acted on these instincts throughout our galaxy? From that conundrum, Fermi’s Paradox emerged.

The American astrophysicist, Frank Drake, later thought about which factors might be necessary to address Fermi’s question and, in particular, how many technological civilizations, emitting electromagnetic signals, might exist among the stars of just our galaxy alone. These became known as Drake’s Equation, and offer a way to calculate the number of civilizations in the Milky Way based on seven variables.* Although scientists can’t yet insert firm numbers for the variables, I think Drake’s effort remains a worthy first attempt at eventually quantifying an answer to Fermi’s question. Especially given that the physical laws of evolution could well differ among far-flung, unfamiliarly diverse chemical, biological, and physical conditions and constraints, yielding singularly different intelligent species.

Many ‘what if’ hypotheses exist by way of possible answers to Fermi’s deceptively simple question. For example, perhaps technology-based civilizations and species with sophisticated intelligence are too far separated by space and time, measured even in thousands of light-years to reveal any presence. Or perhaps, because of the finely grained conditions necessary for life with high intelligence to evolve (the ‘anthropic principle’), civilizations are so rare and scattered that it’s difficult to find each other. Certainly it seems that our own sending-receiving (and space-faring) technologies are too primitive to matter much yet in the sophisticated game of cosmic outreach. Or just perhaps other civilizations have potted us, but rregard humankind as too biologically and intellectually primitive a species to bother with whom to show their hand. Or perhaps they regard humankind as a prototypically warring species, never-endingly engaged in small-minded, lethal belligerence over territory, resources, and power. Perhaps all intelligent species tend toward self-isolating wariness that outweighs curiosity about ‘the other’. Perhaps Thucydides’ theis that established and rising powers are compelled to go to war applies even on the interplanetary scale.

All that said, should there eventually be confirmation of alien intelligent species that are endowed with far higher levels of consciousness and intelligence than humankind — qualities having evolved over histories hundreds of thousands or millions of years older than ours — then the consequence would be culturally tectonic shifting. As a species, perhaps lulled by so easily triumphing over so many of our Earthly competitors, we’re prone to indulging in flights of ‘exceptionalism’. We’re predisposed to looking at our reflection in life’s mirror and — more often looking down, not up — seeing only reasons to preen over our capacity for rationality, creativity, and imagination. To be unseated, with a thud, by an alien species’ cognitive prowess — and the benefits to its civilization — could prove unsettling for humankind’s indulgences in unchallenged exceptionalism.

At the very least, discovery of our sudden non-uniqueness might compel re-examination of basic principles. It might lead to fundamentally questioning religious texts, customs, tenets, rituals, codes of morality, ‘spirituality’, and dicta. If so, the result may be to rethink and rewrite the underlying explanations and descriptions, widening out the aperture of religious philosophy and theology to take into account the new realities of not being alone in the galaxy and in larger cosmos. At the heart of such teleological investigation and reinvention might be questions, which never go away, about humankind’s purpose: about why we are here.

The stunning space-time topography of this universe isn’t hubristically ours alone. I venture it’s a matter of when, not whether, the ‘code’ to Fermi’s Paradox will be cracked.

---

*Drake’s equation, as in our image, is typically shown as follows:

N = R* fp ne fl fi fc L,

Here N is the number of civilizations in the Milky Way whose electromagnetic emissions are detectable; R* is the rate of formation of stars suitable for the development of intelligent life; fp is the fraction of those stars with planetary systems; ne is the number of planets, per solar system, with an environment suitable for life (the habitable, ‘Goldilocks’ zones around their suns); fl is the fraction of suitable planets on which life actually appears; fi is the fraction of life-bearing planets on which intelligent life emerges; fc is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space; and L is the length of time such civilizations release detectable signals into space.

Fermi's Paradox . . . But What If?

Posted by Keith Tidman

Seven decades ago, the physicist-of-atomic-bomb-fame, Enrico Fermi, pondered with his lunchtime companions at Los Alamos whether other intelligent life forms populate planets around the Milky Way, and if so, why we have no evidence of them? He purportedly asked, “Where are they?”, meaning, of course, the alien beings. Because if other complex, intelligent, technology-clever life forms have even a fraction of humankind’s proclivity toward curiosity and, let’s say, colonization, then why is there no evidence of them having acted on these instincts throughout our galaxy? From that conundrum, Fermi’s Paradox emerged.

The American astrophysicist, Frank Drake, later thought about which factors might be necessary to address Fermi’s question and, in particular, how many technological civilizations, emitting electromagnetic signals, might exist among the stars of just our galaxy alone. These became known as Drake’s Equation, and offer a way to calculate the number of civilizations in the Milky Way based on seven variables.* Although scientists can’t yet insert firm numbers for the variables, I think Drake’s effort remains a worthy first attempt at eventually quantifying an answer to Fermi’s question. Especially given that the physical laws of evolution could well differ among far-flung, unfamiliarly diverse chemical, biological, and physical conditions and constraints, yielding singularly different intelligent species.

Many ‘what if’ hypotheses exist by way of possible answers to Fermi’s deceptively simple question. For example, perhaps technology-based civilizations and species with sophisticated intelligence are too far separated by space and time, measured even in thousands of light-years to reveal any presence. Or perhaps, because of the finely grained conditions necessary for life with high intelligence to evolve (the ‘anthropic principle’), civilizations are so rare and scattered that it’s difficult to find each other. Certainly it seems that our own sending-receiving (and space-faring) technologies are too primitive to matter much yet in the sophisticated game of cosmic outreach. Or just perhaps other civilizations have spotted us, but regard humankind as too biologically and intellectually primitive a species to bother with whom to show their hand. Or perhaps they regard humankind as a prototypically warring species, never-endingly engaged in small-minded, lethal belligerence over territory, resources, and power. Perhaps all intelligent species tend toward self-isolating wariness that outweighs curiosity about ‘the other’. Perhaps Thucydides’ thesis that established and rising powers are compelled to go to war applies even on the interplanetary scale.

All that said, should there eventually be confirmation of alien intelligent species that are endowed with far higher levels of consciousness and intelligence than humankind — qualities having evolved over histories hundreds of thousands or millions of years older than ours — then the consequence would be culturally tectonic shifting. As a species, perhaps lulled by so easily triumphing over so many of our Earthly competitors, we’re prone to indulging in flights of ‘exceptionalism’. We’re predisposed to looking at our reflection in life’s mirror and — more often looking down, not up — seeing only reasons to preen over our capacity for rationality, creativity, and imagination. To be unseated, with a thud, by an alien species’ cognitive prowess — and the benefits to its civilization — could prove unsettling for humankind’s indulgences in unchallenged exceptionalism.

At the very least, discovery of our sudden non-uniqueness might compel reexamination of basic principles. It might lead to fundamentally questioning religious texts, customs, tenets, rituals, codes of morality, ‘spirituality’, and dicta. If so, the result may be to rethink and rewrite the underlying explanations and descriptions, widening out the aperture of religious philosophy and theology to take into account the new realities of not being alone in the galaxy and in larger cosmos. At the heart of such teleological investigation and reinvention might be questions, which never go away, about humankind’s purpose: about why we are here.

The stunning space-time topography of this universe isn’t hubristically ours alone. I venture it’s a matter of when, not whether, the ‘code’ to Fermi’s Paradox will be cracked.

---

*Drake’s equation, as in our image, is typically shown as follows:

N = R* fp ne fl fi fc L,

Here N is the number of civilizations in the Milky Way whose electromagnetic emissions are detectable; R* is the rate of formation of stars suitable for the development of intelligent life; fp is the fraction of those stars with planetary systems; ne is the number of planets, per solar system, with an environment suitable for life (the habitable, ‘Goldilocks’ zones around their suns); fl is the fraction of suitable planets on which life actually appears; fi is the fraction of life-bearing planets on which intelligent life emerges; fc is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space; and L is the length of time such civilizations release detectable signals into space.

Impoverished

By Tioti Timon *

In January 2018, in Kiribati, nearly 100 people, of whom 22 school children, tragically went missing on the high seas between Nonouti and Tarawa when a ferry sank. A comparable tragedy in the United States would have seen ¼-million people lost at sea. After four days, a New Zealand Defence Force Orion aircraft found seven survivors.

The Australian Broadcasting Network (ABC) reported on the tragedy—setting it in context by describing Kiribati as “a remote, impoverished nation of thirty-three atolls that is home to about 108,000 people”. Pi approached Tioti Timon of Kiribati for comment on the word “impoverished”.  He replied with free verse:

Impoverished

Impoverished
the word as presented globally
is a discriminatory term
rooted in colonial language
that has treated our people
inhumanly

Australia is a rich country
but there are poor people
begging in the street.
They are rich
but they are poor
in their culture.

Kiribati is a poor country
but we don’t have people
begging in the street.
We are poor
but we are rich
in reciprocity and family support.

What is the meaning
of impoverished,
when we have
the vast ocean around us
and our lives are not dependent
on money.

What is the meaning
of impoverished,
when we have
a material culture
of delightful sophistication
of thousands of years.

All Kiribati people
have their lands
and live subsistently
on their islands
enjoying life,
feasting, dancing, and singing.

We are living in a paradise
that we cannot experience
in an individualistic Australia.

Impoverished
I don't understand this word
applied to our country
especially
in this sad situation
where the lives of our people are lost.

---

* Tioti Timon has been at the forefront of raising awareness of the effects of globalisation on his people, and their precarious position in view of climate change.  He extends his sincere condolences to the families and friends of those who were lost. The ABC news report is here.

Picture Post #33: Bourgeois Reminiscence

'Because things don’t appear to be the known thing; they aren’t what they seemed to be neither will they become what they might appear to become.'

Posted by Tessa den Uyl and Martin Cohen

Mercato di Sant'Ambrogio . Florence . Italy

 Picture credit: Antonio Borrani, 2017

  

Fragments of appearance are offered in the form of leftovers, sold at a market stall by the ounce. Not by the weight per square metre, as used by some manufactures, or by the linear yard. In any case, most likely these surplus fabrics, extras left over after use, could not reach those required measurements.

So instead here we find the evidence of what is left. Fragments not big enough to decorate an entire sofa, but maybe for a cushion it will do. Limited quantities for limited decoration.

The leftover fabric is a measured out merchandise until complete exhaustion. An excess to be sold anew. But this is not the defence of the poor, but rather of a poverty that, solely by its unoffending presence (when permitted) constitutes a critique of possession -- respects the form of private property.

Making such sense of self through this projection into an external referent is a form of psychosis, or to use a Lacanian term, foreclosure. The relation of the subject to the Other is one of dialectic exclusion. Is aspiring to images that offer a make-believe form of prestige a way to enhance an illusion, or to add to alienation?

For sure, we do not find cushions cut from this cloth in the iconic depiction of The Potato Eaters by Van Gogh…

Poetry: On Name-dropping

Posted by Chengde Chen *

On Name-dropping

Don’t keep dropping those great names
Showing off is self-abasing
Being tall may look remarkable, but
Not by lengthening your shadow in the setting sun

If you happen to be associated with a great name
You only 'happen to be' associated with it
Beethoven’s siblings didn’t necessarily compose
Nor must Einstein’s descendants understand physics

To drink liquor you can’t rely on others’ capacity
To sign a cheque you have to use your own name
The more borrowed jewellery you wear
The more should you feel like a beggar!

---

* Chengde Chen is the author of Five Themes of Today, Open Gate Press, London. chengde@sipgroup.com

The Deceptions of Mathematics

by Thomas Scarborough

Galileo Galilei, a man of formidable scientific ability, once wrote that ‘the universe cannot be read until we have learned the (mathematical) language.’  Mathematics, he suggested, would reveal the secrets of the entire cosmos.  It is a common view – yet it is deceptive.  In fact, it may reveal little more than hubris.

On the surface of it, mathematics – even more than science – would seem to be thoroughly objective.  Here there are no failed experiments, no false interpretations, no paradigm shifts.  In mathematics – so it is frequently assumed – there is perfect certainty.

1 + 1 = 2
the logarithm of 1 = 0
the square root of 1 = 1
and so on.

Yet we overlook something, which would seem as simple as one-two-three.  We apply mathematics, by and large, to things in the real world (pure mathematics being the exception to the rule) – and in order so to apply it, we identify units of quantity.  This identification of units of quantity begins with ‘quantification’ – we map our human sense observations into units of quantity, or simply, quantity. 

On first impressions, it might seem to us then that units of quantity come ready made.  Apples come in ones, oranges come in ones – so do people, animals, days, nights, doors, windows, and a great deal more.  And if they do not come in ones, then we may make them into ones: one kilogram, one litre, one block, and so on.  On this basis, we quantify things and perform various mathematical operations on them. 

However, it is not this simple – and even a child might know it.  Our ‘ones’ may really be anything at all – say, clouds with noses (‘I saw three of them today’), ants which fall off the wall (dozens), or dogs which wag their tails, and so on to infinity.  In each case we are dealing with the mathematical unit ‘one’.

The theoretical physicist Albert Einstein would surely have agreed.  He considered that a unit ‘singles out a complex from nature’.  This surely seems a contradiction in terms.  A complex consists of many different and connected parts – parts (plural) which get ‘singled’, out.  That is, one takes a bundle of things or properties, and one defines them as one.  Therefore, various things and various properties may all at once hide inside one and the same single mathematical unit. 

Now this opens up an obvious question.  Who then is to say that our mathematical units – those complexes which we have ‘singled’, out – are precisely the complexes we need for the purpose of our calculations?  Supposing that we really ought to have added something to a complex which we call ‘one’ – or that we really should have taken something out – before we began to make use of it? 

Besides, does one really find such a thing as a complex which is self-contained and closed?  Is not every singled out complex-cum-unit criss-crossed by associations and influences without number?

When we think on it, this is true even of the simplest things in this world.  For instance, we might temporarily assume that the complex ‘hamster’ does not include food or water – it merely refers to a rodent, of which there are so and so many millions in the world.  Yet this complex breaks down at a certain point, as some children can tragically relate, who forgot the food or water.

Consider a thought experiment – as if it had never been conducted before.  Supposing it is true that our complexes might leave things out – or squeeze things in that really ought to be left out.  What then would the logical consequences be?  Of course, high on the list would be that our mathematics may not fit reality, because our mathematical units are ‘not quite right’.  Not only that, but we should easily find examples of this in the world. 

And so it is.  The mathematics of circular orbits and epicycles had to be replaced with the mathematics of elliptical orbits – the mathematics of scalars, then vectors, had to be replaced by the mathematics of tensors.  The mathematics of classical thermodynamics had to be replaced by the mathematics of generalised thermodynamics – and so on.  In fact our complexes may contain an entire world-view which needs to be overhauled – for example, Newtonian physics.  Yet even with the new, we would do well to remember that we have now carved up our world into four mathematical models.

The nineteenth century American philosopher Charles Sanders Peirce saw that ‘every new concept first comes to the mind in a judgment.’  He was saying, apparently, that our ‘ones’ are simply creations of the mind.

On this basis, we may assume that even the simplest of mathematics is not as straightforward as it seems.  In fact mathematics, writes the pioneering statistician William Briggs, requires ‘slow, maturing thought’.  It is not just about numbers, but about wisdom and expansive thinking.

The deceptions are, therefore, that mathematics is objective – and that being objective, it makes an excellent fit with our world – perhaps a perfect fit with the cosmos, as Galileo suggested.   No.  On the contrary, we should see mathematics as a very flawed and very subjective tool – always too simplistic, always in some way violating the totality of the reality in which we live. Mathematics, at the least, should be handled with great humility.

What Are ‘Facts’?

On the trail of the Higgs Boson

Posted by Keith Tidman

What are 'facts'? The ages-long history of deception and sleights of hand and mind — including propaganda and political and psychological legerdemain — demonstrates just one of the many applications of false facts. But similar presentations of falsities meant to deceive, sow discord, or distract have been even more rife today, via the handiness and global ubiquity of the Internet. An enabler is the too-frequent lack of judicious curation and vetting of facts. And, in the process of democratizing access to facts, self-serving individuals may take advantage of those consumers of information who are ill-equipped or disinclined (unmotivated) to discern whether or not content is true. Spurious facts dot the Internet landscape, steering beliefs, driving confirmation bias, and conjuring tangible outcomes such as voting decisions. Interpretations of facts become all the more confounding in political arenas, where interpretations (the understanding) of facts among differently minded politicians becomes muddled, and ‘what’s actually the case’ remains opaque.

And yet surely it is the total anthology of facts — meaning things (their properties), concepts, and their interrelationships — that composes reality. Facts have multiple dimensions, including what one knows (epistemological aspects), how one semantically describes what’s known (linguistic aspects), and what meaning and purpose one attributes to what’s known (metaphysical aspects).

Facts are known on a sliding scale of certainty. An example that seems compelling to me comes from just a few years ago, when scientists announced that they had confirmed the existence of the Higgs boson, whose field generates mass through its interaction with other particles. The Higgs’s existence had been postulated earlier in mathematical terms, but empirical evidence was tantalizingly sought over a few decades. The ultimate confirmation was given a certainty of ‘five sigma’: that there was less than 1 chance in 3.5 million that what was detected was instead a random fluctuation. Impressive enough from an empirical standpoint to conclude discovery (a fact), yet still short of absolute certainty. With resort to empiricism, there is no case where some measure of doubt (of a counterfactual), no matter how infinitesimally small, is excluded.

Mathematics, meantime, provides an even higher level of certainty (rigor of method and of results) in applying facts to describe reality: Newtonian, Einsteinian, quantum theoretical, and other models of scientific realism. Indeed, mathematics, in its precise syntax, universal vocabulary, and singular purpose, is sometimes referred to as the language of reality. Indeed, as opposed to the world’s many natural languages (whose known shortcomings limit understanding), mathematics is the best, and sometimes the only, language for describing select facts of science (mathematical Platonism) — whereby mathematics is less invented than it is discovered as a special case of realism.

Facts are also contingent. Consider another example from science: Immediately following the singularity of the Big Bang, an inflationary period occurred (lasting a tiny fraction of a second). During that inflationary period, the universe — that is, the edges of space-time (not the things within space-time) — expanded faster than the speed of light, resulting in the first step toward the cosmos’s eventual lumpiness, in the form of galaxies, stars, planets. The laws — that is, the facts — of physics were different during the inflation than what scientists are familiar with today — today’s laws of physics breaking down as one looks back closer and closer to the singularity. In this cosmological paradigm, facts are contingent on the peculiar circumstances of the inflationary epoch. This realization points broadly to something capable of being a fact even if we don’t fully understand it.

The sliding scale of certainty and facts’ contingency apply all the more acutely when venturing into other fields. Specifically, the recording of historical events, personages, and ideas, no matter the scholarly intent, often contain biases — judgments, symbols, interpretations — brought to the page by those historians whose contemporaneous accounts may be tailored to self-serving purposes, tilting facts and analyses. In natural course, follow-on historians inadvertently adopt those original biases while not uncommonly folding in their own. Add to this mix the dynamic, complex, and unpredictable (chaotic) nature of human affairs, and the result is all the more shambolic. The accretion of biases over the decades, centuries, and millennia doesn’t of course change reality as such— what happened historically has an underlying matter-of-factness, even if it lingers between hard and impossible to tease out. But the accretion does distort (and on occasion even falsify) what’s understood.

This latter point suggests that what’s a fact and what’s true might either intersect or diverge; nothing excludes either possibility. That is, facts may be true (describe reality) or false (don’t describe reality), depending on their content. (Fairies don’t exist in physical form — in that sense, are false — but do exist nonetheless, legendarily woven into elaborate cultural lore — and in that sense, are true.) What’s true or false will always necessitate the presence of facts, to aid determinations about truth-values. Whereas facts simply stand out there: entirely indifferent to what’s true or false, or what’s believed or known, or what’s formally proven, or what’s wanted and sought after, or what’s observable. That is, absent litmus tests of verifiability. In this sense, given that facts don’t necessarily have to be about something that exists, ‘facts’ and ‘statements’ serve interchangeably.

Facts’ contingency also hinges in some measured, relativistic way on culture. Not as a universally  normative standard for all facts or for all that’s true, of course, but in ways that matter and give shared purpose to citizens of a particular society. Acknowledged facts as to core values — good versus evil, spirituality, integrity, humanitarianism, honesty, trustworthiness, love, environmental stewardship, fairness, justice, and so forth — often become rooted in society. Accordingly, not everyone’s facts are everyone else’s: facts are shaped and shaded both by society and by the individual. The result is the culture-specific normalising of values — what one ‘ought’ to do, ideally. As such, there is no fact-value dilemma. In this vein, values don’t have to be objective to be factual — foundational beliefs, for example, suffice. Facts related to moral realism, unlike scientific and mathematical realism, have to be invented; they’re not discoverable as already-existing phenomena.

Facts are indispensable to describing reality, in both its idealistic (abstract) and realistic (physical) forms. There is no single, exclusive way to define facts; rationalism, empiricism, and idealism all pertain. Yet subsets of facts, and their multifaceted relationships that intricately bear on each other’s truth or falsity, enable knowledge and meaning (purpose) to emerge — an understanding, however imperfect, of slices of abstract and physical reality that our minds piece together as a mosaic. 

In short, the complete anthology of facts relates to all possible forms of reality, ranging the breadth of possibilities, from figments to suppositions to the verifiable phenomenal world.